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or trademarks of Motorola, Inc.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#
# freal.s:
# This file is appended to the top of the 060FPSP package
# and contains the entry points into the package. The user, in
# effect, branches to one of the branch table entries located
# after _060FPSP_TABLE.
# Also, subroutine stubs exist in this file (_fpsp_done for
# example) that are referenced by the FPSP package itself in order
# to call a given routine. The stub routine actually performs the
# callout. The FPSP code does a "bsr" to the stub routine. This
# extra layer of hierarchy adds a slight performance penalty but
# it makes the FPSP code easier to read and more mainatinable.
#
set _off_bsun, 0x00 set _off_snan, 0x04 set _off_operr, 0x08 set _off_ovfl, 0x0c set _off_unfl, 0x10 set _off_dz, 0x14 set _off_inex, 0x18 set _off_fline, 0x1c set _off_fpu_dis, 0x20 set _off_trap, 0x24 set _off_trace, 0x28 set _off_access, 0x2c set _off_done, 0x30
set _off_imr, 0x40 set _off_dmr, 0x44 set _off_dmw, 0x48 set _off_irw, 0x4c set _off_irl, 0x50 set _off_drb, 0x54 set _off_drw, 0x58 set _off_drl, 0x5c set _off_dwb, 0x60 set _off_dww, 0x64 set _off_dwl, 0x68
# Here's the table of ENTRY POINTS for those linking the package.
bra.l _fpsp_snan
short 0x0000
bra.l _fpsp_operr
short 0x0000
bra.l _fpsp_ovfl
short 0x0000
bra.l _fpsp_unfl
short 0x0000
bra.l _fpsp_dz
short 0x0000
bra.l _fpsp_inex
short 0x0000
bra.l _fpsp_fline
short 0x0000
bra.l _fpsp_unsupp
short 0x0000
bra.l _fpsp_effadd
short 0x0000
#
# This file contains a set of define statements for constants
# in order to promote readability within the corecode itself.
#
set LOCAL_SIZE, 192 # stack frame size(bytes) set LV, -LOCAL_SIZE # stack offset
set EXC_SR, 0x4 # stack status register set EXC_PC, 0x6 # stack pc set EXC_VOFF, 0xa # stacked vector offset set EXC_EA, 0xc # stacked <ea>
set EXC_FP, 0x0 # frame pointer
set EXC_AREGS, -68 # offset of all address regs set EXC_DREGS, -100 # offset of all data regs set EXC_FPREGS, -36 # offset of all fp regs
set EXC_A7, EXC_AREGS+(7*4) # offset of saved a7 set OLD_A7, EXC_AREGS+(6*4) # extra copy of saved a7 set EXC_A6, EXC_AREGS+(6*4) # offset of saved a6 set EXC_A5, EXC_AREGS+(5*4) set EXC_A4, EXC_AREGS+(4*4) set EXC_A3, EXC_AREGS+(3*4) set EXC_A2, EXC_AREGS+(2*4) set EXC_A1, EXC_AREGS+(1*4) set EXC_A0, EXC_AREGS+(0*4) set EXC_D7, EXC_DREGS+(7*4) set EXC_D6, EXC_DREGS+(6*4) set EXC_D5, EXC_DREGS+(5*4) set EXC_D4, EXC_DREGS+(4*4) set EXC_D3, EXC_DREGS+(3*4) set EXC_D2, EXC_DREGS+(2*4) set EXC_D1, EXC_DREGS+(1*4) set EXC_D0, EXC_DREGS+(0*4)
set EXC_FP0, EXC_FPREGS+(0*12) # offset of saved fp0 set EXC_FP1, EXC_FPREGS+(1*12) # offset of saved fp1 set EXC_FP2, EXC_FPREGS+(2*12) # offset of saved fp2 (not used)
set FP_SCR1, LV+80 # fp scratch 1 set FP_SCR1_EX, FP_SCR1+0 set FP_SCR1_SGN, FP_SCR1+2 set FP_SCR1_HI, FP_SCR1+4 set FP_SCR1_LO, FP_SCR1+8
set FP_SCR0, LV+68 # fp scratch 0 set FP_SCR0_EX, FP_SCR0+0 set FP_SCR0_SGN, FP_SCR0+2 set FP_SCR0_HI, FP_SCR0+4 set FP_SCR0_LO, FP_SCR0+8
set FP_DST, LV+56 # fp destination operand set FP_DST_EX, FP_DST+0 set FP_DST_SGN, FP_DST+2 set FP_DST_HI, FP_DST+4 set FP_DST_LO, FP_DST+8
set FP_SRC, LV+44 # fp source operand set FP_SRC_EX, FP_SRC+0 set FP_SRC_SGN, FP_SRC+2 set FP_SRC_HI, FP_SRC+4 set FP_SRC_LO, FP_SRC+8
set USER_FPIAR, LV+40 # FP instr address register
set USER_FPSR, LV+36 # FP status register set FPSR_CC, USER_FPSR+0 # FPSR condition codes set FPSR_QBYTE, USER_FPSR+1 # FPSR qoutient byte set FPSR_EXCEPT, USER_FPSR+2 # FPSR exception status byte set FPSR_AEXCEPT, USER_FPSR+3 # FPSR accrued exception byte
set USER_FPCR, LV+32 # FP control register set FPCR_ENABLE, USER_FPCR+2 # FPCR exception enable set FPCR_MODE, USER_FPCR+3 # FPCR rounding mode control
set L_SCR3, LV+28 # integer scratch 3 set L_SCR2, LV+24 # integer scratch 2 set L_SCR1, LV+20 # integer scratch 1
set STORE_FLG, LV+19 # flag: operand store (ie. not fcmp/ftst)
set EXC_TEMP2, LV+24 # temporary space set EXC_TEMP, LV+16 # temporary space
set DTAG, LV+15 # destination operand type set STAG, LV+14 # source operand type
set SPCOND_FLG, LV+10 # flag: special case (see below)
set EXC_CC, LV+8 # saved condition codes set EXC_EXTWPTR, LV+4 # saved current PC (active) set EXC_EXTWORD, LV+2 # saved extension word set EXC_CMDREG, LV+2 # saved extension word set EXC_OPWORD, LV+0 # saved operation word
################################
# Helpful macros
set FTEMP, 0 # offsets within an set FTEMP_EX, 0 # extended precision set FTEMP_SGN, 2 # value saved in memory. set FTEMP_HI, 4 set FTEMP_LO, 8 set FTEMP_GRS, 12
set LOCAL, 0 # offsets within an set LOCAL_EX, 0 # extended precision set LOCAL_SGN, 2 # value saved in memory. set LOCAL_HI, 4 set LOCAL_LO, 8 set LOCAL_GRS, 12
set DST, 0 # offsets within an set DST_EX, 0 # extended precision set DST_HI, 4 # value saved in memory. set DST_LO, 8
set SRC, 0 # offsets within an set SRC_EX, 0 # extended precision set SRC_HI, 4 # value saved in memory. set SRC_LO, 8
set SGL_LO, 0x3f81 # min sgl prec exponent set SGL_HI, 0x407e # max sgl prec exponent set DBL_LO, 0x3c01 # min dbl prec exponent set DBL_HI, 0x43fe # max dbl prec exponent set EXT_LO, 0x0 # min ext prec exponent set EXT_HI, 0x7ffe # max ext prec exponent
set EXT_BIAS, 0x3fff # extended precision bias set SGL_BIAS, 0x007f # single precision bias set DBL_BIAS, 0x03ff # double precision bias
set NORM, 0x00 # operand type for STAG/DTAG set ZERO, 0x01 # operand type for STAG/DTAG set INF, 0x02 # operand type for STAG/DTAG set QNAN, 0x03 # operand type for STAG/DTAG set DENORM, 0x04 # operand type for STAG/DTAG set SNAN, 0x05 # operand type for STAG/DTAG set UNNORM, 0x06 # operand type for STAG/DTAG
##################
# FPSR/FPCR bits #
################## set neg_bit, 0x3 # negative result set z_bit, 0x2 # zero result set inf_bit, 0x1 # infinite result set nan_bit, 0x0 # NAN result
set q_sn_bit, 0x7 # sign bit of quotient byte
set bsun_bit, 7 # branch on unordered set snan_bit, 6 # signalling NAN set operr_bit, 5 # operand error set ovfl_bit, 4 # overflow set unfl_bit, 3 # underflow set dz_bit, 2 # divide by zero set inex2_bit, 1 # inexact result 2 set inex1_bit, 0 # inexact result 1
set aiop_bit, 7 # accrued inexact operation bit set aovfl_bit, 6 # accrued overflow bit set aunfl_bit, 5 # accrued underflow bit set adz_bit, 4 # accrued dz bit set ainex_bit, 3 # accrued inexact bit
#############################
# FPSR individual bit masks #
############################# set neg_mask, 0x08000000 # negative bit mask (lw) set inf_mask, 0x02000000 # infinity bit mask (lw) set z_mask, 0x04000000 # zero bit mask (lw) set nan_mask, 0x01000000 # nan bit mask (lw)
set neg_bmask, 0x08 # negative bit mask (byte) set inf_bmask, 0x02 # infinity bit mask (byte) set z_bmask, 0x04 # zero bit mask (byte) set nan_bmask, 0x01 # nan bit mask (byte)
set bsun_mask, 0x00008000 # bsun exception mask set snan_mask, 0x00004000 # snan exception mask set operr_mask, 0x00002000 # operr exception mask set ovfl_mask, 0x00001000 # overflow exception mask set unfl_mask, 0x00000800 # underflow exception mask set dz_mask, 0x00000400 # dz exception mask set inex2_mask, 0x00000200 # inex2 exception mask set inex1_mask, 0x00000100 # inex1 exception mask
set aiop_mask, 0x00000080 # accrued illegal operation set aovfl_mask, 0x00000040 # accrued overflow set aunfl_mask, 0x00000020 # accrued underflow set adz_mask, 0x00000010 # accrued divide by zero set ainex_mask, 0x00000008 # accrued inexact
######################################
# FPSR combinations used in the FPSP #
###################################### set dzinf_mask, inf_mask+dz_mask+adz_mask set opnan_mask, nan_mask+operr_mask+aiop_mask set nzi_mask, 0x01ffffff #clears N, Z, and I set unfinx_mask, unfl_mask+inex2_mask+aunfl_mask+ainex_mask set unf2inx_mask, unfl_mask+inex2_mask+ainex_mask set ovfinx_mask, ovfl_mask+inex2_mask+aovfl_mask+ainex_mask set inx1a_mask, inex1_mask+ainex_mask set inx2a_mask, inex2_mask+ainex_mask set snaniop_mask, nan_mask+snan_mask+aiop_mask set snaniop2_mask, snan_mask+aiop_mask set naniop_mask, nan_mask+aiop_mask set neginf_mask, neg_mask+inf_mask set infaiop_mask, inf_mask+aiop_mask set negz_mask, neg_mask+z_mask set opaop_mask, operr_mask+aiop_mask set unfl_inx_mask, unfl_mask+aunfl_mask+ainex_mask set ovfl_inx_mask, ovfl_mask+aovfl_mask+ainex_mask
#########
# misc. #
######### set rnd_stky_bit, 29 # stky bit pos in longword
set sign_bit, 0x7 # sign bit set signan_bit, 0x6 # signalling nan bit
set sgl_thresh, 0x3f81 # minimum sgl exponent set dbl_thresh, 0x3c01 # minimum dbl exponent
set x_mode, 0x0 # extended precision set s_mode, 0x4 # single precision set d_mode, 0x8 # double precision
set rn_mode, 0x0 # round-to-nearest set rz_mode, 0x1 # round-to-zero set rm_mode, 0x2 # round-tp-minus-infinity set rp_mode, 0x3 # round-to-plus-infinity
set BSUN_VEC, 0xc0 # bsun vector offset set INEX_VEC, 0xc4 # inexact vector offset set DZ_VEC, 0xc8 # dz vector offset set UNFL_VEC, 0xcc # unfl vector offset set OPERR_VEC, 0xd0 # operr vector offset set OVFL_VEC, 0xd4 # ovfl vector offset set SNAN_VEC, 0xd8 # snan vector offset
###########################
# SPecial CONDition FLaGs #
########################### set ftrapcc_flg, 0x01 # flag bit: ftrapcc exception set fbsun_flg, 0x02 # flag bit: bsun exception set mia7_flg, 0x04 # flag bit: (a7)+ <ea> set mda7_flg, 0x08 # flag bit: -(a7) <ea> set fmovm_flg, 0x40 # flag bit: fmovm instruction set immed_flg, 0x80 # flag bit: &<data> <ea>
set ftrapcc_bit, 0x0 set fbsun_bit, 0x1 set mia7_bit, 0x2 set mda7_bit, 0x3 set immed_bit, 0x7
##################################
# TRANSCENDENTAL "LAST-OP" FLAGS #
################################## set FMUL_OP, 0x0 # fmul instr performed last set FDIV_OP, 0x1 # fdiv performed last set FADD_OP, 0x2 # fadd performed last set FMOV_OP, 0x3 # fmov performed last
#############
# CONSTANTS #
#############
T1: long 0x40C62D38,0xD3D64634 # 16381 LOG2 LEAD
T2: long 0x3D6F90AE,0xB1E75CC7 # 16381 LOG2 TRAIL
PI: long 0x40000000,0xC90FDAA2,0x2168C235,0x00000000
PIBY2: long 0x3FFF0000,0xC90FDAA2,0x2168C235,0x00000000
TWOBYPI:
long 0x3FE45F30,0x6DC9C883
#########################################################################
# XDEF **************************************************************** #
# _fpsp_ovfl(): 060FPSP entry point for FP Overflow exception. #
# #
# This handler should be the first code executed upon taking the #
# FP Overflow exception in an operating system. #
# #
# XREF **************************************************************** #
# _imem_read_long() - read instruction longword #
# fix_skewed_ops() - adjust src operand in fsave frame #
# set_tag_x() - determine optype of src/dst operands #
# store_fpreg() - store opclass 0 or 2 result to FP regfile #
# unnorm_fix() - change UNNORM operands to NORM or ZERO #
# load_fpn2() - load dst operand from FP regfile #
# fout() - emulate an opclass 3 instruction #
# tbl_unsupp - add of table of emulation routines for opclass 0,2 #
# _fpsp_done() - "callout" for 060FPSP exit (all work done!) #
# _real_ovfl() - "callout" for Overflow exception enabled code #
# _real_inex() - "callout" for Inexact exception enabled code #
# _real_trace() - "callout" for Trace exception code #
# #
# INPUT *************************************************************** #
# - The system stack contains the FP Ovfl exception stack frame #
# - The fsave frame contains the source operand #
# #
# OUTPUT ************************************************************** #
# Overflow Exception enabled: #
# - The system stack is unchanged #
# - The fsave frame contains the adjusted src op for opclass 0,2 #
# Overflow Exception disabled: #
# - The system stack is unchanged #
# - The "exception present" flag in the fsave frame is cleared #
# #
# ALGORITHM *********************************************************** #
# On the 060, if an FP overflow is present as the result of any #
# instruction, the 060 will take an overflow exception whether the #
# exception is enabled or disabled in the FPCR. For the disabled case, #
# This handler emulates the instruction to determine what the correct #
# default result should be for the operation. This default result is #
# then stored in either the FP regfile, data regfile, or memory. #
# Finally, the handler exits through the "callout" _fpsp_done() #
# denoting that no exceptional conditions exist within the machine. #
# If the exception is enabled, then this handler must create the #
# exceptional operand and plave it in the fsave state frame, and store #
# the default result (only if the instruction is opclass 3). For #
# exceptions enabled, this handler must exit through the "callout" #
# _real_ovfl() so that the operating system enabled overflow handler #
# can handle this case. #
# Two other conditions exist. First, if overflow was disabled #
# but the inexact exception was enabled, this handler must exit #
# through the "callout" _real_inex() regardless of whether the result #
# was inexact. #
# Also, in the case of an opclass three instruction where #
# overflow was disabled and the trace exception was enabled, this #
# handler must exit through the "callout" _real_trace(). #
# #
#########################################################################
global _fpsp_ovfl
_fpsp_ovfl:
#$# sub.l &24,%sp # make room for src/dst
link.w %a6,&-LOCAL_SIZE # init stack frame
fsave FP_SRC(%a6) # grab the "busy" frame
movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1
fmovm.l %fpcr,%fpsr,%fpiar,USER_FPCR(%a6) # save ctrl regs
fmovm.x &0xc0,EXC_FPREGS(%a6) # save fp0-fp1 on stack
# the FPIAR holds the "current PC" of the faulting instruction
mov.l USER_FPIAR(%a6),EXC_EXTWPTR(%a6)
mov.l EXC_EXTWPTR(%a6),%a0 # fetch instruction addr
addq.l &0x4,EXC_EXTWPTR(%a6) # incr instruction ptr
bsr.l _imem_read_long # fetch the instruction words
mov.l %d0,EXC_OPWORD(%a6)
btst &0x5,EXC_CMDREG(%a6) # is instr an fmove out?
bne.w fovfl_out
lea FP_SRC(%a6),%a0 # pass: ptr to src op
bsr.l fix_skewed_ops # fix src op
# since, I believe, only NORMs and DENORMs can come through here,
# maybe we can avoid the subroutine call.
lea FP_SRC(%a6),%a0 # pass: ptr to src op
bsr.l set_tag_x # tag the operand type
mov.b %d0,STAG(%a6) # maybe NORM,DENORM
# bit five of the fp extension word separates the monadic and dyadic operations
# that can pass through fpsp_ovfl(). remember that fcmp, ftst, and fsincos
# will never take this exception.
btst &0x5,1+EXC_CMDREG(%a6) # is operation monadic or dyadic?
beq.b fovfl_extract # monadic
lea FP_DST(%a6),%a0 # pass: ptr to dst op
bsr.l set_tag_x # tag the operand type
cmpi.b %d0,&UNNORM # is operand an UNNORM?
bne.b fovfl_op2_done # no
bsr.l unnorm_fix # yes; convert to NORM,DENORM,or ZERO
fovfl_op2_done:
mov.b %d0,DTAG(%a6) # save dst optype tag
andi.l &0x00ff01ff,USER_FPSR(%a6) # zero all but accured field
fmov.l &0x0,%fpcr # zero current control regs
fmov.l &0x0,%fpsr
lea FP_SRC(%a6),%a0
lea FP_DST(%a6),%a1
# maybe we can make these entry points ONLY the OVFL entry points of each routine.
mov.l (tbl_unsupp.l,%pc,%d1.w*4),%d1 # fetch routine addr
jsr (tbl_unsupp.l,%pc,%d1.l*1)
# the operation has been emulated. the result is in fp0.
# the EXOP, if an exception occurred, is in fp1.
# we must save the default result regardless of whether
# traps are enabled or disabled.
bfextu EXC_CMDREG(%a6){&6:&3},%d0
bsr.l store_fpreg
# the exceptional possibilities we have left ourselves with are ONLY overflow
# and inexact. and, the inexact is such that overflow occurred and was disabled
# but inexact was enabled.
btst &ovfl_bit,FPCR_ENABLE(%a6)
bne.b fovfl_ovfl_on
# overflow is enabled AND overflow, of course, occurred. so, we have the EXOP
# in fp1. now, simply jump to _real_ovfl()!
fovfl_ovfl_on:
fmovm.x &0x40,FP_SRC(%a6) # save EXOP (fp1) to stack
btst &0x7,(%sp) # is trace on?
beq.l _fpsp_done # no
fmov.l %fpiar,0x8(%sp) # "Current PC" is in FPIAR
mov.w &0x2024,0x6(%sp) # stk fmt = 0x2; voff = 0x024
bra.l _real_trace
#########################################################################
# XDEF **************************************************************** #
# _fpsp_unfl(): 060FPSP entry point for FP Underflow exception. #
# #
# This handler should be the first code executed upon taking the #
# FP Underflow exception in an operating system. #
# #
# XREF **************************************************************** #
# _imem_read_long() - read instruction longword #
# fix_skewed_ops() - adjust src operand in fsave frame #
# set_tag_x() - determine optype of src/dst operands #
# store_fpreg() - store opclass 0 or 2 result to FP regfile #
# unnorm_fix() - change UNNORM operands to NORM or ZERO #
# load_fpn2() - load dst operand from FP regfile #
# fout() - emulate an opclass 3 instruction #
# tbl_unsupp - add of table of emulation routines for opclass 0,2 #
# _fpsp_done() - "callout" for 060FPSP exit (all work done!) #
# _real_ovfl() - "callout" for Overflow exception enabled code #
# _real_inex() - "callout" for Inexact exception enabled code #
# _real_trace() - "callout" for Trace exception code #
# #
# INPUT *************************************************************** #
# - The system stack contains the FP Unfl exception stack frame #
# - The fsave frame contains the source operand #
# #
# OUTPUT ************************************************************** #
# Underflow Exception enabled: #
# - The system stack is unchanged #
# - The fsave frame contains the adjusted src op for opclass 0,2 #
# Underflow Exception disabled: #
# - The system stack is unchanged #
# - The "exception present" flag in the fsave frame is cleared #
# #
# ALGORITHM *********************************************************** #
# On the 060, if an FP underflow is present as the result of any #
# instruction, the 060 will take an underflow exception whether the #
# exception is enabled or disabled in the FPCR. For the disabled case, #
# This handler emulates the instruction to determine what the correct #
# default result should be for the operation. This default result is #
# then stored in either the FP regfile, data regfile, or memory. #
# Finally, the handler exits through the "callout" _fpsp_done() #
# denoting that no exceptional conditions exist within the machine. #
# If the exception is enabled, then this handler must create the #
# exceptional operand and plave it in the fsave state frame, and store #
# the default result (only if the instruction is opclass 3). For #
# exceptions enabled, this handler must exit through the "callout" #
# _real_unfl() so that the operating system enabled overflow handler #
# can handle this case. #
# Two other conditions exist. First, if underflow was disabled #
# but the inexact exception was enabled and the result was inexact, #
# this handler must exit through the "callout" _real_inex(). #
# was inexact. #
# Also, in the case of an opclass three instruction where #
# underflow was disabled and the trace exception was enabled, this #
# handler must exit through the "callout" _real_trace(). #
# #
#########################################################################
global _fpsp_unfl
_fpsp_unfl:
#$# sub.l &24,%sp # make room for src/dst
link.w %a6,&-LOCAL_SIZE # init stack frame
fsave FP_SRC(%a6) # grab the "busy" frame
movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1
fmovm.l %fpcr,%fpsr,%fpiar,USER_FPCR(%a6) # save ctrl regs
fmovm.x &0xc0,EXC_FPREGS(%a6) # save fp0-fp1 on stack
# the FPIAR holds the "current PC" of the faulting instruction
mov.l USER_FPIAR(%a6),EXC_EXTWPTR(%a6)
mov.l EXC_EXTWPTR(%a6),%a0 # fetch instruction addr
addq.l &0x4,EXC_EXTWPTR(%a6) # incr instruction ptr
bsr.l _imem_read_long # fetch the instruction words
mov.l %d0,EXC_OPWORD(%a6)
btst &0x5,EXC_CMDREG(%a6) # is instr an fmove out?
bne.w funfl_out
lea FP_SRC(%a6),%a0 # pass: ptr to src op
bsr.l fix_skewed_ops # fix src op
lea FP_SRC(%a6),%a0 # pass: ptr to src op
bsr.l set_tag_x # tag the operand type
mov.b %d0,STAG(%a6) # maybe NORM,DENORM
# bit five of the fp ext word separates the monadic and dyadic operations
# that can pass through fpsp_unfl(). remember that fcmp, and ftst
# will never take this exception.
btst &0x5,1+EXC_CMDREG(%a6) # is op monadic or dyadic?
beq.b funfl_extract # monadic
# now, what's left that's not dyadic is fsincos. we can distinguish it
# from all dyadics by the '0110xxx pattern
btst &0x4,1+EXC_CMDREG(%a6) # is op an fsincos?
bne.b funfl_extract # yes
lea FP_DST(%a6),%a0 # pass: ptr to dst op
bsr.l set_tag_x # tag the operand type
cmpi.b %d0,&UNNORM # is operand an UNNORM?
bne.b funfl_op2_done # no
bsr.l unnorm_fix # yes; convert to NORM,DENORM,or ZERO
funfl_op2_done:
mov.b %d0,DTAG(%a6) # save dst optype tag
fmov.l &0x0,%fpcr # zero current control regs
fmov.l &0x0,%fpsr
lea FP_SRC(%a6),%a0
lea FP_DST(%a6),%a1
# maybe we can make these entry points ONLY the OVFL entry points of each routine.
mov.l (tbl_unsupp.l,%pc,%d1.w*4),%d1 # fetch routine addr
jsr (tbl_unsupp.l,%pc,%d1.l*1)
# The `060 FPU multiplier hardware is such that if the result of a
# multiply operation is the smallest possible normalized number
# (0x00000000_80000000_00000000), then the machine will take an
# underflow exception. Since this is incorrect, we need to check
# if our emulation, after re-doing the operation, decided that
# no underflow was called for. We do these checks only in
# funfl_{unfl,inex}_on() because w/ both exceptions disabled, this
# special case will simply exit gracefully with the correct result.
# the exceptional possibilities we have left ourselves with are ONLY overflow
# and inexact. and, the inexact is such that overflow occurred and was disabled
# but inexact was enabled.
btst &unfl_bit,FPCR_ENABLE(%a6)
bne.b funfl_unfl_on
# overflow is enabled AND overflow, of course, occurred. so, we have the EXOP
# in fp1 (don't forget to save fp0). what to do now?
# well, we simply have to get to go to _real_unfl()!
funfl_unfl_on:
# The `060 FPU multiplier hardware is such that if the result of a
# multiply operation is the smallest possible normalized number
# (0x00000000_80000000_00000000), then the machine will take an
# underflow exception. Since this is incorrect, we check here to see
# if our emulation, after re-doing the operation, decided that
# no underflow was called for.
btst &unfl_bit,FPSR_EXCEPT(%a6)
beq.w funfl_chkinex
funfl_unfl_on2:
fmovm.x &0x40,FP_SRC(%a6) # save EXOP (fp1) to stack
frestore FP_SRC(%a6) # do this after fmovm,other f<op>s!
unlk %a6
bra.l _real_unfl
# underflow occurred but is disabled. meanwhile, inexact is enabled. Therefore,
# we must jump to real_inex().
funfl_inex_on:
# The `060 FPU multiplier hardware is such that if the result of a
# multiply operation is the smallest possible normalized number
# (0x00000000_80000000_00000000), then the machine will take an
# underflow exception.
# But, whether bogus or not, if inexact is enabled AND it occurred,
# then we have to branch to real_inex.
btst &inex2_bit,FPSR_EXCEPT(%a6)
beq.w funfl_exit
funfl_inex_on2:
fmovm.x &0x40,FP_SRC(%a6) # save EXOP to stack
mov.b &0xc4,1+EXC_VOFF(%a6) # vector offset = 0xc4
mov.w &0xe001,2+FP_SRC(%a6) # save exc status
btst &0x7,(%sp) # is trace on?
beq.l _fpsp_done # no
fmov.l %fpiar,0x8(%sp) # "Current PC" is in FPIAR
mov.w &0x2024,0x6(%sp) # stk fmt = 0x2; voff = 0x024
bra.l _real_trace
#########################################################################
# XDEF **************************************************************** #
# _fpsp_unsupp(): 060FPSP entry point for FP "Unimplemented #
# Data Type" exception. #
# #
# This handler should be the first code executed upon taking the #
# FP Unimplemented Data Type exception in an operating system. #
# #
# XREF **************************************************************** #
# _imem_read_{word,long}() - read instruction word/longword #
# fix_skewed_ops() - adjust src operand in fsave frame #
# set_tag_x() - determine optype of src/dst operands #
# store_fpreg() - store opclass 0 or 2 result to FP regfile #
# unnorm_fix() - change UNNORM operands to NORM or ZERO #
# load_fpn2() - load dst operand from FP regfile #
# load_fpn1() - load src operand from FP regfile #
# fout() - emulate an opclass 3 instruction #
# tbl_unsupp - add of table of emulation routines for opclass 0,2 #
# _real_inex() - "callout" to operating system inexact handler #
# _fpsp_done() - "callout" for exit; work all done #
# _real_trace() - "callout" for Trace enabled exception #
# funimp_skew() - adjust fsave src ops to "incorrect" value #
# _real_snan() - "callout" for SNAN exception #
# _real_operr() - "callout" for OPERR exception #
# _real_ovfl() - "callout" for OVFL exception #
# _real_unfl() - "callout" for UNFL exception #
# get_packed() - fetch packed operand from memory #
# #
# INPUT *************************************************************** #
# - The system stack contains the "Unimp Data Type" stk frame #
# - The fsave frame contains the ssrc op (for UNNORM/DENORM) #
# #
# OUTPUT ************************************************************** #
# If Inexact exception (opclass 3): #
# - The system stack is changed to an Inexact exception stk frame #
# If SNAN exception (opclass 3): #
# - The system stack is changed to an SNAN exception stk frame #
# If OPERR exception (opclass 3): #
# - The system stack is changed to an OPERR exception stk frame #
# If OVFL exception (opclass 3): #
# - The system stack is changed to an OVFL exception stk frame #
# If UNFL exception (opclass 3): #
# - The system stack is changed to an UNFL exception stack frame #
# If Trace exception enabled: #
# - The system stack is changed to a Trace exception stack frame #
# Else: (normal case) #
# - Correct result has been stored as appropriate #
# #
# ALGORITHM *********************************************************** #
# Two main instruction types can enter here: (1) DENORM or UNNORM #
# unimplemented data types. These can be either opclass 0,2 or 3 #
# instructions, and (2) PACKED unimplemented data format instructions #
# also of opclasses 0,2, or 3. #
# For UNNORM/DENORM opclass 0 and 2, the handler fetches the src #
# operand from the fsave state frame and the dst operand (if dyadic) #
# from the FP register file. The instruction is then emulated by #
# choosing an emulation routine from a table of routines indexed by #
# instruction type. Once the instruction has been emulated and result #
# saved, then we check to see if any enabled exceptions resulted from #
# instruction emulation. If none, then we exit through the "callout" #
# _fpsp_done(). If there is an enabled FP exception, then we insert #
# this exception into the FPU in the fsave state frame and then exit #
# through _fpsp_done(). #
# PACKED opclass 0 and 2 is similar in how the instruction is #
# emulated and exceptions handled. The differences occur in how the #
# handler loads the packed op (by calling get_packed() routine) and #
# by the fact that a Trace exception could be pending for PACKED ops. #
# If a Trace exception is pending, then the current exception stack #
# frame is changed to a Trace exception stack frame and an exit is #
# made through _real_trace(). #
# For UNNORM/DENORM opclass 3, the actual move out to memory is #
# performed by calling the routine fout(). If no exception should occur #
# as the result of emulation, then an exit either occurs through #
# _fpsp_done() or through _real_trace() if a Trace exception is pending #
# (a Trace stack frame must be created here, too). If an FP exception #
# should occur, then we must create an exception stack frame of that #
# type and jump to either _real_snan(), _real_operr(), _real_inex(), #
# _real_unfl(), or _real_ovfl() as appropriate. PACKED opclass 3 #
# emulation is performed in a similar manner. #
# #
#########################################################################
#
# (1) DENORM and UNNORM (unimplemented) data types:
#
# post-instruction
# *****************
# * EA *
# pre-instruction * *
# ***************** *****************
# * 0x0 * 0x0dc * * 0x3 * 0x0dc *
# ***************** *****************
# * Next * * Next *
# * PC * * PC *
# ***************** *****************
# * SR * * SR *
# ***************** *****************
#
# (2) PACKED format (unsupported) opclasses two and three:
# *****************
# * EA *
# * *
# *****************
# * 0x2 * 0x0dc *
# *****************
# * Next *
# * PC *
# *****************
# * SR *
# *****************
# global _fpsp_unsupp
_fpsp_unsupp:
link.w %a6,&-LOCAL_SIZE # init stack frame
fsave FP_SRC(%a6) # save fp state
movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1
fmovm.l %fpcr,%fpsr,%fpiar,USER_FPCR(%a6) # save ctrl regs
fmovm.x &0xc0,EXC_FPREGS(%a6) # save fp0-fp1 on stack
btst &0x5,EXC_SR(%a6) # user or supervisor mode?
bne.b fu_s
fu_u:
mov.l %usp,%a0 # fetch user stack pointer
mov.l %a0,EXC_A7(%a6) # save on stack
bra.b fu_cont
# if the exception is an opclass zero or two unimplemented data type
# exception, then the a7' calculated here is wrong since it doesn't
# stack an ea. however, we don't need an a7' for this case anyways.
fu_s:
lea 0x4+EXC_EA(%a6),%a0 # load old a7'
mov.l %a0,EXC_A7(%a6) # save on stack
fu_cont:
# the FPIAR holds the "current PC" of the faulting instruction
# the FPIAR should be set correctly for ALL exceptions passing through
# this point.
mov.l USER_FPIAR(%a6),EXC_EXTWPTR(%a6)
mov.l EXC_EXTWPTR(%a6),%a0 # fetch instruction addr
addq.l &0x4,EXC_EXTWPTR(%a6) # incr instruction ptr
bsr.l _imem_read_long # fetch the instruction words
mov.l %d0,EXC_OPWORD(%a6) # store OPWORD and EXTWORD
############################
clr.b SPCOND_FLG(%a6) # clear special condition flag
# Separate opclass three (fpn-to-mem) ops since they have a different
# stack frame and protocol.
btst &0x5,EXC_CMDREG(%a6) # is it an fmove out?
bne.w fu_out # yes
# Separate packed opclass two instructions.
bfextu EXC_CMDREG(%a6){&0:&6},%d0
cmpi.b %d0,&0x13
beq.w fu_in_pack
# I'm not sure at this point what FPSR bits are valid for this instruction.
# so, since the emulation routines re-create them anyways, zero exception field
andi.l &0x00ff00ff,USER_FPSR(%a6) # zero exception field
fmov.l &0x0,%fpcr # zero current control regs
fmov.l &0x0,%fpsr
# Opclass two w/ memory-to-fpn operation will have an incorrect extended
# precision format if the src format was single or double and the
# source data type was an INF, NAN, DENORM, or UNNORM
lea FP_SRC(%a6),%a0 # pass ptr to input
bsr.l fix_skewed_ops
# we don't know whether the src operand or the dst operand (or both) is the
# UNNORM or DENORM. call the function that tags the operand type. if the
# input is an UNNORM, then convert it to a NORM, DENORM, or ZERO.
lea FP_SRC(%a6),%a0 # pass: ptr to src op
bsr.l set_tag_x # tag the operand type
cmpi.b %d0,&UNNORM # is operand an UNNORM?
bne.b fu_op2 # no
bsr.l unnorm_fix # yes; convert to NORM,DENORM,or ZERO
# bit five of the fp extension word separates the monadic and dyadic operations
# at this point
btst &0x5,1+EXC_CMDREG(%a6) # is operation monadic or dyadic?
beq.b fu_extract # monadic
cmpi.b 1+EXC_CMDREG(%a6),&0x3a # is operation an ftst?
beq.b fu_extract # yes, so it's monadic, too
bsr.l load_fpn2 # load dst into FP_DST
lea FP_DST(%a6),%a0 # pass: ptr to dst op
bsr.l set_tag_x # tag the operand type
cmpi.b %d0,&UNNORM # is operand an UNNORM?
bne.b fu_op2_done # no
bsr.l unnorm_fix # yes; convert to NORM,DENORM,or ZERO
fu_op2_done:
mov.b %d0,DTAG(%a6) # save dst optype tag
#
# Exceptions in order of precedence:
# BSUN : none
# SNAN : all dyadic ops
# OPERR : fsqrt(-NORM)
# OVFL : all except ftst,fcmp
# UNFL : all except ftst,fcmp
# DZ : fdiv
# INEX2 : all except ftst,fcmp
# INEX1 : none (packed doesn't go through here)
#
# we determine the highest priority exception(if any) set by the
# emulation routine that has also been enabled by the user.
mov.b FPCR_ENABLE(%a6),%d0 # fetch exceptions set
bne.b fu_in_ena # some are enabled
fu_in_cont:
# fcmp and ftst do not store any result.
mov.b 1+EXC_CMDREG(%a6),%d0 # fetch extension
andi.b &0x38,%d0 # extract bits 3-5
cmpi.b %d0,&0x38 # is instr fcmp or ftst?
beq.b fu_in_exit # yes
bfextu EXC_CMDREG(%a6){&6:&3},%d0 # dyadic; load dst reg
bsr.l store_fpreg # store the result
fu_in_ena:
and.b FPSR_EXCEPT(%a6),%d0 # keep only ones enabled
bfffo %d0{&24:&8},%d0 # find highest priority exception
bne.b fu_in_exc # there is at least one set
#
# No exceptions occurred that were also enabled. Now:
#
# if (OVFL && ovfl_disabled && inexact_enabled) {
# branch to _real_inex() (even if the result was exact!);
# } else {
# save the result in the proper fp reg (unless the op is fcmp or ftst);
# return;
# }
#
btst &ovfl_bit,FPSR_EXCEPT(%a6) # was overflow set?
beq.b fu_in_cont # no
fu_in_ovflchk:
btst &inex2_bit,FPCR_ENABLE(%a6) # was inexact enabled?
beq.b fu_in_cont # no
bra.w fu_in_exc_ovfl # go insert overflow frame
#
# An exception occurred and that exception was enabled:
#
# shift enabled exception field into lo byte of d0;
# if (((INEX2 || INEX1) && inex_enabled && OVFL && ovfl_disabled) ||
# ((INEX2 || INEX1) && inex_enabled && UNFL && unfl_disabled)) {
# /* # * this is the case where we must call _real_inex() now or else # * there will be no other way to pass it the exceptional operand
# */
# call _real_inex();
# } else {
# restore exc state (SNAN||OPERR||OVFL||UNFL||DZ||INEX) into the FPU;
# }
#
fu_in_exc:
subi.l &24,%d0 # fix offset to be 0-8
cmpi.b %d0,&0x6 # is exception INEX? (6)
bne.b fu_in_exc_exit # no
# the enabled exception was inexact
btst &unfl_bit,FPSR_EXCEPT(%a6) # did disabled underflow occur?
bne.w fu_in_exc_unfl # yes
btst &ovfl_bit,FPSR_EXCEPT(%a6) # did disabled overflow occur?
bne.w fu_in_exc_ovfl # yes
# here, we insert the correct fsave status value into the fsave frame for the
# corresponding exception. the operand in the fsave frame should be the original
# src operand.
fu_in_exc_exit:
mov.l %d0,-(%sp) # save d0
bsr.l funimp_skew # skew sgl or dbl inputs
mov.l (%sp)+,%d0 # restore d0
mov.w (tbl_except.b,%pc,%d0.w*2),2+FP_SRC(%a6) # create exc status
# If the input operand to this operation was opclass two and a single
# or double precision denorm, inf, or nan, the operand needs to be
# "corrected" in order to have the proper equivalent extended precision
# number. global fix_skewed_ops
fix_skewed_ops:
bfextu EXC_CMDREG(%a6){&0:&6},%d0 # extract opclass,src fmt
cmpi.b %d0,&0x11 # is class = 2 & fmt = sgl?
beq.b fso_sgl # yes
cmpi.b %d0,&0x15 # is class = 2 & fmt = dbl?
beq.b fso_dbl # yes
rts # no
fso_sgl_dnrm_zero:
andi.l &0x7fffffff,LOCAL_HI(%a0) # clear j-bit
beq.b fso_zero # it's a skewed zero
fso_sgl_dnrm:
# here, we count on norm not to alter a0...
bsr.l norm # normalize mantissa
neg.w %d0 # -shft amt
addi.w &0x3f81,%d0 # adjust new exponent
andi.w &0x8000,LOCAL_EX(%a0) # clear old exponent
or.w %d0,LOCAL_EX(%a0) # insert new exponent
rts
fso_dbl_dnrm_zero:
andi.l &0x7fffffff,LOCAL_HI(%a0) # clear j-bit
bne.b fso_dbl_dnrm # it's a skewed denorm
tst.l LOCAL_LO(%a0) # is it a zero?
beq.b fso_zero # yes
fso_dbl_dnrm:
# here, we count on norm not to alter a0...
bsr.l norm # normalize mantissa
neg.w %d0 # -shft amt
addi.w &0x3c01,%d0 # adjust new exponent
andi.w &0x8000,LOCAL_EX(%a0) # clear old exponent
or.w %d0,LOCAL_EX(%a0) # insert new exponent
rts
# fmove out took an unimplemented data type exception.
# the src operand is in FP_SRC. Call _fout() to write out the result and
# to determine which exceptions, if any, to take.
fu_out:
# Separate packed move outs from the UNNORM and DENORM move outs.
bfextu EXC_CMDREG(%a6){&3:&3},%d0
cmpi.b %d0,&0x3
beq.w fu_out_pack
cmpi.b %d0,&0x7
beq.w fu_out_pack
# I'm not sure at this point what FPSR bits are valid for this instruction.
# so, since the emulation routines re-create them anyways, zero exception field.
# fmove out doesn't affect ccodes.
and.l &0xffff00ff,USER_FPSR(%a6) # zero exception field
fmov.l &0x0,%fpcr # zero current control regs
fmov.l &0x0,%fpsr
# the src can ONLY be a DENORM or an UNNORM! so, don't make any big subroutine
# call here. just figure out what it is...
mov.w FP_SRC_EX(%a6),%d0 # get exponent
andi.w &0x7fff,%d0 # strip sign
beq.b fu_out_denorm # it's a DENORM
lea FP_SRC(%a6),%a0
bsr.l unnorm_fix # yes; fix it
mov.l (%a6),EXC_A6(%a6) # in case a6 changes
bsr.l fout # call fmove out routine
# Exceptions in order of precedence:
# BSUN : none
# SNAN : none
# OPERR : fmove.{b,w,l} out of large UNNORM
# OVFL : fmove.{s,d}
# UNFL : fmove.{s,d,x}
# DZ : none
# INEX2 : all
# INEX1 : none (packed doesn't travel through here)
# determine the highest priority exception(if any) set by the
# emulation routine that has also been enabled by the user.
mov.b FPCR_ENABLE(%a6),%d0 # fetch exceptions enabled
bne.w fu_out_ena # some are enabled
fu_out_done:
mov.l EXC_A6(%a6),(%a6) # in case a6 changed
# on extended precision opclass three instructions using pre-decrement or
# post-increment addressing mode, the address register is not updated. is the
# address register was the stack pointer used from user mode, then let's update
# it here. if it was used from supervisor mode, then we have to handle this
# as a special case.
btst &0x5,EXC_SR(%a6)
bne.b fu_out_done_s
btst &0x7,(%sp) # is trace on?
bne.b fu_out_trace # yes
bra.l _fpsp_done
# is the ea mode pre-decrement of the stack pointer from supervisor mode?
# ("fmov.x fpm,-(a7)") if so,
fu_out_done_s:
cmpi.b SPCOND_FLG(%a6),&mda7_flg
bne.b fu_out_done_cont
# the extended precision result is still in fp0. but, we need to save it
# somewhere on the stack until we can copy it to its final resting place.
# here, we're counting on the top of the stack to be the old place-holders
# for fp0/fp1 which have already been restored. that way, we can write
# over those destinations with the shifted stack frame.
fmovm.x &0x80,FP_SRC(%a6) # put answer on stack
# now, copy the result to the proper place on the stack
mov.l LOCAL_SIZE+FP_SRC_EX(%sp),LOCAL_SIZE+EXC_SR+0x0(%sp)
mov.l LOCAL_SIZE+FP_SRC_HI(%sp),LOCAL_SIZE+EXC_SR+0x4(%sp)
mov.l LOCAL_SIZE+FP_SRC_LO(%sp),LOCAL_SIZE+EXC_SR+0x8(%sp)
add.l &LOCAL_SIZE-0x8,%sp
btst &0x7,(%sp)
bne.b fu_out_trace
bra.l _fpsp_done
fu_out_ena:
and.b FPSR_EXCEPT(%a6),%d0 # keep only ones enabled
bfffo %d0{&24:&8},%d0 # find highest priority exception
bne.b fu_out_exc # there is at least one set
# no exceptions were set.
# if a disabled overflow occurred and inexact was enabled but the result
# was exact, then a branch to _real_inex() is made.
btst &ovfl_bit,FPSR_EXCEPT(%a6) # was overflow set?
beq.w fu_out_done # no
fu_out_ovflchk:
btst &inex2_bit,FPCR_ENABLE(%a6) # was inexact enabled?
beq.w fu_out_done # no
bra.w fu_inex # yes
#
# The fp move out that took the "Unimplemented Data Type" exception was
# being traced. Since the stack frames are similar, get the "current" PC
# from FPIAR and put it in the trace stack frame then jump to _real_trace().
#
# UNSUPP FRAME TRACE FRAME
# ***************** *****************
# * EA * * Current *
# * * * PC *
# ***************** *****************
# * 0x3 * 0x0dc * * 0x2 * 0x024 *
# ***************** *****************
# * Next * * Next *
# * PC * * PC *
# ***************** *****************
# * SR * * SR *
# ***************** *****************
#
fu_out_trace:
mov.w &0x2024,0x6(%sp)
fmov.l %fpiar,0x8(%sp)
bra.l _real_trace
# an exception occurred and that exception was enabled.
fu_out_exc:
subi.l &24,%d0 # fix offset to be 0-8
# we don't mess with the existing fsave frame. just re-insert it and
# jump to the "_real_{}()" handler...
mov.w (tbl_fu_out.b,%pc,%d0.w*2),%d0
jmp (tbl_fu_out.b,%pc,%d0.w*1)
swbeg &0x8
tbl_fu_out:
short tbl_fu_out - tbl_fu_out # BSUN can't happen
short tbl_fu_out - tbl_fu_out # SNAN can't happen
short fu_operr - tbl_fu_out # OPERR
short fu_ovfl - tbl_fu_out # OVFL
short fu_unfl - tbl_fu_out # UNFL
short tbl_fu_out - tbl_fu_out # DZ can't happen
short fu_inex - tbl_fu_out # INEX2
short tbl_fu_out - tbl_fu_out # INEX1 won't make it here
# for snan,operr,ovfl,unfl, src op is still in FP_SRC so just
# frestore it.
fu_snan:
fmovm.x EXC_FPREGS(%a6),&0xc0 # restore fp0/fp1
fmovm.l USER_FPCR(%a6),%fpcr,%fpsr,%fpiar # restore ctrl regs
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
# underflow can happen for extended precision. extended precision opclass
# three instruction exceptions don't update the stack pointer. so, if the
# exception occurred from user mode, then simply update a7 and exit normally.
# if the exception occurred from supervisor mode, check if
fu_unfl:
mov.l EXC_A6(%a6),(%a6) # restore a6
btst &0x5,EXC_SR(%a6)
bne.w fu_unfl_s
mov.l EXC_A7(%a6),%a0 # restore a7 whether we need
mov.l %a0,%usp # to or not...
fu_unfl_cont:
fmovm.x &0x40,FP_SRC(%a6) # save EXOP to the stack
fu_unfl_s:
cmpi.b SPCOND_FLG(%a6),&mda7_flg # was the <ea> mode -(sp)?
bne.b fu_unfl_cont
# the extended precision result is still in fp0. but, we need to save it
# somewhere on the stack until we can copy it to its final resting place
# (where the exc frame is currently). make sure it's not at the top of the
# frame or it will get overwritten when the exc stack frame is shifted "down".
fmovm.x &0x80,FP_SRC(%a6) # put answer on stack
fmovm.x &0x40,FP_DST(%a6) # put EXOP on stack
# now, copy the result to the proper place on the stack
mov.l LOCAL_SIZE+FP_SRC_EX(%sp),LOCAL_SIZE+EXC_SR+0x0(%sp)
mov.l LOCAL_SIZE+FP_SRC_HI(%sp),LOCAL_SIZE+EXC_SR+0x4(%sp)
mov.l LOCAL_SIZE+FP_SRC_LO(%sp),LOCAL_SIZE+EXC_SR+0x8(%sp)
add.l &LOCAL_SIZE-0x8,%sp
bra.l _real_unfl
# fmove in and out enter here.
fu_inex:
fmovm.x &0x40,FP_SRC(%a6) # save EXOP to the stack
# I'm not sure at this point what FPSR bits are valid for this instruction.
# so, since the emulation routines re-create them anyways, zero exception field
andi.l &0x0ff00ff,USER_FPSR(%a6) # zero exception field
fmov.l &0x0,%fpcr # zero current control regs
fmov.l &0x0,%fpsr
bsr.l get_packed # fetch packed src operand
lea FP_SRC(%a6),%a0 # pass ptr to src
bsr.l set_tag_x # set src optype tag
# bit five of the fp extension word separates the monadic and dyadic operations
# at this point
btst &0x5,1+EXC_CMDREG(%a6) # is operation monadic or dyadic?
beq.b fu_extract_p # monadic
cmpi.b 1+EXC_CMDREG(%a6),&0x3a # is operation an ftst?
beq.b fu_extract_p # yes, so it's monadic, too
bsr.l load_fpn2 # load dst into FP_DST
lea FP_DST(%a6),%a0 # pass: ptr to dst op
bsr.l set_tag_x # tag the operand type
cmpi.b %d0,&UNNORM # is operand an UNNORM?
bne.b fu_op2_done_p # no
bsr.l unnorm_fix # yes; convert to NORM,DENORM,or ZERO
fu_op2_done_p:
mov.b %d0,DTAG(%a6) # save dst optype tag
#
# Exceptions in order of precedence:
# BSUN : none
# SNAN : all dyadic ops
# OPERR : fsqrt(-NORM)
# OVFL : all except ftst,fcmp
# UNFL : all except ftst,fcmp
# DZ : fdiv
# INEX2 : all except ftst,fcmp
# INEX1 : all
#
# we determine the highest priority exception(if any) set by the
# emulation routine that has also been enabled by the user.
mov.b FPCR_ENABLE(%a6),%d0 # fetch exceptions enabled
bne.w fu_in_ena_p # some are enabled
fu_in_cont_p:
# fcmp and ftst do not store any result.
mov.b 1+EXC_CMDREG(%a6),%d0 # fetch extension
andi.b &0x38,%d0 # extract bits 3-5
cmpi.b %d0,&0x38 # is instr fcmp or ftst?
beq.b fu_in_exit_p # yes
bfextu EXC_CMDREG(%a6){&6:&3},%d0 # dyadic; load dst reg
bsr.l store_fpreg # store the result
fu_in_exit_p:
btst &0x5,EXC_SR(%a6) # user or supervisor?
bne.w fu_in_exit_s_p # supervisor
mov.l EXC_A7(%a6),%a0 # update user a7
mov.l %a0,%usp
btst &0x7,(%sp) # is trace on?
bne.w fu_trace_p # yes
bra.l _fpsp_done # exit to os
# the exception occurred in supervisor mode. check to see if the
# addressing mode was (a7)+. if so, we'll need to shift the
# stack frame "up".
fu_in_exit_s_p:
btst &mia7_bit,SPCOND_FLG(%a6) # was ea mode (a7)+
beq.b fu_in_exit_cont_p # no
# shift the stack frame "up". we don't really care about the <ea> field.
mov.l 0x4(%sp),0x10(%sp)
mov.l 0x0(%sp),0xc(%sp)
add.l &0xc,%sp
btst &0x7,(%sp) # is trace on?
bne.w fu_trace_p # yes
bra.l _fpsp_done # exit to os
fu_in_ena_p:
and.b FPSR_EXCEPT(%a6),%d0 # keep only ones enabled & set
bfffo %d0{&24:&8},%d0 # find highest priority exception
bne.b fu_in_exc_p # at least one was set
#
# No exceptions occurred that were also enabled. Now:
#
# if (OVFL && ovfl_disabled && inexact_enabled) {
# branch to _real_inex() (even if the result was exact!);
# } else {
# save the result in the proper fp reg (unless the op is fcmp or ftst);
# return;
# }
#
btst &ovfl_bit,FPSR_EXCEPT(%a6) # was overflow set?
beq.w fu_in_cont_p # no
fu_in_ovflchk_p:
btst &inex2_bit,FPCR_ENABLE(%a6) # was inexact enabled?
beq.w fu_in_cont_p # no
bra.w fu_in_exc_ovfl_p # do _real_inex() now
#
# An exception occurred and that exception was enabled:
#
# shift enabled exception field into lo byte of d0;
# if (((INEX2 || INEX1) && inex_enabled && OVFL && ovfl_disabled) ||
# ((INEX2 || INEX1) && inex_enabled && UNFL && unfl_disabled)) {
# /* # * this is the case where we must call _real_inex() now or else # * there will be no other way to pass it the exceptional operand
# */
# call _real_inex();
# } else {
# restore exc state (SNAN||OPERR||OVFL||UNFL||DZ||INEX) into the FPU;
# }
#
fu_in_exc_p:
subi.l &24,%d0 # fix offset to be 0-8
cmpi.b %d0,&0x6 # is exception INEX? (6 or 7)
blt.b fu_in_exc_exit_p # no
# the enabled exception was inexact
btst &unfl_bit,FPSR_EXCEPT(%a6) # did disabled underflow occur?
bne.w fu_in_exc_unfl_p # yes
btst &ovfl_bit,FPSR_EXCEPT(%a6) # did disabled overflow occur?
bne.w fu_in_exc_ovfl_p # yes
# here, we insert the correct fsave status value into the fsave frame for the
# corresponding exception. the operand in the fsave frame should be the original
# src operand.
# as a reminder for future predicted pain and agony, we are passing in fsave the
# "non-skewed" operand for cases of sgl and dbl src INFs,NANs, and DENORMs.
# this is INCORRECT for enabled SNAN which would give to the user the skewed SNAN!!!
fu_in_exc_exit_p:
btst &0x5,EXC_SR(%a6) # user or supervisor?
bne.w fu_in_exc_exit_s_p # supervisor
mov.l EXC_A7(%a6),%a0 # update user a7
mov.l %a0,%usp
# shift stack frame "up". who cares about <ea> field.
mov.l 0x4(%sp),0x10(%sp)
mov.l 0x0(%sp),0xc(%sp)
add.l &0xc,%sp
btst &0x7,(%sp) # is trace on?
bne.b fu_trace_p # yes
bra.l _fpsp_done # exit to os
#
# The opclass two PACKED instruction that took an "Unimplemented Data Type"
# exception was being traced. Make the "current" PC the FPIAR and put it in the
# trace stack frame then jump to _real_trace().
#
# UNSUPP FRAME TRACE FRAME
# ***************** *****************
# * EA * * Current *
# * * * PC *
# ***************** *****************
# * 0x2 * 0x0dc * * 0x2 * 0x024 *
# ***************** *****************
# * Next * * Next *
# * PC * * PC *
# ***************** *****************
# * SR * * SR *
# ***************** *****************
fu_trace_p:
mov.w &0x2024,0x6(%sp)
fmov.l %fpiar,0x8(%sp)
# I'm not sure at this point what FPSR bits are valid for this instruction.
# so, since the emulation routines re-create them anyways, zero exception field.
# fmove out doesn't affect ccodes.
and.l &0xffff00ff,USER_FPSR(%a6) # zero exception field
fmov.l &0x0,%fpcr # zero current control regs
fmov.l &0x0,%fpsr
bfextu EXC_CMDREG(%a6){&6:&3},%d0
bsr.l load_fpn1
# unlike other opclass 3, unimplemented data type exceptions, packed must be
# able to detect all operand types.
lea FP_SRC(%a6),%a0
bsr.l set_tag_x # tag the operand type
cmpi.b %d0,&UNNORM # is operand an UNNORM?
bne.b fu_op2_p # no
bsr.l unnorm_fix # yes; convert to NORM,DENORM,or ZERO
fu_op2_p:
mov.b %d0,STAG(%a6) # save src optype tag
mov.l (%a6),EXC_A6(%a6) # in case a6 changes
bsr.l fout # call fmove out routine
# Exceptions in order of precedence:
# BSUN : no
# SNAN : yes
# OPERR : if ((k_factor > +17) || (dec. exp exceeds 3 digits))
# OVFL : no
# UNFL : no
# DZ : no
# INEX2 : yes
# INEX1 : no
# determine the highest priority exception(if any) set by the
# emulation routine that has also been enabled by the user.
mov.b FPCR_ENABLE(%a6),%d0 # fetch exceptions enabled
bne.w fu_out_ena_p # some are enabled
btst &0x7,(%sp) # is trace on?
bne.w fu_trace_p # yes
bra.l _fpsp_done # exit to os
# the exception occurred in supervisor mode. check to see if the
# addressing mode was -(a7). if so, we'll need to shift the
# stack frame "down".
fu_out_exit_s_p:
btst &mda7_bit,SPCOND_FLG(%a6) # was ea mode -(a7)
beq.b fu_out_exit_cont_p # no
# now, copy the result to the proper place on the stack
mov.l LOCAL_SIZE+FP_DST_EX(%sp),LOCAL_SIZE+EXC_SR+0x0(%sp)
mov.l LOCAL_SIZE+FP_DST_HI(%sp),LOCAL_SIZE+EXC_SR+0x4(%sp)
mov.l LOCAL_SIZE+FP_DST_LO(%sp),LOCAL_SIZE+EXC_SR+0x8(%sp)
# an exception occurred and that exception was enabled.
# the only exception possible on packed move out are INEX, OPERR, and SNAN.
fu_out_exc_p:
cmpi.b %d0,&0x1a
bgt.w fu_inex_p2
beq.w fu_operr_p
# the instruction was "fmove.p fpn,-(a7)" from supervisor mode.
# the strategy is to move the exception frame "down" 12 bytes. then, we
# can store the default result where the exception frame was.
fmovm.x EXC_FPREGS(%a6),&0xc0 # restore fp0/fp1
fmovm.l USER_FPCR(%a6),%fpcr,%fpsr,%fpiar # restore ctrl regs
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
mov.w &0x30d8,EXC_VOFF(%a6) # vector offset = 0xd0
mov.w &0xe006,2+FP_SRC(%a6) # set fsave status
# now, we copy the default result to its proper location
mov.l LOCAL_SIZE+FP_DST_EX(%sp),LOCAL_SIZE+0x4(%sp)
mov.l LOCAL_SIZE+FP_DST_HI(%sp),LOCAL_SIZE+0x8(%sp)
mov.l LOCAL_SIZE+FP_DST_LO(%sp),LOCAL_SIZE+0xc(%sp)
# the instruction was "fmove.p fpn,-(a7)" from supervisor mode.
# the strategy is to move the exception frame "down" 12 bytes. then, we
# can store the default result where the exception frame was.
fmovm.x EXC_FPREGS(%a6),&0xc0 # restore fp0/fp1
fmovm.l USER_FPCR(%a6),%fpcr,%fpsr,%fpiar # restore ctrl regs
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
mov.w &0x30d0,EXC_VOFF(%a6) # vector offset = 0xd0
mov.w &0xe004,2+FP_SRC(%a6) # set fsave status
# now, we copy the default result to its proper location
mov.l LOCAL_SIZE+FP_DST_EX(%sp),LOCAL_SIZE+0x4(%sp)
mov.l LOCAL_SIZE+FP_DST_HI(%sp),LOCAL_SIZE+0x8(%sp)
mov.l LOCAL_SIZE+FP_DST_LO(%sp),LOCAL_SIZE+0xc(%sp)
# the instruction was "fmove.p fpn,-(a7)" from supervisor mode.
# the strategy is to move the exception frame "down" 12 bytes. then, we
# can store the default result where the exception frame was.
fmovm.x EXC_FPREGS(%a6),&0xc0 # restore fp0/fp1
fmovm.l USER_FPCR(%a6),%fpcr,%fpsr,%fpiar # restore ctrl regs
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
mov.w &0x30c4,EXC_VOFF(%a6) # vector offset = 0xc4
mov.w &0xe001,2+FP_SRC(%a6) # set fsave status
# now, we copy the default result to its proper location
mov.l LOCAL_SIZE+FP_DST_EX(%sp),LOCAL_SIZE+0x4(%sp)
mov.l LOCAL_SIZE+FP_DST_HI(%sp),LOCAL_SIZE+0x8(%sp)
mov.l LOCAL_SIZE+FP_DST_LO(%sp),LOCAL_SIZE+0xc(%sp)
#
# if we're stuffing a source operand back into an fsave frame then we
# have to make sure that for single or double source operands that the
# format stuffed is as weird as the hardware usually makes it.
# global funimp_skew
funimp_skew:
bfextu EXC_EXTWORD(%a6){&3:&3},%d0 # extract src specifier
cmpi.b %d0,&0x1 # was src sgl?
beq.b funimp_skew_sgl # yes
cmpi.b %d0,&0x5 # was src dbl?
beq.b funimp_skew_dbl # yes
rts
funimp_skew_sgl:
mov.w FP_SRC_EX(%a6),%d0 # fetch DENORM exponent
andi.w &0x7fff,%d0 # strip sign
beq.b funimp_skew_sgl_not
cmpi.w %d0,&0x3f80
bgt.b funimp_skew_sgl_not
neg.w %d0 # make exponent negative
addi.w &0x3f81,%d0 # find amt to shift
mov.l FP_SRC_HI(%a6),%d1 # fetch DENORM hi(man)
lsr.l %d0,%d1 # shift it
bset &31,%d1 # set j-bit
mov.l %d1,FP_SRC_HI(%a6) # insert new hi(man)
andi.w &0x8000,FP_SRC_EX(%a6) # clear old exponent
ori.w &0x3f80,FP_SRC_EX(%a6) # insert new "skewed" exponent
funimp_skew_sgl_not:
rts
#########################################################################
# XDEF **************************************************************** #
# _fpsp_effadd(): 060FPSP entry point for FP "Unimplemented #
# effective address" exception. #
# #
# This handler should be the first code executed upon taking the #
# FP Unimplemented Effective Address exception in an operating #
# system. #
# #
# XREF **************************************************************** #
# _imem_read_long() - read instruction longword #
# fix_skewed_ops() - adjust src operand in fsave frame #
# set_tag_x() - determine optype of src/dst operands #
# store_fpreg() - store opclass 0 or 2 result to FP regfile #
# unnorm_fix() - change UNNORM operands to NORM or ZERO #
# load_fpn2() - load dst operand from FP regfile #
# tbl_unsupp - add of table of emulation routines for opclass 0,2 #
# decbin() - convert packed data to FP binary data #
# _real_fpu_disabled() - "callout" for "FPU disabled" exception #
# _real_access() - "callout" for access error exception #
# _mem_read() - read extended immediate operand from memory #
# _fpsp_done() - "callout" for exit; work all done #
# _real_trace() - "callout" for Trace enabled exception #
# fmovm_dynamic() - emulate dynamic fmovm instruction #
# fmovm_ctrl() - emulate fmovm control instruction #
# #
# INPUT *************************************************************** #
# - The system stack contains the "Unimplemented <ea>" stk frame #
# #
# OUTPUT ************************************************************** #
# If access error: #
# - The system stack is changed to an access error stack frame #
# If FPU disabled: #
# - The system stack is changed to an FPU disabled stack frame #
# If Trace exception enabled: #
# - The system stack is changed to a Trace exception stack frame #
# Else: (normal case) #
# - None (correct result has been stored as appropriate) #
# #
# ALGORITHM *********************************************************** #
# This exception handles 3 types of operations: #
# (1) FP Instructions using extended precision or packed immediate #
# addressing mode. #
# (2) The "fmovm.x" instruction w/ dynamic register specification. #
# (3) The "fmovm.l" instruction w/ 2 or 3 control registers. #
# #
# For immediate data operations, the data is read in w/ a #
# _mem_read() "callout", converted to FP binary (if packed), and used #
# as the source operand to the instruction specified by the instruction #
# word. If no FP exception should be reported ads a result of the #
# emulation, then the result is stored to the destination register and #
# the handler exits through _fpsp_done(). If an enabled exc has been #
# signalled as a result of emulation, then an fsave state frame #
# corresponding to the FP exception type must be entered into the 060 #
# FPU before exiting. In either the enabled or disabled cases, we #
# must also check if a Trace exception is pending, in which case, we #
# must create a Trace exception stack frame from the current exception #
# stack frame. If no Trace is pending, we simply exit through #
# _fpsp_done(). #
# For "fmovm.x", call the routine fmovm_dynamic() which will #
# decode and emulate the instruction. No FP exceptions can be pending #
# as a result of this operation emulation. A Trace exception can be #
# pending, though, which means the current stack frame must be changed #
# to a Trace stack frame and an exit made through _real_trace(). #
# For the case of "fmovm.x Dn,-(a7)", where the offending instruction #
# was executed from supervisor mode, this handler must store the FP #
# register file values to the system stack by itself since #
# fmovm_dynamic() can't handle this. A normal exit is made through #
# fpsp_done(). #
# For "fmovm.l", fmovm_ctrl() is used to emulate the instruction. #
# Again, a Trace exception may be pending and an exit made through #
# _real_trace(). Else, a normal exit is made through _fpsp_done(). #
# #
# Before any of the above is attempted, it must be checked to #
# see if the FPU is disabled. Since the "Unimp <ea>" exception is taken #
# before the "FPU disabled" exception, but the "FPU disabled" exception #
# has higher priority, we check the disabled bit in the PCR. If set, #
# then we must create an 8 word"FPU disabled" exception stack frame #
# from the current 4 word exception stack frame. This includes #
# reproducing the effective address of the instruction to put on the #
# new stack frame. #
# #
# In the process of all emulation work, if a _mem_read() #
# "callout" returns a failing result indicating an access error, then #
# we must create an access error stack frame from the current stack #
# frame. This information includes a faulting address and a fault- #
# status-longword. These are created within this handler. #
# #
#########################################################################
global _fpsp_effadd
_fpsp_effadd:
# This exception type takes priority over the "Line F Emulator"
# exception. Therefore, the FPU could be disabled when entering here.
# So, we must check to see if it's disabled and handle that case separately.
mov.l %d0,-(%sp) # save d0
movc %pcr,%d0 # load proc cr
btst &0x1,%d0 # is FPU disabled?
bne.w iea_disabled # yes
mov.l (%sp)+,%d0 # restore d0
link %a6,&-LOCAL_SIZE # init stack frame
movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1
fmovm.l %fpcr,%fpsr,%fpiar,USER_FPCR(%a6) # save ctrl regs
fmovm.x &0xc0,EXC_FPREGS(%a6) # save fp0-fp1 on stack
# PC of instruction that took the exception is the PC in the frame
mov.l EXC_PC(%a6),EXC_EXTWPTR(%a6)
mov.l EXC_EXTWPTR(%a6),%a0 # fetch instruction addr
addq.l &0x4,EXC_EXTWPTR(%a6) # incr instruction ptr
bsr.l _imem_read_long # fetch the instruction words
mov.l %d0,EXC_OPWORD(%a6) # store OPWORD and EXTWORD
tst.w %d0 # is operation fmovem?
bmi.w iea_fmovm # yes
#
# here, we will have:
# fabs fdabs fsabs facos fmod
# fadd fdadd fsadd fasin frem
# fcmp fatan fscale
# fdiv fddiv fsdiv fatanh fsin
# fint fcos fsincos
# fintrz fcosh fsinh
# fmove fdmove fsmove fetox ftan
# fmul fdmul fsmul fetoxm1 ftanh
# fneg fdneg fsneg fgetexp ftentox
# fsgldiv fgetman ftwotox
# fsglmul flog10
# fsqrt flog2
# fsub fdsub fssub flogn
# ftst flognp1
# which can all use f<op>.{x,p}
# so, now it's immediate data extended precision AND PACKED FORMAT!
#
iea_op:
andi.l &0x00ff00ff,USER_FPSR(%a6)
btst &0xa,%d0 # is src fmt x or p?
bne.b iea_op_pack # packed
mov.l EXC_EXTWPTR(%a6),%a0 # pass: ptr to #<data>
lea FP_SRC(%a6),%a1 # pass: ptr to super addr
mov.l &0xc,%d0 # pass: 12 bytes
bsr.l _imem_read # read extended immediate
tst.l %d1 # did ifetch fail?
bne.w iea_iacc # yes
bra.b iea_op_setsrc
iea_op_pack:
mov.l EXC_EXTWPTR(%a6),%a0 # pass: ptr to #<data>
lea FP_SRC(%a6),%a1 # pass: ptr to super dst
mov.l &0xc,%d0 # pass: 12 bytes
bsr.l _imem_read # read packed operand
tst.l %d1 # did ifetch fail?
bne.w iea_iacc # yes
# The packed operand is an INF or a NAN if the exponent field is all ones.
bfextu FP_SRC(%a6){&1:&15},%d0 # get exp
cmpi.w %d0,&0x7fff # INF or NAN?
beq.b iea_op_setsrc # operand is an INF or NAN
# The packed operand is a zero if the mantissa is all zero, else it's
# a normal packed op.
mov.b 3+FP_SRC(%a6),%d0 # get byte 4
andi.b &0x0f,%d0 # clear all but last nybble
bne.b iea_op_gp_not_spec # not a zero
tst.l FP_SRC_HI(%a6) # is lw 2 zero?
bne.b iea_op_gp_not_spec # not a zero
tst.l FP_SRC_LO(%a6) # is lw 3 zero?
beq.b iea_op_setsrc # operand is a ZERO
iea_op_gp_not_spec:
lea FP_SRC(%a6),%a0 # pass: ptr to packed op
bsr.l decbin # convert to extended
fmovm.x &0x80,FP_SRC(%a6) # make this the srcop
iea_op_setsrc:
addi.l &0xc,EXC_EXTWPTR(%a6) # update extension word pointer
# FP_SRC now holds the src operand.
lea FP_SRC(%a6),%a0 # pass: ptr to src op
bsr.l set_tag_x # tag the operand type
mov.b %d0,STAG(%a6) # could be ANYTHING!!!
cmpi.b %d0,&UNNORM # is operand an UNNORM?
bne.b iea_op_getdst # no
bsr.l unnorm_fix # yes; convert to NORM/DENORM/ZERO
mov.b %d0,STAG(%a6) # set new optype tag
iea_op_getdst: clr.b STORE_FLG(%a6) # clear "store result" boolean
btst &0x5,1+EXC_CMDREG(%a6) # is operation monadic or dyadic?
beq.b iea_op_extract # monadic
btst &0x4,1+EXC_CMDREG(%a6) # is operation fsincos,ftst,fcmp?
bne.b iea_op_spec # yes
lea FP_DST(%a6),%a0 # pass: ptr to dst op
bsr.l set_tag_x # tag the operand type
mov.b %d0,DTAG(%a6) # could be ANYTHING!!!
cmpi.b %d0,&UNNORM # is operand an UNNORM?
bne.b iea_op_extract # no
bsr.l unnorm_fix # yes; convert to NORM/DENORM/ZERO
mov.b %d0,DTAG(%a6) # set new optype tag
bra.b iea_op_extract
# the operation is fsincos, ftst, or fcmp. only fcmp is dyadic
iea_op_spec:
btst &0x3,1+EXC_CMDREG(%a6) # is operation fsincos?
beq.b iea_op_extract # yes
# now, we're left with ftst and fcmp. so, first let's tag them so that they don't
# store a result. then, only fcmp will branch back and pick up a dst operand. st STORE_FLG(%a6) # don't store a final result
btst &0x1,1+EXC_CMDREG(%a6) # is operation fcmp?
beq.b iea_op_loaddst # yes
#
# Exceptions in order of precedence:
# BSUN : none
# SNAN : all operations
# OPERR : all reg-reg or mem-reg operations that can normally operr
# OVFL : same as OPERR
# UNFL : same as OPERR
# DZ : same as OPERR
# INEX2 : same as OPERR
# INEX1 : all packed immediate operations
#
# we determine the highest priority exception(if any) set by the
# emulation routine that has also been enabled by the user.
mov.b FPCR_ENABLE(%a6),%d0 # fetch exceptions enabled
bne.b iea_op_ena # some are enabled
# now, we save the result, unless, of course, the operation was ftst or fcmp.
# these don't save results.
iea_op_save:
tst.b STORE_FLG(%a6) # does this op store a result?
bne.b iea_op_exit1 # exit with no frestore
iea_op_store:
bfextu EXC_CMDREG(%a6){&6:&3},%d0 # fetch dst regno
bsr.l store_fpreg # store the result
iea_op_exit1:
mov.l EXC_PC(%a6),USER_FPIAR(%a6) # set FPIAR to "Current PC"
mov.l EXC_EXTWPTR(%a6),EXC_PC(%a6) # set"Next PC" in exc frame
btst &0x7,(%sp) # is trace on?
bne.w iea_op_trace # yes
bra.l _fpsp_done # exit to os
iea_op_ena:
and.b FPSR_EXCEPT(%a6),%d0 # keep only ones enable and set
bfffo %d0{&24:&8},%d0 # find highest priority exception
bne.b iea_op_exc # at least one was set
# no exception occurred. now, did a disabled, exact overflow occur with inexact
# enabled? if so, then we have to stuff an overflow frame into the FPU.
btst &ovfl_bit,FPSR_EXCEPT(%a6) # did overflow occur?
beq.b iea_op_save
iea_op_ovfl:
btst &inex2_bit,FPCR_ENABLE(%a6) # is inexact enabled?
beq.b iea_op_store # no
bra.b iea_op_exc_ovfl # yes
# an enabled exception occurred. we have to insert the exception type back into
# the machine.
iea_op_exc:
subi.l &24,%d0 # fix offset to be 0-8
cmpi.b %d0,&0x6 # is exception INEX?
bne.b iea_op_exc_force # no
# the enabled exception was inexact. so, if it occurs with an overflow
# or underflow that was disabled, then we have to force an overflow or
# underflow frame.
btst &ovfl_bit,FPSR_EXCEPT(%a6) # did overflow occur?
bne.b iea_op_exc_ovfl # yes
btst &unfl_bit,FPSR_EXCEPT(%a6) # did underflow occur?
bne.b iea_op_exc_unfl # yes
iea_op_exc_force:
mov.w (tbl_iea_except.b,%pc,%d0.w*2),2+FP_SRC(%a6)
bra.b iea_op_exit2 # exit with frestore
tbl_iea_except:
short 0xe002, 0xe006, 0xe004, 0xe005
short 0xe003, 0xe002, 0xe001, 0xe001
btst &0x7,(%sp) # is trace on?
bne.b iea_op_trace # yes
bra.l _fpsp_done # exit to os
#
# The opclass two instruction that took an "Unimplemented Effective Address"
# exception was being traced. Make the "current" PC the FPIAR and put it in
# the trace stack frame then jump to _real_trace().
#
# UNIMP EA FRAME TRACE FRAME
# ***************** *****************
# * 0x0 * 0x0f0 * * Current *
# ***************** * PC *
# * Current * *****************
# * PC * * 0x2 * 0x024 *
# ***************** *****************
# * SR * * Next *
# ***************** * PC *
# *****************
# * SR *
# *****************
iea_op_trace:
mov.l (%sp),-(%sp) # shift stack frame "down"
mov.w 0x8(%sp),0x4(%sp)
mov.w &0x2024,0x6(%sp) # stk fmt = 0x2; voff = 0x024
fmov.l %fpiar,0x8(%sp) # "Current PC" is in FPIAR
bra.l _real_trace
#########################################################################
iea_fmovm:
btst &14,%d0 # ctrl or data reg
beq.w iea_fmovm_ctrl
iea_fmovm_data:
btst &0x5,EXC_SR(%a6) # user or supervisor mode
bne.b iea_fmovm_data_s
iea_fmovm_data_u:
mov.l %usp,%a0
mov.l %a0,EXC_A7(%a6) # store current a7
bsr.l fmovm_dynamic # do dynamic fmovm
mov.l EXC_A7(%a6),%a0 # load possibly new a7
mov.l %a0,%usp # update usp
bra.w iea_fmovm_exit
# right now, d0 = the size.
# the data has been fetched from the supervisor stack, but we have not
# incremented the stack pointer by the appropriate number of bytes.
# do it here.
iea_fmovm_data_postinc:
btst &0x7,EXC_SR(%a6)
bne.b iea_fmovm_data_pi_trace
btst &0x7,EXC_SR(%a6) # is trace on?
bne.b iea_fmovm_trace # yes
mov.l EXC_EXTWPTR(%a6),EXC_PC(%a6) # set Next PC
unlk %a6 # unravel the frame
bra.l _fpsp_done # exit to os
#
# The control reg instruction that took an "Unimplemented Effective Address"
# exception was being traced. The "Current PC" for the trace frame is the
# PC stacked for Unimp EA. The "Next PC" is in EXC_EXTWPTR.
# After fixing the stack frame, jump to _real_trace().
#
# UNIMP EA FRAME TRACE FRAME
# ***************** *****************
# * 0x0 * 0x0f0 * * Current *
# ***************** * PC *
# * Current * *****************
# * PC * * 0x2 * 0x024 *
# ***************** *****************
# * SR * * Next *
# ***************** * PC *
# *****************
# * SR *
# *****************
# this ain't a pretty solution, but it works:
# -restore a6 (not with unlk)
# -shift stack frame down over where old a6 used to be
# -add LOCAL_SIZE to stack pointer
iea_fmovm_trace:
mov.l (%a6),%a6 # restore frame pointer
mov.w EXC_SR+LOCAL_SIZE(%sp),0x0+LOCAL_SIZE(%sp)
mov.l EXC_PC+LOCAL_SIZE(%sp),0x8+LOCAL_SIZE(%sp)
mov.l EXC_EXTWPTR+LOCAL_SIZE(%sp),0x2+LOCAL_SIZE(%sp)
mov.w &0x2024,0x6+LOCAL_SIZE(%sp) # stk fmt = 0x2; voff = 0x024
add.l &LOCAL_SIZE,%sp # clear stack frame
bra.l _real_trace
#########################################################################
# The FPU is disabled and so we should really have taken the "Line
# F Emulator" exception. So, here we create an 8-word stack frame
# from our 4-word stack frame. This means we must calculate the length
# the faulting instruction to get the "next PC". This is trivial for
# immediate operands but requires some extra work for fmovm dynamic
# which can use most addressing modes.
iea_disabled:
mov.l (%sp)+,%d0 # restore d0
link %a6,&-LOCAL_SIZE # init stack frame
movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1
# PC of instruction that took the exception is the PC in the frame
mov.l EXC_PC(%a6),EXC_EXTWPTR(%a6)
mov.l EXC_EXTWPTR(%a6),%a0 # fetch instruction addr
addq.l &0x4,EXC_EXTWPTR(%a6) # incr instruction ptr
bsr.l _imem_read_long # fetch the instruction words
mov.l %d0,EXC_OPWORD(%a6) # store OPWORD and EXTWORD
tst.w %d0 # is instr fmovm?
bmi.b iea_dis_fmovm # yes
# instruction is using an extended precision immediate operand. Therefore,
# the total instruction length is 16 bytes.
iea_dis_immed:
mov.l &0x10,%d0 # 16 bytes of instruction
bra.b iea_dis_cont
iea_dis_fmovm:
btst &0xe,%d0 # is instr fmovm ctrl
bne.b iea_dis_fmovm_data # no
# the instruction is a fmovm.l with 2 or 3 registers.
bfextu %d0{&19:&3},%d1
mov.l &0xc,%d0
cmpi.b %d1,&0x7 # move all regs?
bne.b iea_dis_cont
addq.l &0x4,%d0
bra.b iea_dis_cont
# the instruction is an fmovm.x dynamic which can use many addressing
# modes and thus can have several different total instruction lengths.
# call fmovm_calc_ea which will go through the ea calc process and,
# as a by-product, will tell us how long the instruction is.
iea_dis_fmovm_data: clr.l %d0
bsr.l fmovm_calc_ea
mov.l EXC_EXTWPTR(%a6),%d0 sub.l EXC_PC(%a6),%d0
iea_dis_cont:
mov.w %d0,EXC_VOFF(%a6) # store stack shift value
# here, we actually create the 8-word frame from the 4-word frame,
# with the "next PC" as additional info.
# the <ea> field is let as undefined.
subq.l &0x8,%sp # make room for new stack
mov.l %d0,-(%sp) # save d0
mov.w 0xc(%sp),0x4(%sp) # move SR
mov.l 0xe(%sp),0x6(%sp) # move Current PC clr.l %d0
mov.w 0x12(%sp),%d0
mov.l 0x6(%sp),0x10(%sp) # move Current PC
add.l %d0,0x6(%sp) # make Next PC
mov.w &0x402c,0xa(%sp) # insert offset,frame format
mov.l (%sp)+,%d0 # restore d0
subq.w &0x8,%sp # make stack frame bigger
mov.l 0x8(%sp),(%sp) # store SR,hi(PC)
mov.w 0xc(%sp),0x4(%sp) # store lo(PC)
mov.w &0x4008,0x6(%sp) # store voff
mov.l 0x2(%sp),0x8(%sp) # store ea
mov.l &0x09428001,0xc(%sp) # store fslw
iea_acc_done:
btst &0x5,(%sp) # user or supervisor mode?
beq.b iea_acc_done2 # user
bset &0x2,0xd(%sp) # set supervisor TM bit
#########################################################################
# XDEF **************************************************************** #
# _fpsp_operr(): 060FPSP entry point for FP Operr exception. #
# #
# This handler should be the first code executed upon taking the #
# FP Operand Error exception in an operating system. #
# #
# XREF **************************************************************** #
# _imem_read_long() - read instruction longword #
# fix_skewed_ops() - adjust src operand in fsave frame #
# _real_operr() - "callout" to operating system operr handler #
# _dmem_write_{byte,word,long}() - store data to mem (opclass 3) #
# store_dreg_{b,w,l}() - store data to data regfile (opclass 3) #
# facc_out_{b,w,l}() - store to memory took access error (opcl 3) #
# #
# INPUT *************************************************************** #
# - The system stack contains the FP Operr exception frame #
# - The fsave frame contains the source operand #
# #
# OUTPUT ************************************************************** #
# No access error: #
# - The system stack is unchanged #
# - The fsave frame contains the adjusted src op for opclass 0,2 #
# #
# ALGORITHM *********************************************************** #
# In a system where the FP Operr exception is enabled, the goal #
# is to get to the handler specified at _real_operr(). But, on the 060, #
# for opclass zero and two instruction taking this exception, the #
# input operand in the fsave frame may be incorrect for some cases #
# and needs to be corrected. This handler calls fix_skewed_ops() to #
# do just this and then exits through _real_operr(). #
# For opclass 3 instructions, the 060 doesn't store the default #
# operr result out to memory or data register file as it should. #
# This code must emulate the move out before finally exiting through #
# _real_inex(). The move out, if to memory, is performed using #
# _mem_write() "callout" routines that may return a failing result. #
# In this special case, the handler must exit through facc_out() #
# which creates an access error stack frame from the current operr #
# stack frame. #
# #
#########################################################################
global _fpsp_operr
_fpsp_operr:
link.w %a6,&-LOCAL_SIZE # init stack frame
fsave FP_SRC(%a6) # grab the "busy" frame
movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1
fmovm.l %fpcr,%fpsr,%fpiar,USER_FPCR(%a6) # save ctrl regs
fmovm.x &0xc0,EXC_FPREGS(%a6) # save fp0-fp1 on stack
# the FPIAR holds the "current PC" of the faulting instruction
mov.l USER_FPIAR(%a6),EXC_EXTWPTR(%a6)
btst &13,%d0 # is instr an fmove out?
bne.b foperr_out # fmove out
# here, we simply see if the operand in the fsave frame needs to be "unskewed".
# this would be the case for opclass two operations with a source infinity or
# denorm operand in the sgl or dbl format. NANs also become skewed, but can't
# cause an operr so we don't need to check for them here.
lea FP_SRC(%a6),%a0 # pass: ptr to src op
bsr.l fix_skewed_ops # fix src op
#
# the hardware does not save the default result to memory on enabled
# operand error exceptions. we do this here before passing control to
# the user operand error handler.
#
# byte, word, and long destination format operations can pass
# through here. we simply need to test the sign of the src
# operand and save the appropriate minimum or maximum integer value
# to the effective address as pointed to by the stacked effective address.
#
# although packed opclass three operations can take operand error
# exceptions, they won't pass through here since they are caught
# first by the unsupported data format exception handler. that handler
# sends them directly to _real_operr() if necessary.
#
foperr_out:
mov.w FP_SRC_EX(%a6),%d1 # fetch exponent
andi.w &0x7fff,%d1
cmpi.w %d1,&0x7fff
bne.b foperr_out_not_qnan
# the operand is either an infinity or a QNAN.
tst.l FP_SRC_LO(%a6)
bne.b foperr_out_qnan
mov.l FP_SRC_HI(%a6),%d1
andi.l &0x7fffffff,%d1
beq.b foperr_out_not_qnan
foperr_out_qnan:
mov.l FP_SRC_HI(%a6),L_SCR1(%a6)
bra.b foperr_out_jmp
foperr_out_jmp:
bfextu %d0{&19:&3},%d0 # extract dst format field
mov.b 1+EXC_OPWORD(%a6),%d1 # extract <ea> mode,reg
mov.w (tbl_operr.b,%pc,%d0.w*2),%a0
jmp (tbl_operr.b,%pc,%a0)
tbl_operr:
short foperr_out_l - tbl_operr # long word integer
short tbl_operr - tbl_operr # sgl prec shouldn't happen
short tbl_operr - tbl_operr # ext prec shouldn't happen
short foperr_exit - tbl_operr # packed won't enter here
short foperr_out_w - tbl_operr # word integer
short tbl_operr - tbl_operr # dbl prec shouldn't happen
short foperr_out_b - tbl_operr # byte integer
short tbl_operr - tbl_operr # packed won't enter here
foperr_out_b:
mov.b L_SCR1(%a6),%d0 # load positive default result
cmpi.b %d1,&0x7 # is <ea> mode a data reg?
ble.b foperr_out_b_save_dn # yes
mov.l EXC_EA(%a6),%a0 # pass: <ea> of default result
bsr.l _dmem_write_byte # write the default result
tst.l %d1 # did dstore fail?
bne.l facc_out_b # yes
bra.w foperr_exit
foperr_out_b_save_dn:
andi.w &0x0007,%d1
bsr.l store_dreg_b # store result to regfile
bra.w foperr_exit
foperr_out_w:
mov.w L_SCR1(%a6),%d0 # load positive default result
cmpi.b %d1,&0x7 # is <ea> mode a data reg?
ble.b foperr_out_w_save_dn # yes
mov.l EXC_EA(%a6),%a0 # pass: <ea> of default result
bsr.l _dmem_write_word # write the default result
tst.l %d1 # did dstore fail?
bne.l facc_out_w # yes
bra.w foperr_exit
foperr_out_w_save_dn:
andi.w &0x0007,%d1
bsr.l store_dreg_w # store result to regfile
bra.w foperr_exit
foperr_out_l:
mov.l L_SCR1(%a6),%d0 # load positive default result
cmpi.b %d1,&0x7 # is <ea> mode a data reg?
ble.b foperr_out_l_save_dn # yes
mov.l EXC_EA(%a6),%a0 # pass: <ea> of default result
bsr.l _dmem_write_long # write the default result
tst.l %d1 # did dstore fail?
bne.l facc_out_l # yes
bra.w foperr_exit
foperr_out_l_save_dn:
andi.w &0x0007,%d1
bsr.l store_dreg_l # store result to regfile
bra.w foperr_exit
#########################################################################
# XDEF **************************************************************** #
# _fpsp_snan(): 060FPSP entry point for FP SNAN exception. #
# #
# This handler should be the first code executed upon taking the #
# FP Signalling NAN exception in an operating system. #
# #
# XREF **************************************************************** #
# _imem_read_long() - read instruction longword #
# fix_skewed_ops() - adjust src operand in fsave frame #
# _real_snan() - "callout" to operating system SNAN handler #
# _dmem_write_{byte,word,long}() - store data to mem (opclass 3) #
# store_dreg_{b,w,l}() - store data to data regfile (opclass 3) #
# facc_out_{b,w,l,d,x}() - store to mem took acc error (opcl 3) #
# _calc_ea_fout() - fix An if <ea> is -() or ()+; also get <ea> #
# #
# INPUT *************************************************************** #
# - The system stack contains the FP SNAN exception frame #
# - The fsave frame contains the source operand #
# #
# OUTPUT ************************************************************** #
# No access error: #
# - The system stack is unchanged #
# - The fsave frame contains the adjusted src op for opclass 0,2 #
# #
# ALGORITHM *********************************************************** #
# In a system where the FP SNAN exception is enabled, the goal #
# is to get to the handler specified at _real_snan(). But, on the 060, #
# for opclass zero and two instructions taking this exception, the #
# input operand in the fsave frame may be incorrect for some cases #
# and needs to be corrected. This handler calls fix_skewed_ops() to #
# do just this and then exits through _real_snan(). #
# For opclass 3 instructions, the 060 doesn't store the default #
# SNAN result out to memory or data register file as it should. #
# This code must emulate the move out before finally exiting through #
# _real_snan(). The move out, if to memory, is performed using #
# _mem_write() "callout" routines that may return a failing result. #
# In this special case, the handler must exit through facc_out() #
# which creates an access error stack frame from the current SNAN #
# stack frame. #
# For the case of an extended precision opclass 3 instruction, #
# if the effective addressing mode was -() or ()+, then the address #
# register must get updated by calling _calc_ea_fout(). If the <ea> #
# was -(a7) from supervisor mode, then the exception frame currently #
# on the system stack must be carefully moved "down" to make room #
# for the operand being moved. #
# #
#########################################################################
global _fpsp_snan
_fpsp_snan:
link.w %a6,&-LOCAL_SIZE # init stack frame
fsave FP_SRC(%a6) # grab the "busy" frame
movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1
fmovm.l %fpcr,%fpsr,%fpiar,USER_FPCR(%a6) # save ctrl regs
fmovm.x &0xc0,EXC_FPREGS(%a6) # save fp0-fp1 on stack
# the FPIAR holds the "current PC" of the faulting instruction
mov.l USER_FPIAR(%a6),EXC_EXTWPTR(%a6)
btst &13,%d0 # is instr an fmove out?
bne.w fsnan_out # fmove out
# here, we simply see if the operand in the fsave frame needs to be "unskewed".
# this would be the case for opclass two operations with a source infinity or
# denorm operand in the sgl or dbl format. NANs also become skewed and must be
# fixed here.
lea FP_SRC(%a6),%a0 # pass: ptr to src op
bsr.l fix_skewed_ops # fix src op
#
# the hardware does not save the default result to memory on enabled
# snan exceptions. we do this here before passing control to
# the user snan handler.
#
# byte, word, long, and packed destination format operations can pass
# through here. since packed format operations already were handled by
# fpsp_unsupp(), then we need to do nothing else for them here.
# for byte, word, and long, we simply need to test the sign of the src
# operand and save the appropriate minimum or maximum integer value
# to the effective address as pointed to by the stacked effective address.
#
fsnan_out:
bfextu %d0{&19:&3},%d0 # extract dst format field
mov.b 1+EXC_OPWORD(%a6),%d1 # extract <ea> mode,reg
mov.w (tbl_snan.b,%pc,%d0.w*2),%a0
jmp (tbl_snan.b,%pc,%a0)
tbl_snan:
short fsnan_out_l - tbl_snan # long word integer
short fsnan_out_s - tbl_snan # sgl prec shouldn't happen
short fsnan_out_x - tbl_snan # ext prec shouldn't happen
short tbl_snan - tbl_snan # packed needs no help
short fsnan_out_w - tbl_snan # word integer
short fsnan_out_d - tbl_snan # dbl prec shouldn't happen
short fsnan_out_b - tbl_snan # byte integer
short tbl_snan - tbl_snan # packed needs no help
fsnan_out_b:
mov.b FP_SRC_HI(%a6),%d0 # load upper byte of SNAN
bset &6,%d0 # set SNAN bit
cmpi.b %d1,&0x7 # is <ea> mode a data reg?
ble.b fsnan_out_b_dn # yes
mov.l EXC_EA(%a6),%a0 # pass: <ea> of default result
bsr.l _dmem_write_byte # write the default result
tst.l %d1 # did dstore fail?
bne.l facc_out_b # yes
bra.w fsnan_exit
fsnan_out_b_dn:
andi.w &0x0007,%d1
bsr.l store_dreg_b # store result to regfile
bra.w fsnan_exit
fsnan_out_w:
mov.w FP_SRC_HI(%a6),%d0 # load upper word of SNAN
bset &14,%d0 # set SNAN bit
cmpi.b %d1,&0x7 # is <ea> mode a data reg?
ble.b fsnan_out_w_dn # yes
mov.l EXC_EA(%a6),%a0 # pass: <ea> of default result
bsr.l _dmem_write_word # write the default result
tst.l %d1 # did dstore fail?
bne.l facc_out_w # yes
bra.w fsnan_exit
fsnan_out_w_dn:
andi.w &0x0007,%d1
bsr.l store_dreg_w # store result to regfile
bra.w fsnan_exit
fsnan_out_l:
mov.l FP_SRC_HI(%a6),%d0 # load upper longword of SNAN
bset &30,%d0 # set SNAN bit
cmpi.b %d1,&0x7 # is <ea> mode a data reg?
ble.b fsnan_out_l_dn # yes
mov.l EXC_EA(%a6),%a0 # pass: <ea> of default result
bsr.l _dmem_write_long # write the default result
tst.l %d1 # did dstore fail?
bne.l facc_out_l # yes
bra.w fsnan_exit
fsnan_out_l_dn:
andi.w &0x0007,%d1
bsr.l store_dreg_l # store result to regfile
bra.w fsnan_exit
fsnan_out_s:
cmpi.b %d1,&0x7 # is <ea> mode a data reg?
ble.b fsnan_out_d_dn # yes
mov.l FP_SRC_EX(%a6),%d0 # fetch SNAN sign
andi.l &0x80000000,%d0 # keep sign
ori.l &0x7fc00000,%d0 # insert new exponent,SNAN bit
mov.l FP_SRC_HI(%a6),%d1 # load mantissa
lsr.l &0x8,%d1 # shift mantissa for sgl
or.l %d1,%d0 # create sgl SNAN
mov.l EXC_EA(%a6),%a0 # pass: <ea> of default result
bsr.l _dmem_write_long # write the default result
tst.l %d1 # did dstore fail?
bne.l facc_out_l # yes
bra.w fsnan_exit
fsnan_out_d_dn:
mov.l FP_SRC_EX(%a6),%d0 # fetch SNAN sign
andi.l &0x80000000,%d0 # keep sign
ori.l &0x7fc00000,%d0 # insert new exponent,SNAN bit
mov.l %d1,-(%sp)
mov.l FP_SRC_HI(%a6),%d1 # load mantissa
lsr.l &0x8,%d1 # shift mantissa for sgl
or.l %d1,%d0 # create sgl SNAN
mov.l (%sp)+,%d1
andi.w &0x0007,%d1
bsr.l store_dreg_l # store result to regfile
bra.w fsnan_exit
fsnan_out_d:
mov.l FP_SRC_EX(%a6),%d0 # fetch SNAN sign
andi.l &0x80000000,%d0 # keep sign
ori.l &0x7ff80000,%d0 # insert new exponent,SNAN bit
mov.l FP_SRC_HI(%a6),%d1 # load hi mantissa
mov.l %d0,FP_SCR0_EX(%a6) # store to temp space
mov.l &11,%d0 # load shift amt
lsr.l %d0,%d1
or.l %d1,FP_SCR0_EX(%a6) # create dbl hi
mov.l FP_SRC_HI(%a6),%d1 # load hi mantissa
andi.l &0x000007ff,%d1
ror.l %d0,%d1
mov.l %d1,FP_SCR0_HI(%a6) # store to temp space
mov.l FP_SRC_LO(%a6),%d1 # load lo mantissa
lsr.l %d0,%d1
or.l %d1,FP_SCR0_HI(%a6) # create dbl lo
lea FP_SCR0(%a6),%a0 # pass: ptr to operand
mov.l EXC_EA(%a6),%a1 # pass: dst addr
movq.l &0x8,%d0 # pass: size of 8 bytes
bsr.l _dmem_write # write the default result
tst.l %d1 # did dstore fail?
bne.l facc_out_d # yes
bra.w fsnan_exit
# for extended precision, if the addressing mode is pre-decrement or
# post-increment, then the address register did not get updated.
# in addition, for pre-decrement, the stacked <ea> is incorrect.
fsnan_out_x: clr.b SPCOND_FLG(%a6) # clear special case flag
#########################################################################
# XDEF **************************************************************** #
# _fpsp_inex(): 060FPSP entry point for FP Inexact exception. #
# #
# This handler should be the first code executed upon taking the #
# FP Inexact exception in an operating system. #
# #
# XREF **************************************************************** #
# _imem_read_long() - read instruction longword #
# fix_skewed_ops() - adjust src operand in fsave frame #
# set_tag_x() - determine optype of src/dst operands #
# store_fpreg() - store opclass 0 or 2 result to FP regfile #
# unnorm_fix() - change UNNORM operands to NORM or ZERO #
# load_fpn2() - load dst operand from FP regfile #
# smovcr() - emulate an "fmovcr" instruction #
# fout() - emulate an opclass 3 instruction #
# tbl_unsupp - add of table of emulation routines for opclass 0,2 #
# _real_inex() - "callout" to operating system inexact handler #
# #
# INPUT *************************************************************** #
# - The system stack contains the FP Inexact exception frame #
# - The fsave frame contains the source operand #
# #
# OUTPUT ************************************************************** #
# - The system stack is unchanged #
# - The fsave frame contains the adjusted src op for opclass 0,2 #
# #
# ALGORITHM *********************************************************** #
# In a system where the FP Inexact exception is enabled, the goal #
# is to get to the handler specified at _real_inex(). But, on the 060, #
# for opclass zero and two instruction taking this exception, the #
# hardware doesn't store the correct result to the destination FP #
# register as did the '040 and '881/2. This handler must emulate the #
# instruction in order to get this value and then store it to the #
# correct register before calling _real_inex(). #
# For opclass 3 instructions, the 060 doesn't store the default #
# inexact result out to memory or data register file as it should. #
# This code must emulate the move out by calling fout() before finally #
# exiting through _real_inex(). #
# #
#########################################################################
global _fpsp_inex
_fpsp_inex:
link.w %a6,&-LOCAL_SIZE # init stack frame
fsave FP_SRC(%a6) # grab the "busy" frame
movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1
fmovm.l %fpcr,%fpsr,%fpiar,USER_FPCR(%a6) # save ctrl regs
fmovm.x &0xc0,EXC_FPREGS(%a6) # save fp0-fp1 on stack
# the FPIAR holds the "current PC" of the faulting instruction
mov.l USER_FPIAR(%a6),EXC_EXTWPTR(%a6)
btst &13,%d0 # is instr an fmove out?
bne.w finex_out # fmove out
# the hardware, for "fabs" and "fneg" w/ a long source format, puts the
# longword integer directly into the upper longword of the mantissa along
# w/ an exponent value of 0x401e. we convert this to extended precision here.
bfextu %d0{&19:&3},%d0 # fetch instr size
bne.b finex_cont # instr size is not long
cmpi.w FP_SRC_EX(%a6),&0x401e # is exponent 0x401e?
bne.b finex_cont # no
fmov.l &0x0,%fpcr
fmov.l FP_SRC_HI(%a6),%fp0 # load integer src
fmov.x %fp0,FP_SRC(%a6) # store integer as extended precision
mov.w &0xe001,0x2+FP_SRC(%a6)
finex_cont:
lea FP_SRC(%a6),%a0 # pass: ptr to src op
bsr.l fix_skewed_ops # fix src op
# Here, we zero the ccode and exception byte field since we're going to
# emulate the whole instruction. Notice, though, that we don't kill the
# INEX1 bit. This is because a packed op has long since been converted
# to extended before arriving here. Therefore, we need to retain the
# INEX1 bit from when the operand was first converted.
andi.l &0x00ff01ff,USER_FPSR(%a6) # zero all but accured field
fmov.l &0x0,%fpcr # zero current control regs
fmov.l &0x0,%fpsr
bfextu EXC_EXTWORD(%a6){&0:&6},%d1 # extract upper 6 of cmdreg
cmpi.b %d1,&0x17 # is op an fmovecr?
beq.w finex_fmovcr # yes
lea FP_SRC(%a6),%a0 # pass: ptr to src op
bsr.l set_tag_x # tag the operand type
mov.b %d0,STAG(%a6) # maybe NORM,DENORM
# bits four and five of the fp extension word separate the monadic and dyadic
# operations that can pass through fpsp_inex(). remember that fcmp and ftst
# will never take this exception, but fsincos will.
btst &0x5,1+EXC_CMDREG(%a6) # is operation monadic or dyadic?
beq.b finex_extract # monadic
btst &0x4,1+EXC_CMDREG(%a6) # is operation an fsincos?
bne.b finex_extract # yes
lea FP_DST(%a6),%a0 # pass: ptr to dst op
bsr.l set_tag_x # tag the operand type
cmpi.b %d0,&UNNORM # is operand an UNNORM?
bne.b finex_op2_done # no
bsr.l unnorm_fix # yes; convert to NORM,DENORM,or ZERO
finex_op2_done:
mov.b %d0,DTAG(%a6) # save dst optype tag
#
# the hardware does not save the default result to memory on enabled
# inexact exceptions. we do this here before passing control to
# the user inexact handler.
#
# byte, word, and long destination format operations can pass
# through here. so can double and single precision.
# although packed opclass three operations can take inexact
# exceptions, they won't pass through here since they are caught
# first by the unsupported data format exception handler. that handler
# sends them directly to _real_inex() if necessary.
#
finex_out:
andi.l &0xffff00ff,USER_FPSR(%a6) # zero exception field
lea FP_SRC(%a6),%a0 # pass ptr to src operand
bsr.l fout # store the default result
bra.b finex_exit
#########################################################################
# XDEF **************************************************************** #
# _fpsp_dz(): 060FPSP entry point for FP DZ exception. #
# #
# This handler should be the first code executed upon taking #
# the FP DZ exception in an operating system. #
# #
# XREF **************************************************************** #
# _imem_read_long() - read instruction longword from memory #
# fix_skewed_ops() - adjust fsave operand #
# _real_dz() - "callout" exit point from FP DZ handler #
# #
# INPUT *************************************************************** #
# - The system stack contains the FP DZ exception stack. #
# - The fsave frame contains the source operand. #
# #
# OUTPUT ************************************************************** #
# - The system stack contains the FP DZ exception stack. #
# - The fsave frame contains the adjusted source operand. #
# #
# ALGORITHM *********************************************************** #
# In a system where the DZ exception is enabled, the goal is to #
# get to the handler specified at _real_dz(). But, on the 060, when the #
# exception is taken, the input operand in the fsave state frame may #
# be incorrect for some cases and need to be adjusted. So, this package #
# adjusts the operand using fix_skewed_ops() and then branches to #
# _real_dz(). #
# #
#########################################################################
global _fpsp_dz
_fpsp_dz:
link.w %a6,&-LOCAL_SIZE # init stack frame
fsave FP_SRC(%a6) # grab the "busy" frame
movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1
fmovm.l %fpcr,%fpsr,%fpiar,USER_FPCR(%a6) # save ctrl regs
fmovm.x &0xc0,EXC_FPREGS(%a6) # save fp0-fp1 on stack
# the FPIAR holds the "current PC" of the faulting instruction
mov.l USER_FPIAR(%a6),EXC_EXTWPTR(%a6)
# here, we simply see if the operand in the fsave frame needs to be "unskewed".
# this would be the case for opclass two operations with a source zero
# in the sgl or dbl format.
lea FP_SRC(%a6),%a0 # pass: ptr to src op
bsr.l fix_skewed_ops # fix src op
#########################################################################
# XDEF **************************************************************** #
# _fpsp_fline(): 060FPSP entry point for "Line F emulator" exc. #
# #
# This handler should be the first code executed upon taking the #
# "Line F Emulator" exception in an operating system. #
# #
# XREF **************************************************************** #
# _fpsp_unimp() - handle "FP Unimplemented" exceptions #
# _real_fpu_disabled() - handle "FPU disabled" exceptions #
# _real_fline() - handle "FLINE" exceptions #
# _imem_read_long() - read instruction longword #
# #
# INPUT *************************************************************** #
# - The system stack contains a "Line F Emulator" exception #
# stack frame. #
# #
# OUTPUT ************************************************************** #
# - The system stack is unchanged #
# #
# ALGORITHM *********************************************************** #
# When a "Line F Emulator" exception occurs, there are 3 possible #
# exception types, denoted by the exception stack frame format number: #
# (1) FPU unimplemented instruction (6 word stack frame) #
# (2) FPU disabled (8 word stack frame) #
# (3) Line F (4 word stack frame) #
# #
# This module determines which and forks the flow off to the #
# appropriate "callout" (for "disabled" and "Line F") or to the #
# correct emulation code (for "FPU unimplemented"). #
# This code also must check for "fmovecr" instructions w/ a #
# non-zero <ea> field. These may get flagged as "Line F" but should #
# really be flagged as "FPU Unimplemented". (This is a "feature" on #
# the '060. #
# #
#########################################################################
global _fpsp_fline
_fpsp_fline:
# check to see if this exception is a "FP Unimplemented Instruction"
# exception. if so, branch directly to that handler's entry point.
cmpi.w 0x6(%sp),&0x202c
beq.l _fpsp_unimp
# check to see if the FPU is disabled. if so, jump to the OS entry
# point for that condition.
cmpi.w 0x6(%sp),&0x402c
beq.l _real_fpu_disabled
# the exception was an "F-Line Illegal" exception. we check to see
# if the F-Line instruction is an "fmovecr" w/ a non-zero <ea>. if
# so, convert the F-Line exception stack frame to an FP Unimplemented
# Instruction exception stack frame else branch to the OS entry
# point for the F-Line exception handler.
link.w %a6,&-LOCAL_SIZE # init stack frame
bfextu %d0{&0:&10},%d1 # is it an fmovecr?
cmpi.w %d1,&0x03c8
bne.b fline_fline # no
bfextu %d0{&16:&6},%d1 # is it an fmovecr?
cmpi.b %d1,&0x17
bne.b fline_fline # no
# it's an fmovecr w/ a non-zero <ea> that has entered through
# the F-Line Illegal exception.
# so, we need to convert the F-Line exception stack frame into an
# FP Unimplemented Instruction stack frame and jump to that entry
# point.
#
# but, if the FPU is disabled, then we need to jump to the FPU disabled
# entry point.
movc %pcr,%d0
btst &0x1,%d0
beq.b fline_fmovcr
#########################################################################
# XDEF **************************************************************** #
# _fpsp_unimp(): 060FPSP entry point for FP "Unimplemented #
# Instruction" exception. #
# #
# This handler should be the first code executed upon taking the #
# FP Unimplemented Instruction exception in an operating system. #
# #
# XREF **************************************************************** #
# _imem_read_{word,long}() - read instruction word/longword #
# load_fop() - load src/dst ops from memory and/or FP regfile #
# store_fpreg() - store opclass 0 or 2 result to FP regfile #
# tbl_trans - addr of table of emulation routines for trnscndls #
# _real_access() - "callout" for access error exception #
# _fpsp_done() - "callout" for exit; work all done #
# _real_trace() - "callout" for Trace enabled exception #
# smovcr() - emulate "fmovecr" instruction #
# funimp_skew() - adjust fsave src ops to "incorrect" value #
# _ftrapcc() - emulate an "ftrapcc" instruction #
# _fdbcc() - emulate an "fdbcc" instruction #
# _fscc() - emulate an "fscc" instruction #
# _real_trap() - "callout" for Trap exception #
# _real_bsun() - "callout" for enabled Bsun exception #
# #
# INPUT *************************************************************** #
# - The system stack contains the "Unimplemented Instr" stk frame #
# #
# OUTPUT ************************************************************** #
# If access error: #
# - The system stack is changed to an access error stack frame #
# If Trace exception enabled: #
# - The system stack is changed to a Trace exception stack frame #
# Else: (normal case) #
# - Correct result has been stored as appropriate #
# #
# ALGORITHM *********************************************************** #
# There are two main cases of instructions that may enter here to #
# be emulated: (1) the FPgen instructions, most of which were also #
# unimplemented on the 040, and (2) "ftrapcc", "fscc", and "fdbcc". #
# For the first set, this handler calls the routine load_fop() #
# to load the source and destination (for dyadic) operands to be used #
# for instruction emulation. The correct emulation routine is then #
# chosen by decoding the instruction type and indexing into an #
# emulation subroutine index table. After emulation returns, this #
# handler checks to see if an exception should occur as a result of the #
# FP instruction emulation. If so, then an FP exception of the correct #
# type is inserted into the FPU state frame using the "frestore" #
# instruction before exiting through _fpsp_done(). In either the #
# exceptional or non-exceptional cases, we must check to see if the #
# Trace exception is enabled. If so, then we must create a Trace #
# exception frame from the current exception frame and exit through #
# _real_trace(). #
# For "fdbcc", "ftrapcc", and "fscc", the emulation subroutines #
# _fdbcc(), _ftrapcc(), and _fscc() respectively are used. All three #
# may flag that a BSUN exception should be taken. If so, then the #
# current exception stack frame is converted into a BSUN exception #
# stack frame and an exit is made through _real_bsun(). If the #
# instruction was "ftrapcc" and a Trap exception should result, a Trap #
# exception stack frame is created from the current frame and an exit #
# is made through _real_trap(). If a Trace exception is pending, then #
# a Trace exception frame is created from the current frame and a jump #
# is made to _real_trace(). Finally, if none of these conditions exist, #
# then the handler exits though the callout _fpsp_done(). #
# #
# In any of the above scenarios, if a _mem_read() or _mem_write() #
# "callout" returns a failing value, then an access error stack frame #
# is created from the current stack frame and an exit is made through #
# _real_access(). #
# #
#########################################################################
#
# FP UNIMPLEMENTED INSTRUCTION STACK FRAME:
#
# *****************
# * * => <ea> of fp unimp instr.
# - EA -
# * *
# *****************
# * 0x2 * 0x02c * => frame format and vector offset(vector #11)
# *****************
# * *
# - Next PC - => PC of instr to execute after exc handling
# * *
# *****************
# * SR * => SR at the time the exception was taken
# *****************
#
# Note: the !NULL bit does not get set in the fsave frame when the
# machine encounters an fp unimp exception. Therefore, it must be set
# before leaving this handler.
# global _fpsp_unimp
_fpsp_unimp:
link.w %a6,&-LOCAL_SIZE # init stack frame
movm.l &0x0303,EXC_DREGS(%a6) # save d0-d1/a0-a1
fmovm.l %fpcr,%fpsr,%fpiar,USER_FPCR(%a6) # save ctrl regs
fmovm.x &0xc0,EXC_FPREGS(%a6) # save fp0-fp1
# save the value of the user stack pointer onto the stack frame
funimp_u:
mov.l %usp,%a0 # fetch user stack pointer
mov.l %a0,EXC_A7(%a6) # store in stack frame
bra.b funimp_cont
# store the value of the supervisor stack pointer BEFORE the exc occurred.
# old_sp is address just above stacked effective address.
funimp_s:
lea 4+EXC_EA(%a6),%a0 # load old a7'
mov.l %a0,EXC_A7(%a6) # store a7'
mov.l %a0,OLD_A7(%a6) # make a copy
funimp_cont:
# the FPIAR holds the "current PC" of the faulting instruction.
mov.l USER_FPIAR(%a6),EXC_EXTWPTR(%a6)
# Divide the fp instructions into 8 types based on the TYPE field in
# bits 6-8 of the opword(classes 6,7 are undefined).
# (for the '060, only two types can take this exception)
# bftst %d0{&7:&3} # test TYPE
btst &22,%d0 # type 0 or 1 ?
bne.w funimp_misc # type 1
#########################################
# TYPE == 0: General instructions #
#########################################
funimp_gen:
clr.b STORE_FLG(%a6) # clear "store result" flag
# clear the ccode byte and exception status byte
andi.l &0x00ff00ff,USER_FPSR(%a6)
bfextu %d0{&16:&6},%d1 # extract upper 6 of cmdreg
cmpi.b %d1,&0x17 # is op an fmovecr?
beq.w funimp_fmovcr # yes
funimp_gen_exit_cmp:
cmpi.b SPCOND_FLG(%a6),&mia7_flg # was the ea mode (sp)+ ?
beq.b funimp_gen_exit_a7 # yes
cmpi.b SPCOND_FLG(%a6),&mda7_flg # was the ea mode -(sp) ?
beq.b funimp_gen_exit_a7 # yes
funimp_gen_exit_cont:
unlk %a6
funimp_gen_exit_cont2:
btst &0x7,(%sp) # is trace on?
beq.l _fpsp_done # no
# this catches a problem with the case where an exception will be re-inserted
# into the machine. the frestore has already been executed...so, the fmov.l
# alone of the control register would trigger an unwanted exception.
# until I feel like fixing this, we'll sidestep the exception.
fsave -(%sp)
fmov.l %fpiar,0x14(%sp) # "Current PC" is in FPIAR
frestore (%sp)+
mov.w &0x2024,0x6(%sp) # stk fmt = 0x2; voff = 0x24
bra.l _real_trace
funimp_gen_exit_a7:
btst &0x5,EXC_SR(%a6) # supervisor or user mode?
bne.b funimp_gen_exit_a7_s # supervisor
# if the instruction was executed from supervisor mode and the addressing
# mode was (a7)+, then the stack frame for the rte must be shifted "up"
# "n" bytes where "n" is the size of the src operand type.
# f<op>.{b,w,l,s,d,x,p}
funimp_gen_exit_a7_s:
mov.l %d0,-(%sp) # save d0
mov.l EXC_A7(%a6),%d0 # load new a7' sub.l OLD_A7(%a6),%d0 # subtract old a7'
mov.l 0x2+EXC_PC(%a6),(0x2+EXC_PC,%a6,%d0) # shift stack frame
mov.l EXC_SR(%a6),(EXC_SR,%a6,%d0) # shift stack frame
mov.w %d0,EXC_SR(%a6) # store incr number
mov.l (%sp)+,%d0 # restore d0
#
# the user has enabled some exceptions. we figure not to see this too
# often so that's why it gets lower priority.
#
funimp_ena:
# was an exception set that was also enabled?
and.b FPSR_EXCEPT(%a6),%d0 # keep only ones enabled and set
bfffo %d0{&24:&8},%d0 # find highest priority exception
bne.b funimp_exc # at least one was set
# no exception that was enabled was set BUT if we got an exact overflow
# and overflow wasn't enabled but inexact was (yech!) then this is
# an inexact exception; otherwise, return to normal non-exception flow.
btst &ovfl_bit,FPSR_EXCEPT(%a6) # did overflow occur?
beq.w funimp_store # no; return to normal flow
# the overflow w/ exact result happened but was inexact set in the FPCR?
funimp_ovfl:
btst &inex2_bit,FPCR_ENABLE(%a6) # is inexact enabled?
beq.w funimp_store # no; return to normal flow
bra.b funimp_exc_ovfl # yes
# some exception happened that was actually enabled.
# we'll insert this new exception into the FPU and then return.
funimp_exc:
subi.l &24,%d0 # fix offset to be 0-8
cmpi.b %d0,&0x6 # is exception INEX?
bne.b funimp_exc_force # no
# the enabled exception was inexact. so, if it occurs with an overflow
# or underflow that was disabled, then we have to force an overflow or
# underflow frame. the eventual overflow or underflow handler will see that
# it's actually an inexact and act appropriately. this is the only easy
# way to have the EXOP available for the enabled inexact handler when
# a disabled overflow or underflow has also happened.
btst &ovfl_bit,FPSR_EXCEPT(%a6) # did overflow occur?
bne.b funimp_exc_ovfl # yes
btst &unfl_bit,FPSR_EXCEPT(%a6) # did underflow occur?
bne.b funimp_exc_unfl # yes
# force the fsave exception status bits to signal an exception of the
# appropriate type. don't forget to "skew" the source operand in case we
# "unskewed" the one the hardware initially gave us.
funimp_exc_force:
mov.l %d0,-(%sp) # save d0
bsr.l funimp_skew # check for special case
mov.l (%sp)+,%d0 # restore d0
mov.w (tbl_funimp_except.b,%pc,%d0.w*2),2+FP_SRC(%a6)
bra.b funimp_gen_exit2 # exit with frestore
tbl_funimp_except:
short 0xe002, 0xe006, 0xe004, 0xe005
short 0xe003, 0xe002, 0xe001, 0xe001
# insert an overflow frame
funimp_exc_ovfl:
bsr.l funimp_skew # check for special case
mov.w &0xe005,2+FP_SRC(%a6)
bra.b funimp_gen_exit2
# insert an underflow frame
funimp_exc_unfl:
bsr.l funimp_skew # check for special case
mov.w &0xe003,2+FP_SRC(%a6)
# this is the general exit point for an enabled exception that will be
# restored into the machine for the instruction just emulated.
funimp_gen_exit2:
fmovm.x EXC_FP0(%a6),&0xc0 # restore fp0-fp1
fmovm.l USER_FPCR(%a6),%fpcr,%fpsr,%fpiar # restore ctrl regs
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
#
# TYPE == 1: FDB<cc>, FS<cc>, FTRAP<cc>
#
# These instructions were implemented on the '881/2 and '040 in hardware but
# are emulated in software on the '060.
#
funimp_misc:
bfextu %d0{&10:&3},%d1 # extract mode field
cmpi.b %d1,&0x1 # is it an fdb<cc>?
beq.w funimp_fdbcc # yes
cmpi.b %d1,&0x7 # is it an fs<cc>?
bne.w funimp_fscc # yes
bfextu %d0{&13:&3},%d1
cmpi.b %d1,&0x2 # is it an fs<cc>?
blt.w funimp_fscc # yes
cmpi.b SPCOND_FLG(%a6),&ftrapcc_flg # should a trap occur?
bne.w funimp_done # no
# FP UNIMP FRAME TRAP FRAME
# ***************** *****************
# ** <EA> ** ** Current PC **
# ***************** *****************
# * 0x2 * 0x02c * * 0x2 * 0x01c *
# ***************** *****************
# ** Next PC ** ** Next PC **
# ***************** *****************
# * SR * * SR *
# ***************** *****************
# (6 words) (6 words)
#
# the ftrapcc instruction should take a trap. so, here we must create a
# trap stack frame from an unimplemented fp instruction stack frame and
# jump to the user supplied entry point for the trap exception
funimp_ftrapcc_tp:
mov.l USER_FPIAR(%a6),EXC_EA(%a6) # Address = Current PC
mov.w &0x201c,EXC_VOFF(%a6) # Vector Offset = 0x01c
# I am assuming here that an "fs<cc>.b -(An)" or "fs<cc>.b (An)+" instruction
# does not need to update "An" before taking a bsun exception.
cmpi.b SPCOND_FLG(%a6),&fbsun_flg # is enabled bsun occurring?
beq.w funimp_bsun
btst &0x5,EXC_SR(%a6) # yes; is it a user mode exception?
bne.b funimp_fscc_s # no
funimp_fscc_u:
mov.l EXC_A7(%a6),%a0 # yes; set new USP
mov.l %a0,%usp
bra.w funimp_done # branch to finish
# remember, I'm assuming that post-increment is bogus...(it IS!!!)
# so, the least significant WORD of the stacked effective address got
# overwritten by the "fs<cc> -(An)". We must shift the stack frame "down"
# so that the rte will work correctly without destroying the result.
# even though the operation size is byte, the stack ptr is decr by 2.
#
# remember, also, this instruction may be traced.
funimp_fscc_s:
cmpi.b SPCOND_FLG(%a6),&mda7_flg # was a7 modified?
bne.w funimp_done # no
#
# The ftrap<cc>, fs<cc>, or fdb<cc> is to take an enabled bsun. we must convert
# the fp unimplemented instruction exception stack frame into a bsun stack frame,
# restore a bsun exception into the machine, and branch to the user
# supplied bsun hook.
#
# FP UNIMP FRAME BSUN FRAME
# ***************** *****************
# ** <EA> ** * 0x0 * 0x0c0 *
# ***************** *****************
# * 0x2 * 0x02c * ** Current PC **
# ***************** *****************
# ** Next PC ** * SR *
# ***************** *****************
# * SR * (4 words)
# *****************
# (6 words)
#
funimp_bsun:
mov.w &0x00c0,2+EXC_EA(%a6) # Fmt = 0x0; Vector Offset = 0x0c0
mov.l USER_FPIAR(%a6),EXC_VOFF(%a6) # PC = Current PC
mov.w EXC_SR(%a6),2+EXC_PC(%a6) # shift SR "up"
#
# all ftrapcc/fscc/fdbcc processing has been completed. unwind the stack frame
# and return.
#
# as usual, we have to check for trace mode being on here. since instructions
# modifying the supervisor stack frame don't pass through here, this is a
# relatively easy task.
#
funimp_done:
fmovm.x EXC_FP0(%a6),&0xc0 # restore fp0-fp1
fmovm.l USER_FPCR(%a6),%fpcr,%fpsr,%fpiar # restore ctrl regs
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
unlk %a6
btst &0x7,(%sp) # is trace enabled?
bne.b funimp_trace # yes
bra.l _fpsp_done
# FP UNIMP FRAME TRACE FRAME
# ***************** *****************
# ** <EA> ** ** Current PC **
# ***************** *****************
# * 0x2 * 0x02c * * 0x2 * 0x024 *
# ***************** *****************
# ** Next PC ** ** Next PC **
# ***************** *****************
# * SR * * SR *
# ***************** *****************
# (6 words) (6 words)
#
# the fscc instruction should take a trace trap. so, here we must create a
# trace stack frame from an unimplemented fp instruction stack frame and
# jump to the user supplied entry point for the trace exception
funimp_trace:
fmov.l %fpiar,0x8(%sp) # current PC is in fpiar
mov.b &0x24,0x7(%sp) # vector offset = 0x024
global tbl_trans
swbeg &0x1c0
tbl_trans:
short tbl_trans - tbl_trans # $00-0 fmovecr all
short tbl_trans - tbl_trans # $00-1 fmovecr all
short tbl_trans - tbl_trans # $00-2 fmovecr all
short tbl_trans - tbl_trans # $00-3 fmovecr all
short tbl_trans - tbl_trans # $00-4 fmovecr all
short tbl_trans - tbl_trans # $00-5 fmovecr all
short tbl_trans - tbl_trans # $00-6 fmovecr all
short tbl_trans - tbl_trans # $00-7 fmovecr all
short tbl_trans - tbl_trans # $01-0 fint norm
short tbl_trans - tbl_trans # $01-1 fint zero
short tbl_trans - tbl_trans # $01-2 fint inf
short tbl_trans - tbl_trans # $01-3 fint qnan
short tbl_trans - tbl_trans # $01-5 fint denorm
short tbl_trans - tbl_trans # $01-4 fint snan
short tbl_trans - tbl_trans # $01-6 fint unnorm
short tbl_trans - tbl_trans # $01-7 ERROR
short ssinh - tbl_trans # $02-0 fsinh norm
short src_zero - tbl_trans # $02-1 fsinh zero
short src_inf - tbl_trans # $02-2 fsinh inf
short src_qnan - tbl_trans # $02-3 fsinh qnan
short ssinhd - tbl_trans # $02-5 fsinh denorm
short src_snan - tbl_trans # $02-4 fsinh snan
short tbl_trans - tbl_trans # $02-6 fsinh unnorm
short tbl_trans - tbl_trans # $02-7 ERROR
short tbl_trans - tbl_trans # $03-0 fintrz norm
short tbl_trans - tbl_trans # $03-1 fintrz zero
short tbl_trans - tbl_trans # $03-2 fintrz inf
short tbl_trans - tbl_trans # $03-3 fintrz qnan
short tbl_trans - tbl_trans # $03-5 fintrz denorm
short tbl_trans - tbl_trans # $03-4 fintrz snan
short tbl_trans - tbl_trans # $03-6 fintrz unnorm
short tbl_trans - tbl_trans # $03-7 ERROR
short tbl_trans - tbl_trans # $04-0 fsqrt norm
short tbl_trans - tbl_trans # $04-1 fsqrt zero
short tbl_trans - tbl_trans # $04-2 fsqrt inf
short tbl_trans - tbl_trans # $04-3 fsqrt qnan
short tbl_trans - tbl_trans # $04-5 fsqrt denorm
short tbl_trans - tbl_trans # $04-4 fsqrt snan
short tbl_trans - tbl_trans # $04-6 fsqrt unnorm
short tbl_trans - tbl_trans # $04-7 ERROR
short tbl_trans - tbl_trans # $05-0 ERROR
short tbl_trans - tbl_trans # $05-1 ERROR
short tbl_trans - tbl_trans # $05-2 ERROR
short tbl_trans - tbl_trans # $05-3 ERROR
short tbl_trans - tbl_trans # $05-4 ERROR
short tbl_trans - tbl_trans # $05-5 ERROR
short tbl_trans - tbl_trans # $05-6 ERROR
short tbl_trans - tbl_trans # $05-7 ERROR
short slognp1 - tbl_trans # $06-0 flognp1 norm
short src_zero - tbl_trans # $06-1 flognp1 zero
short sopr_inf - tbl_trans # $06-2 flognp1 inf
short src_qnan - tbl_trans # $06-3 flognp1 qnan
short slognp1d - tbl_trans # $06-5 flognp1 denorm
short src_snan - tbl_trans # $06-4 flognp1 snan
short tbl_trans - tbl_trans # $06-6 flognp1 unnorm
short tbl_trans - tbl_trans # $06-7 ERROR
short tbl_trans - tbl_trans # $07-0 ERROR
short tbl_trans - tbl_trans # $07-1 ERROR
short tbl_trans - tbl_trans # $07-2 ERROR
short tbl_trans - tbl_trans # $07-3 ERROR
short tbl_trans - tbl_trans # $07-4 ERROR
short tbl_trans - tbl_trans # $07-5 ERROR
short tbl_trans - tbl_trans # $07-6 ERROR
short tbl_trans - tbl_trans # $07-7 ERROR
short setoxm1 - tbl_trans # $08-0 fetoxm1 norm
short src_zero - tbl_trans # $08-1 fetoxm1 zero
short setoxm1i - tbl_trans # $08-2 fetoxm1 inf
short src_qnan - tbl_trans # $08-3 fetoxm1 qnan
short setoxm1d - tbl_trans # $08-5 fetoxm1 denorm
short src_snan - tbl_trans # $08-4 fetoxm1 snan
short tbl_trans - tbl_trans # $08-6 fetoxm1 unnorm
short tbl_trans - tbl_trans # $08-7 ERROR
short stanh - tbl_trans # $09-0 ftanh norm
short src_zero - tbl_trans # $09-1 ftanh zero
short src_one - tbl_trans # $09-2 ftanh inf
short src_qnan - tbl_trans # $09-3 ftanh qnan
short stanhd - tbl_trans # $09-5 ftanh denorm
short src_snan - tbl_trans # $09-4 ftanh snan
short tbl_trans - tbl_trans # $09-6 ftanh unnorm
short tbl_trans - tbl_trans # $09-7 ERROR
short satan - tbl_trans # $0a-0 fatan norm
short src_zero - tbl_trans # $0a-1 fatan zero
short spi_2 - tbl_trans # $0a-2 fatan inf
short src_qnan - tbl_trans # $0a-3 fatan qnan
short satand - tbl_trans # $0a-5 fatan denorm
short src_snan - tbl_trans # $0a-4 fatan snan
short tbl_trans - tbl_trans # $0a-6 fatan unnorm
short tbl_trans - tbl_trans # $0a-7 ERROR
short tbl_trans - tbl_trans # $0b-0 ERROR
short tbl_trans - tbl_trans # $0b-1 ERROR
short tbl_trans - tbl_trans # $0b-2 ERROR
short tbl_trans - tbl_trans # $0b-3 ERROR
short tbl_trans - tbl_trans # $0b-4 ERROR
short tbl_trans - tbl_trans # $0b-5 ERROR
short tbl_trans - tbl_trans # $0b-6 ERROR
short tbl_trans - tbl_trans # $0b-7 ERROR
short sasin - tbl_trans # $0c-0 fasin norm
short src_zero - tbl_trans # $0c-1 fasin zero
short t_operr - tbl_trans # $0c-2 fasin inf
short src_qnan - tbl_trans # $0c-3 fasin qnan
short sasind - tbl_trans # $0c-5 fasin denorm
short src_snan - tbl_trans # $0c-4 fasin snan
short tbl_trans - tbl_trans # $0c-6 fasin unnorm
short tbl_trans - tbl_trans # $0c-7 ERROR
short satanh - tbl_trans # $0d-0 fatanh norm
short src_zero - tbl_trans # $0d-1 fatanh zero
short t_operr - tbl_trans # $0d-2 fatanh inf
short src_qnan - tbl_trans # $0d-3 fatanh qnan
short satanhd - tbl_trans # $0d-5 fatanh denorm
short src_snan - tbl_trans # $0d-4 fatanh snan
short tbl_trans - tbl_trans # $0d-6 fatanh unnorm
short tbl_trans - tbl_trans # $0d-7 ERROR
short ssin - tbl_trans # $0e-0 fsin norm
short src_zero - tbl_trans # $0e-1 fsin zero
short t_operr - tbl_trans # $0e-2 fsin inf
short src_qnan - tbl_trans # $0e-3 fsin qnan
short ssind - tbl_trans # $0e-5 fsin denorm
short src_snan - tbl_trans # $0e-4 fsin snan
short tbl_trans - tbl_trans # $0e-6 fsin unnorm
short tbl_trans - tbl_trans # $0e-7 ERROR
short stan - tbl_trans # $0f-0 ftan norm
short src_zero - tbl_trans # $0f-1 ftan zero
short t_operr - tbl_trans # $0f-2 ftan inf
short src_qnan - tbl_trans # $0f-3 ftan qnan
short stand - tbl_trans # $0f-5 ftan denorm
short src_snan - tbl_trans # $0f-4 ftan snan
short tbl_trans - tbl_trans # $0f-6 ftan unnorm
short tbl_trans - tbl_trans # $0f-7 ERROR
short setox - tbl_trans # $10-0 fetox norm
short ld_pone - tbl_trans # $10-1 fetox zero
short szr_inf - tbl_trans # $10-2 fetox inf
short src_qnan - tbl_trans # $10-3 fetox qnan
short setoxd - tbl_trans # $10-5 fetox denorm
short src_snan - tbl_trans # $10-4 fetox snan
short tbl_trans - tbl_trans # $10-6 fetox unnorm
short tbl_trans - tbl_trans # $10-7 ERROR
short stwotox - tbl_trans # $11-0 ftwotox norm
short ld_pone - tbl_trans # $11-1 ftwotox zero
short szr_inf - tbl_trans # $11-2 ftwotox inf
short src_qnan - tbl_trans # $11-3 ftwotox qnan
short stwotoxd - tbl_trans # $11-5 ftwotox denorm
short src_snan - tbl_trans # $11-4 ftwotox snan
short tbl_trans - tbl_trans # $11-6 ftwotox unnorm
short tbl_trans - tbl_trans # $11-7 ERROR
short stentox - tbl_trans # $12-0 ftentox norm
short ld_pone - tbl_trans # $12-1 ftentox zero
short szr_inf - tbl_trans # $12-2 ftentox inf
short src_qnan - tbl_trans # $12-3 ftentox qnan
short stentoxd - tbl_trans # $12-5 ftentox denorm
short src_snan - tbl_trans # $12-4 ftentox snan
short tbl_trans - tbl_trans # $12-6 ftentox unnorm
short tbl_trans - tbl_trans # $12-7 ERROR
short tbl_trans - tbl_trans # $13-0 ERROR
short tbl_trans - tbl_trans # $13-1 ERROR
short tbl_trans - tbl_trans # $13-2 ERROR
short tbl_trans - tbl_trans # $13-3 ERROR
short tbl_trans - tbl_trans # $13-4 ERROR
short tbl_trans - tbl_trans # $13-5 ERROR
short tbl_trans - tbl_trans # $13-6 ERROR
short tbl_trans - tbl_trans # $13-7 ERROR
short slogn - tbl_trans # $14-0 flogn norm
short t_dz2 - tbl_trans # $14-1 flogn zero
short sopr_inf - tbl_trans # $14-2 flogn inf
short src_qnan - tbl_trans # $14-3 flogn qnan
short slognd - tbl_trans # $14-5 flogn denorm
short src_snan - tbl_trans # $14-4 flogn snan
short tbl_trans - tbl_trans # $14-6 flogn unnorm
short tbl_trans - tbl_trans # $14-7 ERROR
short slog10 - tbl_trans # $15-0 flog10 norm
short t_dz2 - tbl_trans # $15-1 flog10 zero
short sopr_inf - tbl_trans # $15-2 flog10 inf
short src_qnan - tbl_trans # $15-3 flog10 qnan
short slog10d - tbl_trans # $15-5 flog10 denorm
short src_snan - tbl_trans # $15-4 flog10 snan
short tbl_trans - tbl_trans # $15-6 flog10 unnorm
short tbl_trans - tbl_trans # $15-7 ERROR
short slog2 - tbl_trans # $16-0 flog2 norm
short t_dz2 - tbl_trans # $16-1 flog2 zero
short sopr_inf - tbl_trans # $16-2 flog2 inf
short src_qnan - tbl_trans # $16-3 flog2 qnan
short slog2d - tbl_trans # $16-5 flog2 denorm
short src_snan - tbl_trans # $16-4 flog2 snan
short tbl_trans - tbl_trans # $16-6 flog2 unnorm
short tbl_trans - tbl_trans # $16-7 ERROR
short tbl_trans - tbl_trans # $17-0 ERROR
short tbl_trans - tbl_trans # $17-1 ERROR
short tbl_trans - tbl_trans # $17-2 ERROR
short tbl_trans - tbl_trans # $17-3 ERROR
short tbl_trans - tbl_trans # $17-4 ERROR
short tbl_trans - tbl_trans # $17-5 ERROR
short tbl_trans - tbl_trans # $17-6 ERROR
short tbl_trans - tbl_trans # $17-7 ERROR
short tbl_trans - tbl_trans # $18-0 fabs norm
short tbl_trans - tbl_trans # $18-1 fabs zero
short tbl_trans - tbl_trans # $18-2 fabs inf
short tbl_trans - tbl_trans # $18-3 fabs qnan
short tbl_trans - tbl_trans # $18-5 fabs denorm
short tbl_trans - tbl_trans # $18-4 fabs snan
short tbl_trans - tbl_trans # $18-6 fabs unnorm
short tbl_trans - tbl_trans # $18-7 ERROR
short scosh - tbl_trans # $19-0 fcosh norm
short ld_pone - tbl_trans # $19-1 fcosh zero
short ld_pinf - tbl_trans # $19-2 fcosh inf
short src_qnan - tbl_trans # $19-3 fcosh qnan
short scoshd - tbl_trans # $19-5 fcosh denorm
short src_snan - tbl_trans # $19-4 fcosh snan
short tbl_trans - tbl_trans # $19-6 fcosh unnorm
short tbl_trans - tbl_trans # $19-7 ERROR
short tbl_trans - tbl_trans # $1a-0 fneg norm
short tbl_trans - tbl_trans # $1a-1 fneg zero
short tbl_trans - tbl_trans # $1a-2 fneg inf
short tbl_trans - tbl_trans # $1a-3 fneg qnan
short tbl_trans - tbl_trans # $1a-5 fneg denorm
short tbl_trans - tbl_trans # $1a-4 fneg snan
short tbl_trans - tbl_trans # $1a-6 fneg unnorm
short tbl_trans - tbl_trans # $1a-7 ERROR
short tbl_trans - tbl_trans # $1b-0 ERROR
short tbl_trans - tbl_trans # $1b-1 ERROR
short tbl_trans - tbl_trans # $1b-2 ERROR
short tbl_trans - tbl_trans # $1b-3 ERROR
short tbl_trans - tbl_trans # $1b-4 ERROR
short tbl_trans - tbl_trans # $1b-5 ERROR
short tbl_trans - tbl_trans # $1b-6 ERROR
short tbl_trans - tbl_trans # $1b-7 ERROR
short sacos - tbl_trans # $1c-0 facos norm
short ld_ppi2 - tbl_trans # $1c-1 facos zero
short t_operr - tbl_trans # $1c-2 facos inf
short src_qnan - tbl_trans # $1c-3 facos qnan
short sacosd - tbl_trans # $1c-5 facos denorm
short src_snan - tbl_trans # $1c-4 facos snan
short tbl_trans - tbl_trans # $1c-6 facos unnorm
short tbl_trans - tbl_trans # $1c-7 ERROR
short scos - tbl_trans # $1d-0 fcos norm
short ld_pone - tbl_trans # $1d-1 fcos zero
short t_operr - tbl_trans # $1d-2 fcos inf
short src_qnan - tbl_trans # $1d-3 fcos qnan
short scosd - tbl_trans # $1d-5 fcos denorm
short src_snan - tbl_trans # $1d-4 fcos snan
short tbl_trans - tbl_trans # $1d-6 fcos unnorm
short tbl_trans - tbl_trans # $1d-7 ERROR
short sgetexp - tbl_trans # $1e-0 fgetexp norm
short src_zero - tbl_trans # $1e-1 fgetexp zero
short t_operr - tbl_trans # $1e-2 fgetexp inf
short src_qnan - tbl_trans # $1e-3 fgetexp qnan
short sgetexpd - tbl_trans # $1e-5 fgetexp denorm
short src_snan - tbl_trans # $1e-4 fgetexp snan
short tbl_trans - tbl_trans # $1e-6 fgetexp unnorm
short tbl_trans - tbl_trans # $1e-7 ERROR
short sgetman - tbl_trans # $1f-0 fgetman norm
short src_zero - tbl_trans # $1f-1 fgetman zero
short t_operr - tbl_trans # $1f-2 fgetman inf
short src_qnan - tbl_trans # $1f-3 fgetman qnan
short sgetmand - tbl_trans # $1f-5 fgetman denorm
short src_snan - tbl_trans # $1f-4 fgetman snan
short tbl_trans - tbl_trans # $1f-6 fgetman unnorm
short tbl_trans - tbl_trans # $1f-7 ERROR
short tbl_trans - tbl_trans # $20-0 fdiv norm
short tbl_trans - tbl_trans # $20-1 fdiv zero
short tbl_trans - tbl_trans # $20-2 fdiv inf
short tbl_trans - tbl_trans # $20-3 fdiv qnan
short tbl_trans - tbl_trans # $20-5 fdiv denorm
short tbl_trans - tbl_trans # $20-4 fdiv snan
short tbl_trans - tbl_trans # $20-6 fdiv unnorm
short tbl_trans - tbl_trans # $20-7 ERROR
short smod_snorm - tbl_trans # $21-0 fmod norm
short smod_szero - tbl_trans # $21-1 fmod zero
short smod_sinf - tbl_trans # $21-2 fmod inf
short sop_sqnan - tbl_trans # $21-3 fmod qnan
short smod_sdnrm - tbl_trans # $21-5 fmod denorm
short sop_ssnan - tbl_trans # $21-4 fmod snan
short tbl_trans - tbl_trans # $21-6 fmod unnorm
short tbl_trans - tbl_trans # $21-7 ERROR
short tbl_trans - tbl_trans # $22-0 fadd norm
short tbl_trans - tbl_trans # $22-1 fadd zero
short tbl_trans - tbl_trans # $22-2 fadd inf
short tbl_trans - tbl_trans # $22-3 fadd qnan
short tbl_trans - tbl_trans # $22-5 fadd denorm
short tbl_trans - tbl_trans # $22-4 fadd snan
short tbl_trans - tbl_trans # $22-6 fadd unnorm
short tbl_trans - tbl_trans # $22-7 ERROR
short tbl_trans - tbl_trans # $23-0 fmul norm
short tbl_trans - tbl_trans # $23-1 fmul zero
short tbl_trans - tbl_trans # $23-2 fmul inf
short tbl_trans - tbl_trans # $23-3 fmul qnan
short tbl_trans - tbl_trans # $23-5 fmul denorm
short tbl_trans - tbl_trans # $23-4 fmul snan
short tbl_trans - tbl_trans # $23-6 fmul unnorm
short tbl_trans - tbl_trans # $23-7 ERROR
short tbl_trans - tbl_trans # $24-0 fsgldiv norm
short tbl_trans - tbl_trans # $24-1 fsgldiv zero
short tbl_trans - tbl_trans # $24-2 fsgldiv inf
short tbl_trans - tbl_trans # $24-3 fsgldiv qnan
short tbl_trans - tbl_trans # $24-5 fsgldiv denorm
short tbl_trans - tbl_trans # $24-4 fsgldiv snan
short tbl_trans - tbl_trans # $24-6 fsgldiv unnorm
short tbl_trans - tbl_trans # $24-7 ERROR
short srem_snorm - tbl_trans # $25-0 frem norm
short srem_szero - tbl_trans # $25-1 frem zero
short srem_sinf - tbl_trans # $25-2 frem inf
short sop_sqnan - tbl_trans # $25-3 frem qnan
short srem_sdnrm - tbl_trans # $25-5 frem denorm
short sop_ssnan - tbl_trans # $25-4 frem snan
short tbl_trans - tbl_trans # $25-6 frem unnorm
short tbl_trans - tbl_trans # $25-7 ERROR
short sscale_snorm - tbl_trans # $26-0 fscale norm
short sscale_szero - tbl_trans # $26-1 fscale zero
short sscale_sinf - tbl_trans # $26-2 fscale inf
short sop_sqnan - tbl_trans # $26-3 fscale qnan
short sscale_sdnrm - tbl_trans # $26-5 fscale denorm
short sop_ssnan - tbl_trans # $26-4 fscale snan
short tbl_trans - tbl_trans # $26-6 fscale unnorm
short tbl_trans - tbl_trans # $26-7 ERROR
short tbl_trans - tbl_trans # $27-0 fsglmul norm
short tbl_trans - tbl_trans # $27-1 fsglmul zero
short tbl_trans - tbl_trans # $27-2 fsglmul inf
short tbl_trans - tbl_trans # $27-3 fsglmul qnan
short tbl_trans - tbl_trans # $27-5 fsglmul denorm
short tbl_trans - tbl_trans # $27-4 fsglmul snan
short tbl_trans - tbl_trans # $27-6 fsglmul unnorm
short tbl_trans - tbl_trans # $27-7 ERROR
short tbl_trans - tbl_trans # $28-0 fsub norm
short tbl_trans - tbl_trans # $28-1 fsub zero
short tbl_trans - tbl_trans # $28-2 fsub inf
short tbl_trans - tbl_trans # $28-3 fsub qnan
short tbl_trans - tbl_trans # $28-5 fsub denorm
short tbl_trans - tbl_trans # $28-4 fsub snan
short tbl_trans - tbl_trans # $28-6 fsub unnorm
short tbl_trans - tbl_trans # $28-7 ERROR
short tbl_trans - tbl_trans # $29-0 ERROR
short tbl_trans - tbl_trans # $29-1 ERROR
short tbl_trans - tbl_trans # $29-2 ERROR
short tbl_trans - tbl_trans # $29-3 ERROR
short tbl_trans - tbl_trans # $29-4 ERROR
short tbl_trans - tbl_trans # $29-5 ERROR
short tbl_trans - tbl_trans # $29-6 ERROR
short tbl_trans - tbl_trans # $29-7 ERROR
short tbl_trans - tbl_trans # $2a-0 ERROR
short tbl_trans - tbl_trans # $2a-1 ERROR
short tbl_trans - tbl_trans # $2a-2 ERROR
short tbl_trans - tbl_trans # $2a-3 ERROR
short tbl_trans - tbl_trans # $2a-4 ERROR
short tbl_trans - tbl_trans # $2a-5 ERROR
short tbl_trans - tbl_trans # $2a-6 ERROR
short tbl_trans - tbl_trans # $2a-7 ERROR
short tbl_trans - tbl_trans # $2b-0 ERROR
short tbl_trans - tbl_trans # $2b-1 ERROR
short tbl_trans - tbl_trans # $2b-2 ERROR
short tbl_trans - tbl_trans # $2b-3 ERROR
short tbl_trans - tbl_trans # $2b-4 ERROR
short tbl_trans - tbl_trans # $2b-5 ERROR
short tbl_trans - tbl_trans # $2b-6 ERROR
short tbl_trans - tbl_trans # $2b-7 ERROR
short tbl_trans - tbl_trans # $2c-0 ERROR
short tbl_trans - tbl_trans # $2c-1 ERROR
short tbl_trans - tbl_trans # $2c-2 ERROR
short tbl_trans - tbl_trans # $2c-3 ERROR
short tbl_trans - tbl_trans # $2c-4 ERROR
short tbl_trans - tbl_trans # $2c-5 ERROR
short tbl_trans - tbl_trans # $2c-6 ERROR
short tbl_trans - tbl_trans # $2c-7 ERROR
short tbl_trans - tbl_trans # $2d-0 ERROR
short tbl_trans - tbl_trans # $2d-1 ERROR
short tbl_trans - tbl_trans # $2d-2 ERROR
short tbl_trans - tbl_trans # $2d-3 ERROR
short tbl_trans - tbl_trans # $2d-4 ERROR
short tbl_trans - tbl_trans # $2d-5 ERROR
short tbl_trans - tbl_trans # $2d-6 ERROR
short tbl_trans - tbl_trans # $2d-7 ERROR
short tbl_trans - tbl_trans # $2e-0 ERROR
short tbl_trans - tbl_trans # $2e-1 ERROR
short tbl_trans - tbl_trans # $2e-2 ERROR
short tbl_trans - tbl_trans # $2e-3 ERROR
short tbl_trans - tbl_trans # $2e-4 ERROR
short tbl_trans - tbl_trans # $2e-5 ERROR
short tbl_trans - tbl_trans # $2e-6 ERROR
short tbl_trans - tbl_trans # $2e-7 ERROR
short tbl_trans - tbl_trans # $2f-0 ERROR
short tbl_trans - tbl_trans # $2f-1 ERROR
short tbl_trans - tbl_trans # $2f-2 ERROR
short tbl_trans - tbl_trans # $2f-3 ERROR
short tbl_trans - tbl_trans # $2f-4 ERROR
short tbl_trans - tbl_trans # $2f-5 ERROR
short tbl_trans - tbl_trans # $2f-6 ERROR
short tbl_trans - tbl_trans # $2f-7 ERROR
short ssincos - tbl_trans # $30-0 fsincos norm
short ssincosz - tbl_trans # $30-1 fsincos zero
short ssincosi - tbl_trans # $30-2 fsincos inf
short ssincosqnan - tbl_trans # $30-3 fsincos qnan
short ssincosd - tbl_trans # $30-5 fsincos denorm
short ssincossnan - tbl_trans # $30-4 fsincos snan
short tbl_trans - tbl_trans # $30-6 fsincos unnorm
short tbl_trans - tbl_trans # $30-7 ERROR
short ssincos - tbl_trans # $31-0 fsincos norm
short ssincosz - tbl_trans # $31-1 fsincos zero
short ssincosi - tbl_trans # $31-2 fsincos inf
short ssincosqnan - tbl_trans # $31-3 fsincos qnan
short ssincosd - tbl_trans # $31-5 fsincos denorm
short ssincossnan - tbl_trans # $31-4 fsincos snan
short tbl_trans - tbl_trans # $31-6 fsincos unnorm
short tbl_trans - tbl_trans # $31-7 ERROR
short ssincos - tbl_trans # $32-0 fsincos norm
short ssincosz - tbl_trans # $32-1 fsincos zero
short ssincosi - tbl_trans # $32-2 fsincos inf
short ssincosqnan - tbl_trans # $32-3 fsincos qnan
short ssincosd - tbl_trans # $32-5 fsincos denorm
short ssincossnan - tbl_trans # $32-4 fsincos snan
short tbl_trans - tbl_trans # $32-6 fsincos unnorm
short tbl_trans - tbl_trans # $32-7 ERROR
short ssincos - tbl_trans # $33-0 fsincos norm
short ssincosz - tbl_trans # $33-1 fsincos zero
short ssincosi - tbl_trans # $33-2 fsincos inf
short ssincosqnan - tbl_trans # $33-3 fsincos qnan
short ssincosd - tbl_trans # $33-5 fsincos denorm
short ssincossnan - tbl_trans # $33-4 fsincos snan
short tbl_trans - tbl_trans # $33-6 fsincos unnorm
short tbl_trans - tbl_trans # $33-7 ERROR
short ssincos - tbl_trans # $34-0 fsincos norm
short ssincosz - tbl_trans # $34-1 fsincos zero
short ssincosi - tbl_trans # $34-2 fsincos inf
short ssincosqnan - tbl_trans # $34-3 fsincos qnan
short ssincosd - tbl_trans # $34-5 fsincos denorm
short ssincossnan - tbl_trans # $34-4 fsincos snan
short tbl_trans - tbl_trans # $34-6 fsincos unnorm
short tbl_trans - tbl_trans # $34-7 ERROR
short ssincos - tbl_trans # $35-0 fsincos norm
short ssincosz - tbl_trans # $35-1 fsincos zero
short ssincosi - tbl_trans # $35-2 fsincos inf
short ssincosqnan - tbl_trans # $35-3 fsincos qnan
short ssincosd - tbl_trans # $35-5 fsincos denorm
short ssincossnan - tbl_trans # $35-4 fsincos snan
short tbl_trans - tbl_trans # $35-6 fsincos unnorm
short tbl_trans - tbl_trans # $35-7 ERROR
short ssincos - tbl_trans # $36-0 fsincos norm
short ssincosz - tbl_trans # $36-1 fsincos zero
short ssincosi - tbl_trans # $36-2 fsincos inf
short ssincosqnan - tbl_trans # $36-3 fsincos qnan
short ssincosd - tbl_trans # $36-5 fsincos denorm
short ssincossnan - tbl_trans # $36-4 fsincos snan
short tbl_trans - tbl_trans # $36-6 fsincos unnorm
short tbl_trans - tbl_trans # $36-7 ERROR
short ssincos - tbl_trans # $37-0 fsincos norm
short ssincosz - tbl_trans # $37-1 fsincos zero
short ssincosi - tbl_trans # $37-2 fsincos inf
short ssincosqnan - tbl_trans # $37-3 fsincos qnan
short ssincosd - tbl_trans # $37-5 fsincos denorm
short ssincossnan - tbl_trans # $37-4 fsincos snan
short tbl_trans - tbl_trans # $37-6 fsincos unnorm
short tbl_trans - tbl_trans # $37-7 ERROR
##########
# the instruction fetch access for the displacement word for the
# fdbcc emulation failed. here, we create an access error frame
# from the current frame and branch to _real_access().
funimp_iacc:
movm.l EXC_DREGS(%a6),&0x0303 # restore d0-d1/a0-a1
fmovm.l USER_FPCR(%a6),%fpcr,%fpsr,%fpiar # restore ctrl regs
fmovm.x EXC_FPREGS(%a6),&0xc0 # restore fp0-fp1
mov.l USER_FPIAR(%a6),EXC_PC(%a6) # store current PC
unlk %a6
mov.l (%sp),-(%sp) # store SR,hi(PC)
mov.w 0x8(%sp),0x4(%sp) # store lo(PC)
mov.w &0x4008,0x6(%sp) # store voff
mov.l 0x2(%sp),0x8(%sp) # store EA
mov.l &0x09428001,0xc(%sp) # store FSLW
btst &0x5,(%sp) # user or supervisor mode?
beq.b funimp_iacc_end # user
bset &0x2,0xd(%sp) # set supervisor TM bit
funimp_iacc_end:
bra.l _real_access
#########################################################################
# ssin(): computes the sine of a normalized input #
# ssind(): computes the sine of a denormalized input #
# scos(): computes the cosine of a normalized input #
# scosd(): computes the cosine of a denormalized input #
# ssincos(): computes the sine and cosine of a normalized input #
# ssincosd(): computes the sine and cosine of a denormalized input #
# #
# INPUT *************************************************************** #
# a0 = pointer to extended precision input #
# d0 = round precision,mode #
# #
# OUTPUT ************************************************************** #
# fp0 = sin(X) or cos(X) #
# #
# For ssincos(X): #
# fp0 = sin(X) #
# fp1 = cos(X) #
# #
# ACCURACY and MONOTONICITY ******************************************* #
# The returned result is within 1 ulp in 64 significant bit, i.e. #
# within 0.5001 ulp to 53 bits if the result is subsequently #
# rounded to double precision. The result is provably monotonic #
# in double precision. #
# #
# ALGORITHM *********************************************************** #
# #
# SIN and COS: #
# 1. If SIN is invoked, set AdjN := 0; otherwise, set AdjN := 1. #
# #
# 2. If |X| >= 15Pi or |X| < 2**(-40), go to 7. #
# #
# 3. Decompose X as X = N(Pi/2) + r where |r| <= Pi/4. Let #
# k = N mod 4, so in particular, k = 0,1,2,or 3. #
# Overwrite k by k := k + AdjN. #
# #
# 4. If k is even, go to 6. #
# #
# 5. (k is odd) Set j := (k-1)/2, sgn := (-1)**j. #
# Return sgn*cos(r) where cos(r) is approximated by an #
# even polynomial in r, 1 + r*r*(B1+s*(B2+ ... + s*B8)), #
# s = r*r. #
# Exit. #
# #
# 6. (k is even) Set j := k/2, sgn := (-1)**j. Return sgn*sin(r) #
# where sin(r) is approximated by an odd polynomial in r #
# r + r*s*(A1+s*(A2+ ... + s*A7)), s = r*r. #
# Exit. #
# #
# 7. If |X| > 1, go to 9. #
# #
# 8. (|X|<2**(-40)) If SIN is invoked, return X; #
# otherwise return 1. #
# #
# 9. Overwrite X by X := X rem 2Pi. Now that |X| <= Pi, #
# go back to 3. #
# #
# SINCOS: #
# 1. If |X| >= 15Pi or |X| < 2**(-40), go to 6. #
# #
# 2. Decompose X as X = N(Pi/2) + r where |r| <= Pi/4. Let #
# k = N mod 4, so in particular, k = 0,1,2,or 3. #
# #
# 3. If k is even, go to 5. #
# #
# 4. (k is odd) Set j1 := (k-1)/2, j2 := j1 (EOR) (k mod 2), ie. #
# j1 exclusive or with the l.s.b. of k. #
# sgn1 := (-1)**j1, sgn2 := (-1)**j2. #
# SIN(X) = sgn1 * cos(r) and COS(X) = sgn2*sin(r) where #
# sin(r) and cos(r) are computed as odd and even #
# polynomials in r, respectively. Exit #
# #
# 5. (k is even) Set j1 := k/2, sgn1 := (-1)**j1. #
# SIN(X) = sgn1 * sin(r) and COS(X) = sgn1*cos(r) where #
# sin(r) and cos(r) are computed as odd and even #
# polynomials in r, respectively. Exit #
# #
# 6. If |X| > 1, go to 8. #
# #
# 7. (|X|<2**(-40)) SIN(X) = X and COS(X) = 1. Exit. #
# #
# 8. Overwrite X by X := X rem 2Pi. Now that |X| <= Pi, #
# go back to 2. #
# #
#########################################################################
SINA7: long 0xBD6AAA77,0xCCC994F5
SINA6: long 0x3DE61209,0x7AAE8DA1
SINA5: long 0xBE5AE645,0x2A118AE4
SINA4: long 0x3EC71DE3,0xA5341531
SINA3: long 0xBF2A01A0,0x1A018B59,0x00000000,0x00000000
SINA2: long 0x3FF80000,0x88888888,0x888859AF,0x00000000
SINA1: long 0xBFFC0000,0xAAAAAAAA,0xAAAAAA99,0x00000000
COSB8: long 0x3D2AC4D0,0xD6011EE3
COSB7: long 0xBDA9396F,0x9F45AC19
COSB6: long 0x3E21EED9,0x0612C972
COSB5: long 0xBE927E4F,0xB79D9FCF
COSB4: long 0x3EFA01A0,0x1A01D423,0x00000000,0x00000000
COSB3: long 0xBFF50000,0xB60B60B6,0x0B61D438,0x00000000
COSB2: long 0x3FFA0000,0xAAAAAAAA,0xAAAAAB5E
COSB1: long 0xBF000000
set INARG,FP_SCR0
set X,FP_SCR0
# set XDCARE,X+2 set XFRAC,X+4
set RPRIME,FP_SCR0 set SPRIME,FP_SCR1
set POSNEG1,L_SCR1 set TWOTO63,L_SCR1
set ENDFLAG,L_SCR2 set INT,L_SCR2
set ADJN,L_SCR3
############################################ global ssin
ssin:
mov.l &0,ADJN(%a6) # yes; SET ADJN TO 0
bra.b SINBGN
############################################ global scos
scos:
mov.l &1,ADJN(%a6) # yes; SET ADJN TO 1
############################################
SINBGN:
#--SAVE FPCR, FP1. CHECK IF |X| IS TOO SMALL OR LARGE
fmov.x (%a0),%fp0 # LOAD INPUT
fmov.x %fp0,X(%a6) # save input at X
# "COMPACTIFY" X
mov.l (%a0),%d1 # put exp in hiword
mov.w 4(%a0),%d1 # fetch hi(man)
and.l &0x7FFFFFFF,%d1 # strip sign
cmpi.l %d1,&0x3FD78000 # is |X| >= 2**(-40)?
bge.b SOK1 # no
bra.w SINSM # yes; input is very small
SOK1:
cmp.l %d1,&0x4004BC7E # is |X| < 15 PI?
blt.b SINMAIN # no
bra.w SREDUCEX # yes; input is very large
#--THIS IS THE USUAL CASE, |X| <= 15 PI.
#--THE ARGUMENT REDUCTION IS DONE BY TABLE LOOK UP.
SINMAIN:
fmov.x %fp0,%fp1
fmul.d TWOBYPI(%pc),%fp1 # X*2/PI
lea PITBL+0x200(%pc),%a1 # TABLE OF N*PI/2, N = -32,...,32
fmov.l %fp1,INT(%a6) # CONVERT TO INTEGER
mov.l INT(%a6),%d1 # make a copy of N
asl.l &4,%d1 # N *= 16
add.l %d1,%a1 # tbl_addr = a1 + (N*16)
# A1 IS THE ADDRESS OF N*PIBY2
# ...WHICH IS IN TWO PIECES Y1 & Y2
fsub.x (%a1)+,%fp0 # X-Y1
fsub.s (%a1),%fp0 # fp0 = R = (X-Y1)-Y2
SINCONT:
#--continuation from REDUCEX
#--GET N+ADJN AND SEE IF SIN(R) OR COS(R) IS NEEDED
mov.l INT(%a6),%d1
add.l ADJN(%a6),%d1 # SEE IF D0 IS ODD OR EVEN
ror.l &1,%d1 # D0 WAS ODD IFF D0 IS NEGATIVE
cmp.l %d1,&0
blt.w COSPOLY
#--LET J BE THE LEAST SIG. BIT OF D0, LET SGN := (-1)**J.
#--THEN WE RETURN SGN*SIN(R). SGN*SIN(R) IS COMPUTED BY
#--R' + R'*S*(A1 + S(A2 + S(A3 + S(A4 + ... + SA7)))), WHERE
#--R' = SGN*R, S=R*R. THIS CAN BE REWRITTEN AS
#--R' + R'*S*( [A1+T(A3+T(A5+TA7))] + [S(A2+T(A4+TA6))])
#--WHERE T=S*S.
#--NOTE THAT A3 THROUGH A7 ARE STORED IN DOUBLE PRECISION
#--WHILE A1 AND A2 ARE IN DOUBLE-EXTENDED FORMAT.
SINPOLY:
fmovm.x &0x0c,-(%sp) # save fp2/fp3
fmov.x %fp0,X(%a6) # X IS R
fmul.x %fp0,%fp0 # FP0 IS S
fmov.d SINA7(%pc),%fp3
fmov.d SINA6(%pc),%fp2
fmov.x %fp0,%fp1
fmul.x %fp1,%fp1 # FP1 IS T
ror.l &1,%d1
and.l &0x80000000,%d1
# ...LEAST SIG. BIT OF D0 IN SIGN POSITION
eor.l %d1,X(%a6) # X IS NOW R'= SGN*R
fmov.l %d0,%fpcr # restore users round mode,prec
fadd.x X(%a6),%fp0 # last inst - possible exception set
bra t_inx2
#--LET J BE THE LEAST SIG. BIT OF D0, LET SGN := (-1)**J.
#--THEN WE RETURN SGN*COS(R). SGN*COS(R) IS COMPUTED BY
#--SGN + S'*(B1 + S(B2 + S(B3 + S(B4 + ... + SB8)))), WHERE
#--S=R*R AND S'=SGN*S. THIS CAN BE REWRITTEN AS
#--SGN + S'*([B1+T(B3+T(B5+TB7))] + [S(B2+T(B4+T(B6+TB8)))])
#--WHERE T=S*S.
#--NOTE THAT B4 THROUGH B8 ARE STORED IN DOUBLE PRECISION
#--WHILE B2 AND B3 ARE IN DOUBLE-EXTENDED FORMAT, B1 IS -1/2
#--AND IS THEREFORE STORED AS SINGLE PRECISION.
COSPOLY:
fmovm.x &0x0c,-(%sp) # save fp2/fp3
fmul.x %fp0,%fp0 # FP0 IS S
fmov.d COSB8(%pc),%fp2
fmov.d COSB7(%pc),%fp3
fmov.x %fp0,%fp1
fmul.x %fp1,%fp1 # FP1 IS T
fmov.x %fp0,X(%a6) # X IS S
ror.l &1,%d1
and.l &0x80000000,%d1
# ...LEAST SIG. BIT OF D0 IN SIGN POSITION
fmul.x %fp1,%fp2 # TB8
eor.l %d1,X(%a6) # X IS NOW S'= SGN*S
and.l &0x80000000,%d1
fmul.x %fp1,%fp3 # TB7
or.l &0x3F800000,%d1 # D0 IS SGN IN SINGLE
mov.l %d1,POSNEG1(%a6)
fmov.l %d0,%fpcr # restore users round mode,prec
fadd.s POSNEG1(%a6),%fp0 # last inst - possible exception set
bra t_inx2
##############################################
# SINe: Big OR Small?
#--IF |X| > 15PI, WE USE THE GENERAL ARGUMENT REDUCTION.
#--IF |X| < 2**(-40), RETURN X OR 1.
SINBORS:
cmp.l %d1,&0x3FFF8000
bgt.l SREDUCEX
# here, the operation may underflow iff the precision is sgl or dbl.
# extended denorms are handled through another entry point.
SINTINY:
# mov.w &0x0000,XDCARE(%a6) # JUST IN CASE
fmov.l %d0,%fpcr # restore users round mode,prec
mov.b &FMOV_OP,%d1 # last inst is MOVE
fmov.x X(%a6),%fp0 # last inst - possible exception set
bra t_catch
COSTINY:
fmov.s &0x3F800000,%fp0 # fp0 = 1.0
fmov.l %d0,%fpcr # restore users round mode,prec
fadd.s &0x80800000,%fp0 # last inst - possible exception set
bra t_pinx2
################################################ global ssind
#--SIN(X) = X FOR DENORMALIZED X
ssind:
bra t_extdnrm
############################################ global scosd
#--COS(X) = 1 FOR DENORMALIZED X
scosd:
fmov.s &0x3F800000,%fp0 # fp0 = 1.0
bra t_pinx2
fmov.l %d0,%fpcr
fsub.s &0x00800000,%fp1
bsr sto_cos # store cosine result
fmov.l %fpcr,%d0 # d0 must have fpcr,too
mov.b &FMOV_OP,%d1 # last inst is MOVE
fmov.x X(%a6),%fp0
bra t_catch
##############################################
global ssincosd
#--SIN AND COS OF X FOR DENORMALIZED X
ssincosd:
mov.l %d0,-(%sp) # save d0
fmov.s &0x3F800000,%fp1
bsr sto_cos # store cosine result
mov.l (%sp)+,%d0 # restore d0
bra t_extdnrm
############################################
#--WHEN REDUCEX IS USED, THE CODE WILL INEVITABLY BE SLOW.
#--THIS REDUCTION METHOD, HOWEVER, IS MUCH FASTER THAN USING
#--THE REMAINDER INSTRUCTION WHICH IS NOW IN SOFTWARE.
SREDUCEX:
fmovm.x &0x3c,-(%sp) # save {fp2-fp5}
mov.l %d2,-(%sp) # save d2
fmov.s &0x00000000,%fp1 # fp1 = 0
#--If compact form of abs(arg) in d0=$7ffeffff, argument is so large that
#--there is a danger of unwanted overflow in first LOOP iteration. In this
#--case, reduce argument by one remainder step to make subsequent reduction
#--safe.
cmp.l %d1,&0x7ffeffff # is arg dangerously large?
bne.b SLOOP # no
# create low half of 2**16383*PI/2 at FP_SCR1
mov.w &0x7fdc,FP_SCR1_EX(%a6)
mov.l &0x85a308d3,FP_SCR1_HI(%a6) clr.l FP_SCR1_LO(%a6)
ftest.x %fp0 # test sign of argument
fblt.w sred_neg
or.b &0x80,FP_SCR0_EX(%a6) # positive arg
or.b &0x80,FP_SCR1_EX(%a6)
sred_neg:
fadd.x FP_SCR0(%a6),%fp0 # high part of reduction is exact
fmov.x %fp0,%fp1 # save high result in fp1
fadd.x FP_SCR1(%a6),%fp0 # low part of reduction
fsub.x %fp0,%fp1 # determine low component of result
fadd.x FP_SCR1(%a6),%fp1 # fp0/fp1 are reduced argument.
#--ON ENTRY, FP0 IS X, ON RETURN, FP0 IS X REM PI/2, |X| <= PI/4.
#--integer quotient will be stored in N
#--Intermeditate remainder is 66-bit long; (R,r) in (FP0,FP1)
SLOOP:
fmov.x %fp0,INARG(%a6) # +-2**K * F, 1 <= F < 2
mov.w INARG(%a6),%d1
mov.l %d1,%a1 # save a copy of D0
and.l &0x00007FFF,%d1 sub.l &0x00003FFF,%d1 # d0 = K
cmp.l %d1,&28
ble.b SLASTLOOP
SCONTLOOP: sub.l &27,%d1 # d0 = L := K-27
mov.b &0,ENDFLAG(%a6)
bra.b SWORK
SLASTLOOP: clr.l %d1 # d0 = L := 0
mov.b &1,ENDFLAG(%a6)
SWORK:
#--FIND THE REMAINDER OF (R,r) W.R.T. 2**L * (PI/2). L IS SO CHOSEN
#--THAT INT( X * (2/PI) / 2**(L) ) < 2**29.
fmov.x %fp0,%fp2
fmul.x FP_SCR0(%a6),%fp2 # fp2 = X * 2**(-L)*(2/PI)
#--WE MUST NOW FIND INT(FP2). SINCE WE NEED THIS VALUE IN
#--FLOATING POINT FORMAT, THE TWO FMOVE'S FMOVE.L FP <--> N
#--WILL BE TOO INEFFICIENT. THE WAY AROUND IT IS THAT
#--(SIGN(INARG)*2**63 + FP2) - SIGN(INARG)*2**63 WILL GIVE
#--US THE DESIRED VALUE IN FLOATING POINT.
mov.l %a1,%d2
swap %d2
and.l &0x80000000,%d2
or.l &0x5F000000,%d2 # d2 = SIGN(INARG)*2**63 IN SGL
mov.l %d2,TWOTO63(%a6)
fadd.s TWOTO63(%a6),%fp2 # THE FRACTIONAL PART OF FP1 IS ROUNDED
fsub.s TWOTO63(%a6),%fp2 # fp2 = N
# fint.x %fp2
#--CREATING 2**(L)*Piby2_1 and 2**(L)*Piby2_2
mov.l %d1,%d2 # d2 = L
#--We are now ready to perform (R+r) - N*P1 - N*P2, P1 = 2**(L) * Piby2_1 and
#--P2 = 2**(L) * Piby2_2
fmov.x %fp2,%fp4 # fp4 = N
fmul.x FP_SCR0(%a6),%fp4 # fp4 = W = N*P1
fmov.x %fp2,%fp5 # fp5 = N
fmul.x FP_SCR1(%a6),%fp5 # fp5 = w = N*P2
fmov.x %fp4,%fp3 # fp3 = W = N*P1
#--we want P+p = W+w but |p| <= half ulp of P
#--Then, we need to compute A := R-P and a := r-p
fadd.x %fp5,%fp3 # fp3 = P
fsub.x %fp3,%fp4 # fp4 = W-P
fsub.x %fp3,%fp0 # fp0 = A := R - P
fadd.x %fp5,%fp4 # fp4 = p = (W-P)+w
fmov.x %fp0,%fp3 # fp3 = A
fsub.x %fp4,%fp1 # fp1 = a := r - p
#--Now we need to normalize (A,a) to "new (R,r)" where R+r = A+a but
#--|r| <= half ulp of R.
fadd.x %fp1,%fp0 # fp0 = R := A+a
#--No need to calculate r if this is the last loop
cmp.b %d1,&0
bgt.w SRESTORE
#--Need to calculate r
fsub.x %fp0,%fp3 # fp3 = A-R
fadd.x %fp3,%fp1 # fp1 = r := (A-R)+a
bra.w SLOOP
#########################################################################
# stan(): computes the tangent of a normalized input #
# stand(): computes the tangent of a denormalized input #
# #
# INPUT *************************************************************** #
# a0 = pointer to extended precision input #
# d0 = round precision,mode #
# #
# OUTPUT ************************************************************** #
# fp0 = tan(X) #
# #
# ACCURACY and MONOTONICITY ******************************************* #
# The returned result is within 3 ulp in 64 significant bit, i.e. #
# within 0.5001 ulp to 53 bits if the result is subsequently #
# rounded to double precision. The result is provably monotonic #
# in double precision. #
# #
# ALGORITHM *********************************************************** #
# #
# 1. If |X| >= 15Pi or |X| < 2**(-40), go to 6. #
# #
# 2. Decompose X as X = N(Pi/2) + r where |r| <= Pi/4. Let #
# k = N mod 2, so in particular, k = 0 or 1. #
# #
# 3. If k is odd, go to 5. #
# #
# 4. (k is even) Tan(X) = tan(r) and tan(r) is approximated by a #
# rational function U/V where #
# U = r + r*s*(P1 + s*(P2 + s*P3)), and #
# V = 1 + s*(Q1 + s*(Q2 + s*(Q3 + s*Q4))), s = r*r. #
# Exit. #
# #
# 4. (k is odd) Tan(X) = -cot(r). Since tan(r) is approximated by #
# a rational function U/V where #
# U = r + r*s*(P1 + s*(P2 + s*P3)), and #
# V = 1 + s*(Q1 + s*(Q2 + s*(Q3 + s*Q4))), s = r*r, #
# -Cot(r) = -V/U. Exit. #
# #
# 6. If |X| > 1, go to 8. #
# #
# 7. (|X|<2**(-40)) Tan(X) = X. Exit. #
# #
# 8. Overwrite X by X := X rem 2Pi. Now that |X| <= Pi, go back #
# to 2. #
# #
#########################################################################
TANQ4:
long 0x3EA0B759,0xF50F8688
TANP3:
long 0xBEF2BAA5,0xA8924F04
TANQ3:
long 0xBF346F59,0xB39BA65F,0x00000000,0x00000000
TANP2:
long 0x3FF60000,0xE073D3FC,0x199C4A00,0x00000000
TANQ2:
long 0x3FF90000,0xD23CD684,0x15D95FA1,0x00000000
TANP1:
long 0xBFFC0000,0x8895A6C5,0xFB423BCA,0x00000000
TANQ1:
long 0xBFFD0000,0xEEF57E0D,0xA84BC8CE,0x00000000
INVTWOPI:
long 0x3FFC0000,0xA2F9836E,0x4E44152A,0x00000000
TWOPI1:
long 0x40010000,0xC90FDAA2,0x00000000,0x00000000
TWOPI2:
long 0x3FDF0000,0x85A308D4,0x00000000,0x00000000
#--N*PI/2, -32 <= N <= 32, IN A LEADING TERM IN EXT. AND TRAILING
#--TERM IN SGL. NOTE THAT PI IS 64-BIT LONG, THUS N*PI/2 IS AT
#--MOST 69 BITS LONG.
# global PITBL
PITBL:
long 0xC0040000,0xC90FDAA2,0x2168C235,0x21800000
long 0xC0040000,0xC2C75BCD,0x105D7C23,0xA0D00000
long 0xC0040000,0xBC7EDCF7,0xFF523611,0xA1E80000
long 0xC0040000,0xB6365E22,0xEE46F000,0x21480000
long 0xC0040000,0xAFEDDF4D,0xDD3BA9EE,0xA1200000
long 0xC0040000,0xA9A56078,0xCC3063DD,0x21FC0000
long 0xC0040000,0xA35CE1A3,0xBB251DCB,0x21100000
long 0xC0040000,0x9D1462CE,0xAA19D7B9,0xA1580000
long 0xC0040000,0x96CBE3F9,0x990E91A8,0x21E00000
long 0xC0040000,0x90836524,0x88034B96,0x20B00000
long 0xC0040000,0x8A3AE64F,0x76F80584,0xA1880000
long 0xC0040000,0x83F2677A,0x65ECBF73,0x21C40000
long 0xC0030000,0xFB53D14A,0xA9C2F2C2,0x20000000
long 0xC0030000,0xEEC2D3A0,0x87AC669F,0x21380000
long 0xC0030000,0xE231D5F6,0x6595DA7B,0xA1300000
long 0xC0030000,0xD5A0D84C,0x437F4E58,0x9FC00000
long 0xC0030000,0xC90FDAA2,0x2168C235,0x21000000
long 0xC0030000,0xBC7EDCF7,0xFF523611,0xA1680000
long 0xC0030000,0xAFEDDF4D,0xDD3BA9EE,0xA0A00000
long 0xC0030000,0xA35CE1A3,0xBB251DCB,0x20900000
long 0xC0030000,0x96CBE3F9,0x990E91A8,0x21600000
long 0xC0030000,0x8A3AE64F,0x76F80584,0xA1080000
long 0xC0020000,0xFB53D14A,0xA9C2F2C2,0x1F800000
long 0xC0020000,0xE231D5F6,0x6595DA7B,0xA0B00000
long 0xC0020000,0xC90FDAA2,0x2168C235,0x20800000
long 0xC0020000,0xAFEDDF4D,0xDD3BA9EE,0xA0200000
long 0xC0020000,0x96CBE3F9,0x990E91A8,0x20E00000
long 0xC0010000,0xFB53D14A,0xA9C2F2C2,0x1F000000
long 0xC0010000,0xC90FDAA2,0x2168C235,0x20000000
long 0xC0010000,0x96CBE3F9,0x990E91A8,0x20600000
long 0xC0000000,0xC90FDAA2,0x2168C235,0x1F800000
long 0xBFFF0000,0xC90FDAA2,0x2168C235,0x1F000000
long 0x00000000,0x00000000,0x00000000,0x00000000
long 0x3FFF0000,0xC90FDAA2,0x2168C235,0x9F000000
long 0x40000000,0xC90FDAA2,0x2168C235,0x9F800000
long 0x40010000,0x96CBE3F9,0x990E91A8,0xA0600000
long 0x40010000,0xC90FDAA2,0x2168C235,0xA0000000
long 0x40010000,0xFB53D14A,0xA9C2F2C2,0x9F000000
long 0x40020000,0x96CBE3F9,0x990E91A8,0xA0E00000
long 0x40020000,0xAFEDDF4D,0xDD3BA9EE,0x20200000
long 0x40020000,0xC90FDAA2,0x2168C235,0xA0800000
long 0x40020000,0xE231D5F6,0x6595DA7B,0x20B00000
long 0x40020000,0xFB53D14A,0xA9C2F2C2,0x9F800000
long 0x40030000,0x8A3AE64F,0x76F80584,0x21080000
long 0x40030000,0x96CBE3F9,0x990E91A8,0xA1600000
long 0x40030000,0xA35CE1A3,0xBB251DCB,0xA0900000
long 0x40030000,0xAFEDDF4D,0xDD3BA9EE,0x20A00000
long 0x40030000,0xBC7EDCF7,0xFF523611,0x21680000
long 0x40030000,0xC90FDAA2,0x2168C235,0xA1000000
long 0x40030000,0xD5A0D84C,0x437F4E58,0x1FC00000
long 0x40030000,0xE231D5F6,0x6595DA7B,0x21300000
long 0x40030000,0xEEC2D3A0,0x87AC669F,0xA1380000
long 0x40030000,0xFB53D14A,0xA9C2F2C2,0xA0000000
long 0x40040000,0x83F2677A,0x65ECBF73,0xA1C40000
long 0x40040000,0x8A3AE64F,0x76F80584,0x21880000
long 0x40040000,0x90836524,0x88034B96,0xA0B00000
long 0x40040000,0x96CBE3F9,0x990E91A8,0xA1E00000
long 0x40040000,0x9D1462CE,0xAA19D7B9,0x21580000
long 0x40040000,0xA35CE1A3,0xBB251DCB,0xA1100000
long 0x40040000,0xA9A56078,0xCC3063DD,0xA1FC0000
long 0x40040000,0xAFEDDF4D,0xDD3BA9EE,0x21200000
long 0x40040000,0xB6365E22,0xEE46F000,0xA1480000
long 0x40040000,0xBC7EDCF7,0xFF523611,0x21E80000
long 0x40040000,0xC2C75BCD,0x105D7C23,0x20D00000
long 0x40040000,0xC90FDAA2,0x2168C235,0xA1800000
set INARG,FP_SCR0
set TWOTO63,L_SCR1 set INT,L_SCR1 set ENDFLAG,L_SCR2
fmov.l %d0,%fpcr # restore users round mode,prec
fdiv.x (%sp)+,%fp0 # last inst - possible exception set
bra t_inx2
TANBORS:
#--IF |X| > 15PI, WE USE THE GENERAL ARGUMENT REDUCTION.
#--IF |X| < 2**(-40), RETURN X OR 1.
cmp.l %d1,&0x3FFF8000
bgt.b REDUCEX
TANSM:
fmov.x %fp0,-(%sp)
fmov.l %d0,%fpcr # restore users round mode,prec
mov.b &FMOV_OP,%d1 # last inst is MOVE
fmov.x (%sp)+,%fp0 # last inst - posibble exception set
bra t_catch
global stand
#--TAN(X) = X FOR DENORMALIZED X
stand:
bra t_extdnrm
#--WHEN REDUCEX IS USED, THE CODE WILL INEVITABLY BE SLOW.
#--THIS REDUCTION METHOD, HOWEVER, IS MUCH FASTER THAN USING
#--THE REMAINDER INSTRUCTION WHICH IS NOW IN SOFTWARE.
REDUCEX:
fmovm.x &0x3c,-(%sp) # save {fp2-fp5}
mov.l %d2,-(%sp) # save d2
fmov.s &0x00000000,%fp1 # fp1 = 0
#--If compact form of abs(arg) in d0=$7ffeffff, argument is so large that
#--there is a danger of unwanted overflow in first LOOP iteration. In this
#--case, reduce argument by one remainder step to make subsequent reduction
#--safe.
cmp.l %d1,&0x7ffeffff # is arg dangerously large?
bne.b LOOP # no
# create low half of 2**16383*PI/2 at FP_SCR1
mov.w &0x7fdc,FP_SCR1_EX(%a6)
mov.l &0x85a308d3,FP_SCR1_HI(%a6) clr.l FP_SCR1_LO(%a6)
ftest.x %fp0 # test sign of argument
fblt.w red_neg
or.b &0x80,FP_SCR0_EX(%a6) # positive arg
or.b &0x80,FP_SCR1_EX(%a6)
red_neg:
fadd.x FP_SCR0(%a6),%fp0 # high part of reduction is exact
fmov.x %fp0,%fp1 # save high result in fp1
fadd.x FP_SCR1(%a6),%fp0 # low part of reduction
fsub.x %fp0,%fp1 # determine low component of result
fadd.x FP_SCR1(%a6),%fp1 # fp0/fp1 are reduced argument.
#--ON ENTRY, FP0 IS X, ON RETURN, FP0 IS X REM PI/2, |X| <= PI/4.
#--integer quotient will be stored in N
#--Intermeditate remainder is 66-bit long; (R,r) in (FP0,FP1)
LOOP:
fmov.x %fp0,INARG(%a6) # +-2**K * F, 1 <= F < 2
mov.w INARG(%a6),%d1
mov.l %d1,%a1 # save a copy of D0
and.l &0x00007FFF,%d1 sub.l &0x00003FFF,%d1 # d0 = K
cmp.l %d1,&28
ble.b LASTLOOP
CONTLOOP: sub.l &27,%d1 # d0 = L := K-27
mov.b &0,ENDFLAG(%a6)
bra.b WORK
LASTLOOP: clr.l %d1 # d0 = L := 0
mov.b &1,ENDFLAG(%a6)
WORK:
#--FIND THE REMAINDER OF (R,r) W.R.T. 2**L * (PI/2). L IS SO CHOSEN
#--THAT INT( X * (2/PI) / 2**(L) ) < 2**29.
fmov.x %fp0,%fp2
fmul.x FP_SCR0(%a6),%fp2 # fp2 = X * 2**(-L)*(2/PI)
#--WE MUST NOW FIND INT(FP2). SINCE WE NEED THIS VALUE IN
#--FLOATING POINT FORMAT, THE TWO FMOVE'S FMOVE.L FP <--> N
#--WILL BE TOO INEFFICIENT. THE WAY AROUND IT IS THAT
#--(SIGN(INARG)*2**63 + FP2) - SIGN(INARG)*2**63 WILL GIVE
#--US THE DESIRED VALUE IN FLOATING POINT.
mov.l %a1,%d2
swap %d2
and.l &0x80000000,%d2
or.l &0x5F000000,%d2 # d2 = SIGN(INARG)*2**63 IN SGL
mov.l %d2,TWOTO63(%a6)
fadd.s TWOTO63(%a6),%fp2 # THE FRACTIONAL PART OF FP1 IS ROUNDED
fsub.s TWOTO63(%a6),%fp2 # fp2 = N
# fintrz.x %fp2,%fp2
#--CREATING 2**(L)*Piby2_1 and 2**(L)*Piby2_2
mov.l %d1,%d2 # d2 = L
#--We are now ready to perform (R+r) - N*P1 - N*P2, P1 = 2**(L) * Piby2_1 and
#--P2 = 2**(L) * Piby2_2
fmov.x %fp2,%fp4 # fp4 = N
fmul.x FP_SCR0(%a6),%fp4 # fp4 = W = N*P1
fmov.x %fp2,%fp5 # fp5 = N
fmul.x FP_SCR1(%a6),%fp5 # fp5 = w = N*P2
fmov.x %fp4,%fp3 # fp3 = W = N*P1
#--we want P+p = W+w but |p| <= half ulp of P
#--Then, we need to compute A := R-P and a := r-p
fadd.x %fp5,%fp3 # fp3 = P
fsub.x %fp3,%fp4 # fp4 = W-P
fsub.x %fp3,%fp0 # fp0 = A := R - P
fadd.x %fp5,%fp4 # fp4 = p = (W-P)+w
fmov.x %fp0,%fp3 # fp3 = A
fsub.x %fp4,%fp1 # fp1 = a := r - p
#--Now we need to normalize (A,a) to "new (R,r)" where R+r = A+a but
#--|r| <= half ulp of R.
fadd.x %fp1,%fp0 # fp0 = R := A+a
#--No need to calculate r if this is the last loop
cmp.b %d1,&0
bgt.w RESTORE
#--Need to calculate r
fsub.x %fp0,%fp3 # fp3 = A-R
fadd.x %fp3,%fp1 # fp1 = r := (A-R)+a
bra.w LOOP
#########################################################################
# satan(): computes the arctangent of a normalized number #
# satand(): computes the arctangent of a denormalized number #
# #
# INPUT *************************************************************** #
# a0 = pointer to extended precision input #
# d0 = round precision,mode #
# #
# OUTPUT ************************************************************** #
# fp0 = arctan(X) #
# #
# ACCURACY and MONOTONICITY ******************************************* #
# The returned result is within 2 ulps in 64 significant bit, #
# i.e. within 0.5001 ulp to 53 bits if the result is subsequently #
# rounded to double precision. The result is provably monotonic #
# in double precision. #
# #
# ALGORITHM *********************************************************** #
# Step 1. If |X| >= 16 or |X| < 1/16, go to Step 5. #
# #
# Step 2. Let X = sgn * 2**k * 1.xxxxxxxx...x. #
# Note that k = -4, -3,..., or 3. #
# Define F = sgn * 2**k * 1.xxxx1, i.e. the first 5 #
# significant bits of X with a bit-1 attached at the 6-th #
# bit position. Define u to be u = (X-F) / (1 + X*F). #
# #
# Step 3. Approximate arctan(u) by a polynomial poly. #
# #
# Step 4. Return arctan(F) + poly, arctan(F) is fetched from a #
# table of values calculated beforehand. Exit. #
# #
# Step 5. If |X| >= 16, go to Step 7. #
# #
# Step 6. Approximate arctan(X) by an odd polynomial in X. Exit. #
# #
# Step 7. Define X' = -1/X. Approximate arctan(X') by an odd #
# polynomial in X'. #
# Arctan(X) = sign(X)*Pi/2 + arctan(X'). Exit. #
# #
#########################################################################
ATANA3: long 0xBFF6687E,0x314987D8
ATANA2: long 0x4002AC69,0x34A26DB3
ATANA1: long 0xBFC2476F,0x4E1DA28E
ATANB6: long 0x3FB34444,0x7F876989
ATANB5: long 0xBFB744EE,0x7FAF45DB
ATANB4: long 0x3FBC71C6,0x46940220
ATANB3: long 0xBFC24924,0x921872F9
ATANB2: long 0x3FC99999,0x99998FA9
ATANB1: long 0xBFD55555,0x55555555
ATANC5: long 0xBFB70BF3,0x98539E6A
ATANC4: long 0x3FBC7187,0x962D1D7D
ATANC3: long 0xBFC24924,0x827107B8
ATANC2: long 0x3FC99999,0x9996263E
ATANC1: long 0xBFD55555,0x55555536
PPIBY2: long 0x3FFF0000,0xC90FDAA2,0x2168C235,0x00000000
NPIBY2: long 0xBFFF0000,0xC90FDAA2,0x2168C235,0x00000000
PTINY: long 0x00010000,0x80000000,0x00000000,0x00000000
NTINY: long 0x80010000,0x80000000,0x00000000,0x00000000
ATANTBL:
long 0x3FFB0000,0x83D152C5,0x060B7A51,0x00000000
long 0x3FFB0000,0x8BC85445,0x65498B8B,0x00000000
long 0x3FFB0000,0x93BE4060,0x17626B0D,0x00000000
long 0x3FFB0000,0x9BB3078D,0x35AEC202,0x00000000
long 0x3FFB0000,0xA3A69A52,0x5DDCE7DE,0x00000000
long 0x3FFB0000,0xAB98E943,0x62765619,0x00000000
long 0x3FFB0000,0xB389E502,0xF9C59862,0x00000000
long 0x3FFB0000,0xBB797E43,0x6B09E6FB,0x00000000
long 0x3FFB0000,0xC367A5C7,0x39E5F446,0x00000000
long 0x3FFB0000,0xCB544C61,0xCFF7D5C6,0x00000000
long 0x3FFB0000,0xD33F62F8,0x2488533E,0x00000000
long 0x3FFB0000,0xDB28DA81,0x62404C77,0x00000000
long 0x3FFB0000,0xE310A407,0x8AD34F18,0x00000000
long 0x3FFB0000,0xEAF6B0A8,0x188EE1EB,0x00000000
long 0x3FFB0000,0xF2DAF194,0x9DBE79D5,0x00000000
long 0x3FFB0000,0xFABD5813,0x61D47E3E,0x00000000
long 0x3FFC0000,0x8346AC21,0x0959ECC4,0x00000000
long 0x3FFC0000,0x8B232A08,0x304282D8,0x00000000
long 0x3FFC0000,0x92FB70B8,0xD29AE2F9,0x00000000
long 0x3FFC0000,0x9ACF476F,0x5CCD1CB4,0x00000000
long 0x3FFC0000,0xA29E7630,0x4954F23F,0x00000000
long 0x3FFC0000,0xAA68C5D0,0x8AB85230,0x00000000
long 0x3FFC0000,0xB22DFFFD,0x9D539F83,0x00000000
long 0x3FFC0000,0xB9EDEF45,0x3E900EA5,0x00000000
long 0x3FFC0000,0xC1A85F1C,0xC75E3EA5,0x00000000
long 0x3FFC0000,0xC95D1BE8,0x28138DE6,0x00000000
long 0x3FFC0000,0xD10BF300,0x840D2DE4,0x00000000
long 0x3FFC0000,0xD8B4B2BA,0x6BC05E7A,0x00000000
long 0x3FFC0000,0xE0572A6B,0xB42335F6,0x00000000
long 0x3FFC0000,0xE7F32A70,0xEA9CAA8F,0x00000000
long 0x3FFC0000,0xEF888432,0x64ECEFAA,0x00000000
long 0x3FFC0000,0xF7170A28,0xECC06666,0x00000000
long 0x3FFD0000,0x812FD288,0x332DAD32,0x00000000
long 0x3FFD0000,0x88A8D1B1,0x218E4D64,0x00000000
long 0x3FFD0000,0x9012AB3F,0x23E4AEE8,0x00000000
long 0x3FFD0000,0x976CC3D4,0x11E7F1B9,0x00000000
long 0x3FFD0000,0x9EB68949,0x3889A227,0x00000000
long 0x3FFD0000,0xA5EF72C3,0x4487361B,0x00000000
long 0x3FFD0000,0xAD1700BA,0xF07A7227,0x00000000
long 0x3FFD0000,0xB42CBCFA,0xFD37EFB7,0x00000000
long 0x3FFD0000,0xBB303A94,0x0BA80F89,0x00000000
long 0x3FFD0000,0xC22115C6,0xFCAEBBAF,0x00000000
long 0x3FFD0000,0xC8FEF3E6,0x86331221,0x00000000
long 0x3FFD0000,0xCFC98330,0xB4000C70,0x00000000
long 0x3FFD0000,0xD6807AA1,0x102C5BF9,0x00000000
long 0x3FFD0000,0xDD2399BC,0x31252AA3,0x00000000
long 0x3FFD0000,0xE3B2A855,0x6B8FC517,0x00000000
long 0x3FFD0000,0xEA2D764F,0x64315989,0x00000000
long 0x3FFD0000,0xF3BF5BF8,0xBAD1A21D,0x00000000
long 0x3FFE0000,0x801CE39E,0x0D205C9A,0x00000000
long 0x3FFE0000,0x8630A2DA,0xDA1ED066,0x00000000
long 0x3FFE0000,0x8C1AD445,0xF3E09B8C,0x00000000
long 0x3FFE0000,0x91DB8F16,0x64F350E2,0x00000000
long 0x3FFE0000,0x97731420,0x365E538C,0x00000000
long 0x3FFE0000,0x9CE1C8E6,0xA0B8CDBA,0x00000000
long 0x3FFE0000,0xA22832DB,0xCADAAE09,0x00000000
long 0x3FFE0000,0xA746F2DD,0xB7602294,0x00000000
long 0x3FFE0000,0xAC3EC0FB,0x997DD6A2,0x00000000
long 0x3FFE0000,0xB110688A,0xEBDC6F6A,0x00000000
long 0x3FFE0000,0xB5BCC490,0x59ECC4B0,0x00000000
long 0x3FFE0000,0xBA44BC7D,0xD470782F,0x00000000
long 0x3FFE0000,0xBEA94144,0xFD049AAC,0x00000000
long 0x3FFE0000,0xC2EB4ABB,0x661628B6,0x00000000
long 0x3FFE0000,0xC70BD54C,0xE602EE14,0x00000000
long 0x3FFE0000,0xCD000549,0xADEC7159,0x00000000
long 0x3FFE0000,0xD48457D2,0xD8EA4EA3,0x00000000
long 0x3FFE0000,0xDB948DA7,0x12DECE3B,0x00000000
long 0x3FFE0000,0xE23855F9,0x69E8096A,0x00000000
long 0x3FFE0000,0xE8771129,0xC4353259,0x00000000
long 0x3FFE0000,0xEE57C16E,0x0D379C0D,0x00000000
long 0x3FFE0000,0xF3E10211,0xA87C3779,0x00000000
long 0x3FFE0000,0xF919039D,0x758B8D41,0x00000000
long 0x3FFE0000,0xFE058B8F,0x64935FB3,0x00000000
long 0x3FFF0000,0x8155FB49,0x7B685D04,0x00000000
long 0x3FFF0000,0x83889E35,0x49D108E1,0x00000000
long 0x3FFF0000,0x859CFA76,0x511D724B,0x00000000
long 0x3FFF0000,0x87952ECF,0xFF8131E7,0x00000000
long 0x3FFF0000,0x89732FD1,0x9557641B,0x00000000
long 0x3FFF0000,0x8B38CAD1,0x01932A35,0x00000000
long 0x3FFF0000,0x8CE7A8D8,0x301EE6B5,0x00000000
long 0x3FFF0000,0x8F46A39E,0x2EAE5281,0x00000000
long 0x3FFF0000,0x922DA7D7,0x91888487,0x00000000
long 0x3FFF0000,0x94D19FCB,0xDEDF5241,0x00000000
long 0x3FFF0000,0x973AB944,0x19D2A08B,0x00000000
long 0x3FFF0000,0x996FF00E,0x08E10B96,0x00000000
long 0x3FFF0000,0x9B773F95,0x12321DA7,0x00000000
long 0x3FFF0000,0x9D55CC32,0x0F935624,0x00000000
long 0x3FFF0000,0x9F100575,0x006CC571,0x00000000
long 0x3FFF0000,0xA0A9C290,0xD97CC06C,0x00000000
long 0x3FFF0000,0xA22659EB,0xEBC0630A,0x00000000
long 0x3FFF0000,0xA388B4AF,0xF6EF0EC9,0x00000000
long 0x3FFF0000,0xA4D35F10,0x61D292C4,0x00000000
long 0x3FFF0000,0xA60895DC,0xFBE3187E,0x00000000
long 0x3FFF0000,0xA72A51DC,0x7367BEAC,0x00000000
long 0x3FFF0000,0xA83A5153,0x0956168F,0x00000000
long 0x3FFF0000,0xA93A2007,0x7539546E,0x00000000
long 0x3FFF0000,0xAA9E7245,0x023B2605,0x00000000
long 0x3FFF0000,0xAC4C84BA,0x6FE4D58F,0x00000000
long 0x3FFF0000,0xADCE4A4A,0x606B9712,0x00000000
long 0x3FFF0000,0xAF2A2DCD,0x8D263C9C,0x00000000
long 0x3FFF0000,0xB0656F81,0xF22265C7,0x00000000
long 0x3FFF0000,0xB1846515,0x0F71496A,0x00000000
long 0x3FFF0000,0xB28AAA15,0x6F9ADA35,0x00000000
long 0x3FFF0000,0xB37B44FF,0x3766B895,0x00000000
long 0x3FFF0000,0xB458C3DC,0xE9630433,0x00000000
long 0x3FFF0000,0xB525529D,0x562246BD,0x00000000
long 0x3FFF0000,0xB5E2CCA9,0x5F9D88CC,0x00000000
long 0x3FFF0000,0xB692CADA,0x7ACA1ADA,0x00000000
long 0x3FFF0000,0xB736AEA7,0xA6925838,0x00000000
long 0x3FFF0000,0xB7CFAB28,0x7E9F7B36,0x00000000
long 0x3FFF0000,0xB85ECC66,0xCB219835,0x00000000
long 0x3FFF0000,0xB8E4FD5A,0x20A593DA,0x00000000
long 0x3FFF0000,0xB99F41F6,0x4AFF9BB5,0x00000000
long 0x3FFF0000,0xBA7F1E17,0x842BBE7B,0x00000000
long 0x3FFF0000,0xBB471285,0x7637E17D,0x00000000
long 0x3FFF0000,0xBBFABE8A,0x4788DF6F,0x00000000
long 0x3FFF0000,0xBC9D0FAD,0x2B689D79,0x00000000
long 0x3FFF0000,0xBD306A39,0x471ECD86,0x00000000
long 0x3FFF0000,0xBDB6C731,0x856AF18A,0x00000000
long 0x3FFF0000,0xBE31CAC5,0x02E80D70,0x00000000
long 0x3FFF0000,0xBEA2D55C,0xE33194E2,0x00000000
long 0x3FFF0000,0xBF0B10B7,0xC03128F0,0x00000000
long 0x3FFF0000,0xBF6B7A18,0xDACB778D,0x00000000
long 0x3FFF0000,0xBFC4EA46,0x63FA18F6,0x00000000
long 0x3FFF0000,0xC0181BDE,0x8B89A454,0x00000000
long 0x3FFF0000,0xC065B066,0xCFBF6439,0x00000000
long 0x3FFF0000,0xC0AE345F,0x56340AE6,0x00000000
long 0x3FFF0000,0xC0F22291,0x9CB9E6A7,0x00000000
set X,FP_SCR0 set XDCARE,X+2 set XFRAC,X+4 set XFRACLO,X+8
set ATANF,FP_SCR1 set ATANFHI,ATANF+4 set ATANFLO,ATANF+8
global satan
#--ENTRY POINT FOR ATAN(X), HERE X IS FINITE, NON-ZERO, AND NOT NAN'S
satan:
fmov.x (%a0),%fp0 # LOAD INPUT
#--THE MOST LIKELY CASE, |X| IN [1/16, 16). WE USE TABLE TECHNIQUE
#--THE IDEA IS ATAN(X) = ATAN(F) + ATAN( [X-F] / [1+XF] ).
#--SO IF F IS CHOSEN TO BE CLOSE TO X AND ATAN(F) IS STORED IN
#--A TABLE, ALL WE NEED IS TO APPROXIMATE ATAN(U) WHERE
#--U = (X-F)/(1+XF) IS SMALL (REMEMBER F IS CLOSE TO X). IT IS
#--TRUE THAT A DIVIDE IS NOW NEEDED, BUT THE APPROXIMATION FOR
#--ATAN(U) IS A VERY SHORT POLYNOMIAL AND THE INDEXING TO
#--FETCH F AND SAVING OF REGISTERS CAN BE ALL HIDED UNDER THE
#--DIVIDE. IN THE END THIS METHOD IS MUCH FASTER THAN A TRADITIONAL
#--ONE. NOTE ALSO THAT THE TRADITIONAL SCHEME THAT APPROXIMATE
#--ATAN(X) DIRECTLY WILL NEED TO USE A RATIONAL APPROXIMATION
#--(DIVISION NEEDED) ANYWAY BECAUSE A POLYNOMIAL APPROXIMATION
#--WILL INVOLVE A VERY LONG POLYNOMIAL.
#--NOW WE SEE X AS +-2^K * 1.BBBBBBB....B <- 1. + 63 BITS
#--WE CHOSE F TO BE +-2^K * 1.BBBB1
#--THAT IS IT MATCHES THE EXPONENT AND FIRST 5 BITS OF X, THE
#--SIXTH BITS IS SET TO BE 1. SINCE K = -4, -3, ..., 3, THERE
#--ARE ONLY 8 TIMES 16 = 2^7 = 128 |F|'S. SINCE ATAN(-|F|) IS
#-- -ATAN(|F|), WE NEED TO STORE ONLY ATAN(|F|).
ATANMAIN:
and.l &0xF8000000,XFRAC(%a6) # FIRST 5 BITS
or.l &0x04000000,XFRAC(%a6) # SET 6-TH BIT TO 1
mov.l &0x00000000,XFRACLO(%a6) # LOCATION OF X IS NOW F
fmov.x %fp0,%fp1 # FP1 IS X
fmul.x X(%a6),%fp1 # FP1 IS X*F, NOTE THAT X*F > 0
fsub.x X(%a6),%fp0 # FP0 IS X-F
fadd.s &0x3F800000,%fp1 # FP1 IS 1 + X*F
fdiv.x %fp1,%fp0 # FP0 IS U = (X-F)/(1+X*F)
#--WHILE THE DIVISION IS TAKING ITS TIME, WE FETCH ATAN(|F|)
#--CREATE ATAN(F) AND STORE IT IN ATANF, AND
#--SAVE REGISTERS FP2.
mov.l %d2,-(%sp) # SAVE d2 TEMPORARILY
mov.l %d1,%d2 # THE EXP AND 16 BITS OF X
and.l &0x00007800,%d1 # 4 VARYING BITS OF F'S FRACTION
and.l &0x7FFF0000,%d2 # EXPONENT OF F sub.l &0x3FFB0000,%d2 # K+4
asr.l &1,%d2
add.l %d2,%d1 # THE 7 BITS IDENTIFYING F
asr.l &7,%d1 # INDEX INTO TBL OF ATAN(|F|)
lea ATANTBL(%pc),%a1
add.l %d1,%a1 # ADDRESS OF ATAN(|F|)
mov.l (%a1)+,ATANF(%a6)
mov.l (%a1)+,ATANFHI(%a6)
mov.l (%a1)+,ATANFLO(%a6) # ATANF IS NOW ATAN(|F|)
mov.l X(%a6),%d1 # LOAD SIGN AND EXPO. AGAIN
and.l &0x80000000,%d1 # SIGN(F)
or.l %d1,ATANF(%a6) # ATANF IS NOW SIGN(F)*ATAN(|F|)
mov.l (%sp)+,%d2 # RESTORE d2
#--THAT'S ALL I HAVE TO DO FOR NOW,
#--BUT ALAS, THE DIVIDE IS STILL CRANKING!
#--U IN FP0, WE ARE NOW READY TO COMPUTE ATAN(U) AS
#--U + A1*U*V*(A2 + V*(A3 + V)), V = U*U
#--THE POLYNOMIAL MAY LOOK STRANGE, BUT IS NEVERTHELESS CORRECT.
#--THE NATURAL FORM IS U + U*V*(A1 + V*(A2 + V*A3))
#--WHAT WE HAVE HERE IS MERELY A1 = A3, A2 = A1/A3, A3 = A2/A3.
#--THE REASON FOR THIS REARRANGEMENT IS TO MAKE THE INDEPENDENT
#--PARTS A1*U*V AND (A2 + ... STUFF) MORE LOAD-BALANCED
ATANBORS:
#--|X| IS IN d0 IN COMPACT FORM. FP1, d0 SAVED.
#--FP0 IS X AND |X| <= 1/16 OR |X| >= 16.
cmp.l %d1,&0x3FFF8000
bgt.w ATANBIG # I.E. |X| >= 16
ATANSM:
#--|X| <= 1/16
#--IF |X| < 2^(-40), RETURN X AS ANSWER. OTHERWISE, APPROXIMATE
#--ATAN(X) BY X + X*Y*(B1+Y*(B2+Y*(B3+Y*(B4+Y*(B5+Y*B6)))))
#--WHICH IS X + X*Y*( [B1+Z*(B3+Z*B5)] + [Y*(B2+Z*(B4+Z*B6)] )
#--WHERE Y = X*X, AND Z = Y*Y.
cmp.l %d1,&0x3FD78000
blt.w ATANTINY
#--COMPUTE POLYNOMIAL
fmovm.x &0x0c,-(%sp) # save fp2/fp3
fmul.x %fp0,%fp0 # FPO IS Y = X*X
fmov.x %fp0,%fp1
fmul.x %fp1,%fp1 # FP1 IS Z = Y*Y
#--APPROXIMATE ATAN(-1/X) BY
#--X'+X'*Y*(C1+Y*(C2+Y*(C3+Y*(C4+Y*C5)))), X' = -1/X, Y = X'*X'
#--THIS CAN BE RE-WRITTEN AS
#--X'+X'*Y*( [C1+Z*(C3+Z*C5)] + [Y*(C2+Z*C4)] ), Z = Y*Y.
# This catch is added here for the '060 QSP. Originally, the call to
# satan() would handle this case by causing the exception which would
# not be caught until gen_except(). Now, with the exceptions being
# detected inside of satan(), the exception would have been handled there
# instead of inside sasin() as expected.
cmp.l %d1,&0x3FD78000
blt.w ASINTINY
#--THIS IS THE USUAL CASE, |X| < 1
#--ASIN(X) = ATAN( X / SQRT( (1-X)(1+X) ) )
ACOSBIG:
fabs.x %fp0
fcmp.s %fp0,&0x3F800000
fbgt t_operr # cause an operr exception
#--|X| = 1, ACOS(X) = 0 OR PI
tst.b (%a0) # is X positive or negative?
bpl.b ACOSP1
#--X = -1
#Returns PI and inexact exception
ACOSM1:
fmov.x PI(%pc),%fp0 # load PI
fmov.l %d0,%fpcr # load round mode,prec
fadd.s &0x00800000,%fp0 # add a small value
bra t_pinx2
ACOSP1:
bra ld_pzero # answer is positive zero
global sacosd
#--ACOS(X) = PI/2 FOR DENORMALIZED X
sacosd:
fmov.l %d0,%fpcr # load user's rnd mode/prec
fmov.x PIBY2(%pc),%fp0
bra t_pinx2
#########################################################################
# setox(): computes the exponential for a normalized input #
# setoxd(): computes the exponential for a denormalized input #
# setoxm1(): computes the exponential minus 1 for a normalized input #
# setoxm1d(): computes the exponential minus 1 for a denormalized input #
# #
# INPUT *************************************************************** #
# a0 = pointer to extended precision input #
# d0 = round precision,mode #
# #
# OUTPUT ************************************************************** #
# fp0 = exp(X) or exp(X)-1 #
# #
# ACCURACY and MONOTONICITY ******************************************* #
# The returned result is within 0.85 ulps in 64 significant bit, #
# i.e. within 0.5001 ulp to 53 bits if the result is subsequently #
# rounded to double precision. The result is provably monotonic #
# in double precision. #
# #
# ALGORITHM and IMPLEMENTATION **************************************** #
# #
# setoxd #
# ------ #
# Step 1. Set ans := 1.0 #
# #
# Step 2. Return ans := ans + sign(X)*2^(-126). Exit. #
# Notes: This will always generate one exception -- inexact. #
# #
# #
# setox #
# ----- #
# #
# Step 1. Filter out extreme cases of input argument. #
# 1.1 If |X| >= 2^(-65), go to Step 1.3. #
# 1.2 Go to Step 7. #
# 1.3 If |X| < 16380 log(2), go to Step 2. #
# 1.4 Go to Step 8. #
# Notes: The usual case should take the branches 1.1 -> 1.3 -> 2.#
# To avoid the use of floating-point comparisons, a #
# compact representation of |X| is used. This format is a #
# 32-bit integer, the upper (more significant) 16 bits #
# are the sign and biased exponent field of |X|; the #
# lower 16 bits are the 16 most significant fraction #
# (including the explicit bit) bits of |X|. Consequently, #
# the comparisons in Steps 1.1 and 1.3 can be performed #
# by integer comparison. Note also that the constant #
# 16380 log(2) used in Step 1.3 is also in the compact #
# form. Thus taking the branch to Step 2 guarantees #
# |X| < 16380 log(2). There is no harm to have a small #
# number of cases where |X| is less than, but close to, #
# 16380 log(2) and the branch to Step 9 is taken. #
# #
# Step 2. Calculate N = round-to-nearest-int( X * 64/log2 ). #
# 2.1 Set AdjFlag := 0 (indicates the branch 1.3 -> 2 #
# was taken) #
# 2.2 N := round-to-nearest-integer( X * 64/log2 ). #
# 2.3 Calculate J = N mod 64; so J = 0,1,2,..., #
# or 63. #
# 2.4 Calculate M = (N - J)/64; so N = 64M + J. #
# 2.5 Calculate the address of the stored value of #
# 2^(J/64). #
# 2.6 Create the value Scale = 2^M. #
# Notes: The calculation in 2.2 is really performed by #
# Z := X * constant #
# N := round-to-nearest-integer(Z) #
# where #
# constant := single-precision( 64/log 2 ). #
# #
# Using a single-precision constant avoids memory #
# access. Another effect of using a single-precision #
# "constant" is that the calculated value Z is #
# #
# Z = X*(64/log2)*(1+eps), |eps| <= 2^(-24). #
# #
# This error has to be considered later in Steps 3 and 4. #
# #
# Step 3. Calculate X - N*log2/64. #
# 3.1 R := X + N*L1, #
# where L1 := single-precision(-log2/64). #
# 3.2 R := R + N*L2, #
# L2 := extended-precision(-log2/64 - L1).#
# Notes: a) The way L1 and L2 are chosen ensures L1+L2 #
# approximate the value -log2/64 to 88 bits of accuracy. #
# b) N*L1 is exact because N is no longer than 22 bits #
# and L1 is no longer than 24 bits. #
# c) The calculation X+N*L1 is also exact due to #
# cancellation. Thus, R is practically X+N(L1+L2) to full #
# 64 bits. #
# d) It is important to estimate how large can |R| be #
# after Step 3.2. #
# #
# N = rnd-to-int( X*64/log2 (1+eps) ), |eps|<=2^(-24) #
# X*64/log2 (1+eps) = N + f, |f| <= 0.5 #
# X*64/log2 - N = f - eps*X 64/log2 #
# X - N*log2/64 = f*log2/64 - eps*X #
# #
# #
# Now |X| <= 16446 log2, thus #
# #
# |X - N*log2/64| <= (0.5 + 16446/2^(18))*log2/64 #
# <= 0.57 log2/64. #
# This bound will be used in Step 4. #
# #
# Step 4. Approximate exp(R)-1 by a polynomial #
# p = R + R*R*(A1 + R*(A2 + R*(A3 + R*(A4 + R*A5)))) #
# Notes: a) In order to reduce memory access, the coefficients #
# are made as "short" as possible: A1 (which is 1/2), A4 #
# and A5 are single precision; A2 and A3 are double #
# precision. #
# b) Even with the restrictions above, #
# |p - (exp(R)-1)| < 2^(-68.8) for all |R| <= 0.0062. #
# Note that 0.0062 is slightly bigger than 0.57 log2/64. #
# c) To fully utilize the pipeline, p is separated into #
# two independent pieces of roughly equal complexities #
# p = [ R + R*S*(A2 + S*A4) ] + #
# [ S*(A1 + S*(A3 + S*A5)) ] #
# where S = R*R. #
# #
# Step 5. Compute 2^(J/64)*exp(R) = 2^(J/64)*(1+p) by #
# ans := T + ( T*p + t) #
# where T and t are the stored values for 2^(J/64). #
# Notes: 2^(J/64) is stored as T and t where T+t approximates #
# 2^(J/64) to roughly 85 bits; T is in extended precision #
# and t is in single precision. Note also that T is #
# rounded to 62 bits so that the last two bits of T are #
# zero. The reason for such a special form is that T-1, #
# T-2, and T-8 will all be exact --- a property that will #
# give much more accurate computation of the function #
# EXPM1. #
# #
# Step 6. Reconstruction of exp(X) #
# exp(X) = 2^M * 2^(J/64) * exp(R). #
# 6.1 If AdjFlag = 0, go to 6.3 #
# 6.2 ans := ans * AdjScale #
# 6.3 Restore the user FPCR #
# 6.4 Return ans := ans * Scale. Exit. #
# Notes: If AdjFlag = 0, we have X = Mlog2 + Jlog2/64 + R, #
# |M| <= 16380, and Scale = 2^M. Moreover, exp(X) will #
# neither overflow nor underflow. If AdjFlag = 1, that #
# means that #
# X = (M1+M)log2 + Jlog2/64 + R, |M1+M| >= 16380. #
# Hence, exp(X) may overflow or underflow or neither. #
# When that is the case, AdjScale = 2^(M1) where M1 is #
# approximately M. Thus 6.2 will never cause #
# over/underflow. Possible exception in 6.4 is overflow #
# or underflow. The inexact exception is not generated in #
# 6.4. Although one can argue that the inexact flag #
# should always be raised, to simulate that exception #
# cost to much than the flag is worth in practical uses. #
# #
# Step 7. Return 1 + X. #
# 7.1 ans := X #
# 7.2 Restore user FPCR. #
# 7.3 Return ans := 1 + ans. Exit #
# Notes: For non-zero X, the inexact exception will always be #
# raised by 7.3. That is the only exception raised by 7.3.#
# Note also that we use the FMOVEM instruction to move X #
# in Step 7.1 to avoid unnecessary trapping. (Although #
# the FMOVEM may not seem relevant since X is normalized, #
# the precaution will be useful in the library version of #
# this code where the separate entry for denormalized #
# inputs will be done away with.) #
# #
# Step 8. Handle exp(X) where |X| >= 16380log2. #
# 8.1 If |X| > 16480 log2, go to Step 9. #
# (mimic 2.2 - 2.6) #
# 8.2 N := round-to-integer( X * 64/log2 ) #
# 8.3 Calculate J = N mod 64, J = 0,1,...,63 #
# 8.4 K := (N-J)/64, M1 := truncate(K/2), M = K-M1, #
# AdjFlag := 1. #
# 8.5 Calculate the address of the stored value #
# 2^(J/64). #
# 8.6 Create the values Scale = 2^M, AdjScale = 2^M1. #
# 8.7 Go to Step 3. #
# Notes: Refer to notes for 2.2 - 2.6. #
# #
# Step 9. Handle exp(X), |X| > 16480 log2. #
# 9.1 If X < 0, go to 9.3 #
# 9.2 ans := Huge, go to 9.4 #
# 9.3 ans := Tiny. #
# 9.4 Restore user FPCR. #
# 9.5 Return ans := ans * ans. Exit. #
# Notes: Exp(X) will surely overflow or underflow, depending on #
# X's sign. "Huge" and "Tiny" are respectively large/tiny #
# extended-precision numbers whose square over/underflow #
# with an inexact result. Thus, 9.5 always raises the #
# inexact together with either overflow or underflow. #
# #
# setoxm1d #
# -------- #
# #
# Step 1. Set ans := 0 #
# #
# Step 2. Return ans := X + ans. Exit. #
# Notes: This will return X with the appropriate rounding #
# precision prescribed by the user FPCR. #
# #
# setoxm1 #
# ------- #
# #
# Step 1. Check |X| #
# 1.1 If |X| >= 1/4, go to Step 1.3. #
# 1.2 Go to Step 7. #
# 1.3 If |X| < 70 log(2), go to Step 2. #
# 1.4 Go to Step 10. #
# Notes: The usual case should take the branches 1.1 -> 1.3 -> 2.#
# However, it is conceivable |X| can be small very often #
# because EXPM1 is intended to evaluate exp(X)-1 #
# accurately when |X| is small. For further details on #
# the comparisons, see the notes on Step 1 of setox. #
# #
# Step 2. Calculate N = round-to-nearest-int( X * 64/log2 ). #
# 2.1 N := round-to-nearest-integer( X * 64/log2 ). #
# 2.2 Calculate J = N mod 64; so J = 0,1,2,..., #
# or 63. #
# 2.3 Calculate M = (N - J)/64; so N = 64M + J. #
# 2.4 Calculate the address of the stored value of #
# 2^(J/64). #
# 2.5 Create the values Sc = 2^M and #
# OnebySc := -2^(-M). #
# Notes: See the notes on Step 2 of setox. #
# #
# Step 3. Calculate X - N*log2/64. #
# 3.1 R := X + N*L1, #
# where L1 := single-precision(-log2/64). #
# 3.2 R := R + N*L2, #
# L2 := extended-precision(-log2/64 - L1).#
# Notes: Applying the analysis of Step 3 of setox in this case #
# shows that |R| <= 0.0055 (note that |X| <= 70 log2 in #
# this case). #
# #
# Step 4. Approximate exp(R)-1 by a polynomial #
# p = R+R*R*(A1+R*(A2+R*(A3+R*(A4+R*(A5+R*A6))))) #
# Notes: a) In order to reduce memory access, the coefficients #
# are made as "short" as possible: A1 (which is 1/2), A5 #
# and A6 are single precision; A2, A3 and A4 are double #
# precision. #
# b) Even with the restriction above, #
# |p - (exp(R)-1)| < |R| * 2^(-72.7) #
# for all |R| <= 0.0055. #
# c) To fully utilize the pipeline, p is separated into #
# two independent pieces of roughly equal complexity #
# p = [ R*S*(A2 + S*(A4 + S*A6)) ] + #
# [ R + S*(A1 + S*(A3 + S*A5)) ] #
# where S = R*R. #
# #
# Step 5. Compute 2^(J/64)*p by #
# p := T*p #
# where T and t are the stored values for 2^(J/64). #
# Notes: 2^(J/64) is stored as T and t where T+t approximates #
# 2^(J/64) to roughly 85 bits; T is in extended precision #
# and t is in single precision. Note also that T is #
# rounded to 62 bits so that the last two bits of T are #
# zero. The reason for such a special form is that T-1, #
# T-2, and T-8 will all be exact --- a property that will #
# be exploited in Step 6 below. The total relative error #
# in p is no bigger than 2^(-67.7) compared to the final #
# result. #
# #
# Step 6. Reconstruction of exp(X)-1 #
# exp(X)-1 = 2^M * ( 2^(J/64) + p - 2^(-M) ). #
# 6.1 If M <= 63, go to Step 6.3. #
# 6.2 ans := T + (p + (t + OnebySc)). Go to 6.6 #
# 6.3 If M >= -3, go to 6.5. #
# 6.4 ans := (T + (p + t)) + OnebySc. Go to 6.6 #
# 6.5 ans := (T + OnebySc) + (p + t). #
# 6.6 Restore user FPCR. #
# 6.7 Return ans := Sc * ans. Exit. #
# Notes: The various arrangements of the expressions give #
# accurate evaluations. #
# #
# Step 7. exp(X)-1 for |X| < 1/4. #
# 7.1 If |X| >= 2^(-65), go to Step 9. #
# 7.2 Go to Step 8. #
# #
# Step 8. Calculate exp(X)-1, |X| < 2^(-65). #
# 8.1 If |X| < 2^(-16312), goto 8.3 #
# 8.2 Restore FPCR; return ans := X - 2^(-16382). #
# Exit. #
# 8.3 X := X * 2^(140). #
# 8.4 Restore FPCR; ans := ans - 2^(-16382). #
# Return ans := ans*2^(140). Exit #
# Notes: The idea is to return "X - tiny" under the user #
# precision and rounding modes. To avoid unnecessary #
# inefficiency, we stay away from denormalized numbers #
# the best we can. For |X| >= 2^(-16312), the #
# straightforward 8.2 generates the inexact exception as #
# the case warrants. #
# #
# Step 9. Calculate exp(X)-1, |X| < 1/4, by a polynomial #
# p = X + X*X*(B1 + X*(B2 + ... + X*B12)) #
# Notes: a) In order to reduce memory access, the coefficients #
# are made as "short" as possible: B1 (which is 1/2), B9 #
# to B12 are single precision; B3 to B8 are double #
# precision; and B2 is double extended. #
# b) Even with the restriction above, #
# |p - (exp(X)-1)| < |X| 2^(-70.6) #
# for all |X| <= 0.251. #
# Note that 0.251 is slightly bigger than 1/4. #
# c) To fully preserve accuracy, the polynomial is #
# computed as #
# X + ( S*B1 + Q ) where S = X*X and #
# Q = X*S*(B2 + X*(B3 + ... + X*B12)) #
# d) To fully utilize the pipeline, Q is separated into #
# two independent pieces of roughly equal complexity #
# Q = [ X*S*(B2 + S*(B4 + ... + S*B12)) ] + #
# [ S*S*(B3 + S*(B5 + ... + S*B11)) ] #
# #
# Step 10. Calculate exp(X)-1 for |X| >= 70 log 2. #
# 10.1 If X >= 70log2 , exp(X) - 1 = exp(X) for all #
# practical purposes. Therefore, go to Step 1 of setox. #
# 10.2 If X <= -70log2, exp(X) - 1 = -1 for all practical #
# purposes. #
# ans := -1 #
# Restore user FPCR #
# Return ans := ans + 2^(-126). Exit. #
# Notes: 10.2 will always create an inexact and return -1 + tiny #
# in the user rounding precision and mode. #
# #
#########################################################################
L2: long 0x3FDC0000,0x82E30865,0x4361C4C6,0x00000000
EEXPA3: long 0x3FA55555,0x55554CC1
EEXPA2: long 0x3FC55555,0x55554A54
EM1A4: long 0x3F811111,0x11174385
EM1A3: long 0x3FA55555,0x55554F5A
EM1A2: long 0x3FC55555,0x55555555,0x00000000,0x00000000
EM1B8: long 0x3EC71DE3,0xA5774682
EM1B7: long 0x3EFA01A0,0x19D7CB68
EM1B6: long 0x3F2A01A0,0x1A019DF3
EM1B5: long 0x3F56C16C,0x16C170E2
EM1B4: long 0x3F811111,0x11111111
EM1B3: long 0x3FA55555,0x55555555
EM1B2: long 0x3FFC0000,0xAAAAAAAA,0xAAAAAAAB
long 0x00000000
TWO140: long 0x48B00000,0x00000000
TWON140:
long 0x37300000,0x00000000
EEXPTBL:
long 0x3FFF0000,0x80000000,0x00000000,0x00000000
long 0x3FFF0000,0x8164D1F3,0xBC030774,0x9F841A9B
long 0x3FFF0000,0x82CD8698,0xAC2BA1D8,0x9FC1D5B9
long 0x3FFF0000,0x843A28C3,0xACDE4048,0xA0728369
long 0x3FFF0000,0x85AAC367,0xCC487B14,0x1FC5C95C
long 0x3FFF0000,0x871F6196,0x9E8D1010,0x1EE85C9F
long 0x3FFF0000,0x88980E80,0x92DA8528,0x9FA20729
long 0x3FFF0000,0x8A14D575,0x496EFD9C,0xA07BF9AF
long 0x3FFF0000,0x8B95C1E3,0xEA8BD6E8,0xA0020DCF
long 0x3FFF0000,0x8D1ADF5B,0x7E5BA9E4,0x205A63DA
long 0x3FFF0000,0x8EA4398B,0x45CD53C0,0x1EB70051
long 0x3FFF0000,0x9031DC43,0x1466B1DC,0x1F6EB029
long 0x3FFF0000,0x91C3D373,0xAB11C338,0xA0781494
long 0x3FFF0000,0x935A2B2F,0x13E6E92C,0x9EB319B0
long 0x3FFF0000,0x94F4EFA8,0xFEF70960,0x2017457D
long 0x3FFF0000,0x96942D37,0x20185A00,0x1F11D537
long 0x3FFF0000,0x9837F051,0x8DB8A970,0x9FB952DD
long 0x3FFF0000,0x99E04593,0x20B7FA64,0x1FE43087
long 0x3FFF0000,0x9B8D39B9,0xD54E5538,0x1FA2A818
long 0x3FFF0000,0x9D3ED9A7,0x2CFFB750,0x1FDE494D
long 0x3FFF0000,0x9EF53260,0x91A111AC,0x20504890
long 0x3FFF0000,0xA0B0510F,0xB9714FC4,0xA073691C
long 0x3FFF0000,0xA2704303,0x0C496818,0x1F9B7A05
long 0x3FFF0000,0xA43515AE,0x09E680A0,0xA0797126
long 0x3FFF0000,0xA5FED6A9,0xB15138EC,0xA071A140
long 0x3FFF0000,0xA7CD93B4,0xE9653568,0x204F62DA
long 0x3FFF0000,0xA9A15AB4,0xEA7C0EF8,0x1F283C4A
long 0x3FFF0000,0xAB7A39B5,0xA93ED338,0x9F9A7FDC
long 0x3FFF0000,0xAD583EEA,0x42A14AC8,0xA05B3FAC
long 0x3FFF0000,0xAF3B78AD,0x690A4374,0x1FDF2610
long 0x3FFF0000,0xB123F581,0xD2AC2590,0x9F705F90
long 0x3FFF0000,0xB311C412,0xA9112488,0x201F678A
long 0x3FFF0000,0xB504F333,0xF9DE6484,0x1F32FB13
long 0x3FFF0000,0xB6FD91E3,0x28D17790,0x20038B30
long 0x3FFF0000,0xB8FBAF47,0x62FB9EE8,0x200DC3CC
long 0x3FFF0000,0xBAFF5AB2,0x133E45FC,0x9F8B2AE6
long 0x3FFF0000,0xBD08A39F,0x580C36C0,0xA02BBF70
long 0x3FFF0000,0xBF1799B6,0x7A731084,0xA00BF518
long 0x3FFF0000,0xC12C4CCA,0x66709458,0xA041DD41
long 0x3FFF0000,0xC346CCDA,0x24976408,0x9FDF137B
long 0x3FFF0000,0xC5672A11,0x5506DADC,0x201F1568
long 0x3FFF0000,0xC78D74C8,0xABB9B15C,0x1FC13A2E
long 0x3FFF0000,0xC9B9BD86,0x6E2F27A4,0xA03F8F03
long 0x3FFF0000,0xCBEC14FE,0xF2727C5C,0x1FF4907D
long 0x3FFF0000,0xCE248C15,0x1F8480E4,0x9E6E53E4
long 0x3FFF0000,0xD06333DA,0xEF2B2594,0x1FD6D45C
long 0x3FFF0000,0xD2A81D91,0xF12AE45C,0xA076EDB9
long 0x3FFF0000,0xD4F35AAB,0xCFEDFA20,0x9FA6DE21
long 0x3FFF0000,0xD744FCCA,0xD69D6AF4,0x1EE69A2F
long 0x3FFF0000,0xD99D15C2,0x78AFD7B4,0x207F439F
long 0x3FFF0000,0xDBFBB797,0xDAF23754,0x201EC207
long 0x3FFF0000,0xDE60F482,0x5E0E9124,0x9E8BE175
long 0x3FFF0000,0xE0CCDEEC,0x2A94E110,0x20032C4B
long 0x3FFF0000,0xE33F8972,0xBE8A5A50,0x2004DFF5
long 0x3FFF0000,0xE5B906E7,0x7C8348A8,0x1E72F47A
long 0x3FFF0000,0xE8396A50,0x3C4BDC68,0x1F722F22
long 0x3FFF0000,0xEAC0C6E7,0xDD243930,0xA017E945
long 0x3FFF0000,0xED4F301E,0xD9942B84,0x1F401A5B
long 0x3FFF0000,0xEFE4B99B,0xDCDAF5CC,0x9FB9A9E3
long 0x3FFF0000,0xF281773C,0x59FFB138,0x20744C05
long 0x3FFF0000,0xF5257D15,0x2486CC2C,0x1F773A19
long 0x3FFF0000,0xF7D0DF73,0x0AD13BB8,0x1FFE90D5
long 0x3FFF0000,0xFA83B2DB,0x722A033C,0xA041ED22
long 0x3FFF0000,0xFD3E0C0C,0xF486C174,0x1F853F3A
set ADJFLAG,L_SCR2 set SCALE,FP_SCR0 set ADJSCALE,FP_SCR1 set SC,FP_SCR0 set ONEBYSC,FP_SCR1
global setox
setox:
#--entry point for EXP(X), here X is finite, non-zero, and not NaN's
#--Step 1.
mov.l (%a0),%d1 # load part of input X
and.l &0x7FFF0000,%d1 # biased expo. of X
cmp.l %d1,&0x3FBE0000 # 2^(-65)
bge.b EXPC1 # normal case
bra EXPSM
EXPC1:
#--The case |X| >= 2^(-65)
mov.w 4(%a0),%d1 # expo. and partial sig. of |X|
cmp.l %d1,&0x400CB167 # 16380 log2 trunc. 16 bits
blt.b EXPMAIN # normal case
bra EEXPBIG
EXPMAIN:
#--Step 2.
#--This is the normal branch: 2^(-65) <= |X| < 16380 log2.
fmov.x (%a0),%fp0 # load input from (a0)
fmov.x %fp0,%fp1
fmul.s &0x42B8AA3B,%fp0 # 64/log2 * X
fmovm.x &0xc,-(%sp) # save fp2 {%fp2/%fp3}
mov.l &0,ADJFLAG(%a6)
fmov.l %fp0,%d1 # N = int( X * 64/log2 )
lea EEXPTBL(%pc),%a1
fmov.l %d1,%fp0 # convert to floating-format
mov.l %d1,L_SCR1(%a6) # save N temporarily
and.l &0x3F,%d1 # D0 is J = N mod 64
lsl.l &4,%d1
add.l %d1,%a1 # address of 2^(J/64)
mov.l L_SCR1(%a6),%d1
asr.l &6,%d1 # D0 is M
add.w &0x3FFF,%d1 # biased expo. of 2^(M)
mov.w L2(%pc),L_SCR1(%a6) # prefetch L2, no need in CB
EXPCONT1:
#--Step 3.
#--fp1,fp2 saved on the stack. fp0 is N, fp1 is X,
#--a0 points to 2^(J/64), D0 is biased expo. of 2^(M)
fmov.x %fp0,%fp2
fmul.s &0xBC317218,%fp0 # N * L1, L1 = lead(-log2/64)
fmul.x L2(%pc),%fp2 # N * L2, L1+L2 = -log2/64
fadd.x %fp1,%fp0 # X + N*L1
fadd.x %fp2,%fp0 # fp0 is R, reduced arg.
#--Step 4.
#--WE NOW COMPUTE EXP(R)-1 BY A POLYNOMIAL
#-- R + R*R*(A1 + R*(A2 + R*(A3 + R*(A4 + R*A5))))
#--TO FULLY UTILIZE THE PIPELINE, WE COMPUTE S = R*R
#--[R+R*S*(A2+S*A4)] + [S*(A1+S*(A3+S*A5))]
fmov.x %fp0,%fp1
fmul.x %fp1,%fp1 # fp1 IS S = R*R
fmov.s &0x3AB60B70,%fp2 # fp2 IS A5
fmul.x %fp1,%fp2 # fp2 IS S*A5
fmov.x %fp1,%fp3
fmul.s &0x3C088895,%fp3 # fp3 IS S*A4
fadd.d EEXPA3(%pc),%fp2 # fp2 IS A3+S*A5
fadd.d EEXPA2(%pc),%fp3 # fp3 IS A2+S*A4
fmul.x %fp1,%fp2 # fp2 IS S*(A3+S*A5)
mov.w %d1,SCALE(%a6) # SCALE is 2^(M) in extended
mov.l &0x80000000,SCALE+4(%a6) clr.l SCALE+8(%a6)
fmul.x %fp1,%fp3 # fp3 IS S*(A2+S*A4)
fadd.s &0x3F000000,%fp2 # fp2 IS A1+S*(A3+S*A5)
fmul.x %fp0,%fp3 # fp3 IS R*S*(A2+S*A4)
fmul.x %fp1,%fp2 # fp2 IS S*(A1+S*(A3+S*A5))
fadd.x %fp3,%fp0 # fp0 IS R+R*S*(A2+S*A4),
fmov.x (%a1)+,%fp1 # fp1 is lead. pt. of 2^(J/64)
fadd.x %fp2,%fp0 # fp0 is EXP(R) - 1
#--Step 6
tst.l %d1
beq.b NORMAL
ADJUST:
fmul.x ADJSCALE(%a6),%fp0
NORMAL:
fmov.l %d0,%fpcr # restore user FPCR
mov.b &FMUL_OP,%d1 # last inst is MUL
fmul.x SCALE(%a6),%fp0 # multiply 2^(M)
bra t_catch
EXPSM:
#--Step 7
fmovm.x (%a0),&0x80 # load X
fmov.l %d0,%fpcr
fadd.s &0x3F800000,%fp0 # 1+X in user mode
bra t_pinx2
fmov.x %fp0,%fp1
fmul.s &0x42B8AA3B,%fp0 # 64/log2 * X
fmovm.x &0xc,-(%sp) # save fp2 {%fp2/%fp3}
mov.l &1,ADJFLAG(%a6)
fmov.l %fp0,%d1 # N = int( X * 64/log2 )
lea EEXPTBL(%pc),%a1
fmov.l %d1,%fp0 # convert to floating-format
mov.l %d1,L_SCR1(%a6) # save N temporarily
and.l &0x3F,%d1 # D0 is J = N mod 64
lsl.l &4,%d1
add.l %d1,%a1 # address of 2^(J/64)
mov.l L_SCR1(%a6),%d1
asr.l &6,%d1 # D0 is K
mov.l %d1,L_SCR1(%a6) # save K temporarily
asr.l &1,%d1 # D0 is M1 sub.l %d1,L_SCR1(%a6) # a1 is M
add.w &0x3FFF,%d1 # biased expo. of 2^(M1)
mov.w %d1,ADJSCALE(%a6) # ADJSCALE := 2^(M1)
mov.l &0x80000000,ADJSCALE+4(%a6) clr.l ADJSCALE+8(%a6)
mov.l L_SCR1(%a6),%d1 # D0 is M
add.w &0x3FFF,%d1 # biased expo. of 2^(M)
bra.w EXPCONT1 # go back to Step 3
EXP2BIG:
#--Step 9
tst.b (%a0) # is X positive or negative?
bmi t_unfl2
bra t_ovfl2
global setoxd
setoxd:
#--entry point for EXP(X), X is denormalized
mov.l (%a0),-(%sp)
andi.l &0x80000000,(%sp)
ori.l &0x00800000,(%sp) # sign(X)*2^(-126)
fmov.s &0x3F800000,%fp0
fmov.l %d0,%fpcr
fadd.s (%sp)+,%fp0
bra t_pinx2
global setoxm1
setoxm1:
#--entry point for EXPM1(X), here X is finite, non-zero, non-NaN
#--Step 1.
#--Step 1.1
mov.l (%a0),%d1 # load part of input X
and.l &0x7FFF0000,%d1 # biased expo. of X
cmp.l %d1,&0x3FFD0000 # 1/4
bge.b EM1CON1 # |X| >= 1/4
bra EM1SM
EM1CON1:
#--Step 1.3
#--The case |X| >= 1/4
mov.w 4(%a0),%d1 # expo. and partial sig. of |X|
cmp.l %d1,&0x4004C215 # 70log2 rounded up to 16 bits
ble.b EM1MAIN # 1/4 <= |X| <= 70log2
bra EM1BIG
EM1MAIN:
#--Step 2.
#--This is the case: 1/4 <= |X| <= 70 log2.
fmov.x (%a0),%fp0 # load input from (a0)
fmov.x %fp0,%fp1
fmul.s &0x42B8AA3B,%fp0 # 64/log2 * X
fmovm.x &0xc,-(%sp) # save fp2 {%fp2/%fp3}
fmov.l %fp0,%d1 # N = int( X * 64/log2 )
lea EEXPTBL(%pc),%a1
fmov.l %d1,%fp0 # convert to floating-format
mov.l %d1,L_SCR1(%a6) # save N temporarily
and.l &0x3F,%d1 # D0 is J = N mod 64
lsl.l &4,%d1
add.l %d1,%a1 # address of 2^(J/64)
mov.l L_SCR1(%a6),%d1
asr.l &6,%d1 # D0 is M
mov.l %d1,L_SCR1(%a6) # save a copy of M
#--Step 3.
#--fp1,fp2 saved on the stack. fp0 is N, fp1 is X,
#--a0 points to 2^(J/64), D0 and a1 both contain M
fmov.x %fp0,%fp2
fmul.s &0xBC317218,%fp0 # N * L1, L1 = lead(-log2/64)
fmul.x L2(%pc),%fp2 # N * L2, L1+L2 = -log2/64
fadd.x %fp1,%fp0 # X + N*L1
fadd.x %fp2,%fp0 # fp0 is R, reduced arg.
add.w &0x3FFF,%d1 # D0 is biased expo. of 2^M
#--Step 4.
#--WE NOW COMPUTE EXP(R)-1 BY A POLYNOMIAL
#-- R + R*R*(A1 + R*(A2 + R*(A3 + R*(A4 + R*(A5 + R*A6)))))
#--TO FULLY UTILIZE THE PIPELINE, WE COMPUTE S = R*R
#--[R*S*(A2+S*(A4+S*A6))] + [R+S*(A1+S*(A3+S*A5))]
fmov.x %fp0,%fp1
fmul.x %fp1,%fp1 # fp1 IS S = R*R
fmov.s &0x3950097B,%fp2 # fp2 IS a6
fmul.x %fp1,%fp2 # fp2 IS S*A6
fmov.x %fp1,%fp3
fmul.s &0x3AB60B6A,%fp3 # fp3 IS S*A5
fadd.d EM1A4(%pc),%fp2 # fp2 IS A4+S*A6
fadd.d EM1A3(%pc),%fp3 # fp3 IS A3+S*A5
mov.w %d1,SC(%a6) # SC is 2^(M) in extended
mov.l &0x80000000,SC+4(%a6) clr.l SC+8(%a6)
fmul.x %fp1,%fp2 # fp2 IS S*(A4+S*A6)
mov.l L_SCR1(%a6),%d1 # D0 is M
neg.w %d1 # D0 is -M
fmul.x %fp1,%fp3 # fp3 IS S*(A3+S*A5)
add.w &0x3FFF,%d1 # biased expo. of 2^(-M)
fadd.d EM1A2(%pc),%fp2 # fp2 IS A2+S*(A4+S*A6)
fadd.s &0x3F000000,%fp3 # fp3 IS A1+S*(A3+S*A5)
fmul.x %fp1,%fp2 # fp2 IS S*(A2+S*(A4+S*A6))
or.w &0x8000,%d1 # signed/expo. of -2^(-M)
mov.w %d1,ONEBYSC(%a6) # OnebySc is -2^(-M)
mov.l &0x80000000,ONEBYSC+4(%a6) clr.l ONEBYSC+8(%a6)
fmul.x %fp3,%fp1 # fp1 IS S*(A1+S*(A3+S*A5))
fmul.x %fp0,%fp2 # fp2 IS R*S*(A2+S*(A4+S*A6))
fadd.x %fp1,%fp0 # fp0 IS R+S*(A1+S*(A3+S*A5))
fadd.x %fp2,%fp0 # fp0 IS EXP(R)-1
fmovm.x (%sp)+,&0x30 # fp2 restored {%fp2/%fp3}
#--Step 5
#--Compute 2^(J/64)*p
fmul.x (%a1),%fp0 # 2^(J/64)*(Exp(R)-1)
#--Step 6
#--Step 6.1
mov.l L_SCR1(%a6),%d1 # retrieve M
cmp.l %d1,&63
ble.b MLE63
#--Step 6.2 M >= 64
fmov.s 12(%a1),%fp1 # fp1 is t
fadd.x ONEBYSC(%a6),%fp1 # fp1 is t+OnebySc
fadd.x %fp1,%fp0 # p+(t+OnebySc), fp1 released
fadd.x (%a1),%fp0 # T+(p+(t+OnebySc))
bra EM1SCALE
MLE63:
#--Step 6.3 M <= 63
cmp.l %d1,&-3
bge.b MGEN3
MLTN3:
#--Step 6.4 M <= -4
fadd.s 12(%a1),%fp0 # p+t
fadd.x (%a1),%fp0 # T+(p+t)
fadd.x ONEBYSC(%a6),%fp0 # OnebySc + (T+(p+t))
bra EM1SCALE
MGEN3:
#--Step 6.5 -3 <= M <= 63
fmov.x (%a1)+,%fp1 # fp1 is T
fadd.s (%a1),%fp0 # fp0 is p+t
fadd.x ONEBYSC(%a6),%fp1 # fp1 is T+OnebySc
fadd.x %fp1,%fp0 # (T+OnebySc)+(p+t)
EM1SCALE:
#--Step 6.6
fmov.l %d0,%fpcr
fmul.x SC(%a6),%fp0
bra t_inx2
EM1TINY:
#--Step 8 |X| < 2^(-65)
cmp.l %d1,&0x00330000 # 2^(-16312)
blt.b EM12TINY
#--Step 8.2
mov.l &0x80010000,SC(%a6) # SC is -2^(-16382)
mov.l &0x80000000,SC+4(%a6) clr.l SC+8(%a6)
fmov.x (%a0),%fp0
fmov.l %d0,%fpcr
mov.b &FADD_OP,%d1 # last inst is ADD
fadd.x SC(%a6),%fp0
bra t_catch
EM12TINY:
#--Step 8.3
fmov.x (%a0),%fp0
fmul.d TWO140(%pc),%fp0
mov.l &0x80010000,SC(%a6)
mov.l &0x80000000,SC+4(%a6) clr.l SC+8(%a6)
fadd.x SC(%a6),%fp0
fmov.l %d0,%fpcr
mov.b &FMUL_OP,%d1 # last inst is MUL
fmul.d TWON140(%pc),%fp0
bra t_catch
EM1POLY:
#--Step 9 exp(X)-1 by a simple polynomial
fmov.x (%a0),%fp0 # fp0 is X
fmul.x %fp0,%fp0 # fp0 is S := X*X
fmovm.x &0xc,-(%sp) # save fp2 {%fp2/%fp3}
fmov.s &0x2F30CAA8,%fp1 # fp1 is B12
fmul.x %fp0,%fp1 # fp1 is S*B12
fmov.s &0x310F8290,%fp2 # fp2 is B11
fadd.s &0x32D73220,%fp1 # fp1 is B10+S*B12
fmul.x %fp0,%fp2 # fp2 is S*B11
fmul.x %fp0,%fp1 # fp1 is S*(B10 + ...
fadd.s &0x3493F281,%fp2 # fp2 is B9+S*...
fadd.d EM1B8(%pc),%fp1 # fp1 is B8+S*...
fmul.x %fp0,%fp2 # fp2 is S*(B9+...
fmul.x %fp0,%fp1 # fp1 is S*(B8+...
fadd.d EM1B7(%pc),%fp2 # fp2 is B7+S*...
fadd.d EM1B6(%pc),%fp1 # fp1 is B6+S*...
fmul.x %fp0,%fp2 # fp2 is S*(B7+...
fmul.x %fp0,%fp1 # fp1 is S*(B6+...
fadd.d EM1B5(%pc),%fp2 # fp2 is B5+S*...
fadd.d EM1B4(%pc),%fp1 # fp1 is B4+S*...
fmul.x %fp0,%fp2 # fp2 is S*(B5+...
fmul.x %fp0,%fp1 # fp1 is S*(B4+...
fadd.d EM1B3(%pc),%fp2 # fp2 is B3+S*...
fadd.x EM1B2(%pc),%fp1 # fp1 is B2+S*...
fmul.x %fp0,%fp2 # fp2 is S*(B3+...
fmul.x %fp0,%fp1 # fp1 is S*(B2+...
fmul.x %fp0,%fp2 # fp2 is S*S*(B3+...)
fmul.x (%a0),%fp1 # fp1 is X*S*(B2...
fmul.s &0x3F000000,%fp0 # fp0 is S*B1
fadd.x %fp2,%fp1 # fp1 is Q
global setoxm1d
setoxm1d:
#--entry point for EXPM1(X), here X is denormalized
#--Step 0.
bra t_extdnrm
#########################################################################
# sgetexp(): returns the exponent portion of the input argument. #
# The exponent bias is removed and the exponent value is #
# returned as an extended precision number in fp0. #
# sgetexpd(): handles denormalized numbers. #
# #
# sgetman(): extracts the mantissa of the input argument. The #
# mantissa is converted to an extended precision number w/ #
# an exponent of $3fff and is returned in fp0. The range of #
# the result is [1.0 - 2.0). #
# sgetmand(): handles denormalized numbers. #
# #
# INPUT *************************************************************** #
# a0 = pointer to extended precision input #
# #
# OUTPUT ************************************************************** #
# fp0 = exponent(X) or mantissa(X) #
# #
#########################################################################
global sgetexp
sgetexp:
mov.w SRC_EX(%a0),%d0 # get the exponent
bclr &0xf,%d0 # clear the sign bit
subi.w &0x3fff,%d0 # subtract off the bias
fmov.w %d0,%fp0 # return exp in fp0
blt.b sgetexpn # it's negative
rts
sgetexpn:
mov.b &neg_bmask,FPSR_CC(%a6) # set'N' ccode bit
rts
global sgetexpd
sgetexpd:
bsr.l norm # normalize
neg.w %d0 # new exp = -(shft amt)
subi.w &0x3fff,%d0 # subtract off the bias
fmov.w %d0,%fp0 # return exp in fp0
mov.b &neg_bmask,FPSR_CC(%a6) # set'N' ccode bit
rts
global sgetman
sgetman:
mov.w SRC_EX(%a0),%d0 # get the exp
ori.w &0x7fff,%d0 # clear old exp
bclr &0xe,%d0 # make it the new exp +-3fff
# here, we build the result in a tmp location so as not to disturb the input
mov.l SRC_HI(%a0),FP_SCR0_HI(%a6) # copy to tmp loc
mov.l SRC_LO(%a0),FP_SCR0_LO(%a6) # copy to tmp loc
mov.w %d0,FP_SCR0_EX(%a6) # insert new exponent
fmov.x FP_SCR0(%a6),%fp0 # put new value back in fp0
bmi.b sgetmann # it's negative
rts
sgetmann:
mov.b &neg_bmask,FPSR_CC(%a6) # set'N' ccode bit
rts
#
# For denormalized numbers, shift the mantissa until the j-bit = 1,
# then load the exponent with +/1 $3fff.
# global sgetmand
sgetmand:
bsr.l norm # normalize exponent
bra.b sgetman
#########################################################################
# scosh(): computes the hyperbolic cosine of a normalized input #
# scoshd(): computes the hyperbolic cosine of a denormalized input #
# #
# INPUT *************************************************************** #
# a0 = pointer to extended precision input #
# d0 = round precision,mode #
# #
# OUTPUT ************************************************************** #
# fp0 = cosh(X) #
# #
# ACCURACY and MONOTONICITY ******************************************* #
# The returned result is within 3 ulps in 64 significant bit, #
# i.e. within 0.5001 ulp to 53 bits if the result is subsequently #
# rounded to double precision. The result is provably monotonic #
# in double precision. #
# #
# ALGORITHM *********************************************************** #
# #
# COSH #
# 1. If |X| > 16380 log2, go to 3. #
# #
# 2. (|X| <= 16380 log2) Cosh(X) is obtained by the formulae #
# y = |X|, z = exp(Y), and #
# cosh(X) = (1/2)*( z + 1/z ). #
# Exit. #
# #
# 3. (|X| > 16380 log2). If |X| > 16480 log2, go to 5. #
# #
# 4. (16380 log2 < |X| <= 16480 log2) #
# cosh(X) = sign(X) * exp(|X|)/2. #
# However, invoking exp(|X|) may cause premature #
# overflow. Thus, we calculate sinh(X) as follows: #
# Y := |X| #
# Fact := 2**(16380) #
# Y' := Y - 16381 log2 #
# cosh(X) := Fact * exp(Y'). #
# Exit. #
# #
# 5. (|X| > 16480 log2) sinh(X) must overflow. Return #
# Huge*Huge to generate overflow and an infinity with #
# the appropriate sign. Huge is the largest finite number #
# in extended format. Exit. #
# #
#########################################################################
TWO16380:
long 0x7FFB0000,0x80000000,0x00000000,0x00000000
global scosh
scosh:
fmov.x (%a0),%fp0 # LOAD INPUT
mov.l %d0,-(%sp) clr.l %d0
fmovm.x &0x01,-(%sp) # save fp0 to stack
lea (%sp),%a0 # pass ptr to fp0
bsr setox
add.l &0xc,%sp # clear fp0 from stack
mov.l (%sp)+,%d0
fmov.l %d0,%fpcr
mov.b &FMUL_OP,%d1 # last inst is MUL
fmul.x TWO16380(%pc),%fp0
bra t_catch
COSHHUGE:
bra t_ovfl2
global scoshd
#--COSH(X) = 1 FOR DENORMALIZED X
scoshd:
fmov.s &0x3F800000,%fp0
fmov.l %d0,%fpcr
fadd.s &0x00800000,%fp0
bra t_pinx2
#########################################################################
# ssinh(): computes the hyperbolic sine of a normalized input #
# ssinhd(): computes the hyperbolic sine of a denormalized input #
# #
# INPUT *************************************************************** #
# a0 = pointer to extended precision input #
# d0 = round precision,mode #
# #
# OUTPUT ************************************************************** #
# fp0 = sinh(X) #
# #
# ACCURACY and MONOTONICITY ******************************************* #
# The returned result is within 3 ulps in 64 significant bit, #
# i.e. within 0.5001 ulp to 53 bits if the result is subsequently #
# rounded to double precision. The result is provably monotonic #
# in double precision. #
# #
# ALGORITHM *********************************************************** #
# #
# SINH #
# 1. If |X| > 16380 log2, go to 3. #
# #
# 2. (|X| <= 16380 log2) Sinh(X) is obtained by the formula #
# y = |X|, sgn = sign(X), and z = expm1(Y), #
# sinh(X) = sgn*(1/2)*( z + z/(1+z) ). #
# Exit. #
# #
# 3. If |X| > 16480 log2, go to 5. #
# #
# 4. (16380 log2 < |X| <= 16480 log2) #
# sinh(X) = sign(X) * exp(|X|)/2. #
# However, invoking exp(|X|) may cause premature overflow. #
# Thus, we calculate sinh(X) as follows: #
# Y := |X| #
# sgn := sign(X) #
# sgnFact := sgn * 2**(16380) #
# Y' := Y - 16381 log2 #
# sinh(X) := sgnFact * exp(Y'). #
# Exit. #
# #
# 5. (|X| > 16480 log2) sinh(X) must overflow. Return #
# sign(X)*Huge*Huge to generate overflow and an infinity with #
# the appropriate sign. Huge is the largest finite number in #
# extended format. Exit. #
# #
#########################################################################
global ssinh
ssinh:
fmov.x (%a0),%fp0 # LOAD INPUT
#--THIS IS THE USUAL CASE, |X| < 16380 LOG2
#--Y = |X|, Z = EXPM1(Y), SINH(X) = SIGN(X)*(1/2)*( Z + Z/(1+Z) )
fabs.x %fp0 # Y = |X|
movm.l &0x8040,-(%sp) # {a1/d0}
fmovm.x &0x01,-(%sp) # save Y on stack
lea (%sp),%a0 # pass ptr to Y clr.l %d0
bsr setoxm1 # FP0 IS Z = EXPM1(Y)
add.l &0xc,%sp # clear Y from stack
fmov.l &0,%fpcr
movm.l (%sp)+,&0x0201 # {a1/d0}
#--THIS IS THE USUAL CASE
#--Y = 2|X|, Z = EXPM1(Y), TANH(X) = SIGN(X) * Z / (Z+2).
mov.l X(%a6),%d1
mov.l %d1,SGN(%a6)
and.l &0x7FFF0000,%d1
add.l &0x00010000,%d1 # EXPONENT OF 2|X|
mov.l %d1,X(%a6)
and.l &0x80000000,SGN(%a6)
fmov.x X(%a6),%fp0 # FP0 IS Y = 2|X|
mov.l %d0,-(%sp) clr.l %d0
fmovm.x &0x1,-(%sp) # save Y on stack
lea (%sp),%a0 # pass ptr to Y
bsr setoxm1 # FP0 IS Z = EXPM1(Y)
add.l &0xc,%sp # clear Y from stack
mov.l (%sp)+,%d0
mov.l X(%a6),%d1
mov.l %d1,SGN(%a6)
and.l &0x7FFF0000,%d1
add.l &0x00010000,%d1 # EXPO OF 2|X|
mov.l %d1,X(%a6) # Y = 2|X|
and.l &0x80000000,SGN(%a6)
mov.l SGN(%a6),%d1
fmov.x X(%a6),%fp0 # Y = 2|X|
mov.l %d0,-(%sp) clr.l %d0
fmovm.x &0x01,-(%sp) # save Y on stack
lea (%sp),%a0 # pass ptr to Y
bsr setox # FP0 IS EXP(Y)
add.l &0xc,%sp # clear Y from stack
mov.l (%sp)+,%d0
mov.l SGN(%a6),%d1
fadd.s &0x3F800000,%fp0 # EXP(Y)+1
fmov.l %d0,%fpcr # restore users round prec,mode
mov.b &FADD_OP,%d1 # last inst is ADD
fadd.x %fp1,%fp0
bra t_inx2
TANHSM:
fmov.l %d0,%fpcr # restore users round prec,mode
mov.b &FMOV_OP,%d1 # last inst is MOVE
fmov.x X(%a6),%fp0 # last inst - possible exception set
bra t_catch
global stanhd
#--TANH(X) = X FOR DENORMALIZED X
stanhd:
bra t_extdnrm
#########################################################################
# slogn(): computes the natural logarithm of a normalized input #
# slognd(): computes the natural logarithm of a denormalized input #
# slognp1(): computes the log(1+X) of a normalized input #
# slognp1d(): computes the log(1+X) of a denormalized input #
# #
# INPUT *************************************************************** #
# a0 = pointer to extended precision input #
# d0 = round precision,mode #
# #
# OUTPUT ************************************************************** #
# fp0 = log(X) or log(1+X) #
# #
# ACCURACY and MONOTONICITY ******************************************* #
# The returned result is within 2 ulps in 64 significant bit, #
# i.e. within 0.5001 ulp to 53 bits if the result is subsequently #
# rounded to double precision. The result is provably monotonic #
# in double precision. #
# #
# ALGORITHM *********************************************************** #
# LOGN: #
# Step 1. If |X-1| < 1/16, approximate log(X) by an odd #
# polynomial in u, where u = 2(X-1)/(X+1). Otherwise, #
# move on to Step 2. #
# #
# Step 2. X = 2**k * Y where 1 <= Y < 2. Define F to be the first #
# seven significant bits of Y plus 2**(-7), i.e. #
# F = 1.xxxxxx1 in base 2 where the six "x" match those #
# of Y. Note that |Y-F| <= 2**(-7). #
# #
# Step 3. Define u = (Y-F)/F. Approximate log(1+u) by a #
# polynomial in u, log(1+u) = poly. #
# #
# Step 4. Reconstruct #
# log(X) = log( 2**k * Y ) = k*log(2) + log(F) + log(1+u) #
# by k*log(2) + (log(F) + poly). The values of log(F) are #
# calculated beforehand and stored in the program. #
# #
# lognp1: #
# Step 1: If |X| < 1/16, approximate log(1+X) by an odd #
# polynomial in u where u = 2X/(2+X). Otherwise, move on #
# to Step 2. #
# #
# Step 2: Let 1+X = 2**k * Y, where 1 <= Y < 2. Define F as done #
# in Step 2 of the algorithm for LOGN and compute #
# log(1+X) as k*log(2) + log(F) + poly where poly #
# approximates log(1+u), u = (Y-F)/F. #
# #
# Implementation Notes: #
# Note 1. There are 64 different possible values for F, thus 64 #
# log(F)'s need to be tabulated. Moreover, the values of #
# 1/F are also tabulated so that the division in (Y-F)/F #
# can be performed by a multiplication. #
# #
# Note 2. In Step 2 of lognp1, in order to preserved accuracy, #
# the value Y-F has to be calculated carefully when #
# 1/2 <= X < 3/2. #
# #
# Note 3. To fully exploit the pipeline, polynomials are usually #
# separated into two parts evaluated independently before #
# being added up. #
# #
#########################################################################
LOGOF2:
long 0x3FFE0000,0xB17217F7,0xD1CF79AC,0x00000000
one:
long 0x3F800000
zero:
long 0x00000000
infty:
long 0x7F800000
negone:
long 0xBF800000
LOGA6:
long 0x3FC2499A,0xB5E4040B
LOGA5:
long 0xBFC555B5,0x848CB7DB
LOGA4:
long 0x3FC99999,0x987D8730
LOGA3:
long 0xBFCFFFFF,0xFF6F7E97
LOGA2:
long 0x3FD55555,0x555555A4
LOGA1:
long 0xBFE00000,0x00000008
LOGB5:
long 0x3F175496,0xADD7DAD6
LOGB4:
long 0x3F3C71C2,0xFE80C7E0
LOGB3:
long 0x3F624924,0x928BCCFF
LOGB2:
long 0x3F899999,0x999995EC
LOGB1:
long 0x3FB55555,0x55555555
TWO:
long 0x40000000,0x00000000
LTHOLD:
long 0x3f990000,0x80000000,0x00000000,0x00000000
LOGTBL:
long 0x3FFE0000,0xFE03F80F,0xE03F80FE,0x00000000
long 0x3FF70000,0xFF015358,0x833C47E2,0x00000000
long 0x3FFE0000,0xFA232CF2,0x52138AC0,0x00000000
long 0x3FF90000,0xBDC8D83E,0xAD88D549,0x00000000
long 0x3FFE0000,0xF6603D98,0x0F6603DA,0x00000000
long 0x3FFA0000,0x9CF43DCF,0xF5EAFD48,0x00000000
long 0x3FFE0000,0xF2B9D648,0x0F2B9D65,0x00000000
long 0x3FFA0000,0xDA16EB88,0xCB8DF614,0x00000000
long 0x3FFE0000,0xEF2EB71F,0xC4345238,0x00000000
long 0x3FFB0000,0x8B29B775,0x1BD70743,0x00000000
long 0x3FFE0000,0xEBBDB2A5,0xC1619C8C,0x00000000
long 0x3FFB0000,0xA8D839F8,0x30C1FB49,0x00000000
long 0x3FFE0000,0xE865AC7B,0x7603A197,0x00000000
long 0x3FFB0000,0xC61A2EB1,0x8CD907AD,0x00000000
long 0x3FFE0000,0xE525982A,0xF70C880E,0x00000000
long 0x3FFB0000,0xE2F2A47A,0xDE3A18AF,0x00000000
long 0x3FFE0000,0xE1FC780E,0x1FC780E2,0x00000000
long 0x3FFB0000,0xFF64898E,0xDF55D551,0x00000000
long 0x3FFE0000,0xDEE95C4C,0xA037BA57,0x00000000
long 0x3FFC0000,0x8DB956A9,0x7B3D0148,0x00000000
long 0x3FFE0000,0xDBEB61EE,0xD19C5958,0x00000000
long 0x3FFC0000,0x9B8FE100,0xF47BA1DE,0x00000000
long 0x3FFE0000,0xD901B203,0x6406C80E,0x00000000
long 0x3FFC0000,0xA9372F1D,0x0DA1BD17,0x00000000
long 0x3FFE0000,0xD62B80D6,0x2B80D62C,0x00000000
long 0x3FFC0000,0xB6B07F38,0xCE90E46B,0x00000000
long 0x3FFE0000,0xD3680D36,0x80D3680D,0x00000000
long 0x3FFC0000,0xC3FD0329,0x06488481,0x00000000
long 0x3FFE0000,0xD0B69FCB,0xD2580D0B,0x00000000
long 0x3FFC0000,0xD11DE0FF,0x15AB18CA,0x00000000
long 0x3FFE0000,0xCE168A77,0x25080CE1,0x00000000
long 0x3FFC0000,0xDE1433A1,0x6C66B150,0x00000000
long 0x3FFE0000,0xCB8727C0,0x65C393E0,0x00000000
long 0x3FFC0000,0xEAE10B5A,0x7DDC8ADD,0x00000000
long 0x3FFE0000,0xC907DA4E,0x871146AD,0x00000000
long 0x3FFC0000,0xF7856E5E,0xE2C9B291,0x00000000
long 0x3FFE0000,0xC6980C69,0x80C6980C,0x00000000
long 0x3FFD0000,0x82012CA5,0xA68206D7,0x00000000
long 0x3FFE0000,0xC4372F85,0x5D824CA6,0x00000000
long 0x3FFD0000,0x882C5FCD,0x7256A8C5,0x00000000
long 0x3FFE0000,0xC1E4BBD5,0x95F6E947,0x00000000
long 0x3FFD0000,0x8E44C60B,0x4CCFD7DE,0x00000000
long 0x3FFE0000,0xBFA02FE8,0x0BFA02FF,0x00000000
long 0x3FFD0000,0x944AD09E,0xF4351AF6,0x00000000
long 0x3FFE0000,0xBD691047,0x07661AA3,0x00000000
long 0x3FFD0000,0x9A3EECD4,0xC3EAA6B2,0x00000000
long 0x3FFE0000,0xBB3EE721,0xA54D880C,0x00000000
long 0x3FFD0000,0xA0218434,0x353F1DE8,0x00000000
long 0x3FFE0000,0xB92143FA,0x36F5E02E,0x00000000
long 0x3FFD0000,0xA5F2FCAB,0xBBC506DA,0x00000000
long 0x3FFE0000,0xB70FBB5A,0x19BE3659,0x00000000
long 0x3FFD0000,0xABB3B8BA,0x2AD362A5,0x00000000
long 0x3FFE0000,0xB509E68A,0x9B94821F,0x00000000
long 0x3FFD0000,0xB1641795,0xCE3CA97B,0x00000000
long 0x3FFE0000,0xB30F6352,0x8917C80B,0x00000000
long 0x3FFD0000,0xB7047551,0x5D0F1C61,0x00000000
long 0x3FFE0000,0xB11FD3B8,0x0B11FD3C,0x00000000
long 0x3FFD0000,0xBC952AFE,0xEA3D13E1,0x00000000
long 0x3FFE0000,0xAF3ADDC6,0x80AF3ADE,0x00000000
long 0x3FFD0000,0xC2168ED0,0xF458BA4A,0x00000000
long 0x3FFE0000,0xAD602B58,0x0AD602B6,0x00000000
long 0x3FFD0000,0xC788F439,0xB3163BF1,0x00000000
long 0x3FFE0000,0xAB8F69E2,0x8359CD11,0x00000000
long 0x3FFD0000,0xCCECAC08,0xBF04565D,0x00000000
long 0x3FFE0000,0xA9C84A47,0xA07F5638,0x00000000
long 0x3FFD0000,0xD2420487,0x2DD85160,0x00000000
long 0x3FFE0000,0xA80A80A8,0x0A80A80B,0x00000000
long 0x3FFD0000,0xD7894992,0x3BC3588A,0x00000000
long 0x3FFE0000,0xA655C439,0x2D7B73A8,0x00000000
long 0x3FFD0000,0xDCC2C4B4,0x9887DACC,0x00000000
long 0x3FFE0000,0xA4A9CF1D,0x96833751,0x00000000
long 0x3FFD0000,0xE1EEBD3E,0x6D6A6B9E,0x00000000
long 0x3FFE0000,0xA3065E3F,0xAE7CD0E0,0x00000000
long 0x3FFD0000,0xE70D785C,0x2F9F5BDC,0x00000000
long 0x3FFE0000,0xA16B312E,0xA8FC377D,0x00000000
long 0x3FFD0000,0xEC1F392C,0x5179F283,0x00000000
long 0x3FFE0000,0x9FD809FD,0x809FD80A,0x00000000
long 0x3FFD0000,0xF12440D3,0xE36130E6,0x00000000
long 0x3FFE0000,0x9E4CAD23,0xDD5F3A20,0x00000000
long 0x3FFD0000,0xF61CCE92,0x346600BB,0x00000000
long 0x3FFE0000,0x9CC8E160,0xC3FB19B9,0x00000000
long 0x3FFD0000,0xFB091FD3,0x8145630A,0x00000000
long 0x3FFE0000,0x9B4C6F9E,0xF03A3CAA,0x00000000
long 0x3FFD0000,0xFFE97042,0xBFA4C2AD,0x00000000
long 0x3FFE0000,0x99D722DA,0xBDE58F06,0x00000000
long 0x3FFE0000,0x825EFCED,0x49369330,0x00000000
long 0x3FFE0000,0x9868C809,0x868C8098,0x00000000
long 0x3FFE0000,0x84C37A7A,0xB9A905C9,0x00000000
long 0x3FFE0000,0x97012E02,0x5C04B809,0x00000000
long 0x3FFE0000,0x87224C2E,0x8E645FB7,0x00000000
long 0x3FFE0000,0x95A02568,0x095A0257,0x00000000
long 0x3FFE0000,0x897B8CAC,0x9F7DE298,0x00000000
long 0x3FFE0000,0x94458094,0x45809446,0x00000000
long 0x3FFE0000,0x8BCF55DE,0xC4CD05FE,0x00000000
long 0x3FFE0000,0x92F11384,0x0497889C,0x00000000
long 0x3FFE0000,0x8E1DC0FB,0x89E125E5,0x00000000
long 0x3FFE0000,0x91A2B3C4,0xD5E6F809,0x00000000
long 0x3FFE0000,0x9066E68C,0x955B6C9B,0x00000000
long 0x3FFE0000,0x905A3863,0x3E06C43B,0x00000000
long 0x3FFE0000,0x92AADE74,0xC7BE59E0,0x00000000
long 0x3FFE0000,0x8F1779D9,0xFDC3A219,0x00000000
long 0x3FFE0000,0x94E9BFF6,0x15845643,0x00000000
long 0x3FFE0000,0x8DDA5202,0x37694809,0x00000000
long 0x3FFE0000,0x9723A1B7,0x20134203,0x00000000
long 0x3FFE0000,0x8CA29C04,0x6514E023,0x00000000
long 0x3FFE0000,0x995899C8,0x90EB8990,0x00000000
long 0x3FFE0000,0x8B70344A,0x139BC75A,0x00000000
long 0x3FFE0000,0x9B88BDAA,0x3A3DAE2F,0x00000000
long 0x3FFE0000,0x8A42F870,0x5669DB46,0x00000000
long 0x3FFE0000,0x9DB4224F,0xFFE1157C,0x00000000
long 0x3FFE0000,0x891AC73A,0xE9819B50,0x00000000
long 0x3FFE0000,0x9FDADC26,0x8B7A12DA,0x00000000
long 0x3FFE0000,0x87F78087,0xF78087F8,0x00000000
long 0x3FFE0000,0xA1FCFF17,0xCE733BD4,0x00000000
long 0x3FFE0000,0x86D90544,0x7A34ACC6,0x00000000
long 0x3FFE0000,0xA41A9E8F,0x5446FB9F,0x00000000
long 0x3FFE0000,0x85BF3761,0x2CEE3C9B,0x00000000
long 0x3FFE0000,0xA633CD7E,0x6771CD8B,0x00000000
long 0x3FFE0000,0x84A9F9C8,0x084A9F9D,0x00000000
long 0x3FFE0000,0xA8489E60,0x0B435A5E,0x00000000
long 0x3FFE0000,0x83993052,0x3FBE3368,0x00000000
long 0x3FFE0000,0xAA59233C,0xCCA4BD49,0x00000000
long 0x3FFE0000,0x828CBFBE,0xB9A020A3,0x00000000
long 0x3FFE0000,0xAC656DAE,0x6BCC4985,0x00000000
long 0x3FFE0000,0x81848DA8,0xFAF0D277,0x00000000
long 0x3FFE0000,0xAE6D8EE3,0x60BB2468,0x00000000
long 0x3FFE0000,0x80808080,0x80808081,0x00000000
long 0x3FFE0000,0xB07197A2,0x3C46C654,0x00000000
set ADJK,L_SCR1
set X,FP_SCR0 set XDCARE,X+2 set XFRAC,X+4
set F,FP_SCR1 set FFRAC,F+4
set KLOG2,FP_SCR0
set SAVEU,FP_SCR0
global slogn
#--ENTRY POINT FOR LOG(X) FOR X FINITE, NON-ZERO, NOT NAN'S
slogn:
fmov.x (%a0),%fp0 # LOAD INPUT
mov.l &0x00000000,ADJK(%a6)
LOGBGN:
#--FPCR SAVED AND CLEARED, INPUT IS 2^(ADJK)*FP0, FP0 CONTAINS
#--A FINITE, NON-ZERO, NORMALIZED NUMBER.
cmp.l %d1,&0 # CHECK IF X IS NEGATIVE
blt.w LOGNEG # LOG OF NEGATIVE ARGUMENT IS INVALID
# X IS POSITIVE, CHECK IF X IS NEAR 1
cmp.l %d1,&0x3ffef07d # IS X < 15/16?
blt.b LOGMAIN # YES
cmp.l %d1,&0x3fff8841 # IS X > 17/16?
ble.w LOGNEAR1 # NO
LOGMAIN:
#--THIS SHOULD BE THE USUAL CASE, X NOT VERY CLOSE TO 1
#--X = 2^(K) * Y, 1 <= Y < 2. THUS, Y = 1.XXXXXXXX....XX IN BINARY.
#--WE DEFINE F = 1.XXXXXX1, I.E. FIRST 7 BITS OF Y AND ATTACH A 1.
#--THE IDEA IS THAT LOG(X) = K*LOG2 + LOG(Y)
#-- = K*LOG2 + LOG(F) + LOG(1 + (Y-F)/F).
#--NOTE THAT U = (Y-F)/F IS VERY SMALL AND THUS APPROXIMATING
#--LOG(1+U) CAN BE VERY EFFICIENT.
#--ALSO NOTE THAT THE VALUE 1/F IS STORED IN A TABLE SO THAT NO
#--DIVISION IS NEEDED TO CALCULATE (Y-F)/F.
#--GET K, Y, F, AND ADDRESS OF 1/F.
asr.l &8,%d1
asr.l &8,%d1 # SHIFTED 16 BITS, BIASED EXPO. OF X sub.l &0x3FFF,%d1 # THIS IS K
add.l ADJK(%a6),%d1 # ADJUST K, ORIGINAL INPUT MAY BE DENORM.
lea LOGTBL(%pc),%a0 # BASE ADDRESS OF 1/F AND LOG(F)
fmov.l %d1,%fp1 # CONVERT K TO FLOATING-POINT FORMAT
#--WHILE THE CONVERSION IS GOING ON, WE GET F AND ADDRESS OF 1/F
mov.l &0x3FFF0000,X(%a6) # X IS NOW Y, I.E. 2^(-K)*X
mov.l XFRAC(%a6),FFRAC(%a6)
and.l &0xFE000000,FFRAC(%a6) # FIRST 7 BITS OF Y
or.l &0x01000000,FFRAC(%a6) # GET F: ATTACH A 1 AT THE EIGHTH BIT
mov.l FFRAC(%a6),%d1 # READY TO GET ADDRESS OF 1/F
and.l &0x7E000000,%d1
asr.l &8,%d1
asr.l &8,%d1
asr.l &4,%d1 # SHIFTED 20, D0 IS THE DISPLACEMENT
add.l %d1,%a0 # A0 IS THE ADDRESS FOR 1/F
fmov.x X(%a6),%fp0
mov.l &0x3fff0000,F(%a6) clr.l F+8(%a6)
fsub.x F(%a6),%fp0 # Y-F
fmovm.x &0xc,-(%sp) # SAVE FP2-3 WHILE FP0 IS NOT READY
#--SUMMARY: FP0 IS Y-F, A0 IS ADDRESS OF 1/F, FP1 IS K
#--REGISTERS SAVED: FPCR, FP1, FP2
LP1CONT1:
#--AN RE-ENTRY POINT FOR LOGNP1
fmul.x (%a0),%fp0 # FP0 IS U = (Y-F)/F
fmul.x LOGOF2(%pc),%fp1 # GET K*LOG2 WHILE FP0 IS NOT READY
fmov.x %fp0,%fp2
fmul.x %fp2,%fp2 # FP2 IS V=U*U
fmov.x %fp1,KLOG2(%a6) # PUT K*LOG2 IN MEMEORY, FREE FP1
#--LOG(1+U) IS APPROXIMATED BY
#--U + V*(A1+U*(A2+U*(A3+U*(A4+U*(A5+U*A6))))) WHICH IS
#--[U + V*(A1+V*(A3+V*A5))] + [U*V*(A2+V*(A4+V*A6))]
fmov.l %d0,%fpcr
fadd.x KLOG2(%a6),%fp0 # FINAL ADD
bra t_inx2
LOGNEAR1:
# if the input is exactly equal to one, then exit through ld_pzero.
# if these 2 lines weren't here, the correct answer would be returned
# but the INEX2 bit would be set.
fcmp.b %fp0,&0x1 # is it equal to one?
fbeq.l ld_pzero # yes
#--REGISTERS SAVED: FPCR, FP1. FP0 CONTAINS THE INPUT.
fmov.x %fp0,%fp1
fsub.s one(%pc),%fp1 # FP1 IS X-1
fadd.s one(%pc),%fp0 # FP0 IS X+1
fadd.x %fp1,%fp1 # FP1 IS 2(X-1)
#--LOG(X) = LOG(1+U/2)-LOG(1-U/2) WHICH IS AN ODD POLYNOMIAL
#--IN U, U = 2(X-1)/(X+1) = FP1/FP0
LP1CONT2:
#--THIS IS AN RE-ENTRY POINT FOR LOGNP1
fdiv.x %fp0,%fp1 # FP1 IS U
fmovm.x &0xc,-(%sp) # SAVE FP2-3
#--REGISTERS SAVED ARE NOW FPCR,FP1,FP2,FP3
#--LET V=U*U, W=V*V, CALCULATE
#--U + U*V*(B1 + V*(B2 + V*(B3 + V*(B4 + V*B5)))) BY
#--U + U*V*( [B1 + W*(B3 + W*B5)] + [V*(B2 + W*B4)] )
fmov.x %fp1,%fp0
fmul.x %fp0,%fp0 # FP0 IS V
fmov.x %fp1,SAVEU(%a6) # STORE U IN MEMORY, FREE FP1
fmov.x %fp0,%fp1
fmul.x %fp1,%fp1 # FP1 IS W
fmov.l %d0,%fpcr
fadd.x SAVEU(%a6),%fp0
bra t_inx2
#--REGISTERS SAVED FPCR. LOG(-VE) IS INVALID
LOGNEG:
bra t_operr
global slognd
slognd:
#--ENTRY POINT FOR LOG(X) FOR DENORMALIZED INPUT
mov.l &-100,ADJK(%a6) # INPUT = 2^(ADJK) * FP0
#----normalize the input value by left shifting k bits (k to be determined
#----below), adjusting exponent and storing -k to ADJK
#----the value TWOTO100 is no longer needed.
#----Note that this code assumes the denormalized input is NON-ZERO.
movm.l &0x3f00,-(%sp) # save some registers {d2-d7}
mov.l (%a0),%d3 # D3 is exponent of smallest norm. #
mov.l 4(%a0),%d4
mov.l 8(%a0),%d5 # (D4,D5) is (Hi_X,Lo_X) clr.l %d2 # D2 used for holding K
global slognp1
#--ENTRY POINT FOR LOG(1+X) FOR X FINITE, NON-ZERO, NOT NAN'S
slognp1:
fmov.x (%a0),%fp0 # LOAD INPUT
fabs.x %fp0 # test magnitude
fcmp.x %fp0,LTHOLD(%pc) # compare with min threshold
fbgt.w LP1REAL # if greater, continue
fmov.l %d0,%fpcr
mov.b &FMOV_OP,%d1 # last inst is MOVE
fmov.x (%a0),%fp0 # return signed argument
bra t_catch
LP1REAL:
fmov.x (%a0),%fp0 # LOAD INPUT
mov.l &0x00000000,ADJK(%a6)
fmov.x %fp0,%fp1 # FP1 IS INPUT Z
fadd.s one(%pc),%fp0 # X := ROUND(1+Z)
fmov.x %fp0,X(%a6)
mov.w XFRAC(%a6),XDCARE(%a6)
mov.l X(%a6),%d1
cmp.l %d1,&0
ble.w LP1NEG0 # LOG OF ZERO OR -VE
cmp.l %d1,&0x3ffe8000 # IS BOUNDS [1/2,3/2]?
blt.w LOGMAIN
cmp.l %d1,&0x3fffc000
bgt.w LOGMAIN
#--IF 1+Z > 3/2 OR 1+Z < 1/2, THEN X, WHICH IS ROUNDING 1+Z,
#--CONTAINS AT LEAST 63 BITS OF INFORMATION OF Z. IN THAT CASE,
#--SIMPLY INVOKE LOG(X) FOR LOG(1+Z).
LP1NEAR1:
#--NEXT SEE IF EXP(-1/16) < X < EXP(1/16)
cmp.l %d1,&0x3ffef07d
blt.w LP1CARE
cmp.l %d1,&0x3fff8841
bgt.w LP1CARE
LP1ONE16:
#--EXP(-1/16) < X < EXP(1/16). LOG(1+Z) = LOG(1+U/2) - LOG(1-U/2)
#--WHERE U = 2Z/(2+Z) = 2Z/(1+X).
fadd.x %fp1,%fp1 # FP1 IS 2Z
fadd.s one(%pc),%fp0 # FP0 IS 1+X
#--U = FP1/FP0
bra.w LP1CONT2
LP1CARE:
#--HERE WE USE THE USUAL TABLE DRIVEN APPROACH. CARE HAS TO BE
#--TAKEN BECAUSE 1+Z CAN HAVE 67 BITS OF INFORMATION AND WE MUST
#--PRESERVE ALL THE INFORMATION. BECAUSE 1+Z IS IN [1/2,3/2],
#--THERE ARE ONLY TWO CASES.
#--CASE 1: 1+Z < 1, THEN K = -1 AND Y-F = (2-F) + 2Z
#--CASE 2: 1+Z > 1, THEN K = 0 AND Y-F = (1-F) + Z
#--ON RETURNING TO LP1CONT1, WE MUST HAVE K IN FP1, ADDRESS OF
#--(1/F) IN A0, Y-F IN FP0, AND FP2 SAVED.
mov.l XFRAC(%a6),FFRAC(%a6)
and.l &0xFE000000,FFRAC(%a6)
or.l &0x01000000,FFRAC(%a6) # F OBTAINED
cmp.l %d1,&0x3FFF8000 # SEE IF 1+Z > 1
bge.b KISZERO
KISNEG1:
fmov.s TWO(%pc),%fp0
mov.l &0x3fff0000,F(%a6) clr.l F+8(%a6)
fsub.x F(%a6),%fp0 # 2-F
mov.l FFRAC(%a6),%d1
and.l &0x7E000000,%d1
asr.l &8,%d1
asr.l &8,%d1
asr.l &4,%d1 # D0 CONTAINS DISPLACEMENT FOR 1/F
fadd.x %fp1,%fp1 # GET 2Z
fmovm.x &0xc,-(%sp) # SAVE FP2 {%fp2/%fp3}
fadd.x %fp1,%fp0 # FP0 IS Y-F = (2-F)+2Z
lea LOGTBL(%pc),%a0 # A0 IS ADDRESS OF 1/F
add.l %d1,%a0
fmov.s negone(%pc),%fp1 # FP1 IS K = -1
bra.w LP1CONT1
mov.l %d0,-(%sp) # save rnd prec,mode clr.l %d0 # pass ext prec,RN
fmovm.x &0x01,-(%sp) # save Z on stack
lea (%sp),%a0 # pass ptr to Z
bsr slognp1 # LOG1P(Z)
add.l &0xc,%sp # clear Z from stack
mov.l (%sp)+,%d0 # fetch old prec,mode
fmov.l %d0,%fpcr # load it
mov.b &FMUL_OP,%d1 # last inst is MUL
fmul.s (%sp)+,%fp0
bra t_catch
global satanhd
#--ATANH(X) = X FOR DENORMALIZED X
satanhd:
bra t_extdnrm
#########################################################################
# slog10(): computes the base-10 logarithm of a normalized input #
# slog10d(): computes the base-10 logarithm of a denormalized input #
# slog2(): computes the base-2 logarithm of a normalized input #
# slog2d(): computes the base-2 logarithm of a denormalized input #
# #
# INPUT *************************************************************** #
# a0 = pointer to extended precision input #
# d0 = round precision,mode #
# #
# OUTPUT ************************************************************** #
# fp0 = log_10(X) or log_2(X) #
# #
# ACCURACY and MONOTONICITY ******************************************* #
# The returned result is within 1.7 ulps in 64 significant bit, #
# i.e. within 0.5003 ulp to 53 bits if the result is subsequently #
# rounded to double precision. The result is provably monotonic #
# in double precision. #
# #
# ALGORITHM *********************************************************** #
# #
# slog10d: #
# #
# Step 0. If X < 0, create a NaN and raise the invalid operation #
# flag. Otherwise, save FPCR in D1; set FpCR to default. #
# Notes: Default means round-to-nearest mode, no floating-point #
# traps, and precision control = double extended. #
# #
# Step 1. Call slognd to obtain Y = log(X), the natural log of X. #
# Notes: Even if X is denormalized, log(X) is always normalized. #
# #
# Step 2. Compute log_10(X) = log(X) * (1/log(10)). #
# 2.1 Restore the user FPCR #
# 2.2 Return ans := Y * INV_L10. #
# #
# slog10: #
# #
# Step 0. If X < 0, create a NaN and raise the invalid operation #
# flag. Otherwise, save FPCR in D1; set FpCR to default. #
# Notes: Default means round-to-nearest mode, no floating-point #
# traps, and precision control = double extended. #
# #
# Step 1. Call sLogN to obtain Y = log(X), the natural log of X. #
# #
# Step 2. Compute log_10(X) = log(X) * (1/log(10)). #
# 2.1 Restore the user FPCR #
# 2.2 Return ans := Y * INV_L10. #
# #
# sLog2d: #
# #
# Step 0. If X < 0, create a NaN and raise the invalid operation #
# flag. Otherwise, save FPCR in D1; set FpCR to default. #
# Notes: Default means round-to-nearest mode, no floating-point #
# traps, and precision control = double extended. #
# #
# Step 1. Call slognd to obtain Y = log(X), the natural log of X. #
# Notes: Even if X is denormalized, log(X) is always normalized. #
# #
# Step 2. Compute log_10(X) = log(X) * (1/log(2)). #
# 2.1 Restore the user FPCR #
# 2.2 Return ans := Y * INV_L2. #
# #
# sLog2: #
# #
# Step 0. If X < 0, create a NaN and raise the invalid operation #
# flag. Otherwise, save FPCR in D1; set FpCR to default. #
# Notes: Default means round-to-nearest mode, no floating-point #
# traps, and precision control = double extended. #
# #
# Step 1. If X is not an integer power of two, i.e., X != 2^k, #
# go to Step 3. #
# #
# Step 2. Return k. #
# 2.1 Get integer k, X = 2^k. #
# 2.2 Restore the user FPCR. #
# 2.3 Return ans := convert-to-double-extended(k). #
# #
# Step 3. Call sLogN to obtain Y = log(X), the natural log of X. #
# #
# Step 4. Compute log_2(X) = log(X) * (1/log(2)). #
# 4.1 Restore the user FPCR #
# 4.2 Return ans := Y * INV_L2. #
# #
#########################################################################
INV_L10:
long 0x3FFD0000,0xDE5BD8A9,0x37287195,0x00000000
INV_L2:
long 0x3FFF0000,0xB8AA3B29,0x5C17F0BC,0x00000000
global slog10
#--entry point for Log10(X), X is normalized
slog10:
fmov.b &0x1,%fp0
fcmp.x %fp0,(%a0) # if operand == 1,
fbeq.l ld_pzero # return an EXACT zero
mov.l (%a0),%d1
blt.w invalid
mov.l %d0,-(%sp) clr.l %d0
bsr slogn # log(X), X normal.
fmov.l (%sp)+,%fpcr
fmul.x INV_L10(%pc),%fp0
bra t_inx2
global slog10d
#--entry point for Log10(X), X is denormalized
slog10d:
mov.l (%a0),%d1
blt.w invalid
mov.l %d0,-(%sp) clr.l %d0
bsr slognd # log(X), X denorm.
fmov.l (%sp)+,%fpcr
fmul.x INV_L10(%pc),%fp0
bra t_minx2
global slog2
#--entry point for Log2(X), X is normalized
slog2:
mov.l (%a0),%d1
blt.w invalid
continue:
mov.l %d0,-(%sp) clr.l %d0
bsr slogn # log(X), X normal.
fmov.l (%sp)+,%fpcr
fmul.x INV_L2(%pc),%fp0
bra t_inx2
invalid:
bra t_operr
global slog2d
#--entry point for Log2(X), X is denormalized
slog2d:
mov.l (%a0),%d1
blt.w invalid
mov.l %d0,-(%sp) clr.l %d0
bsr slognd # log(X), X denorm.
fmov.l (%sp)+,%fpcr
fmul.x INV_L2(%pc),%fp0
bra t_minx2
#########################################################################
# stwotox(): computes 2**X for a normalized input #
# stwotoxd(): computes 2**X for a denormalized input #
# stentox(): computes 10**X for a normalized input #
# stentoxd(): computes 10**X for a denormalized input #
# #
# INPUT *************************************************************** #
# a0 = pointer to extended precision input #
# d0 = round precision,mode #
# #
# OUTPUT ************************************************************** #
# fp0 = 2**X or 10**X #
# #
# ACCURACY and MONOTONICITY ******************************************* #
# The returned result is within 2 ulps in 64 significant bit, #
# i.e. within 0.5001 ulp to 53 bits if the result is subsequently #
# rounded to double precision. The result is provably monotonic #
# in double precision. #
# #
# ALGORITHM *********************************************************** #
# #
# twotox #
# 1. If |X| > 16480, go to ExpBig. #
# #
# 2. If |X| < 2**(-70), go to ExpSm. #
# #
# 3. Decompose X as X = N/64 + r where |r| <= 1/128. Furthermore #
# decompose N as #
# N = 64(M + M') + j, j = 0,1,2,...,63. #
# #
# 4. Overwrite r := r * log2. Then #
# 2**X = 2**(M') * 2**(M) * 2**(j/64) * exp(r). #
# Go to expr to compute that expression. #
# #
# tentox #
# 1. If |X| > 16480*log_10(2) (base 10 log of 2), go to ExpBig. #
# #
# 2. If |X| < 2**(-70), go to ExpSm. #
# #
# 3. Set y := X*log_2(10)*64 (base 2 log of 10). Set #
# N := round-to-int(y). Decompose N as #
# N = 64(M + M') + j, j = 0,1,2,...,63. #
# #
# 4. Define r as #
# r := ((X - N*L1)-N*L2) * L10 #
# where L1, L2 are the leading and trailing parts of #
# log_10(2)/64 and L10 is the natural log of 10. Then #
# 10**X = 2**(M') * 2**(M) * 2**(j/64) * exp(r). #
# Go to expr to compute that expression. #
# #
# expr #
# 1. Fetch 2**(j/64) from table as Fact1 and Fact2. #
# #
# 2. Overwrite Fact1 and Fact2 by #
# Fact1 := 2**(M) * Fact1 #
# Fact2 := 2**(M) * Fact2 #
# Thus Fact1 + Fact2 = 2**(M) * 2**(j/64). #
# #
# 3. Calculate P where 1 + P approximates exp(r): #
# P = r + r*r*(A1+r*(A2+...+r*A5)). #
# #
# 4. Let AdjFact := 2**(M'). Return #
# AdjFact * ( Fact1 + ((Fact1*P) + Fact2) ). #
# Exit. #
# #
# ExpBig #
# 1. Generate overflow by Huge * Huge if X > 0; otherwise, #
# generate underflow by Tiny * Tiny. #
# #
# ExpSm #
# 1. Return 1 + X. #
# #
#########################################################################
L2TEN64:
long 0x406A934F,0x0979A371 # 64LOG10/LOG2
L10TWO1:
long 0x3F734413,0x509F8000 # LOG2/64LOG10
L10TWO2:
long 0xBFCD0000,0xC0219DC1,0xDA994FD2,0x00000000
LOG10: long 0x40000000,0x935D8DDD,0xAAA8AC17,0x00000000
LOG2: long 0x3FFE0000,0xB17217F7,0xD1CF79AC,0x00000000
EXPA5: long 0x3F56C16D,0x6F7BD0B2
EXPA4: long 0x3F811112,0x302C712C
EXPA3: long 0x3FA55555,0x55554CC1
EXPA2: long 0x3FC55555,0x55554A54
EXPA1: long 0x3FE00000,0x00000000,0x00000000,0x00000000
TEXPTBL:
long 0x3FFF0000,0x80000000,0x00000000,0x3F738000
long 0x3FFF0000,0x8164D1F3,0xBC030773,0x3FBEF7CA
long 0x3FFF0000,0x82CD8698,0xAC2BA1D7,0x3FBDF8A9
long 0x3FFF0000,0x843A28C3,0xACDE4046,0x3FBCD7C9
long 0x3FFF0000,0x85AAC367,0xCC487B15,0xBFBDE8DA
long 0x3FFF0000,0x871F6196,0x9E8D1010,0x3FBDE85C
long 0x3FFF0000,0x88980E80,0x92DA8527,0x3FBEBBF1
long 0x3FFF0000,0x8A14D575,0x496EFD9A,0x3FBB80CA
long 0x3FFF0000,0x8B95C1E3,0xEA8BD6E7,0xBFBA8373
long 0x3FFF0000,0x8D1ADF5B,0x7E5BA9E6,0xBFBE9670
long 0x3FFF0000,0x8EA4398B,0x45CD53C0,0x3FBDB700
long 0x3FFF0000,0x9031DC43,0x1466B1DC,0x3FBEEEB0
long 0x3FFF0000,0x91C3D373,0xAB11C336,0x3FBBFD6D
long 0x3FFF0000,0x935A2B2F,0x13E6E92C,0xBFBDB319
long 0x3FFF0000,0x94F4EFA8,0xFEF70961,0x3FBDBA2B
long 0x3FFF0000,0x96942D37,0x20185A00,0x3FBE91D5
long 0x3FFF0000,0x9837F051,0x8DB8A96F,0x3FBE8D5A
long 0x3FFF0000,0x99E04593,0x20B7FA65,0xBFBCDE7B
long 0x3FFF0000,0x9B8D39B9,0xD54E5539,0xBFBEBAAF
long 0x3FFF0000,0x9D3ED9A7,0x2CFFB751,0xBFBD86DA
long 0x3FFF0000,0x9EF53260,0x91A111AE,0xBFBEBEDD
long 0x3FFF0000,0xA0B0510F,0xB9714FC2,0x3FBCC96E
long 0x3FFF0000,0xA2704303,0x0C496819,0xBFBEC90B
long 0x3FFF0000,0xA43515AE,0x09E6809E,0x3FBBD1DB
long 0x3FFF0000,0xA5FED6A9,0xB15138EA,0x3FBCE5EB
long 0x3FFF0000,0xA7CD93B4,0xE965356A,0xBFBEC274
long 0x3FFF0000,0xA9A15AB4,0xEA7C0EF8,0x3FBEA83C
long 0x3FFF0000,0xAB7A39B5,0xA93ED337,0x3FBECB00
long 0x3FFF0000,0xAD583EEA,0x42A14AC6,0x3FBE9301
long 0x3FFF0000,0xAF3B78AD,0x690A4375,0xBFBD8367
long 0x3FFF0000,0xB123F581,0xD2AC2590,0xBFBEF05F
long 0x3FFF0000,0xB311C412,0xA9112489,0x3FBDFB3C
long 0x3FFF0000,0xB504F333,0xF9DE6484,0x3FBEB2FB
long 0x3FFF0000,0xB6FD91E3,0x28D17791,0x3FBAE2CB
long 0x3FFF0000,0xB8FBAF47,0x62FB9EE9,0x3FBCDC3C
long 0x3FFF0000,0xBAFF5AB2,0x133E45FB,0x3FBEE9AA
long 0x3FFF0000,0xBD08A39F,0x580C36BF,0xBFBEAEFD
long 0x3FFF0000,0xBF1799B6,0x7A731083,0xBFBCBF51
long 0x3FFF0000,0xC12C4CCA,0x66709456,0x3FBEF88A
long 0x3FFF0000,0xC346CCDA,0x24976407,0x3FBD83B2
long 0x3FFF0000,0xC5672A11,0x5506DADD,0x3FBDF8AB
long 0x3FFF0000,0xC78D74C8,0xABB9B15D,0xBFBDFB17
long 0x3FFF0000,0xC9B9BD86,0x6E2F27A3,0xBFBEFE3C
long 0x3FFF0000,0xCBEC14FE,0xF2727C5D,0xBFBBB6F8
long 0x3FFF0000,0xCE248C15,0x1F8480E4,0xBFBCEE53
long 0x3FFF0000,0xD06333DA,0xEF2B2595,0xBFBDA4AE
long 0x3FFF0000,0xD2A81D91,0xF12AE45A,0x3FBC9124
long 0x3FFF0000,0xD4F35AAB,0xCFEDFA1F,0x3FBEB243
long 0x3FFF0000,0xD744FCCA,0xD69D6AF4,0x3FBDE69A
long 0x3FFF0000,0xD99D15C2,0x78AFD7B6,0xBFB8BC61
long 0x3FFF0000,0xDBFBB797,0xDAF23755,0x3FBDF610
long 0x3FFF0000,0xDE60F482,0x5E0E9124,0xBFBD8BE1
long 0x3FFF0000,0xE0CCDEEC,0x2A94E111,0x3FBACB12
long 0x3FFF0000,0xE33F8972,0xBE8A5A51,0x3FBB9BFE
long 0x3FFF0000,0xE5B906E7,0x7C8348A8,0x3FBCF2F4
long 0x3FFF0000,0xE8396A50,0x3C4BDC68,0x3FBEF22F
long 0x3FFF0000,0xEAC0C6E7,0xDD24392F,0xBFBDBF4A
long 0x3FFF0000,0xED4F301E,0xD9942B84,0x3FBEC01A
long 0x3FFF0000,0xEFE4B99B,0xDCDAF5CB,0x3FBE8CAC
long 0x3FFF0000,0xF281773C,0x59FFB13A,0xBFBCBB3F
long 0x3FFF0000,0xF5257D15,0x2486CC2C,0x3FBEF73A
long 0x3FFF0000,0xF7D0DF73,0x0AD13BB9,0xBFB8B795
long 0x3FFF0000,0xFA83B2DB,0x722A033A,0x3FBEF84B
long 0x3FFF0000,0xFD3E0C0C,0xF486C175,0xBFBEF581
set INT,L_SCR1
set X,FP_SCR0 set XDCARE,X+2 set XFRAC,X+4
set ADJFACT,FP_SCR0
set FACT1,FP_SCR0 set FACT1HI,FACT1+4 set FACT1LOW,FACT1+8
set FACT2,FP_SCR1 set FACT2HI,FACT2+4 set FACT2LOW,FACT2+8
global stwotox
#--ENTRY POINT FOR 2**(X), HERE X IS FINITE, NON-ZERO, AND NOT NAN'S
stwotox:
fmovm.x (%a0),&0x80 # LOAD INPUT
fmov.x %fp0,%fp1
fmul.s &0x42800000,%fp1 # 64 * X
fmov.l %fp1,INT(%a6) # N = ROUND-TO-INT(64 X)
mov.l %d2,-(%sp)
lea TEXPTBL(%pc),%a1 # LOAD ADDRESS OF TABLE OF 2^(J/64)
fmov.l INT(%a6),%fp1 # N --> FLOATING FMT
mov.l INT(%a6),%d1
mov.l %d1,%d2
and.l &0x3F,%d1 # D0 IS J
asl.l &4,%d1 # DISPLACEMENT FOR 2^(J/64)
add.l %d1,%a1 # ADDRESS FOR 2^(J/64)
asr.l &6,%d2 # d2 IS L, N = 64L + J
mov.l %d2,%d1
asr.l &1,%d1 # D0 IS M sub.l %d1,%d2 # d2 IS M', N = 64(M+M') + J
add.l &0x3FFF,%d2
#--SUMMARY: a1 IS ADDRESS FOR THE LEADING PORTION OF 2^(J/64),
#--D0 IS M WHERE N = 64(M+M') + J. NOTE THAT |M| <= 16140 BY DESIGN.
#--ADJFACT = 2^(M').
#--REGISTERS SAVED SO FAR ARE (IN ORDER) FPCR, D0, FP1, a1, AND FP2.
fmov.l %d0,%fpcr # restore users round prec,mode
fadd.s &0x3F800000,%fp0 # RETURN 1 + X
bra t_pinx2
TEXPBIG:
#--|X| IS LARGE, GENERATE OVERFLOW IF X > 0; ELSE GENERATE UNDERFLOW
#--REGISTERS SAVE SO FAR ARE FPCR AND D0
mov.l X(%a6),%d1
cmp.l %d1,&0
blt.b EXPNEG
bra t_ovfl2 # t_ovfl expects positive value
EXPNEG:
bra t_unfl2 # t_unfl expects positive value
global stwotoxd
stwotoxd:
#--ENTRY POINT FOR 2**(X) FOR DENORMALIZED ARGUMENT
fmov.l %d0,%fpcr # set user's rounding mode/precision
fmov.s &0x3F800000,%fp0 # RETURN 1 + X
mov.l (%a0),%d1
or.l &0x00800001,%d1
fadd.s %d1,%fp0
bra t_pinx2
global stentox
#--ENTRY POINT FOR 10**(X), HERE X IS FINITE, NON-ZERO, AND NOT NAN'S
stentox:
fmovm.x (%a0),&0x80 # LOAD INPUT
fmov.x %fp0,%fp1
fmul.d L2TEN64(%pc),%fp1 # X*64*LOG10/LOG2
fmov.l %fp1,INT(%a6) # N=INT(X*64*LOG10/LOG2)
mov.l %d2,-(%sp)
lea TEXPTBL(%pc),%a1 # LOAD ADDRESS OF TABLE OF 2^(J/64)
fmov.l INT(%a6),%fp1 # N --> FLOATING FMT
mov.l INT(%a6),%d1
mov.l %d1,%d2
and.l &0x3F,%d1 # D0 IS J
asl.l &4,%d1 # DISPLACEMENT FOR 2^(J/64)
add.l %d1,%a1 # ADDRESS FOR 2^(J/64)
asr.l &6,%d2 # d2 IS L, N = 64L + J
mov.l %d2,%d1
asr.l &1,%d1 # D0 IS M sub.l %d1,%d2 # d2 IS M', N = 64(M+M') + J
add.l &0x3FFF,%d2
#--SUMMARY: a1 IS ADDRESS FOR THE LEADING PORTION OF 2^(J/64),
#--D0 IS M WHERE N = 64(M+M') + J. NOTE THAT |M| <= 16140 BY DESIGN.
#--ADJFACT = 2^(M').
#--REGISTERS SAVED SO FAR ARE (IN ORDER) FPCR, D0, FP1, a1, AND FP2.
fmovm.x &0x0c,-(%sp) # save fp2/fp3
fmul.x LOG10(%pc),%fp0 # FP0 IS R
add.w %d1,FACT1(%a6)
add.w %d1,FACT2(%a6)
expr:
#--FPCR, FP2, FP3 ARE SAVED IN ORDER AS SHOWN.
#--ADJFACT CONTAINS 2**(M'), FACT1 + FACT2 = 2**(M) * 2**(J/64).
#--FP0 IS R. THE FOLLOWING CODE COMPUTES
#-- 2**(M'+M) * 2**(J/64) * EXP(R)
fmov.x %fp0,%fp1
fmul.x %fp1,%fp1 # FP1 IS S = R*R
fmov.d EXPA5(%pc),%fp2 # FP2 IS A5
fmov.d EXPA4(%pc),%fp3 # FP3 IS A4
fmul.x %fp1,%fp2 # FP2 IS S*A5
fmul.x %fp1,%fp3 # FP3 IS S*A4
fadd.d EXPA3(%pc),%fp2 # FP2 IS A3+S*A5
fadd.d EXPA2(%pc),%fp3 # FP3 IS A2+S*A4
fmul.x %fp1,%fp2 # FP2 IS S*(A3+S*A5)
fmul.x %fp1,%fp3 # FP3 IS S*(A2+S*A4)
fadd.d EXPA1(%pc),%fp2 # FP2 IS A1+S*(A3+S*A5)
fmul.x %fp0,%fp3 # FP3 IS R*S*(A2+S*A4)
fmul.x %fp1,%fp2 # FP2 IS S*(A1+S*(A3+S*A5))
fadd.x %fp3,%fp0 # FP0 IS R+R*S*(A2+S*A4)
fadd.x %fp2,%fp0 # FP0 IS EXP(R) - 1
fmovm.x (%sp)+,&0x30 # restore fp2/fp3
#--FINAL RECONSTRUCTION PROCESS
#--EXP(X) = 2^M*2^(J/64) + 2^M*2^(J/64)*(EXP(R)-1) - (1 OR 0)
fmov.l %d0,%fpcr # restore users round prec,mode
mov.w %d2,ADJFACT(%a6) # INSERT EXPONENT
mov.l (%sp)+,%d2
mov.l &0x80000000,ADJFACT+4(%a6) clr.l ADJFACT+8(%a6)
mov.b &FMUL_OP,%d1 # last inst is MUL
fmul.x ADJFACT(%a6),%fp0 # FINAL ADJUSTMENT
bra t_catch
global stentoxd
stentoxd:
#--ENTRY POINT FOR 10**(X) FOR DENORMALIZED ARGUMENT
fmov.l %d0,%fpcr # set user's rounding mode/precision
fmov.s &0x3F800000,%fp0 # RETURN 1 + X
mov.l (%a0),%d1
or.l &0x00800001,%d1
fadd.s %d1,%fp0
bra t_pinx2
#########################################################################
# smovcr(): returns the ROM constant at the offset specified in d1 #
# rounded to the mode and precision specified in d0. #
# #
# INPUT *************************************************************** #
# d0 = rnd prec,mode #
# d1 = ROM offset #
# #
# OUTPUT ************************************************************** #
# fp0 = the ROM constant rounded to the user's rounding mode,prec #
# #
#########################################################################
global smovcr
smovcr:
mov.l %d1,-(%sp) # save rom offset for a sec
lsr.b &0x4,%d0 # shift ctrl bits to lo
mov.l %d0,%d1 # make a copy
andi.w &0x3,%d1 # extract rnd mode
andi.w &0xc,%d0 # extract rnd prec
swap %d0 # put rnd prec in hi
mov.w %d1,%d0 # put rnd mode in lo
mov.l (%sp)+,%d1 # get rom offset
#
# check range of offset
#
tst.b %d1 # if zero, offset is to pi
beq.b pi_tbl # it is pi
cmpi.b %d1,&0x0a # check range $01 - $0a
ble.b z_val # if in this range, return zero
cmpi.b %d1,&0x0e # check range $0b - $0e
ble.b sm_tbl # valid constants in this range
cmpi.b %d1,&0x2f # check range $10 - $2f
ble.b z_val # if in this range, return zero
cmpi.b %d1,&0x3f # check range $30 - $3f
ble.b bg_tbl # valid constants in this range
z_val:
bra.l ld_pzero # return a zero
#
# the answer is PI rounded to the proper precision.
#
# fetch a pointer to the answer table relating to the proper rounding
# precision.
#
pi_tbl:
tst.b %d0 # is rmode RN?
bne.b pi_not_rn # no
pi_rn:
lea.l PIRN(%pc),%a0 # yes; load PI RN table addr
bra.w set_finx
pi_not_rn:
cmpi.b %d0,&rp_mode # is rmode RP?
beq.b pi_rp # yes
pi_rzrm:
lea.l PIRZRM(%pc),%a0 # no; load PI RZ,RM table addr
bra.b set_finx
pi_rp:
lea.l PIRP(%pc),%a0 # load PI RP table addr
bra.b set_finx
#
# the answer is one of:
# $0B log10(2) (inexact)
# $0C e (inexact)
# $0D log2(e) (inexact)
# $0E log10(e) (exact)
#
# fetch a pointer to the answer table relating to the proper rounding
# precision.
#
sm_tbl:
subi.b &0xb,%d1 # make offset in 0-4 range
tst.b %d0 # is rmode RN?
bne.b sm_not_rn # no
sm_rn:
lea.l SMALRN(%pc),%a0 # yes; load RN table addr
sm_tbl_cont:
cmpi.b %d1,&0x2 # is result log10(e)?
ble.b set_finx # no; answer is inexact
bra.b no_finx # yes; answer is exact
sm_not_rn:
cmpi.b %d0,&rp_mode # is rmode RP?
beq.b sm_rp # yes
sm_rzrm:
lea.l SMALRZRM(%pc),%a0 # no; load RZ,RM table addr
bra.b sm_tbl_cont
sm_rp:
lea.l SMALRP(%pc),%a0 # load RP table addr
bra.b sm_tbl_cont
#
# the answer is one of:
# $30 ln(2) (inexact)
# $31 ln(10) (inexact)
# $32 10^0 (exact)
# $33 10^1 (exact)
# $34 10^2 (exact)
# $35 10^4 (exact)
# $36 10^8 (exact)
# $37 10^16 (exact)
# $38 10^32 (inexact)
# $39 10^64 (inexact)
# $3A 10^128 (inexact)
# $3B 10^256 (inexact)
# $3C 10^512 (inexact)
# $3D 10^1024 (inexact)
# $3E 10^2048 (inexact)
# $3F 10^4096 (inexact)
#
# fetch a pointer to the answer table relating to the proper rounding
# precision.
#
bg_tbl:
subi.b &0x30,%d1 # make offset in 0-f range
tst.b %d0 # is rmode RN?
bne.b bg_not_rn # no
bg_rn:
lea.l BIGRN(%pc),%a0 # yes; load RN table addr
bg_tbl_cont:
cmpi.b %d1,&0x1 # is offset <= $31?
ble.b set_finx # yes; answer is inexact
cmpi.b %d1,&0x7 # is $32 <= offset <= $37?
ble.b no_finx # yes; answer is exact
bra.b set_finx # no; answer is inexact
bg_not_rn:
cmpi.b %d0,&rp_mode # is rmode RP?
beq.b bg_rp # yes
bg_rzrm:
lea.l BIGRZRM(%pc),%a0 # no; load RZ,RM table addr
bra.b bg_tbl_cont
bg_rp:
lea.l BIGRP(%pc),%a0 # load RP table addr
bra.b bg_tbl_cont
# answer is inexact, so set INEX2 and AINEX in the user's FPSR.
set_finx:
ori.l &inx2a_mask,USER_FPSR(%a6) # set INEX2/AINEX
no_finx:
mulu.w &0xc,%d1 # offset points into tables
swap %d0 # put rnd prec in loword
tst.b %d0 # is precision extended?
bne.b not_ext # if xprec, do not call round
# Precision is extended
fmovm.x (%a0,%d1.w),&0x80 # return result in fp0
rts
# Precision is single or double
not_ext:
swap %d0 # rnd prec in upper word
# call round() to round the answer to the proper precision.
# exponents out of range for single or double DO NOT cause underflow
# or overflow.
mov.w 0x0(%a0,%d1.w),FP_SCR1_EX(%a6) # load first word
mov.l 0x4(%a0,%d1.w),FP_SCR1_HI(%a6) # load second word
mov.l 0x8(%a0,%d1.w),FP_SCR1_LO(%a6) # load third word
mov.l %d0,%d1 clr.l %d0 # clear g,r,s
lea FP_SCR1(%a6),%a0 # pass ptr to answer clr.w LOCAL_SGN(%a0) # sign always positive
bsr.l _round # round the mantissa
fmovm.x (%a0),&0x80 # return rounded result in fp0
rts
align 0x4
PIRN: long 0x40000000,0xc90fdaa2,0x2168c235 # pi
PIRZRM: long 0x40000000,0xc90fdaa2,0x2168c234 # pi
PIRP: long 0x40000000,0xc90fdaa2,0x2168c235 # pi
SMALRN: long 0x3ffd0000,0x9a209a84,0xfbcff798 # log10(2)
long 0x40000000,0xadf85458,0xa2bb4a9a # e
long 0x3fff0000,0xb8aa3b29,0x5c17f0bc # log2(e)
long 0x3ffd0000,0xde5bd8a9,0x37287195 # log10(e)
long 0x00000000,0x00000000,0x00000000 # 0.0
SMALRZRM:
long 0x3ffd0000,0x9a209a84,0xfbcff798 # log10(2)
long 0x40000000,0xadf85458,0xa2bb4a9a # e
long 0x3fff0000,0xb8aa3b29,0x5c17f0bb # log2(e)
long 0x3ffd0000,0xde5bd8a9,0x37287195 # log10(e)
long 0x00000000,0x00000000,0x00000000 # 0.0
SMALRP: long 0x3ffd0000,0x9a209a84,0xfbcff799 # log10(2)
long 0x40000000,0xadf85458,0xa2bb4a9b # e
long 0x3fff0000,0xb8aa3b29,0x5c17f0bc # log2(e)
long 0x3ffd0000,0xde5bd8a9,0x37287195 # log10(e)
long 0x00000000,0x00000000,0x00000000 # 0.0
BIGRN: long 0x3ffe0000,0xb17217f7,0xd1cf79ac # ln(2)
long 0x40000000,0x935d8ddd,0xaaa8ac17 # ln(10)
long 0x3fff0000,0x80000000,0x00000000 # 10 ^ 0
long 0x40020000,0xA0000000,0x00000000 # 10 ^ 1
long 0x40050000,0xC8000000,0x00000000 # 10 ^ 2
long 0x400C0000,0x9C400000,0x00000000 # 10 ^ 4
long 0x40190000,0xBEBC2000,0x00000000 # 10 ^ 8
long 0x40340000,0x8E1BC9BF,0x04000000 # 10 ^ 16
long 0x40690000,0x9DC5ADA8,0x2B70B59E # 10 ^ 32
long 0x40D30000,0xC2781F49,0xFFCFA6D5 # 10 ^ 64
long 0x41A80000,0x93BA47C9,0x80E98CE0 # 10 ^ 128
long 0x43510000,0xAA7EEBFB,0x9DF9DE8E # 10 ^ 256
long 0x46A30000,0xE319A0AE,0xA60E91C7 # 10 ^ 512
long 0x4D480000,0xC9767586,0x81750C17 # 10 ^ 1024
long 0x5A920000,0x9E8B3B5D,0xC53D5DE5 # 10 ^ 2048
long 0x75250000,0xC4605202,0x8A20979B # 10 ^ 4096
BIGRZRM:
long 0x3ffe0000,0xb17217f7,0xd1cf79ab # ln(2)
long 0x40000000,0x935d8ddd,0xaaa8ac16 # ln(10)
long 0x3fff0000,0x80000000,0x00000000 # 10 ^ 0
long 0x40020000,0xA0000000,0x00000000 # 10 ^ 1
long 0x40050000,0xC8000000,0x00000000 # 10 ^ 2
long 0x400C0000,0x9C400000,0x00000000 # 10 ^ 4
long 0x40190000,0xBEBC2000,0x00000000 # 10 ^ 8
long 0x40340000,0x8E1BC9BF,0x04000000 # 10 ^ 16
long 0x40690000,0x9DC5ADA8,0x2B70B59D # 10 ^ 32
long 0x40D30000,0xC2781F49,0xFFCFA6D5 # 10 ^ 64
long 0x41A80000,0x93BA47C9,0x80E98CDF # 10 ^ 128
long 0x43510000,0xAA7EEBFB,0x9DF9DE8D # 10 ^ 256
long 0x46A30000,0xE319A0AE,0xA60E91C6 # 10 ^ 512
long 0x4D480000,0xC9767586,0x81750C17 # 10 ^ 1024
long 0x5A920000,0x9E8B3B5D,0xC53D5DE4 # 10 ^ 2048
long 0x75250000,0xC4605202,0x8A20979A # 10 ^ 4096
BIGRP:
long 0x3ffe0000,0xb17217f7,0xd1cf79ac # ln(2)
long 0x40000000,0x935d8ddd,0xaaa8ac17 # ln(10)
long 0x3fff0000,0x80000000,0x00000000 # 10 ^ 0
long 0x40020000,0xA0000000,0x00000000 # 10 ^ 1
long 0x40050000,0xC8000000,0x00000000 # 10 ^ 2
long 0x400C0000,0x9C400000,0x00000000 # 10 ^ 4
long 0x40190000,0xBEBC2000,0x00000000 # 10 ^ 8
long 0x40340000,0x8E1BC9BF,0x04000000 # 10 ^ 16
long 0x40690000,0x9DC5ADA8,0x2B70B59E # 10 ^ 32
long 0x40D30000,0xC2781F49,0xFFCFA6D6 # 10 ^ 64
long 0x41A80000,0x93BA47C9,0x80E98CE0 # 10 ^ 128
long 0x43510000,0xAA7EEBFB,0x9DF9DE8E # 10 ^ 256
long 0x46A30000,0xE319A0AE,0xA60E91C7 # 10 ^ 512
long 0x4D480000,0xC9767586,0x81750C18 # 10 ^ 1024
long 0x5A920000,0x9E8B3B5D,0xC53D5DE5 # 10 ^ 2048
long 0x75250000,0xC4605202,0x8A20979B # 10 ^ 4096
#########################################################################
# sscale(): computes the destination operand scaled by the source #
# operand. If the absoulute value of the source operand is #
# >= 2^14, an overflow or underflow is returned. #
# #
# INPUT *************************************************************** #
# a0 = pointer to double-extended source operand X #
# a1 = pointer to double-extended destination operand Y #
# #
# OUTPUT ************************************************************** #
# fp0 = scale(X,Y) #
# #
#########################################################################
set SIGN, L_SCR1
global sscale
sscale:
mov.l %d0,-(%sp) # store off ctrl bits for now
mov.w DST_EX(%a1),%d1 # get dst exponent
smi.b SIGN(%a6) # use SIGN to hold dst sign
andi.l &0x00007fff,%d1 # strip sign from dst exp
mov.w SRC_EX(%a0),%d0 # check src bounds
andi.w &0x7fff,%d0 # clr src sign bit
cmpi.w %d0,&0x3fff # is src ~ ZERO?
blt.w src_small # yes
cmpi.w %d0,&0x400c # no; is src too big?
bgt.w src_out # yes
#
# Source is within 2^14 range.
#
src_ok:
fintrz.x SRC(%a0),%fp0 # calc int of src
fmov.l %fp0,%d0 # int src to d0
# don't want any accrued bits from the fintrz showing up later since
# we may need to read the fpsr for the last fp op in t_catch2().
fmov.l &0x0,%fpsr
tst.b DST_HI(%a1) # is dst denormalized?
bmi.b sok_norm
# the dst is a DENORM. normalize the DENORM and add the adjustment to
# the src value. then, jump to the norm part of the routine.
sok_dnrm:
mov.l %d0,-(%sp) # save src for now
mov.w DST_EX(%a1),FP_SCR0_EX(%a6) # make a copy
mov.l DST_HI(%a1),FP_SCR0_HI(%a6)
mov.l DST_LO(%a1),FP_SCR0_LO(%a6)
lea FP_SCR0(%a6),%a0 # pass ptr to DENORM
bsr.l norm # normalize the DENORM
neg.l %d0
add.l (%sp)+,%d0 # add adjustment to src
cmpi.w %d0,&-0x3fff # is the shft amt really low?
bge.b sok_norm2 # thank goodness no
# the multiply factor that we're trying to create should be a denorm
# for the multiply to work. Therefore, we're going to actually do a
# multiply with a denorm which will cause an unimplemented data type
# exception to be put into the machine which will be caught and corrected
# later. we don't do this with the DENORMs above because this method
# is slower. but, don't fret, I don't see it being used much either.
fmov.l (%sp)+,%fpcr # restore user fpcr
mov.l &0x80000000,%d1 # load normalized mantissa
subi.l &-0x3fff,%d0 # how many should we shift?
neg.l %d0 # make it positive
cmpi.b %d0,&0x20 # is it > 32?
bge.b sok_dnrm_32 # yes
lsr.l %d0,%d1 # no; bit stays in upper lw clr.l -(%sp) # insert zero low mantissa
mov.l %d1,-(%sp) # insert new high mantissa clr.l -(%sp) # make zero exponent
bra.b sok_norm_cont
sok_dnrm_32:
subi.b &0x20,%d0 # get shift count
lsr.l %d0,%d1 # make low mantissa longword
mov.l %d1,-(%sp) # insert new low mantissa clr.l -(%sp) # insert zero high mantissa clr.l -(%sp) # make zero exponent
bra.b sok_norm_cont
# the src will force the dst to a DENORM value or worse. so, let's
# create an fp multiply that will create the result.
sok_norm:
fmovm.x DST(%a1),&0x80 # load fp0 with normalized src
sok_norm2:
fmov.l (%sp)+,%fpcr # restore user fpcr
addi.w &0x3fff,%d0 # turn src amt into exp value
swap %d0 # put exponent in high word clr.l -(%sp) # insert new exponent
mov.l &0x80000000,-(%sp) # insert new high mantissa
mov.l %d0,-(%sp) # insert new lo mantissa
sok_norm_cont:
fmov.l %fpcr,%d0 # d0 needs fpcr for t_catch2
mov.b &FMUL_OP,%d1 # last inst is MUL
fmul.x (%sp)+,%fp0 # do the multiply
bra t_catch2 # catch any exceptions
#
# Source is outside of 2^14 range. Test the sign and branch
# to the appropriate exception handler.
#
src_out:
mov.l (%sp)+,%d0 # restore ctrl bits
exg %a0,%a1 # swap src,dst ptrs
tst.b SRC_EX(%a1) # is src negative?
bmi t_unfl # yes; underflow
bra t_ovfl_sc # no; overflow
#
# The source input is below 1, so we check for denormalized numbers
# and set unfl.
#
src_small:
tst.b DST_HI(%a1) # is dst denormalized?
bpl.b ssmall_done # yes
mov.l (%sp)+,%d0
fmov.l %d0,%fpcr # no; load control bits
mov.b &FMOV_OP,%d1 # last inst is MOVE
fmov.x DST(%a1),%fp0 # simply return dest
bra t_catch2
ssmall_done:
mov.l (%sp)+,%d0 # load control bits into d1
mov.l %a1,%a0 # pass ptr to dst
bra t_resdnrm
#########################################################################
# smod(): computes the fp MOD of the input values X,Y. #
# srem(): computes the fp (IEEE) REM of the input values X,Y. #
# #
# INPUT *************************************************************** #
# a0 = pointer to extended precision input X #
# a1 = pointer to extended precision input Y #
# d0 = round precision,mode #
# #
# The input operands X and Y can be either normalized or #
# denormalized. #
# #
# OUTPUT ************************************************************** #
# fp0 = FREM(X,Y) or FMOD(X,Y) #
# #
# ALGORITHM *********************************************************** #
# #
# Step 1. Save and strip signs of X and Y: signX := sign(X), #
# signY := sign(Y), X := |X|, Y := |Y|, #
# signQ := signX EOR signY. Record whether MOD or REM #
# is requested. #
# #
# Step 2. Set L := expo(X)-expo(Y), k := 0, Q := 0. #
# If (L < 0) then #
# R := X, go to Step 4. #
# else #
# R := 2^(-L)X, j := L. #
# endif #
# #
# Step 3. Perform MOD(X,Y) #
# 3.1 If R = Y, go to Step 9. #
# 3.2 If R > Y, then { R := R - Y, Q := Q + 1} #
# 3.3 If j = 0, go to Step 4. #
# 3.4 k := k + 1, j := j - 1, Q := 2Q, R := 2R. Go to #
# Step 3.1. #
# #
# Step 4. At this point, R = X - QY = MOD(X,Y). Set #
# Last_Subtract := false (used in Step 7 below). If #
# MOD is requested, go to Step 6. #
# #
# Step 5. R = MOD(X,Y), but REM(X,Y) is requested. #
# 5.1 If R < Y/2, then R = MOD(X,Y) = REM(X,Y). Go to #
# Step 6. #
# 5.2 If R > Y/2, then { set Last_Subtract := true, #
# Q := Q + 1, Y := signY*Y }. Go to Step 6. #
# 5.3 This is the tricky case of R = Y/2. If Q is odd, #
# then { Q := Q + 1, signX := -signX }. #
# #
# Step 6. R := signX*R. #
# #
# Step 7. If Last_Subtract = true, R := R - Y. #
# #
# Step 8. Return signQ, last 7 bits of Q, and R as required. #
# #
# Step 9. At this point, R = 2^(-j)*X - Q Y = Y. Thus, #
# X = 2^(j)*(Q+1)Y. set Q := 2^(j)*(Q+1), #
# R := 0. Return signQ, last 7 bits of Q, and R. #
# #
#########################################################################
set Mod_Flag,L_SCR3 set Sc_Flag,L_SCR3+1
set SignY,L_SCR2 set SignX,L_SCR2+2 set SignQ,L_SCR3+2
set Y,FP_SCR0 set Y_Hi,Y+4 set Y_Lo,Y+8
set R,FP_SCR1 set R_Hi,R+4 set R_Lo,R+8
Scale:
long 0x00010000,0x80000000,0x00000000,0x00000000
global smod
smod: clr.b FPSR_QBYTE(%a6)
mov.l %d0,-(%sp) # save ctrl bits clr.b Mod_Flag(%a6)
bra.b Mod_Rem
global srem
srem: clr.b FPSR_QBYTE(%a6)
mov.l %d0,-(%sp) # save ctrl bits
mov.b &0x1,Mod_Flag(%a6)
Mod_Rem:
#..Save sign of X and Y
movm.l &0x3f00,-(%sp) # save data registers
mov.w SRC_EX(%a0),%d3
mov.w %d3,SignY(%a6)
and.l &0x00007FFF,%d3 # Y := |Y|
#
mov.l SRC_HI(%a0),%d4
mov.l SRC_LO(%a0),%d5 # (D3,D4,D5) is |Y|
Mod_Loop_pre:
addq.l &0x4,%sp # erase exp(X)
#..At this point R = 2^(-L)X; Q = 0; k = 0; and k+j = L
Mod_Loop:
tst.l %d6 # test carry bit
bgt.b R_GT_Y
#..At this point carry = 0, R = (D1,D2), Y = (D4,D5)
cmp.l %d1,%d4 # compare hi(R) and hi(Y)
bne.b R_NE_Y
cmp.l %d2,%d5 # compare lo(R) and lo(Y)
bne.b R_NE_Y
#..At this point, R = Y
bra.w Rem_is_0
R_NE_Y:
#..use the borrow of the previous compare
bcs.b R_LT_Y # borrow is set iff R < Y
R_GT_Y:
#..If Carry is set, then Y < (Carry,D1,D2) < 2Y. Otherwise, Carry = 0
#..and Y < (D1,D2) < 2Y. Either way, perform R - Y sub.l %d5,%d2 # lo(R) - lo(Y)
subx.l %d4,%d1 # hi(R) - hi(Y) clr.l %d6 # clear carry
addq.l &1,%d3 # Q := Q + 1
R_LT_Y:
#..At this point, Carry=0, R < Y. R = 2^(k-L)X - QY; k+j = L; j >= 0.
tst.l %d0 # see if j = 0.
beq.b PostLoop
add.l %d3,%d3 # Q := 2Q
add.l %d2,%d2 # lo(R) = 2lo(R)
roxl.l &1,%d1 # hi(R) = 2hi(R) + carry
scs %d6 # set Carry if 2(R) overflows
addq.l &1,%a1 # k := k+1
subq.l &1,%d0 # j := j - 1
#..At this point, R=(Carry,D1,D2) = 2^(k-L)X - QY, j+k=L, j >= 0, R < 2Y.
bra.b Mod_Loop
PostLoop:
#..k = L, j = 0, Carry = 0, R = (D1,D2) = X - QY, R < Y.
#..normalize R.
mov.l L_SCR1(%a6),%d0 # new biased expo of R
tst.l %d1
bne.b HiR_not0
#
Fix_Sign:
#..Get sign of X
mov.w SignX(%a6),%d6
bge.b Get_Q
fneg.x %fp0
#..Get Q
#
Get_Q: clr.l %d6
mov.w SignQ(%a6),%d6 # D6 is sign(Q)
mov.l &8,%d7
lsr.l %d7,%d6
and.l &0x0000007F,%d3 # 7 bits of Q
or.l %d6,%d3 # sign and bits of Q
# swap %d3
# fmov.l %fpsr,%d6
# and.l &0xFF00FFFF,%d6
# or.l %d3,%d6
# fmov.l %d6,%fpsr # put Q in fpsr
mov.b %d3,FPSR_QBYTE(%a6) # put Q in fpsr
#
Restore:
movm.l (%sp)+,&0xfc # {%d2-%d7}
mov.l (%sp)+,%d0
fmov.l %d0,%fpcr
tst.b Sc_Flag(%a6)
beq.b Finish
mov.b &FMUL_OP,%d1 # last inst is MUL
fmul.x Scale(%pc),%fp0 # may cause underflow
bra t_catch2
# the '040 package did this apparently to see if the dst operand for the
# preceding fmul was a denorm. but, it better not have been since the
# algorithm just got done playing with fp0 and expected no exceptions
# as a result. trust me...
# bra t_avoid_unsupp # check for denorm as a
# ;result of the scaling
Finish:
mov.b &FMOV_OP,%d1 # last inst is MOVE
fmov.x %fp0,%fp0 # capture exceptions & round
bra t_catch2
Rem_is_0:
#..R = 2^(-j)X - Q Y = Y, thus R = 0 and quotient = 2^j (Q+1)
addq.l &1,%d3
cmp.l %d0,&8 # D0 is j
bge.b Q_Big
#########################################################################
# XDEF **************************************************************** #
# t_dz(): Handle DZ exception during transcendental emulation. #
# Sets N bit according to sign of source operand. #
# t_dz2(): Handle DZ exception during transcendental emulation. #
# Sets N bit always. #
# #
# XREF **************************************************************** #
# None #
# #
# INPUT *************************************************************** #
# a0 = pointer to source operand #
# #
# OUTPUT ************************************************************** #
# fp0 = default result #
# #
# ALGORITHM *********************************************************** #
# - Store properly signed INF into fp0. #
# - Set FPSR exception status dz bit, ccode inf bit, and #
# accrued dz bit. #
# #
#########################################################################
global t_dz
t_dz:
tst.b SRC_EX(%a0) # no; is src negative?
bmi.b t_dz2 # yes
dz_pinf:
fmov.s &0x7f800000,%fp0 # return +INF in fp0
ori.l &dzinf_mask,USER_FPSR(%a6) # set I/DZ/ADZ
rts
global t_dz2
t_dz2:
fmov.s &0xff800000,%fp0 # return -INF in fp0
ori.l &dzinf_mask+neg_mask,USER_FPSR(%a6) # set N/I/DZ/ADZ
rts
#################################################################
# OPERR exception: #
# - set FPSR exception status operr bit, condition code #
# nan bit; Store default NAN into fp0 #
################################################################# global t_operr
t_operr:
ori.l &opnan_mask,USER_FPSR(%a6) # set NaN/OPERR/AIOP
fmovm.x qnan(%pc),&0x80 # return default NAN in fp0
rts
#################################################################
# Extended DENORM: #
# - For all functions that have a denormalized input and #
# that f(x)=x, this is the entry point. #
# - we only return the EXOP here if either underflow or #
# inexact is enabled. #
#################################################################
# Entry point for scale w/ extended denorm. The function does
# NOT set INEX2/AUNFL/AINEX. global t_resdnrm
t_resdnrm:
ori.l &unfl_mask,USER_FPSR(%a6) # set UNFL
bra.b xdnrm_con
global t_extdnrm
t_extdnrm:
ori.l &unfinx_mask,USER_FPSR(%a6) # set UNFL/INEX2/AUNFL/AINEX
xdnrm_con:
mov.l %a0,%a1 # make copy of src ptr
mov.l %d0,%d1 # make copy of rnd prec,mode
andi.b &0xc0,%d1 # extended precision?
bne.b xdnrm_sd # no
# result precision is extended.
tst.b LOCAL_EX(%a0) # is denorm negative?
bpl.b xdnrm_exit # no
bset &neg_bit,FPSR_CC(%a6) # yes; set'N' ccode bit
bra.b xdnrm_exit
# result precision is single or double
xdnrm_sd:
mov.l %a1,-(%sp)
tst.b LOCAL_EX(%a0) # is denorm pos or neg?
smi.b %d1 # set d0 accordingly
bsr.l unf_sub
mov.l (%sp)+,%a1
xdnrm_exit:
fmovm.x (%a0),&0x80 # return default result in fp0
mov.b FPCR_ENABLE(%a6),%d0
andi.b &0x0a,%d0 # is UNFL or INEX enabled?
bne.b xdnrm_ena # yes
rts
################
# unfl enabled #
################
# we have a DENORM that needs to be converted into an EXOP.
# so, normalize the mantissa, add 0x6000 to the new exponent,
# and return the result in fp1.
xdnrm_ena:
mov.w LOCAL_EX(%a1),FP_SCR0_EX(%a6)
mov.l LOCAL_HI(%a1),FP_SCR0_HI(%a6)
mov.l LOCAL_LO(%a1),FP_SCR0_LO(%a6)
lea FP_SCR0(%a6),%a0
bsr.l norm # normalize mantissa
addi.l &0x6000,%d0 # add extra bias
andi.w &0x8000,FP_SCR0_EX(%a6) # keep old sign
or.w %d0,FP_SCR0_EX(%a6) # insert new exponent
fmovm.x FP_SCR0(%a6),&0x40 # return EXOP in fp1
rts
#################################################################
# UNFL exception: #
# - This routine is for cases where even an EXOP isn't #
# large enough to hold the range of this result. #
# In such a case, the EXOP equals zero. #
# - Return the default result to the proper precision #
# with the sign of this result being the same as that #
# of the src operand. #
# - t_unfl2() is provided to force the result sign to #
# positive which is the desired result for fetox(). #
################################################################# global t_unfl
t_unfl:
ori.l &unfinx_mask,USER_FPSR(%a6) # set UNFL/INEX2/AUNFL/AINEX
tst.b (%a0) # is result pos or neg?
smi.b %d1 # set d1 accordingly
bsr.l unf_sub # calc default unfl result
fmovm.x (%a0),&0x80 # return default result in fp0
fmov.s &0x00000000,%fp1 # return EXOP in fp1
rts
# t_unfl2 ALWAYS tells unf_sub to create a positive result global t_unfl2
t_unfl2:
ori.l &unfinx_mask,USER_FPSR(%a6) # set UNFL/INEX2/AUNFL/AINEX
sf.b %d1 # set d0 to represent positive
bsr.l unf_sub # calc default unfl result
fmovm.x (%a0),&0x80 # return default result in fp0
fmov.s &0x0000000,%fp1 # return EXOP in fp1
rts
#################################################################
# OVFL exception: #
# - This routine is for cases where even an EXOP isn't #
# large enough to hold the range of this result. #
# - Return the default result to the proper precision #
# with the sign of this result being the same as that #
# of the src operand. #
# - t_ovfl2() is provided to force the result sign to #
# positive which is the desired result for fcosh(). #
# - t_ovfl_sc() is provided for scale() which only sets #
# the inexact bits if the number is inexact for the #
# precision indicated. #
#################################################################
global t_ovfl_sc
t_ovfl_sc:
ori.l &ovfl_inx_mask,USER_FPSR(%a6) # set OVFL/AOVFL/AINEX
tst.b LOCAL_HI(%a0) # is dst a DENORM?
bmi.b ovfl_sc_norm # no
# dst op is a DENORM. we have to normalize the mantissa to see if the
# result would be inexact for the given precision. make a copy of the
# dst so we don't screw up the version passed to us.
mov.w LOCAL_EX(%a0),FP_SCR0_EX(%a6)
mov.l LOCAL_HI(%a0),FP_SCR0_HI(%a6)
mov.l LOCAL_LO(%a0),FP_SCR0_LO(%a6)
lea FP_SCR0(%a6),%a0 # pass ptr to FP_SCR0
movm.l &0xc080,-(%sp) # save d0-d1/a0
bsr.l norm # normalize mantissa
movm.l (%sp)+,&0x0103 # restore d0-d1/a0
ovfl_sc_norm:
cmpi.b %d1,&0x40 # is prec dbl?
bne.b ovfl_sc_dbl # no; sgl
ovfl_sc_sgl:
tst.l LOCAL_LO(%a0) # is lo lw of sgl set?
bne.b ovfl_sc_inx # yes
tst.b 3+LOCAL_HI(%a0) # is lo byte of hi lw set?
bne.b ovfl_sc_inx # yes
bra.b ovfl_work # don't set INEX2
ovfl_sc_dbl:
mov.l LOCAL_LO(%a0),%d1 # are any of lo 11 bits of
andi.l &0x7ff,%d1 # dbl mantissa set?
beq.b ovfl_work # no; don't set INEX2
ovfl_sc_inx:
ori.l &inex2_mask,USER_FPSR(%a6) # set INEX2
bra.b ovfl_work # continue
global t_ovfl
t_ovfl:
ori.l &ovfinx_mask,USER_FPSR(%a6) # set OVFL/INEX2/AOVFL/AINEX
ovfl_work:
tst.b LOCAL_EX(%a0) # what is the sign?
smi.b %d1 # set d1 accordingly
bsr.l ovf_res # calc default ovfl result
mov.b %d0,FPSR_CC(%a6) # insert new ccodes
fmovm.x (%a0),&0x80 # return default result in fp0
fmov.s &0x00000000,%fp1 # return EXOP in fp1
rts
# t_ovfl2 ALWAYS tells ovf_res to create a positive result global t_ovfl2
t_ovfl2:
ori.l &ovfinx_mask,USER_FPSR(%a6) # set OVFL/INEX2/AOVFL/AINEX
sf.b %d1 # clear sign flag for positive
bsr.l ovf_res # calc default ovfl result
mov.b %d0,FPSR_CC(%a6) # insert new ccodes
fmovm.x (%a0),&0x80 # return default result in fp0
fmov.s &0x00000000,%fp1 # return EXOP in fp1
rts
#################################################################
# t_catch(): #
# - the last operation of a transcendental emulation #
# routine may have caused an underflow or overflow. #
# we find out if this occurred by doing an fsave and #
# checking the exception bit. if one did occur, then we #
# jump to fgen_except() which creates the default #
# result and EXOP for us. #
################################################################# global t_catch
t_catch:
#################################################################
# INEX2 exception: #
# - The inex2 and ainex bits are set. #
################################################################# global t_inx2
t_inx2:
fblt.w t_minx2
fbeq.w inx2_zero
global t_pinx2
t_pinx2:
ori.w &inx2a_mask,2+USER_FPSR(%a6) # set INEX2/AINEX
rts
global t_minx2
t_minx2:
ori.l &inx2a_mask+neg_mask,USER_FPSR(%a6) # set N/INEX2/AINEX
rts
inx2_zero:
mov.b &z_bmask,FPSR_CC(%a6)
ori.w &inx2a_mask,2+USER_FPSR(%a6) # set INEX2/AINEX
rts
# an underflow or overflow exception occurred.
# we must set INEX/AINEX since the fmul/fdiv/fmov emulation may not!
catch:
ori.w &inx2a_mask,FPSR_EXCEPT(%a6)
catch2:
bsr.l fgen_except
add.l &0xc,%sp
rts
#########################################################################
# src_zero(): Return signed zero according to sign of src operand. #
######################################################################### global src_zero
src_zero:
tst.b SRC_EX(%a0) # get sign of src operand
bmi.b ld_mzero # if neg, load neg zero
#
# ld_pzero(): return a positive zero.
# global ld_pzero
ld_pzero:
fmov.s &0x00000000,%fp0 # load +0
mov.b &z_bmask,FPSR_CC(%a6) # set'Z' ccode bit
rts
#########################################################################
# dst_zero(): Return signed zero according to sign of dst operand. #
######################################################################### global dst_zero
dst_zero:
tst.b DST_EX(%a1) # get sign of dst operand
bmi.b ld_mzero # if neg, load neg zero
bra.b ld_pzero # load positive zero
#########################################################################
# src_inf(): Return signed inf according to sign of src operand. #
######################################################################### global src_inf
src_inf:
tst.b SRC_EX(%a0) # get sign of src operand
bmi.b ld_minf # if negative branch
#
# ld_pinf(): return a positive infinity.
# global ld_pinf
ld_pinf:
fmov.s &0x7f800000,%fp0 # load +INF
mov.b &inf_bmask,FPSR_CC(%a6) # set'INF' ccode bit
rts
#########################################################################
# dst_inf(): Return signed inf according to sign of dst operand. #
######################################################################### global dst_inf
dst_inf:
tst.b DST_EX(%a1) # get sign of dst operand
bmi.b ld_minf # if negative branch
bra.b ld_pinf
global szr_inf
#################################################################
# szr_inf(): Return +ZERO for a negative src operand or #
# +INF for a positive src operand. #
# Routine used for fetox, ftwotox, and ftentox. #
#################################################################
szr_inf:
tst.b SRC_EX(%a0) # check sign of source
bmi.b ld_pzero
bra.b ld_pinf
#########################################################################
# sopr_inf(): Return +INF for a positive src operand or #
# jump to operand error routine for a negative src operand. #
# Routine used for flogn, flognp1, flog10, and flog2. #
######################################################################### global sopr_inf
sopr_inf:
tst.b SRC_EX(%a0) # check sign of source
bmi.w t_operr
bra.b ld_pinf
#################################################################
# setoxm1i(): Return minus one for a negative src operand or #
# positive infinity for a positive src operand. #
# Routine used for fetoxm1. #
################################################################# global setoxm1i
setoxm1i:
tst.b SRC_EX(%a0) # check sign of source
bmi.b ld_mone
bra.b ld_pinf
#########################################################################
# src_one(): Return signed one according to sign of src operand. #
######################################################################### global src_one
src_one:
tst.b SRC_EX(%a0) # check sign of source
bmi.b ld_mone
ppiby2: long 0x3fff0000, 0xc90fdaa2, 0x2168c235
mpiby2: long 0xbfff0000, 0xc90fdaa2, 0x2168c235
#################################################################
# spi_2(): Return signed PI/2 according to sign of src operand. #
################################################################# global spi_2
spi_2:
tst.b SRC_EX(%a0) # check sign of source
bmi.b ld_mpi2
####################################################
# The following routines give support for fsincos. #
####################################################
#
# ssincosz(): When the src operand is ZERO, store a one in the
# cosine register and return a ZERO in fp0 w/ the same sign
# as the src operand.
# global ssincosz
ssincosz:
fmov.s &0x3f800000,%fp1
tst.b SRC_EX(%a0) # test sign
bpl.b sincoszp
fmov.s &0x80000000,%fp0 # return sin result in fp0
mov.b &z_bmask+neg_bmask,FPSR_CC(%a6)
bra.b sto_cos # store cosine result
sincoszp:
fmov.s &0x00000000,%fp0 # return sin result in fp0
mov.b &z_bmask,FPSR_CC(%a6)
bra.b sto_cos # store cosine result
#
# ssincosi(): When the src operand is INF, store a QNAN in the cosine
# register and jump to the operand error routine for negative
# src operands.
# global ssincosi
ssincosi:
fmov.x qnan(%pc),%fp1 # load NAN
bsr.l sto_cos # store cosine result
bra.w t_operr
#
# ssincosqnan(): When the src operand is a QNAN, store the QNAN in the cosine
# register and branch to the src QNAN routine.
# global ssincosqnan
ssincosqnan:
fmov.x LOCAL_EX(%a0),%fp1
bsr.l sto_cos
bra.w src_qnan
#
# ssincossnan(): When the src operand is an SNAN, store the SNAN w/ the SNAN bit set
# in the cosine register and branch to the src SNAN routine.
# global ssincossnan
ssincossnan:
fmov.x LOCAL_EX(%a0),%fp1
bsr.l sto_cos
bra.w src_snan
#########################################################################
# sto_cos(): store fp1 to the fpreg designated by the CMDREG dst field. #
# fp1 holds the result of the cosine portion of ssincos(). #
# the value in fp1 will not take any exceptions when moved. #
# INPUT: #
# fp1 : fp value to store #
# MODIFIED: #
# d0 #
######################################################################### global sto_cos
sto_cos:
mov.b 1+EXC_CMDREG(%a6),%d0
andi.w &0x7,%d0
mov.w (tbl_sto_cos.b,%pc,%d0.w*2),%d0
jmp (tbl_sto_cos.b,%pc,%d0.w*1)
tbl_sto_cos:
short sto_cos_0 - tbl_sto_cos
short sto_cos_1 - tbl_sto_cos
short sto_cos_2 - tbl_sto_cos
short sto_cos_3 - tbl_sto_cos
short sto_cos_4 - tbl_sto_cos
short sto_cos_5 - tbl_sto_cos
short sto_cos_6 - tbl_sto_cos
short sto_cos_7 - tbl_sto_cos
#
# sop_sqnan(): The src op for frem/fmod/fscale was a QNAN.
# global sop_sqnan
sop_sqnan:
mov.b DTAG(%a6),%d1
cmpi.b %d1,&QNAN
beq.b dst_qnan
cmpi.b %d1,&SNAN
beq.b dst_snan
bra.b src_qnan
#
# sop_ssnan(): The src op for frem/fmod/fscale was an SNAN.
# global sop_ssnan
sop_ssnan:
mov.b DTAG(%a6),%d1
cmpi.b %d1,&QNAN
beq.b dst_qnan_src_snan
cmpi.b %d1,&SNAN
beq.b dst_snan
bra.b src_snan
dst_qnan_src_snan:
ori.l &snaniop_mask,USER_FPSR(%a6) # set NAN/SNAN/AIOP
bra.b dst_qnan
#
# dst_qnan(): Return the dst SNAN w/ the SNAN bit set.
# global dst_snan
dst_snan:
fmov.x DST(%a1),%fp0 # the fmove sets the SNAN bit
fmov.l %fpsr,%d0 # catch resulting status
or.l %d0,USER_FPSR(%a6) # store status
rts
#
# dst_qnan(): Return the dst QNAN.
# global dst_qnan
dst_qnan:
fmov.x DST(%a1),%fp0 # return the non-signalling nan
tst.b DST_EX(%a1) # set ccodes according to QNAN sign
bmi.b dst_qnan_m
dst_qnan_p:
mov.b &nan_bmask,FPSR_CC(%a6)
rts
dst_qnan_m:
mov.b &neg_bmask+nan_bmask,FPSR_CC(%a6)
rts
#
# src_snan(): Return the src SNAN w/ the SNAN bit set.
# global src_snan
src_snan:
fmov.x SRC(%a0),%fp0 # the fmove sets the SNAN bit
fmov.l %fpsr,%d0 # catch resulting status
or.l %d0,USER_FPSR(%a6) # store status
rts
#
# src_qnan(): Return the src QNAN.
# global src_qnan
src_qnan:
fmov.x SRC(%a0),%fp0 # return the non-signalling nan
tst.b SRC_EX(%a0) # set ccodes according to QNAN sign
bmi.b dst_qnan_m
src_qnan_p:
mov.b &nan_bmask,FPSR_CC(%a6)
rts
src_qnan_m:
mov.b &neg_bmask+nan_bmask,FPSR_CC(%a6)
rts
#
# fkern2.s:
# These entry points are used by the exception handler
# routines where an instruction is selected by an index into
# a large jump table corresponding to a given instruction which
# has been decoded. Flow continues here where we now decode
# further according to the source operand type.
#
#########################################################################
# XDEF **************************************************************** #
# fgen_except(): catch an exception during transcendental #
# emulation #
# #
# XREF **************************************************************** #
# fmul() - emulate a multiply instruction #
# fadd() - emulate an add instruction #
# fin() - emulate an fmove instruction #
# #
# INPUT *************************************************************** #
# fp0 = destination operand #
# d0 = type of instruction that took exception #
# fsave frame = source operand #
# #
# OUTPUT ************************************************************** #
# fp0 = result #
# fp1 = EXOP #
# #
# ALGORITHM *********************************************************** #
# An exception occurred on the last instruction of the #
# transcendental emulation. hopefully, this won't be happening much #
# because it will be VERY slow. #
# The only exceptions capable of passing through here are #
# Overflow, Underflow, and Unsupported Data Type. #
# #
#########################################################################
global fgen_except
fgen_except:
cmpi.b 0x3(%sp),&0x7 # is exception UNSUPP?
beq.b fge_unsupp # yes
mov.b &NORM,STAG(%a6)
fge_cont:
mov.b &NORM,DTAG(%a6)
# ok, I have a problem with putting the dst op at FP_DST. the emulation
# routines aren't supposed to alter the operands but we've just squashed
# FP_DST here...
# 8/17/93 - this turns out to be more of a "cleanliness" standpoint
# then a potential bug. to begin with, only the dyadic functions
# frem,fmod, and fscale would get the dst trashed here. But, for
# the 060SP, the FP_DST is never used again anyways.
fmovm.x &0x80,FP_DST(%a6) # dst op is in fp0
lea 0x4(%sp),%a0 # pass: ptr to src op
lea FP_DST(%a6),%a1 # pass: ptr to dst op
cmpi.b %d1,&FMOV_OP
beq.b fge_fin # it was an "fmov"
cmpi.b %d1,&FADD_OP
beq.b fge_fadd # it was an "fadd"
fge_fmul:
bsr.l fmul
rts
fge_fadd:
bsr.l fadd
rts
fge_fin:
bsr.l fin
rts
#
# This table holds the offsets of the emulation routines for each individual
# math operation relative to the address of this table. Included are
# routines like fadd/fmul/fabs as well as the transcendentals.
# The location within the table is determined by the extension bits of the
# operation longword.
#
swbeg &109
tbl_unsupp:
long fin - tbl_unsupp # 00: fmove
long fint - tbl_unsupp # 01: fint
long fsinh - tbl_unsupp # 02: fsinh
long fintrz - tbl_unsupp # 03: fintrz
long fsqrt - tbl_unsupp # 04: fsqrt
long tbl_unsupp - tbl_unsupp
long flognp1 - tbl_unsupp # 06: flognp1
long tbl_unsupp - tbl_unsupp
long fetoxm1 - tbl_unsupp # 08: fetoxm1
long ftanh - tbl_unsupp # 09: ftanh
long fatan - tbl_unsupp # 0a: fatan
long tbl_unsupp - tbl_unsupp
long fasin - tbl_unsupp # 0c: fasin
long fatanh - tbl_unsupp # 0d: fatanh
long fsine - tbl_unsupp # 0e: fsin
long ftan - tbl_unsupp # 0f: ftan
long fetox - tbl_unsupp # 10: fetox
long ftwotox - tbl_unsupp # 11: ftwotox
long ftentox - tbl_unsupp # 12: ftentox
long tbl_unsupp - tbl_unsupp
long flogn - tbl_unsupp # 14: flogn
long flog10 - tbl_unsupp # 15: flog10
long flog2 - tbl_unsupp # 16: flog2
long tbl_unsupp - tbl_unsupp
long fabs - tbl_unsupp # 18: fabs
long fcosh - tbl_unsupp # 19: fcosh
long fneg - tbl_unsupp # 1a: fneg
long tbl_unsupp - tbl_unsupp
long facos - tbl_unsupp # 1c: facos
long fcos - tbl_unsupp # 1d: fcos
long fgetexp - tbl_unsupp # 1e: fgetexp
long fgetman - tbl_unsupp # 1f: fgetman
long fdiv - tbl_unsupp # 20: fdiv
long fmod - tbl_unsupp # 21: fmod
long fadd - tbl_unsupp # 22: fadd
long fmul - tbl_unsupp # 23: fmul
long fsgldiv - tbl_unsupp # 24: fsgldiv
long frem - tbl_unsupp # 25: frem
long fscale - tbl_unsupp # 26: fscale
long fsglmul - tbl_unsupp # 27: fsglmul
long fsub - tbl_unsupp # 28: fsub
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long fsincos - tbl_unsupp # 30: fsincos
long fsincos - tbl_unsupp # 31: fsincos
long fsincos - tbl_unsupp # 32: fsincos
long fsincos - tbl_unsupp # 33: fsincos
long fsincos - tbl_unsupp # 34: fsincos
long fsincos - tbl_unsupp # 35: fsincos
long fsincos - tbl_unsupp # 36: fsincos
long fsincos - tbl_unsupp # 37: fsincos
long fcmp - tbl_unsupp # 38: fcmp
long tbl_unsupp - tbl_unsupp
long ftst - tbl_unsupp # 3a: ftst
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long fsin - tbl_unsupp # 40: fsmove
long fssqrt - tbl_unsupp # 41: fssqrt
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long fdin - tbl_unsupp # 44: fdmove
long fdsqrt - tbl_unsupp # 45: fdsqrt
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long fsabs - tbl_unsupp # 58: fsabs
long tbl_unsupp - tbl_unsupp
long fsneg - tbl_unsupp # 5a: fsneg
long tbl_unsupp - tbl_unsupp
long fdabs - tbl_unsupp # 5c: fdabs
long tbl_unsupp - tbl_unsupp
long fdneg - tbl_unsupp # 5e: fdneg
long tbl_unsupp - tbl_unsupp
long fsdiv - tbl_unsupp # 60: fsdiv
long tbl_unsupp - tbl_unsupp
long fsadd - tbl_unsupp # 62: fsadd
long fsmul - tbl_unsupp # 63: fsmul
long fddiv - tbl_unsupp # 64: fddiv
long tbl_unsupp - tbl_unsupp
long fdadd - tbl_unsupp # 66: fdadd
long fdmul - tbl_unsupp # 67: fdmul
long fssub - tbl_unsupp # 68: fssub
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long tbl_unsupp - tbl_unsupp
long fdsub - tbl_unsupp # 6c: fdsub
#########################################################################
# XDEF **************************************************************** #
# fmul(): emulates the fmul instruction #
# fsmul(): emulates the fsmul instruction #
# fdmul(): emulates the fdmul instruction #
# #
# XREF **************************************************************** #
# scale_to_zero_src() - scale src exponent to zero #
# scale_to_zero_dst() - scale dst exponent to zero #
# unf_res() - return default underflow result #
# ovf_res() - return default overflow result #
# res_qnan() - return QNAN result #
# res_snan() - return SNAN result #
# #
# INPUT *************************************************************** #
# a0 = pointer to extended precision source operand #
# a1 = pointer to extended precision destination operand #
# d0 rnd prec,mode #
# #
# OUTPUT ************************************************************** #
# fp0 = result #
# fp1 = EXOP (if exception occurred) #
# #
# ALGORITHM *********************************************************** #
# Handle NANs, infinities, and zeroes as special cases. Divide #
# norms/denorms into ext/sgl/dbl precision. #
# For norms/denorms, scale the exponents such that a multiply #
# instruction won't cause an exception. Use the regular fmul to #
# compute a result. Check if the regular operands would have taken #
# an exception. If so, return the default overflow/underflow result #
# and return the EXOP if exceptions are enabled. Else, scale the #
# result operand to the proper exponent. #
# #
#########################################################################
align 0x10
tbl_fmul_ovfl:
long 0x3fff - 0x7ffe # ext_max
long 0x3fff - 0x407e # sgl_max
long 0x3fff - 0x43fe # dbl_max
tbl_fmul_unfl:
long 0x3fff + 0x0001 # ext_unfl
long 0x3fff - 0x3f80 # sgl_unfl
long 0x3fff - 0x3c00 # dbl_unfl
mov.w 2+L_SCR3(%a6),%d1 # fetch precision
lsr.b &0x6,%d1 # shift to lo bits
mov.l (%sp)+,%d0 # load S.F.
cmp.l %d0,(tbl_fmul_ovfl.w,%pc,%d1.w*4) # would result ovfl?
beq.w fmul_may_ovfl # result may rnd to overflow
blt.w fmul_ovfl # result will overflow
cmp.l %d0,(tbl_fmul_unfl.w,%pc,%d1.w*4) # would result unfl?
beq.w fmul_may_unfl # result may rnd to no unfl
bgt.w fmul_unfl # result will underflow
#
# NORMAL:
# - the result of the multiply operation will neither overflow nor underflow.
# - do the multiply to the proper precision and rounding mode.
# - scale the result exponent using the scale factor. if both operands were
# normalized then we really don't need to go through this scaling. but for now,
# this will do.
#
fmul_normal:
fmovm.x FP_SCR1(%a6),&0x80 # load dst operand
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fmov.l &0x0,%fpsr # clear FPSR
fmul.x FP_SCR0(%a6),%fp0 # execute multiply
fmov.l %fpsr,%d1 # save status
fmov.l &0x0,%fpcr # clear FPCR
or.l %d1,USER_FPSR(%a6) # save INEX2,N
fmul_normal_exit:
fmovm.x &0x80,FP_SCR0(%a6) # store out result
mov.l %d2,-(%sp) # save d2
mov.w FP_SCR0_EX(%a6),%d1 # load {sgn,exp}
mov.l %d1,%d2 # make a copy
andi.l &0x7fff,%d1 # strip sign
andi.w &0x8000,%d2 # keep old sign sub.l %d0,%d1 # add scale factor
or.w %d2,%d1 # concat old sign,new exp
mov.w %d1,FP_SCR0_EX(%a6) # insert new exponent
mov.l (%sp)+,%d2 # restore d2
fmovm.x FP_SCR0(%a6),&0x80 # return default result in fp0
rts
#
# OVERFLOW:
# - the result of the multiply operation is an overflow.
# - do the multiply to the proper precision and rounding mode in order to
# set the inexact bits.
# - calculate the default result and return it in fp0.
# - if overflow or inexact is enabled, we need a multiply result rounded to
# extended precision. if the original operation was extended, then we have this
# result. if the original operation was single or double, we have to do another
# multiply using extended precision and the correct rounding mode. the result
# of this operation then has its exponent scaled by -0x6000 to create the
# exceptional operand.
#
fmul_ovfl:
fmovm.x FP_SCR1(%a6),&0x80 # load dst operand
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fmov.l &0x0,%fpsr # clear FPSR
fmul.x FP_SCR0(%a6),%fp0 # execute multiply
fmov.l %fpsr,%d1 # save status
fmov.l &0x0,%fpcr # clear FPCR
or.l %d1,USER_FPSR(%a6) # save INEX2,N
# save setting this until now because this is where fmul_may_ovfl may jump in
fmul_ovfl_tst:
or.l &ovfl_inx_mask,USER_FPSR(%a6) # set ovfl/aovfl/ainex
mov.b FPCR_ENABLE(%a6),%d1
andi.b &0x13,%d1 # is OVFL or INEX enabled?
bne.b fmul_ovfl_ena # yes
# calculate the default result
fmul_ovfl_dis:
btst &neg_bit,FPSR_CC(%a6) # is result negative?
sne %d1 # set sign param accordingly
mov.l L_SCR3(%a6),%d0 # pass rnd prec,mode
bsr.l ovf_res # calculate default result
or.b %d0,FPSR_CC(%a6) # set INF,N if applicable
fmovm.x (%a0),&0x80 # return default result in fp0
rts
#
# OVFL is enabled; Create EXOP:
# - if precision is extended, then we have the EXOP. simply bias the exponent
# with an extra -0x6000. if the precision is single or double, we need to
# calculate a result rounded to extended precision.
#
fmul_ovfl_ena:
mov.l L_SCR3(%a6),%d1
andi.b &0xc0,%d1 # test the rnd prec
bne.b fmul_ovfl_ena_sd # it's sgl or dbl
fmul_ovfl_ena_cont:
fmovm.x &0x80,FP_SCR0(%a6) # move result to stack
mov.l %d2,-(%sp) # save d2
mov.w FP_SCR0_EX(%a6),%d1 # fetch {sgn,exp}
mov.w %d1,%d2 # make a copy
andi.l &0x7fff,%d1 # strip sign sub.l %d0,%d1 # add scale factor
subi.l &0x6000,%d1 # subtract bias
andi.w &0x7fff,%d1 # clear sign bit
andi.w &0x8000,%d2 # keep old sign
or.w %d2,%d1 # concat old sign,new exp
mov.w %d1,FP_SCR0_EX(%a6) # insert new exponent
mov.l (%sp)+,%d2 # restore d2
fmovm.x FP_SCR0(%a6),&0x40 # return EXOP in fp1
bra.b fmul_ovfl_dis
#
# may OVERFLOW:
# - the result of the multiply operation MAY overflow.
# - do the multiply to the proper precision and rounding mode in order to
# set the inexact bits.
# - calculate the default result and return it in fp0.
#
fmul_may_ovfl:
fmovm.x FP_SCR1(%a6),&0x80 # load dst op
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fmov.l &0x0,%fpsr # clear FPSR
fmul.x FP_SCR0(%a6),%fp0 # execute multiply
fmov.l %fpsr,%d1 # save status
fmov.l &0x0,%fpcr # clear FPCR
or.l %d1,USER_FPSR(%a6) # save INEX2,N
fabs.x %fp0,%fp1 # make a copy of result
fcmp.b %fp1,&0x2 # is |result| >= 2.b?
fbge.w fmul_ovfl_tst # yes; overflow has occurred
# no, it didn't overflow; we have correct result
bra.w fmul_normal_exit
#
# UNDERFLOW:
# - the result of the multiply operation is an underflow.
# - do the multiply to the proper precision and rounding mode in order to
# set the inexact bits.
# - calculate the default result and return it in fp0.
# - if overflow or inexact is enabled, we need a multiply result rounded to
# extended precision. if the original operation was extended, then we have this
# result. if the original operation was single or double, we have to do another
# multiply using extended precision and the correct rounding mode. the result
# of this operation then has its exponent scaled by -0x6000 to create the
# exceptional operand.
#
fmul_unfl:
bset &unfl_bit,FPSR_EXCEPT(%a6) # set unfl exc bit
# for fun, let's use only extended precision, round to zero. then, let
# the unf_res() routine figure out all the rest.
# will we get the correct answer.
fmovm.x FP_SCR1(%a6),&0x80 # load dst operand
fmov.l &rz_mode*0x10,%fpcr # set FPCR
fmov.l &0x0,%fpsr # clear FPSR
fmul.x FP_SCR0(%a6),%fp0 # execute multiply
fmov.l %fpsr,%d1 # save status
fmov.l &0x0,%fpcr # clear FPCR
or.l %d1,USER_FPSR(%a6) # save INEX2,N
mov.b FPCR_ENABLE(%a6),%d1
andi.b &0x0b,%d1 # is UNFL or INEX enabled?
bne.b fmul_unfl_ena # yes
fmul_unfl_dis:
fmovm.x &0x80,FP_SCR0(%a6) # store out result
lea FP_SCR0(%a6),%a0 # pass: result addr
mov.l L_SCR3(%a6),%d1 # pass: rnd prec,mode
bsr.l unf_res # calculate default result
or.b %d0,FPSR_CC(%a6) # unf_res2 may have set'Z'
fmovm.x FP_SCR0(%a6),&0x80 # return default result in fp0
rts
#
# UNFL is enabled.
#
fmul_unfl_ena:
fmovm.x FP_SCR1(%a6),&0x40 # load dst op
mov.l L_SCR3(%a6),%d1
andi.b &0xc0,%d1 # is precision extended?
bne.b fmul_unfl_ena_sd # no, sgl or dbl
# if the rnd mode is anything but RZ, then we have to re-do the above
# multiplication because we used RZ for all.
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fmovm.x &0x40,FP_SCR0(%a6) # save result to stack
mov.l %d2,-(%sp) # save d2
mov.w FP_SCR0_EX(%a6),%d1 # fetch {sgn,exp}
mov.l %d1,%d2 # make a copy
andi.l &0x7fff,%d1 # strip sign
andi.w &0x8000,%d2 # keep old sign sub.l %d0,%d1 # add scale factor
addi.l &0x6000,%d1 # add bias
andi.w &0x7fff,%d1
or.w %d2,%d1 # concat old sign,new exp
mov.w %d1,FP_SCR0_EX(%a6) # insert new exponent
mov.l (%sp)+,%d2 # restore d2
fmovm.x FP_SCR0(%a6),&0x40 # return EXOP in fp1
bra.w fmul_unfl_dis
fmul_unfl_ena_sd:
mov.l L_SCR3(%a6),%d1
andi.b &0x30,%d1 # use only rnd mode
fmov.l %d1,%fpcr # set FPCR
bra.b fmul_unfl_ena_cont
# MAY UNDERFLOW:
# -use the correct rounding mode and precision. this code favors operations
# that do not underflow.
fmul_may_unfl:
fmovm.x FP_SCR1(%a6),&0x80 # load dst operand
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fmov.l &0x0,%fpsr # clear FPSR
fmul.x FP_SCR0(%a6),%fp0 # execute multiply
fmov.l %fpsr,%d1 # save status
fmov.l &0x0,%fpcr # clear FPCR
or.l %d1,USER_FPSR(%a6) # save INEX2,N
fabs.x %fp0,%fp1 # make a copy of result
fcmp.b %fp1,&0x2 # is |result| > 2.b?
fbgt.w fmul_normal_exit # no; no underflow occurred
fblt.w fmul_unfl # yes; underflow occurred
#
# we still don't know if underflow occurred. result is ~ equal to 2. but,
# we don't know if the result was an underflow that rounded up to a 2 or
# a normalized number that rounded down to a 2. so, redo the entire operation
# using RZ as the rounding mode to see what the pre-rounded result is.
# this case should be relatively rare.
#
fmovm.x FP_SCR1(%a6),&0x40 # load dst operand
#
# Multiply: inputs are not both normalized; what are they?
#
fmul_not_norm:
mov.w (tbl_fmul_op.b,%pc,%d1.w*2),%d1
jmp (tbl_fmul_op.b,%pc,%d1.w)
swbeg &48
tbl_fmul_op:
short fmul_norm - tbl_fmul_op # NORM x NORM
short fmul_zero - tbl_fmul_op # NORM x ZERO
short fmul_inf_src - tbl_fmul_op # NORM x INF
short fmul_res_qnan - tbl_fmul_op # NORM x QNAN
short fmul_norm - tbl_fmul_op # NORM x DENORM
short fmul_res_snan - tbl_fmul_op # NORM x SNAN
short tbl_fmul_op - tbl_fmul_op #
short tbl_fmul_op - tbl_fmul_op #
short fmul_zero - tbl_fmul_op # ZERO x NORM
short fmul_zero - tbl_fmul_op # ZERO x ZERO
short fmul_res_operr - tbl_fmul_op # ZERO x INF
short fmul_res_qnan - tbl_fmul_op # ZERO x QNAN
short fmul_zero - tbl_fmul_op # ZERO x DENORM
short fmul_res_snan - tbl_fmul_op # ZERO x SNAN
short tbl_fmul_op - tbl_fmul_op #
short tbl_fmul_op - tbl_fmul_op #
short fmul_inf_dst - tbl_fmul_op # INF x NORM
short fmul_res_operr - tbl_fmul_op # INF x ZERO
short fmul_inf_dst - tbl_fmul_op # INF x INF
short fmul_res_qnan - tbl_fmul_op # INF x QNAN
short fmul_inf_dst - tbl_fmul_op # INF x DENORM
short fmul_res_snan - tbl_fmul_op # INF x SNAN
short tbl_fmul_op - tbl_fmul_op #
short tbl_fmul_op - tbl_fmul_op #
short fmul_res_qnan - tbl_fmul_op # QNAN x NORM
short fmul_res_qnan - tbl_fmul_op # QNAN x ZERO
short fmul_res_qnan - tbl_fmul_op # QNAN x INF
short fmul_res_qnan - tbl_fmul_op # QNAN x QNAN
short fmul_res_qnan - tbl_fmul_op # QNAN x DENORM
short fmul_res_snan - tbl_fmul_op # QNAN x SNAN
short tbl_fmul_op - tbl_fmul_op #
short tbl_fmul_op - tbl_fmul_op #
short fmul_norm - tbl_fmul_op # NORM x NORM
short fmul_zero - tbl_fmul_op # NORM x ZERO
short fmul_inf_src - tbl_fmul_op # NORM x INF
short fmul_res_qnan - tbl_fmul_op # NORM x QNAN
short fmul_norm - tbl_fmul_op # NORM x DENORM
short fmul_res_snan - tbl_fmul_op # NORM x SNAN
short tbl_fmul_op - tbl_fmul_op #
short tbl_fmul_op - tbl_fmul_op #
short fmul_res_snan - tbl_fmul_op # SNAN x NORM
short fmul_res_snan - tbl_fmul_op # SNAN x ZERO
short fmul_res_snan - tbl_fmul_op # SNAN x INF
short fmul_res_snan - tbl_fmul_op # SNAN x QNAN
short fmul_res_snan - tbl_fmul_op # SNAN x DENORM
short fmul_res_snan - tbl_fmul_op # SNAN x SNAN
short tbl_fmul_op - tbl_fmul_op #
short tbl_fmul_op - tbl_fmul_op #
#
# Multiply: (Zero x Zero) || (Zero x norm) || (Zero x denorm)
# global fmul_zero # global for fsglmul
fmul_zero:
mov.b SRC_EX(%a0),%d0 # exclusive or the signs
mov.b DST_EX(%a1),%d1
eor.b %d0,%d1
bpl.b fmul_zero_p # result ZERO is pos.
fmul_zero_n:
fmov.s &0x80000000,%fp0 # load -ZERO
mov.b &z_bmask+neg_bmask,FPSR_CC(%a6) # set Z/N
rts
fmul_zero_p:
fmov.s &0x00000000,%fp0 # load +ZERO
mov.b &z_bmask,FPSR_CC(%a6) # set Z
rts
#
# Multiply: (inf x inf) || (inf x norm) || (inf x denorm)
#
# Note: The j-bit for an infinity is a don't-care. However, to be
# strictly compatible w/ the 68881/882, we make sure to return an
# INF w/ the j-bit set if the input INF j-bit was set. Destination
# INFs take priority.
# global fmul_inf_dst # global for fsglmul
fmul_inf_dst:
fmovm.x DST(%a1),&0x80 # return INF result in fp0
mov.b SRC_EX(%a0),%d0 # exclusive or the signs
mov.b DST_EX(%a1),%d1
eor.b %d0,%d1
bpl.b fmul_inf_dst_p # result INF is pos.
fmul_inf_dst_n:
fabs.x %fp0 # clear result sign
fneg.x %fp0 # set result sign
mov.b &inf_bmask+neg_bmask,FPSR_CC(%a6) # set INF/N
rts
fmul_inf_dst_p:
fabs.x %fp0 # clear result sign
mov.b &inf_bmask,FPSR_CC(%a6) # set INF
rts
global fmul_inf_src # global for fsglmul
fmul_inf_src:
fmovm.x SRC(%a0),&0x80 # return INF result in fp0
mov.b SRC_EX(%a0),%d0 # exclusive or the signs
mov.b DST_EX(%a1),%d1
eor.b %d0,%d1
bpl.b fmul_inf_dst_p # result INF is pos.
bra.b fmul_inf_dst_n
#########################################################################
# XDEF **************************************************************** #
# fin(): emulates the fmove instruction #
# fsin(): emulates the fsmove instruction #
# fdin(): emulates the fdmove instruction #
# #
# XREF **************************************************************** #
# norm() - normalize mantissa for EXOP on denorm #
# scale_to_zero_src() - scale src exponent to zero #
# ovf_res() - return default overflow result #
# unf_res() - return default underflow result #
# res_qnan_1op() - return QNAN result #
# res_snan_1op() - return SNAN result #
# #
# INPUT *************************************************************** #
# a0 = pointer to extended precision source operand #
# d0 = round prec/mode #
# #
# OUTPUT ************************************************************** #
# fp0 = result #
# fp1 = EXOP (if exception occurred) #
# #
# ALGORITHM *********************************************************** #
# Handle NANs, infinities, and zeroes as special cases. Divide #
# norms into extended, single, and double precision. #
# Norms can be emulated w/ a regular fmove instruction. For #
# sgl/dbl, must scale exponent and perform an "fmove". Check to see #
# if the result would have overflowed/underflowed. If so, use unf_res() #
# or ovf_res() to return the default result. Also return EXOP if #
# exception is enabled. If no exception, return the default result. #
# Unnorms don't pass through here. #
# #
#########################################################################
global fsin
fsin:
andi.b &0x30,%d0 # clear rnd prec
ori.b &s_mode*0x10,%d0 # insert sgl precision
bra.b fin
global fin
fin:
mov.l %d0,L_SCR3(%a6) # store rnd info
mov.b STAG(%a6),%d1 # fetch src optype tag
bne.w fin_not_norm # optimize on non-norm input
#
# FP MOVE IN: NORMs and DENORMs ONLY!
#
fin_norm:
andi.b &0xc0,%d0 # is precision extended?
bne.w fin_not_ext # no, so go handle dbl or sgl
#
# precision selected is extended. so...we cannot get an underflow
# or overflow because of rounding to the correct precision. so...
# skip the scaling and unscaling...
#
tst.b SRC_EX(%a0) # is the operand negative?
bpl.b fin_norm_done # no
bset &neg_bit,FPSR_CC(%a6) # yes, so set'N' ccode bit
fin_norm_done:
fmovm.x SRC(%a0),&0x80 # return result in fp0
rts
#
# for an extended precision DENORM, the UNFL exception bit is set
# the accrued bit is NOT set in this instance(no inexactness!)
#
fin_denorm:
andi.b &0xc0,%d0 # is precision extended?
bne.w fin_not_ext # no, so go handle dbl or sgl
bset &unfl_bit,FPSR_EXCEPT(%a6) # set unfl exc bit
tst.b SRC_EX(%a0) # is the operand negative?
bpl.b fin_denorm_done # no
bset &neg_bit,FPSR_CC(%a6) # yes, so set'N' ccode bit
fin_denorm_done:
fmovm.x SRC(%a0),&0x80 # return result in fp0
btst &unfl_bit,FPCR_ENABLE(%a6) # is UNFL enabled?
bne.b fin_denorm_unfl_ena # yes
rts
#
# the input is an extended DENORM and underflow is enabled in the FPCR.
# normalize the mantissa and add the bias of 0x6000 to the resulting negative
# exponent and insert back into the operand.
#
fin_denorm_unfl_ena:
mov.w SRC_EX(%a0),FP_SCR0_EX(%a6)
mov.l SRC_HI(%a0),FP_SCR0_HI(%a6)
mov.l SRC_LO(%a0),FP_SCR0_LO(%a6)
lea FP_SCR0(%a6),%a0 # pass: ptr to operand
bsr.l norm # normalize result
neg.w %d0 # new exponent = -(shft val)
addi.w &0x6000,%d0 # add new bias to exponent
mov.w FP_SCR0_EX(%a6),%d1 # fetch old sign,exp
andi.w &0x8000,%d1 # keep old sign
andi.w &0x7fff,%d0 # clear sign position
or.w %d1,%d0 # concat new exo,old sign
mov.w %d0,FP_SCR0_EX(%a6) # insert new exponent
fmovm.x FP_SCR0(%a6),&0x40 # return EXOP in fp1
rts
#
# operand is to be rounded to single or double precision
#
fin_not_ext:
cmpi.b %d0,&s_mode*0x10 # separate sgl/dbl prec
bne.b fin_dbl
#
# operand is to be rounded to single precision
#
fin_sgl:
mov.w SRC_EX(%a0),FP_SCR0_EX(%a6)
mov.l SRC_HI(%a0),FP_SCR0_HI(%a6)
mov.l SRC_LO(%a0),FP_SCR0_LO(%a6)
bsr.l scale_to_zero_src # calculate scale factor
cmpi.l %d0,&0x3fff-0x3f80 # will move in underflow?
bge.w fin_sd_unfl # yes; go handle underflow
cmpi.l %d0,&0x3fff-0x407e # will move in overflow?
beq.w fin_sd_may_ovfl # maybe; go check
blt.w fin_sd_ovfl # yes; go handle overflow
#
# operand will NOT overflow or underflow when moved into the fp reg file
#
fin_sd_normal:
fmov.l &0x0,%fpsr # clear FPSR
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fmov.x FP_SCR0(%a6),%fp0 # perform move
fmov.l %fpsr,%d1 # save FPSR
fmov.l &0x0,%fpcr # clear FPCR
or.l %d1,USER_FPSR(%a6) # save INEX2,N
fin_sd_normal_exit:
mov.l %d2,-(%sp) # save d2
fmovm.x &0x80,FP_SCR0(%a6) # store out result
mov.w FP_SCR0_EX(%a6),%d1 # load {sgn,exp}
mov.w %d1,%d2 # make a copy
andi.l &0x7fff,%d1 # strip sign sub.l %d0,%d1 # add scale factor
andi.w &0x8000,%d2 # keep old sign
or.w %d1,%d2 # concat old sign,new exponent
mov.w %d2,FP_SCR0_EX(%a6) # insert new exponent
mov.l (%sp)+,%d2 # restore d2
fmovm.x FP_SCR0(%a6),&0x80 # return result in fp0
rts
#
# operand is to be rounded to double precision
#
fin_dbl:
mov.w SRC_EX(%a0),FP_SCR0_EX(%a6)
mov.l SRC_HI(%a0),FP_SCR0_HI(%a6)
mov.l SRC_LO(%a0),FP_SCR0_LO(%a6)
bsr.l scale_to_zero_src # calculate scale factor
cmpi.l %d0,&0x3fff-0x3c00 # will move in underflow?
bge.w fin_sd_unfl # yes; go handle underflow
cmpi.l %d0,&0x3fff-0x43fe # will move in overflow?
beq.w fin_sd_may_ovfl # maybe; go check
blt.w fin_sd_ovfl # yes; go handle overflow
bra.w fin_sd_normal # no; ho handle normalized op
#
# operand WILL underflow when moved in to the fp register file
#
fin_sd_unfl:
bset &unfl_bit,FPSR_EXCEPT(%a6) # set unfl exc bit
tst.b FP_SCR0_EX(%a6) # is operand negative?
bpl.b fin_sd_unfl_tst
bset &neg_bit,FPSR_CC(%a6) # set'N' ccode bit
# if underflow or inexact is enabled, then go calculate the EXOP first.
fin_sd_unfl_tst:
mov.b FPCR_ENABLE(%a6),%d1
andi.b &0x0b,%d1 # is UNFL or INEX enabled?
bne.b fin_sd_unfl_ena # yes
fin_sd_unfl_dis:
lea FP_SCR0(%a6),%a0 # pass: result addr
mov.l L_SCR3(%a6),%d1 # pass: rnd prec,mode
bsr.l unf_res # calculate default result
or.b %d0,FPSR_CC(%a6) # unf_res may have set'Z'
fmovm.x FP_SCR0(%a6),&0x80 # return default result in fp0
rts
#
# operand will underflow AND underflow or inexact is enabled.
# Therefore, we must return the result rounded to extended precision.
#
fin_sd_unfl_ena:
mov.l FP_SCR0_HI(%a6),FP_SCR1_HI(%a6)
mov.l FP_SCR0_LO(%a6),FP_SCR1_LO(%a6)
mov.w FP_SCR0_EX(%a6),%d1 # load current exponent
mov.l %d2,-(%sp) # save d2
mov.w %d1,%d2 # make a copy
andi.l &0x7fff,%d1 # strip sign sub.l %d0,%d1 # subtract scale factor
andi.w &0x8000,%d2 # extract old sign
addi.l &0x6000,%d1 # add new bias
andi.w &0x7fff,%d1
or.w %d1,%d2 # concat old sign,new exp
mov.w %d2,FP_SCR1_EX(%a6) # insert new exponent
fmovm.x FP_SCR1(%a6),&0x40 # return EXOP in fp1
mov.l (%sp)+,%d2 # restore d2
bra.b fin_sd_unfl_dis
#
# operand WILL overflow.
#
fin_sd_ovfl:
fmov.l &0x0,%fpsr # clear FPSR
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fmov.x FP_SCR0(%a6),%fp0 # perform move
fmov.l &0x0,%fpcr # clear FPCR
fmov.l %fpsr,%d1 # save FPSR
or.l %d1,USER_FPSR(%a6) # save INEX2,N
fin_sd_ovfl_tst:
or.l &ovfl_inx_mask,USER_FPSR(%a6) # set ovfl/aovfl/ainex
mov.b FPCR_ENABLE(%a6),%d1
andi.b &0x13,%d1 # is OVFL or INEX enabled?
bne.b fin_sd_ovfl_ena # yes
#
# OVFL is not enabled; therefore, we must create the default result by
# calling ovf_res().
#
fin_sd_ovfl_dis:
btst &neg_bit,FPSR_CC(%a6) # is result negative?
sne %d1 # set sign param accordingly
mov.l L_SCR3(%a6),%d0 # pass: prec,mode
bsr.l ovf_res # calculate default result
or.b %d0,FPSR_CC(%a6) # set INF,N if applicable
fmovm.x (%a0),&0x80 # return default result in fp0
rts
#
# OVFL is enabled.
# the INEX2 bit has already been updated by the round to the correct precision.
# now, round to extended(and don't alter the FPSR).
#
fin_sd_ovfl_ena:
mov.l %d2,-(%sp) # save d2
mov.w FP_SCR0_EX(%a6),%d1 # fetch {sgn,exp}
mov.l %d1,%d2 # make a copy
andi.l &0x7fff,%d1 # strip sign
andi.w &0x8000,%d2 # keep old sign sub.l %d0,%d1 # add scale factor sub.l &0x6000,%d1 # subtract bias
andi.w &0x7fff,%d1
or.w %d2,%d1
mov.w %d1,FP_SCR0_EX(%a6) # insert new exponent
mov.l (%sp)+,%d2 # restore d2
fmovm.x FP_SCR0(%a6),&0x40 # return EXOP in fp1
bra.b fin_sd_ovfl_dis
#
# the move in MAY overflow. so...
#
fin_sd_may_ovfl:
fmov.l &0x0,%fpsr # clear FPSR
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fmov.x FP_SCR0(%a6),%fp0 # perform the move
fmov.l %fpsr,%d1 # save status
fmov.l &0x0,%fpcr # clear FPCR
or.l %d1,USER_FPSR(%a6) # save INEX2,N
fabs.x %fp0,%fp1 # make a copy of result
fcmp.b %fp1,&0x2 # is |result| >= 2.b?
fbge.w fin_sd_ovfl_tst # yes; overflow has occurred
# no, it didn't overflow; we have correct result
bra.w fin_sd_normal_exit
#
# operand is not a NORM: check its optype and branch accordingly
#
fin_not_norm:
cmpi.b %d1,&DENORM # weed out DENORM
beq.w fin_denorm
cmpi.b %d1,&SNAN # weed out SNANs
beq.l res_snan_1op
cmpi.b %d1,&QNAN # weed out QNANs
beq.l res_qnan_1op
#
# do the fmove in; at this point, only possible ops are ZERO and INF.
# use fmov to determine ccodes.
# prec:mode should be zero at this point but it won't affect answer anyways.
#
fmov.x SRC(%a0),%fp0 # do fmove in
fmov.l %fpsr,%d0 # no exceptions possible
rol.l &0x8,%d0 # put ccodes in lo byte
mov.b %d0,FPSR_CC(%a6) # insert correct ccodes
rts
#########################################################################
# XDEF **************************************************************** #
# fdiv(): emulates the fdiv instruction #
# fsdiv(): emulates the fsdiv instruction #
# fddiv(): emulates the fddiv instruction #
# #
# XREF **************************************************************** #
# scale_to_zero_src() - scale src exponent to zero #
# scale_to_zero_dst() - scale dst exponent to zero #
# unf_res() - return default underflow result #
# ovf_res() - return default overflow result #
# res_qnan() - return QNAN result #
# res_snan() - return SNAN result #
# #
# INPUT *************************************************************** #
# a0 = pointer to extended precision source operand #
# a1 = pointer to extended precision destination operand #
# d0 rnd prec,mode #
# #
# OUTPUT ************************************************************** #
# fp0 = result #
# fp1 = EXOP (if exception occurred) #
# #
# ALGORITHM *********************************************************** #
# Handle NANs, infinities, and zeroes as special cases. Divide #
# norms/denorms into ext/sgl/dbl precision. #
# For norms/denorms, scale the exponents such that a divide #
# instruction won't cause an exception. Use the regular fdiv to #
# compute a result. Check if the regular operands would have taken #
# an exception. If so, return the default overflow/underflow result #
# and return the EXOP if exceptions are enabled. Else, scale the #
# result operand to the proper exponent. #
# #
#########################################################################
align 0x10
tbl_fdiv_unfl:
long 0x3fff - 0x0000 # ext_unfl
long 0x3fff - 0x3f81 # sgl_unfl
long 0x3fff - 0x3c01 # dbl_unfl
tbl_fdiv_ovfl:
long 0x3fff - 0x7ffe # ext overflow exponent
long 0x3fff - 0x407e # sgl overflow exponent
long 0x3fff - 0x43fe # dbl overflow exponent
mov.w 2+L_SCR3(%a6),%d1 # fetch precision
lsr.b &0x6,%d1 # shift to lo bits
mov.l (%sp)+,%d0 # load S.F.
cmp.l %d0,(tbl_fdiv_ovfl.b,%pc,%d1.w*4) # will result overflow?
ble.w fdiv_may_ovfl # result will overflow
cmp.l %d0,(tbl_fdiv_unfl.w,%pc,%d1.w*4) # will result underflow?
beq.w fdiv_may_unfl # maybe
bgt.w fdiv_unfl # yes; go handle underflow
fdiv_normal:
fmovm.x FP_SCR1(%a6),&0x80 # load dst op
fmov.l L_SCR3(%a6),%fpcr # save FPCR
fmov.l &0x0,%fpsr # clear FPSR
fdiv.x FP_SCR0(%a6),%fp0 # perform divide
fmov.l %fpsr,%d1 # save FPSR
fmov.l &0x0,%fpcr # clear FPCR
or.l %d1,USER_FPSR(%a6) # save INEX2,N
fdiv_normal_exit:
fmovm.x &0x80,FP_SCR0(%a6) # store result on stack
mov.l %d2,-(%sp) # store d2
mov.w FP_SCR0_EX(%a6),%d1 # load {sgn,exp}
mov.l %d1,%d2 # make a copy
andi.l &0x7fff,%d1 # strip sign
andi.w &0x8000,%d2 # keep old sign sub.l %d0,%d1 # add scale factor
or.w %d2,%d1 # concat old sign,new exp
mov.w %d1,FP_SCR0_EX(%a6) # insert new exponent
mov.l (%sp)+,%d2 # restore d2
fmovm.x FP_SCR0(%a6),&0x80 # return result in fp0
rts
tbl_fdiv_ovfl2:
long 0x7fff
long 0x407f
long 0x43ff
fdiv_unfl:
bset &unfl_bit,FPSR_EXCEPT(%a6) # set unfl exc bit
fmovm.x FP_SCR1(%a6),&0x80 # load dst op
fmov.l &rz_mode*0x10,%fpcr # set FPCR
fmov.l &0x0,%fpsr # clear FPSR
fdiv.x FP_SCR0(%a6),%fp0 # execute divide
fmov.l %fpsr,%d1 # save status
fmov.l &0x0,%fpcr # clear FPCR
or.l %d1,USER_FPSR(%a6) # save INEX2,N
mov.b FPCR_ENABLE(%a6),%d1
andi.b &0x0b,%d1 # is UNFL or INEX enabled?
bne.b fdiv_unfl_ena # yes
fdiv_unfl_dis:
fmovm.x &0x80,FP_SCR0(%a6) # store out result
lea FP_SCR0(%a6),%a0 # pass: result addr
mov.l L_SCR3(%a6),%d1 # pass: rnd prec,mode
bsr.l unf_res # calculate default result
or.b %d0,FPSR_CC(%a6) # 'Z' may have been set
fmovm.x FP_SCR0(%a6),&0x80 # return default result in fp0
rts
#
# UNFL is enabled.
#
fdiv_unfl_ena:
fmovm.x FP_SCR1(%a6),&0x40 # load dst op
mov.l L_SCR3(%a6),%d1
andi.b &0xc0,%d1 # is precision extended?
bne.b fdiv_unfl_ena_sd # no, sgl or dbl
fmovm.x &0x40,FP_SCR0(%a6) # save result to stack
mov.l %d2,-(%sp) # save d2
mov.w FP_SCR0_EX(%a6),%d1 # fetch {sgn,exp}
mov.l %d1,%d2 # make a copy
andi.l &0x7fff,%d1 # strip sign
andi.w &0x8000,%d2 # keep old sign sub.l %d0,%d1 # add scale factoer
addi.l &0x6000,%d1 # add bias
andi.w &0x7fff,%d1
or.w %d2,%d1 # concat old sign,new exp
mov.w %d1,FP_SCR0_EX(%a6) # insert new exp
mov.l (%sp)+,%d2 # restore d2
fmovm.x FP_SCR0(%a6),&0x40 # return EXOP in fp1
bra.w fdiv_unfl_dis
fdiv_unfl_ena_sd:
mov.l L_SCR3(%a6),%d1
andi.b &0x30,%d1 # use only rnd mode
fmov.l %d1,%fpcr # set FPCR
bra.b fdiv_unfl_ena_cont
#
# the divide operation MAY underflow:
#
fdiv_may_unfl:
fmovm.x FP_SCR1(%a6),&0x80 # load dst op
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fmov.l &0x0,%fpsr # clear FPSR
fdiv.x FP_SCR0(%a6),%fp0 # execute divide
fmov.l %fpsr,%d1 # save status
fmov.l &0x0,%fpcr # clear FPCR
or.l %d1,USER_FPSR(%a6) # save INEX2,N
fabs.x %fp0,%fp1 # make a copy of result
fcmp.b %fp1,&0x1 # is |result| > 1.b?
fbgt.w fdiv_normal_exit # no; no underflow occurred
fblt.w fdiv_unfl # yes; underflow occurred
#
# we still don't know if underflow occurred. result is ~ equal to 1. but,
# we don't know if the result was an underflow that rounded up to a 1
# or a normalized number that rounded down to a 1. so, redo the entire
# operation using RZ as the rounding mode to see what the pre-rounded
# result is. this case should be relatively rare.
#
fmovm.x FP_SCR1(%a6),&0x40 # load dst op into fp1
#
# Divide: inputs are not both normalized; what are they?
#
fdiv_not_norm:
mov.w (tbl_fdiv_op.b,%pc,%d1.w*2),%d1
jmp (tbl_fdiv_op.b,%pc,%d1.w*1)
swbeg &48
tbl_fdiv_op:
short fdiv_norm - tbl_fdiv_op # NORM / NORM
short fdiv_inf_load - tbl_fdiv_op # NORM / ZERO
short fdiv_zero_load - tbl_fdiv_op # NORM / INF
short fdiv_res_qnan - tbl_fdiv_op # NORM / QNAN
short fdiv_norm - tbl_fdiv_op # NORM / DENORM
short fdiv_res_snan - tbl_fdiv_op # NORM / SNAN
short tbl_fdiv_op - tbl_fdiv_op #
short tbl_fdiv_op - tbl_fdiv_op #
short fdiv_zero_load - tbl_fdiv_op # ZERO / NORM
short fdiv_res_operr - tbl_fdiv_op # ZERO / ZERO
short fdiv_zero_load - tbl_fdiv_op # ZERO / INF
short fdiv_res_qnan - tbl_fdiv_op # ZERO / QNAN
short fdiv_zero_load - tbl_fdiv_op # ZERO / DENORM
short fdiv_res_snan - tbl_fdiv_op # ZERO / SNAN
short tbl_fdiv_op - tbl_fdiv_op #
short tbl_fdiv_op - tbl_fdiv_op #
short fdiv_inf_dst - tbl_fdiv_op # INF / NORM
short fdiv_inf_dst - tbl_fdiv_op # INF / ZERO
short fdiv_res_operr - tbl_fdiv_op # INF / INF
short fdiv_res_qnan - tbl_fdiv_op # INF / QNAN
short fdiv_inf_dst - tbl_fdiv_op # INF / DENORM
short fdiv_res_snan - tbl_fdiv_op # INF / SNAN
short tbl_fdiv_op - tbl_fdiv_op #
short tbl_fdiv_op - tbl_fdiv_op #
short fdiv_res_qnan - tbl_fdiv_op # QNAN / NORM
short fdiv_res_qnan - tbl_fdiv_op # QNAN / ZERO
short fdiv_res_qnan - tbl_fdiv_op # QNAN / INF
short fdiv_res_qnan - tbl_fdiv_op # QNAN / QNAN
short fdiv_res_qnan - tbl_fdiv_op # QNAN / DENORM
short fdiv_res_snan - tbl_fdiv_op # QNAN / SNAN
short tbl_fdiv_op - tbl_fdiv_op #
short tbl_fdiv_op - tbl_fdiv_op #
short fdiv_norm - tbl_fdiv_op # DENORM / NORM
short fdiv_inf_load - tbl_fdiv_op # DENORM / ZERO
short fdiv_zero_load - tbl_fdiv_op # DENORM / INF
short fdiv_res_qnan - tbl_fdiv_op # DENORM / QNAN
short fdiv_norm - tbl_fdiv_op # DENORM / DENORM
short fdiv_res_snan - tbl_fdiv_op # DENORM / SNAN
short tbl_fdiv_op - tbl_fdiv_op #
short tbl_fdiv_op - tbl_fdiv_op #
short fdiv_res_snan - tbl_fdiv_op # SNAN / NORM
short fdiv_res_snan - tbl_fdiv_op # SNAN / ZERO
short fdiv_res_snan - tbl_fdiv_op # SNAN / INF
short fdiv_res_snan - tbl_fdiv_op # SNAN / QNAN
short fdiv_res_snan - tbl_fdiv_op # SNAN / DENORM
short fdiv_res_snan - tbl_fdiv_op # SNAN / SNAN
short tbl_fdiv_op - tbl_fdiv_op #
short tbl_fdiv_op - tbl_fdiv_op #
global fdiv_zero_load # global for fsgldiv
fdiv_zero_load:
mov.b SRC_EX(%a0),%d0 # result sign is exclusive
mov.b DST_EX(%a1),%d1 # or of input signs.
eor.b %d0,%d1
bpl.b fdiv_zero_load_p # result is positive
fmov.s &0x80000000,%fp0 # load a -ZERO
mov.b &z_bmask+neg_bmask,FPSR_CC(%a6) # set Z/N
rts
fdiv_zero_load_p:
fmov.s &0x00000000,%fp0 # load a +ZERO
mov.b &z_bmask,FPSR_CC(%a6) # set Z
rts
#
# The destination was In Range and the source was a ZERO. The result,
# Therefore, is an INF w/ the proper sign.
# So, determine the sign and return a new INF (w/ the j-bit cleared).
# global fdiv_inf_load # global for fsgldiv
fdiv_inf_load:
ori.w &dz_mask+adz_mask,2+USER_FPSR(%a6) # no; set DZ/ADZ
mov.b SRC_EX(%a0),%d0 # load both signs
mov.b DST_EX(%a1),%d1
eor.b %d0,%d1
bpl.b fdiv_inf_load_p # result is positive
fmov.s &0xff800000,%fp0 # make result -INF
mov.b &inf_bmask+neg_bmask,FPSR_CC(%a6) # set INF/N
rts
fdiv_inf_load_p:
fmov.s &0x7f800000,%fp0 # make result +INF
mov.b &inf_bmask,FPSR_CC(%a6) # set INF
rts
#
# The destination was an INF w/ an In Range or ZERO source, the result is
# an INF w/ the proper sign.
# The 68881/882 returns the destination INF w/ the new sign(if the j-bit of the
# dst INF is set, then then j-bit of the result INF is also set).
# global fdiv_inf_dst # global for fsgldiv
fdiv_inf_dst:
mov.b DST_EX(%a1),%d0 # load both signs
mov.b SRC_EX(%a0),%d1
eor.b %d0,%d1
bpl.b fdiv_inf_dst_p # result is positive
fmovm.x DST(%a1),&0x80 # return result in fp0
fabs.x %fp0 # clear sign bit
fneg.x %fp0 # set sign bit
mov.b &inf_bmask+neg_bmask,FPSR_CC(%a6) # set INF/NEG
rts
fdiv_inf_dst_p:
fmovm.x DST(%a1),&0x80 # return result in fp0
fabs.x %fp0 # return positive INF
mov.b &inf_bmask,FPSR_CC(%a6) # set INF
rts
#########################################################################
# XDEF **************************************************************** #
# fneg(): emulates the fneg instruction #
# fsneg(): emulates the fsneg instruction #
# fdneg(): emulates the fdneg instruction #
# #
# XREF **************************************************************** #
# norm() - normalize a denorm to provide EXOP #
# scale_to_zero_src() - scale sgl/dbl source exponent #
# ovf_res() - return default overflow result #
# unf_res() - return default underflow result #
# res_qnan_1op() - return QNAN result #
# res_snan_1op() - return SNAN result #
# #
# INPUT *************************************************************** #
# a0 = pointer to extended precision source operand #
# d0 = rnd prec,mode #
# #
# OUTPUT ************************************************************** #
# fp0 = result #
# fp1 = EXOP (if exception occurred) #
# #
# ALGORITHM *********************************************************** #
# Handle NANs, zeroes, and infinities as special cases. Separate #
# norms/denorms into ext/sgl/dbl precisions. Extended precision can be #
# emulated by simply setting sign bit. Sgl/dbl operands must be scaled #
# and an actual fneg performed to see if overflow/underflow would have #
# occurred. If so, return default underflow/overflow result. Else, #
# scale the result exponent and return result. FPSR gets set based on #
# the result value. #
# #
#########################################################################
global fneg
fneg:
mov.l %d0,L_SCR3(%a6) # store rnd info
mov.b STAG(%a6),%d1
bne.w fneg_not_norm # optimize on non-norm input
#
# NEGATE SIGN : norms and denorms ONLY!
#
fneg_norm:
andi.b &0xc0,%d0 # is precision extended?
bne.w fneg_not_ext # no; go handle sgl or dbl
#
# precision selected is extended. so...we can not get an underflow
# or overflow because of rounding to the correct precision. so...
# skip the scaling and unscaling...
#
mov.l SRC_HI(%a0),FP_SCR0_HI(%a6)
mov.l SRC_LO(%a0),FP_SCR0_LO(%a6)
mov.w SRC_EX(%a0),%d0
eori.w &0x8000,%d0 # negate sign
bpl.b fneg_norm_load # sign is positive
mov.b &neg_bmask,FPSR_CC(%a6) # set'N' ccode bit
fneg_norm_load:
mov.w %d0,FP_SCR0_EX(%a6)
fmovm.x FP_SCR0(%a6),&0x80 # return result in fp0
rts
#
# for an extended precision DENORM, the UNFL exception bit is set
# the accrued bit is NOT set in this instance(no inexactness!)
#
fneg_denorm:
andi.b &0xc0,%d0 # is precision extended?
bne.b fneg_not_ext # no; go handle sgl or dbl
bset &unfl_bit,FPSR_EXCEPT(%a6) # set unfl exc bit
mov.l SRC_HI(%a0),FP_SCR0_HI(%a6)
mov.l SRC_LO(%a0),FP_SCR0_LO(%a6)
mov.w SRC_EX(%a0),%d0
eori.w &0x8000,%d0 # negate sign
bpl.b fneg_denorm_done # no
mov.b &neg_bmask,FPSR_CC(%a6) # yes, set'N' ccode bit
fneg_denorm_done:
mov.w %d0,FP_SCR0_EX(%a6)
fmovm.x FP_SCR0(%a6),&0x80 # return default result in fp0
#
# the input is an extended DENORM and underflow is enabled in the FPCR.
# normalize the mantissa and add the bias of 0x6000 to the resulting negative
# exponent and insert back into the operand.
#
fneg_ext_unfl_ena:
lea FP_SCR0(%a6),%a0 # pass: ptr to operand
bsr.l norm # normalize result
neg.w %d0 # new exponent = -(shft val)
addi.w &0x6000,%d0 # add new bias to exponent
mov.w FP_SCR0_EX(%a6),%d1 # fetch old sign,exp
andi.w &0x8000,%d1 # keep old sign
andi.w &0x7fff,%d0 # clear sign position
or.w %d1,%d0 # concat old sign, new exponent
mov.w %d0,FP_SCR0_EX(%a6) # insert new exponent
fmovm.x FP_SCR0(%a6),&0x40 # return EXOP in fp1
rts
#
# operand is either single or double
#
fneg_not_ext:
cmpi.b %d0,&s_mode*0x10 # separate sgl/dbl prec
bne.b fneg_dbl
#
# operand is to be rounded to single precision
#
fneg_sgl:
mov.w SRC_EX(%a0),FP_SCR0_EX(%a6)
mov.l SRC_HI(%a0),FP_SCR0_HI(%a6)
mov.l SRC_LO(%a0),FP_SCR0_LO(%a6)
bsr.l scale_to_zero_src # calculate scale factor
cmpi.l %d0,&0x3fff-0x3f80 # will move in underflow?
bge.w fneg_sd_unfl # yes; go handle underflow
cmpi.l %d0,&0x3fff-0x407e # will move in overflow?
beq.w fneg_sd_may_ovfl # maybe; go check
blt.w fneg_sd_ovfl # yes; go handle overflow
#
# operand will NOT overflow or underflow when moved in to the fp reg file
#
fneg_sd_normal:
fmov.l &0x0,%fpsr # clear FPSR
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fneg.x FP_SCR0(%a6),%fp0 # perform negation
fmov.l %fpsr,%d1 # save FPSR
fmov.l &0x0,%fpcr # clear FPCR
or.l %d1,USER_FPSR(%a6) # save INEX2,N
fneg_sd_normal_exit:
mov.l %d2,-(%sp) # save d2
fmovm.x &0x80,FP_SCR0(%a6) # store out result
mov.w FP_SCR0_EX(%a6),%d1 # load sgn,exp
mov.w %d1,%d2 # make a copy
andi.l &0x7fff,%d1 # strip sign sub.l %d0,%d1 # add scale factor
andi.w &0x8000,%d2 # keep old sign
or.w %d1,%d2 # concat old sign,new exp
mov.w %d2,FP_SCR0_EX(%a6) # insert new exponent
mov.l (%sp)+,%d2 # restore d2
fmovm.x FP_SCR0(%a6),&0x80 # return result in fp0
rts
#
# operand is to be rounded to double precision
#
fneg_dbl:
mov.w SRC_EX(%a0),FP_SCR0_EX(%a6)
mov.l SRC_HI(%a0),FP_SCR0_HI(%a6)
mov.l SRC_LO(%a0),FP_SCR0_LO(%a6)
bsr.l scale_to_zero_src # calculate scale factor
cmpi.l %d0,&0x3fff-0x3c00 # will move in underflow?
bge.b fneg_sd_unfl # yes; go handle underflow
cmpi.l %d0,&0x3fff-0x43fe # will move in overflow?
beq.w fneg_sd_may_ovfl # maybe; go check
blt.w fneg_sd_ovfl # yes; go handle overflow
bra.w fneg_sd_normal # no; ho handle normalized op
#
# operand WILL underflow when moved in to the fp register file
#
fneg_sd_unfl:
bset &unfl_bit,FPSR_EXCEPT(%a6) # set unfl exc bit
# if underflow or inexact is enabled, go calculate EXOP first.
fneg_sd_unfl_tst:
mov.b FPCR_ENABLE(%a6),%d1
andi.b &0x0b,%d1 # is UNFL or INEX enabled?
bne.b fneg_sd_unfl_ena # yes
fneg_sd_unfl_dis:
lea FP_SCR0(%a6),%a0 # pass: result addr
mov.l L_SCR3(%a6),%d1 # pass: rnd prec,mode
bsr.l unf_res # calculate default result
or.b %d0,FPSR_CC(%a6) # unf_res may have set'Z'
fmovm.x FP_SCR0(%a6),&0x80 # return default result in fp0
rts
#
# operand will underflow AND underflow is enabled.
# Therefore, we must return the result rounded to extended precision.
#
fneg_sd_unfl_ena:
mov.l FP_SCR0_HI(%a6),FP_SCR1_HI(%a6)
mov.l FP_SCR0_LO(%a6),FP_SCR1_LO(%a6)
mov.w FP_SCR0_EX(%a6),%d1 # load current exponent
mov.l %d2,-(%sp) # save d2
mov.l %d1,%d2 # make a copy
andi.l &0x7fff,%d1 # strip sign
andi.w &0x8000,%d2 # keep old sign sub.l %d0,%d1 # subtract scale factor
addi.l &0x6000,%d1 # add new bias
andi.w &0x7fff,%d1
or.w %d2,%d1 # concat new sign,new exp
mov.w %d1,FP_SCR1_EX(%a6) # insert new exp
fmovm.x FP_SCR1(%a6),&0x40 # return EXOP in fp1
mov.l (%sp)+,%d2 # restore d2
bra.b fneg_sd_unfl_dis
#
# operand WILL overflow.
#
fneg_sd_ovfl:
fmov.l &0x0,%fpsr # clear FPSR
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fneg.x FP_SCR0(%a6),%fp0 # perform negation
fmov.l &0x0,%fpcr # clear FPCR
fmov.l %fpsr,%d1 # save FPSR
or.l %d1,USER_FPSR(%a6) # save INEX2,N
fneg_sd_ovfl_tst:
or.l &ovfl_inx_mask,USER_FPSR(%a6) # set ovfl/aovfl/ainex
mov.b FPCR_ENABLE(%a6),%d1
andi.b &0x13,%d1 # is OVFL or INEX enabled?
bne.b fneg_sd_ovfl_ena # yes
#
# OVFL is not enabled; therefore, we must create the default result by
# calling ovf_res().
#
fneg_sd_ovfl_dis:
btst &neg_bit,FPSR_CC(%a6) # is result negative?
sne %d1 # set sign param accordingly
mov.l L_SCR3(%a6),%d0 # pass: prec,mode
bsr.l ovf_res # calculate default result
or.b %d0,FPSR_CC(%a6) # set INF,N if applicable
fmovm.x (%a0),&0x80 # return default result in fp0
rts
#
# OVFL is enabled.
# the INEX2 bit has already been updated by the round to the correct precision.
# now, round to extended(and don't alter the FPSR).
#
fneg_sd_ovfl_ena:
mov.l %d2,-(%sp) # save d2
mov.w FP_SCR0_EX(%a6),%d1 # fetch {sgn,exp}
mov.l %d1,%d2 # make a copy
andi.l &0x7fff,%d1 # strip sign
andi.w &0x8000,%d2 # keep old sign sub.l %d0,%d1 # add scale factor
subi.l &0x6000,%d1 # subtract bias
andi.w &0x7fff,%d1
or.w %d2,%d1 # concat sign,exp
mov.w %d1,FP_SCR0_EX(%a6) # insert new exponent
fmovm.x FP_SCR0(%a6),&0x40 # return EXOP in fp1
mov.l (%sp)+,%d2 # restore d2
bra.b fneg_sd_ovfl_dis
#
# the move in MAY underflow. so...
#
fneg_sd_may_ovfl:
fmov.l &0x0,%fpsr # clear FPSR
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fneg.x FP_SCR0(%a6),%fp0 # perform negation
fmov.l %fpsr,%d1 # save status
fmov.l &0x0,%fpcr # clear FPCR
or.l %d1,USER_FPSR(%a6) # save INEX2,N
fabs.x %fp0,%fp1 # make a copy of result
fcmp.b %fp1,&0x2 # is |result| >= 2.b?
fbge.w fneg_sd_ovfl_tst # yes; overflow has occurred
# no, it didn't overflow; we have correct result
bra.w fneg_sd_normal_exit
#
# input is not normalized; what is it?
#
fneg_not_norm:
cmpi.b %d1,&DENORM # weed out DENORM
beq.w fneg_denorm
cmpi.b %d1,&SNAN # weed out SNAN
beq.l res_snan_1op
cmpi.b %d1,&QNAN # weed out QNAN
beq.l res_qnan_1op
#
# do the fneg; at this point, only possible ops are ZERO and INF.
# use fneg to determine ccodes.
# prec:mode should be zero at this point but it won't affect answer anyways.
#
fneg.x SRC_EX(%a0),%fp0 # do fneg
fmov.l %fpsr,%d0
rol.l &0x8,%d0 # put ccodes in lo byte
mov.b %d0,FPSR_CC(%a6) # insert correct ccodes
rts
#########################################################################
# XDEF **************************************************************** #
# ftst(): emulates the ftest instruction #
# #
# XREF **************************************************************** #
# res{s,q}nan_1op() - set NAN result for monadic instruction #
# #
# INPUT *************************************************************** #
# a0 = pointer to extended precision source operand #
# #
# OUTPUT ************************************************************** #
# none #
# #
# ALGORITHM *********************************************************** #
# Check the source operand tag (STAG) and set the FPCR according #
# to the operand type and sign. #
# #
#########################################################################
global ftst
ftst:
mov.b STAG(%a6),%d1
bne.b ftst_not_norm # optimize on non-norm input
#
# input is not normalized; what is it?
#
ftst_not_norm:
cmpi.b %d1,&ZERO # weed out ZERO
beq.b ftst_zero
cmpi.b %d1,&INF # weed out INF
beq.b ftst_inf
cmpi.b %d1,&SNAN # weed out SNAN
beq.l res_snan_1op
cmpi.b %d1,&QNAN # weed out QNAN
beq.l res_qnan_1op
#########################################################################
# XDEF **************************************************************** #
# fint(): emulates the fint instruction #
# #
# XREF **************************************************************** #
# res_{s,q}nan_1op() - set NAN result for monadic operation #
# #
# INPUT *************************************************************** #
# a0 = pointer to extended precision source operand #
# d0 = round precision/mode #
# #
# OUTPUT ************************************************************** #
# fp0 = result #
# #
# ALGORITHM *********************************************************** #
# Separate according to operand type. Unnorms don't pass through #
# here. For norms, load the rounding mode/prec, execute a "fint", then #
# store the resulting FPSR bits. #
# For denorms, force the j-bit to a one and do the same as for #
# norms. Denorms are so low that the answer will either be a zero or a #
# one. #
# For zeroes/infs/NANs, return the same while setting the FPSR #
# as appropriate. #
# #
#########################################################################
global fint
fint:
mov.b STAG(%a6),%d1
bne.b fint_not_norm # optimize on non-norm input
fmov.l %d0,%fpcr # set FPCR
fmov.l &0x0,%fpsr # clear FPSR
fint.x SRC(%a0),%fp0 # execute fint
fmov.l &0x0,%fpcr # clear FPCR
fmov.l %fpsr,%d0 # save FPSR
or.l %d0,USER_FPSR(%a6) # set exception bits
rts
#
# input is not normalized; what is it?
#
fint_not_norm:
cmpi.b %d1,&ZERO # weed out ZERO
beq.b fint_zero
cmpi.b %d1,&INF # weed out INF
beq.b fint_inf
cmpi.b %d1,&DENORM # weed out DENORM
beq.b fint_denorm
cmpi.b %d1,&SNAN # weed out SNAN
beq.l res_snan_1op
bra.l res_qnan_1op # weed out QNAN
#
# Denorm:
#
# for DENORMs, the result will be either (+/-)ZERO or (+/-)1.
# also, the INEX2 and AINEX exception bits will be set.
# so, we could either set these manually or force the DENORM
# to a very small NORM and ship it to the NORM routine.
# I do the latter.
#
fint_denorm:
mov.w SRC_EX(%a0),FP_SCR0_EX(%a6) # copy sign, zero exp
mov.b &0x80,FP_SCR0_HI(%a6) # force DENORM ==> small NORM
lea FP_SCR0(%a6),%a0
bra.b fint_norm
#
# Zero:
#
fint_zero:
tst.b SRC_EX(%a0) # is ZERO negative?
bmi.b fint_zero_m # yes
fint_zero_p:
fmov.s &0x00000000,%fp0 # return +ZERO in fp0
mov.b &z_bmask,FPSR_CC(%a6) # set'Z' ccode bit
rts
fint_zero_m:
fmov.s &0x80000000,%fp0 # return -ZERO in fp0
mov.b &z_bmask+neg_bmask,FPSR_CC(%a6) # set'Z','N' ccode bits
rts
#
# Infinity:
#
fint_inf:
fmovm.x SRC(%a0),&0x80 # return result in fp0
tst.b SRC_EX(%a0) # is INF negative?
bmi.b fint_inf_m # yes
fint_inf_p:
mov.b &inf_bmask,FPSR_CC(%a6) # set'I' ccode bit
rts
fint_inf_m:
mov.b &inf_bmask+neg_bmask,FPSR_CC(%a6) # set'N','I' ccode bits
rts
#########################################################################
# XDEF **************************************************************** #
# fintrz(): emulates the fintrz instruction #
# #
# XREF **************************************************************** #
# res_{s,q}nan_1op() - set NAN result for monadic operation #
# #
# INPUT *************************************************************** #
# a0 = pointer to extended precision source operand #
# d0 = round precision/mode #
# #
# OUTPUT ************************************************************** #
# fp0 = result #
# #
# ALGORITHM *********************************************************** #
# Separate according to operand type. Unnorms don't pass through #
# here. For norms, load the rounding mode/prec, execute a "fintrz", #
# then store the resulting FPSR bits. #
# For denorms, force the j-bit to a one and do the same as for #
# norms. Denorms are so low that the answer will either be a zero or a #
# one. #
# For zeroes/infs/NANs, return the same while setting the FPSR #
# as appropriate. #
# #
#########################################################################
global fintrz
fintrz:
mov.b STAG(%a6),%d1
bne.b fintrz_not_norm # optimize on non-norm input
fmov.l %fpsr,%d0 # save FPSR
or.l %d0,USER_FPSR(%a6) # set exception bits
rts
#
# input is not normalized; what is it?
#
fintrz_not_norm:
cmpi.b %d1,&ZERO # weed out ZERO
beq.b fintrz_zero
cmpi.b %d1,&INF # weed out INF
beq.b fintrz_inf
cmpi.b %d1,&DENORM # weed out DENORM
beq.b fintrz_denorm
cmpi.b %d1,&SNAN # weed out SNAN
beq.l res_snan_1op
bra.l res_qnan_1op # weed out QNAN
#
# Denorm:
#
# for DENORMs, the result will be (+/-)ZERO.
# also, the INEX2 and AINEX exception bits will be set.
# so, we could either set these manually or force the DENORM
# to a very small NORM and ship it to the NORM routine.
# I do the latter.
#
fintrz_denorm:
mov.w SRC_EX(%a0),FP_SCR0_EX(%a6) # copy sign, zero exp
mov.b &0x80,FP_SCR0_HI(%a6) # force DENORM ==> small NORM
lea FP_SCR0(%a6),%a0
bra.b fintrz_norm
#
# Zero:
#
fintrz_zero:
tst.b SRC_EX(%a0) # is ZERO negative?
bmi.b fintrz_zero_m # yes
fintrz_zero_p:
fmov.s &0x00000000,%fp0 # return +ZERO in fp0
mov.b &z_bmask,FPSR_CC(%a6) # set'Z' ccode bit
rts
fintrz_zero_m:
fmov.s &0x80000000,%fp0 # return -ZERO in fp0
mov.b &z_bmask+neg_bmask,FPSR_CC(%a6) # set'Z','N' ccode bits
rts
#
# Infinity:
#
fintrz_inf:
fmovm.x SRC(%a0),&0x80 # return result in fp0
tst.b SRC_EX(%a0) # is INF negative?
bmi.b fintrz_inf_m # yes
fintrz_inf_p:
mov.b &inf_bmask,FPSR_CC(%a6) # set'I' ccode bit
rts
fintrz_inf_m:
mov.b &inf_bmask+neg_bmask,FPSR_CC(%a6) # set'N','I' ccode bits
rts
#########################################################################
# XDEF **************************************************************** #
# fabs(): emulates the fabs instruction #
# fsabs(): emulates the fsabs instruction #
# fdabs(): emulates the fdabs instruction #
# #
# XREF **************************************************************** #
# norm() - normalize denorm mantissa to provide EXOP #
# scale_to_zero_src() - make exponent. = 0; get scale factor #
# unf_res() - calculate underflow result #
# ovf_res() - calculate overflow result #
# res_{s,q}nan_1op() - set NAN result for monadic operation #
# #
# INPUT *************************************************************** #
# a0 = pointer to extended precision source operand #
# d0 = rnd precision/mode #
# #
# OUTPUT ************************************************************** #
# fp0 = result #
# fp1 = EXOP (if exception occurred) #
# #
# ALGORITHM *********************************************************** #
# Handle NANs, infinities, and zeroes as special cases. Divide #
# norms into extended, single, and double precision. #
# Simply clear sign for extended precision norm. Ext prec denorm #
# gets an EXOP created for it since it's an underflow. #
# Double and single precision can overflow and underflow. First, #
# scale the operand such that the exponent is zero. Perform an "fabs" #
# using the correct rnd mode/prec. Check to see if the original #
# exponent would take an exception. If so, use unf_res() or ovf_res() #
# to calculate the default result. Also, create the EXOP for the #
# exceptional case. If no exception should occur, insert the correct #
# result exponent and return. #
# Unnorms don't pass through here. #
# #
#########################################################################
global fabs
fabs:
mov.l %d0,L_SCR3(%a6) # store rnd info
mov.b STAG(%a6),%d1
bne.w fabs_not_norm # optimize on non-norm input
#
# ABSOLUTE VALUE: norms and denorms ONLY!
#
fabs_norm:
andi.b &0xc0,%d0 # is precision extended?
bne.b fabs_not_ext # no; go handle sgl or dbl
#
# precision selected is extended. so...we can not get an underflow
# or overflow because of rounding to the correct precision. so...
# skip the scaling and unscaling...
#
mov.l SRC_HI(%a0),FP_SCR0_HI(%a6)
mov.l SRC_LO(%a0),FP_SCR0_LO(%a6)
mov.w SRC_EX(%a0),%d1
bclr &15,%d1 # force absolute value
mov.w %d1,FP_SCR0_EX(%a6) # insert exponent
fmovm.x FP_SCR0(%a6),&0x80 # return result in fp0
rts
#
# for an extended precision DENORM, the UNFL exception bit is set
# the accrued bit is NOT set in this instance(no inexactness!)
#
fabs_denorm:
andi.b &0xc0,%d0 # is precision extended?
bne.b fabs_not_ext # no
bset &unfl_bit,FPSR_EXCEPT(%a6) # set unfl exc bit
fmovm.x FP_SCR0(%a6),&0x80 # return default result in fp0
btst &unfl_bit,FPCR_ENABLE(%a6) # is UNFL enabled?
bne.b fabs_ext_unfl_ena
rts
#
# the input is an extended DENORM and underflow is enabled in the FPCR.
# normalize the mantissa and add the bias of 0x6000 to the resulting negative
# exponent and insert back into the operand.
#
fabs_ext_unfl_ena:
lea FP_SCR0(%a6),%a0 # pass: ptr to operand
bsr.l norm # normalize result
neg.w %d0 # new exponent = -(shft val)
addi.w &0x6000,%d0 # add new bias to exponent
mov.w FP_SCR0_EX(%a6),%d1 # fetch old sign,exp
andi.w &0x8000,%d1 # keep old sign
andi.w &0x7fff,%d0 # clear sign position
or.w %d1,%d0 # concat old sign, new exponent
mov.w %d0,FP_SCR0_EX(%a6) # insert new exponent
fmovm.x FP_SCR0(%a6),&0x40 # return EXOP in fp1
rts
#
# operand is either single or double
#
fabs_not_ext:
cmpi.b %d0,&s_mode*0x10 # separate sgl/dbl prec
bne.b fabs_dbl
#
# operand is to be rounded to single precision
#
fabs_sgl:
mov.w SRC_EX(%a0),FP_SCR0_EX(%a6)
mov.l SRC_HI(%a0),FP_SCR0_HI(%a6)
mov.l SRC_LO(%a0),FP_SCR0_LO(%a6)
bsr.l scale_to_zero_src # calculate scale factor
cmpi.l %d0,&0x3fff-0x3f80 # will move in underflow?
bge.w fabs_sd_unfl # yes; go handle underflow
cmpi.l %d0,&0x3fff-0x407e # will move in overflow?
beq.w fabs_sd_may_ovfl # maybe; go check
blt.w fabs_sd_ovfl # yes; go handle overflow
#
# operand will NOT overflow or underflow when moved in to the fp reg file
#
fabs_sd_normal:
fmov.l &0x0,%fpsr # clear FPSR
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fabs.x FP_SCR0(%a6),%fp0 # perform absolute
fmov.l %fpsr,%d1 # save FPSR
fmov.l &0x0,%fpcr # clear FPCR
or.l %d1,USER_FPSR(%a6) # save INEX2,N
fabs_sd_normal_exit:
mov.l %d2,-(%sp) # save d2
fmovm.x &0x80,FP_SCR0(%a6) # store out result
mov.w FP_SCR0_EX(%a6),%d1 # load sgn,exp
mov.l %d1,%d2 # make a copy
andi.l &0x7fff,%d1 # strip sign sub.l %d0,%d1 # add scale factor
andi.w &0x8000,%d2 # keep old sign
or.w %d1,%d2 # concat old sign,new exp
mov.w %d2,FP_SCR0_EX(%a6) # insert new exponent
mov.l (%sp)+,%d2 # restore d2
fmovm.x FP_SCR0(%a6),&0x80 # return result in fp0
rts
#
# operand is to be rounded to double precision
#
fabs_dbl:
mov.w SRC_EX(%a0),FP_SCR0_EX(%a6)
mov.l SRC_HI(%a0),FP_SCR0_HI(%a6)
mov.l SRC_LO(%a0),FP_SCR0_LO(%a6)
bsr.l scale_to_zero_src # calculate scale factor
cmpi.l %d0,&0x3fff-0x3c00 # will move in underflow?
bge.b fabs_sd_unfl # yes; go handle underflow
cmpi.l %d0,&0x3fff-0x43fe # will move in overflow?
beq.w fabs_sd_may_ovfl # maybe; go check
blt.w fabs_sd_ovfl # yes; go handle overflow
bra.w fabs_sd_normal # no; ho handle normalized op
#
# operand WILL underflow when moved in to the fp register file
#
fabs_sd_unfl:
bset &unfl_bit,FPSR_EXCEPT(%a6) # set unfl exc bit
bclr &0x7,FP_SCR0_EX(%a6) # force absolute value
# if underflow or inexact is enabled, go calculate EXOP first.
mov.b FPCR_ENABLE(%a6),%d1
andi.b &0x0b,%d1 # is UNFL or INEX enabled?
bne.b fabs_sd_unfl_ena # yes
fabs_sd_unfl_dis:
lea FP_SCR0(%a6),%a0 # pass: result addr
mov.l L_SCR3(%a6),%d1 # pass: rnd prec,mode
bsr.l unf_res # calculate default result
or.b %d0,FPSR_CC(%a6) # set possible 'Z' ccode
fmovm.x FP_SCR0(%a6),&0x80 # return default result in fp0
rts
#
# operand will underflow AND underflow is enabled.
# Therefore, we must return the result rounded to extended precision.
#
fabs_sd_unfl_ena:
mov.l FP_SCR0_HI(%a6),FP_SCR1_HI(%a6)
mov.l FP_SCR0_LO(%a6),FP_SCR1_LO(%a6)
mov.w FP_SCR0_EX(%a6),%d1 # load current exponent
mov.l %d2,-(%sp) # save d2
mov.l %d1,%d2 # make a copy
andi.l &0x7fff,%d1 # strip sign
andi.w &0x8000,%d2 # keep old sign sub.l %d0,%d1 # subtract scale factor
addi.l &0x6000,%d1 # add new bias
andi.w &0x7fff,%d1
or.w %d2,%d1 # concat new sign,new exp
mov.w %d1,FP_SCR1_EX(%a6) # insert new exp
fmovm.x FP_SCR1(%a6),&0x40 # return EXOP in fp1
mov.l (%sp)+,%d2 # restore d2
bra.b fabs_sd_unfl_dis
#
# operand WILL overflow.
#
fabs_sd_ovfl:
fmov.l &0x0,%fpsr # clear FPSR
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fabs.x FP_SCR0(%a6),%fp0 # perform absolute
fmov.l &0x0,%fpcr # clear FPCR
fmov.l %fpsr,%d1 # save FPSR
or.l %d1,USER_FPSR(%a6) # save INEX2,N
fabs_sd_ovfl_tst:
or.l &ovfl_inx_mask,USER_FPSR(%a6) # set ovfl/aovfl/ainex
mov.b FPCR_ENABLE(%a6),%d1
andi.b &0x13,%d1 # is OVFL or INEX enabled?
bne.b fabs_sd_ovfl_ena # yes
#
# OVFL is not enabled; therefore, we must create the default result by
# calling ovf_res().
#
fabs_sd_ovfl_dis:
btst &neg_bit,FPSR_CC(%a6) # is result negative?
sne %d1 # set sign param accordingly
mov.l L_SCR3(%a6),%d0 # pass: prec,mode
bsr.l ovf_res # calculate default result
or.b %d0,FPSR_CC(%a6) # set INF,N if applicable
fmovm.x (%a0),&0x80 # return default result in fp0
rts
#
# OVFL is enabled.
# the INEX2 bit has already been updated by the round to the correct precision.
# now, round to extended(and don't alter the FPSR).
#
fabs_sd_ovfl_ena:
mov.l %d2,-(%sp) # save d2
mov.w FP_SCR0_EX(%a6),%d1 # fetch {sgn,exp}
mov.l %d1,%d2 # make a copy
andi.l &0x7fff,%d1 # strip sign
andi.w &0x8000,%d2 # keep old sign sub.l %d0,%d1 # add scale factor
subi.l &0x6000,%d1 # subtract bias
andi.w &0x7fff,%d1
or.w %d2,%d1 # concat sign,exp
mov.w %d1,FP_SCR0_EX(%a6) # insert new exponent
fmovm.x FP_SCR0(%a6),&0x40 # return EXOP in fp1
mov.l (%sp)+,%d2 # restore d2
bra.b fabs_sd_ovfl_dis
#
# the move in MAY underflow. so...
#
fabs_sd_may_ovfl:
fmov.l &0x0,%fpsr # clear FPSR
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fabs.x FP_SCR0(%a6),%fp0 # perform absolute
fmov.l %fpsr,%d1 # save status
fmov.l &0x0,%fpcr # clear FPCR
or.l %d1,USER_FPSR(%a6) # save INEX2,N
fabs.x %fp0,%fp1 # make a copy of result
fcmp.b %fp1,&0x2 # is |result| >= 2.b?
fbge.w fabs_sd_ovfl_tst # yes; overflow has occurred
# no, it didn't overflow; we have correct result
bra.w fabs_sd_normal_exit
#
# input is not normalized; what is it?
#
fabs_not_norm:
cmpi.b %d1,&DENORM # weed out DENORM
beq.w fabs_denorm
cmpi.b %d1,&SNAN # weed out SNAN
beq.l res_snan_1op
cmpi.b %d1,&QNAN # weed out QNAN
beq.l res_qnan_1op
fabs.x SRC(%a0),%fp0 # force absolute value
cmpi.b %d1,&INF # weed out INF
beq.b fabs_inf
fabs_zero:
mov.b &z_bmask,FPSR_CC(%a6) # set'Z' ccode bit
rts
fabs_inf:
mov.b &inf_bmask,FPSR_CC(%a6) # set'I' ccode bit
rts
#########################################################################
# XDEF **************************************************************** #
# fcmp(): fp compare op routine #
# #
# XREF **************************************************************** #
# res_qnan() - return QNAN result #
# res_snan() - return SNAN result #
# #
# INPUT *************************************************************** #
# a0 = pointer to extended precision source operand #
# a1 = pointer to extended precision destination operand #
# d0 = round prec/mode #
# #
# OUTPUT ************************************************************** #
# None #
# #
# ALGORITHM *********************************************************** #
# Handle NANs and denorms as special cases. For everything else, #
# just use the actual fcmp instruction to produce the correct condition #
# codes. #
# #
#########################################################################
global fcmp
fcmp: clr.w %d1
mov.b DTAG(%a6),%d1
lsl.b &0x3,%d1
or.b STAG(%a6),%d1
bne.b fcmp_not_norm # optimize on non-norm input
#
# COMPARE FP OPs : NORMs, ZEROs, INFs, and "corrected" DENORMs
#
fcmp_norm:
fmovm.x DST(%a1),&0x80 # load dst op
fcmp.x %fp0,SRC(%a0) # do compare
fmov.l %fpsr,%d0 # save FPSR
rol.l &0x8,%d0 # extract ccode bits
mov.b %d0,FPSR_CC(%a6) # set ccode bits(no exc bits are set)
rts
#
# fcmp: inputs are not both normalized; what are they?
#
fcmp_not_norm:
mov.w (tbl_fcmp_op.b,%pc,%d1.w*2),%d1
jmp (tbl_fcmp_op.b,%pc,%d1.w*1)
swbeg &48
tbl_fcmp_op:
short fcmp_norm - tbl_fcmp_op # NORM - NORM
short fcmp_norm - tbl_fcmp_op # NORM - ZERO
short fcmp_norm - tbl_fcmp_op # NORM - INF
short fcmp_res_qnan - tbl_fcmp_op # NORM - QNAN
short fcmp_nrm_dnrm - tbl_fcmp_op # NORM - DENORM
short fcmp_res_snan - tbl_fcmp_op # NORM - SNAN
short tbl_fcmp_op - tbl_fcmp_op #
short tbl_fcmp_op - tbl_fcmp_op #
short fcmp_norm - tbl_fcmp_op # ZERO - NORM
short fcmp_norm - tbl_fcmp_op # ZERO - ZERO
short fcmp_norm - tbl_fcmp_op # ZERO - INF
short fcmp_res_qnan - tbl_fcmp_op # ZERO - QNAN
short fcmp_dnrm_s - tbl_fcmp_op # ZERO - DENORM
short fcmp_res_snan - tbl_fcmp_op # ZERO - SNAN
short tbl_fcmp_op - tbl_fcmp_op #
short tbl_fcmp_op - tbl_fcmp_op #
short fcmp_norm - tbl_fcmp_op # INF - NORM
short fcmp_norm - tbl_fcmp_op # INF - ZERO
short fcmp_norm - tbl_fcmp_op # INF - INF
short fcmp_res_qnan - tbl_fcmp_op # INF - QNAN
short fcmp_dnrm_s - tbl_fcmp_op # INF - DENORM
short fcmp_res_snan - tbl_fcmp_op # INF - SNAN
short tbl_fcmp_op - tbl_fcmp_op #
short tbl_fcmp_op - tbl_fcmp_op #
short fcmp_res_qnan - tbl_fcmp_op # QNAN - NORM
short fcmp_res_qnan - tbl_fcmp_op # QNAN - ZERO
short fcmp_res_qnan - tbl_fcmp_op # QNAN - INF
short fcmp_res_qnan - tbl_fcmp_op # QNAN - QNAN
short fcmp_res_qnan - tbl_fcmp_op # QNAN - DENORM
short fcmp_res_snan - tbl_fcmp_op # QNAN - SNAN
short tbl_fcmp_op - tbl_fcmp_op #
short tbl_fcmp_op - tbl_fcmp_op #
short fcmp_dnrm_nrm - tbl_fcmp_op # DENORM - NORM
short fcmp_dnrm_d - tbl_fcmp_op # DENORM - ZERO
short fcmp_dnrm_d - tbl_fcmp_op # DENORM - INF
short fcmp_res_qnan - tbl_fcmp_op # DENORM - QNAN
short fcmp_dnrm_sd - tbl_fcmp_op # DENORM - DENORM
short fcmp_res_snan - tbl_fcmp_op # DENORM - SNAN
short tbl_fcmp_op - tbl_fcmp_op #
short tbl_fcmp_op - tbl_fcmp_op #
short fcmp_res_snan - tbl_fcmp_op # SNAN - NORM
short fcmp_res_snan - tbl_fcmp_op # SNAN - ZERO
short fcmp_res_snan - tbl_fcmp_op # SNAN - INF
short fcmp_res_snan - tbl_fcmp_op # SNAN - QNAN
short fcmp_res_snan - tbl_fcmp_op # SNAN - DENORM
short fcmp_res_snan - tbl_fcmp_op # SNAN - SNAN
short tbl_fcmp_op - tbl_fcmp_op #
short tbl_fcmp_op - tbl_fcmp_op #
# unlike all other functions for QNAN and SNAN, fcmp does NOT set the
# 'N' bit for a negative QNAN or SNAN input so we must squelch it here.
fcmp_res_qnan:
bsr.l res_qnan
andi.b &0xf7,FPSR_CC(%a6)
rts
fcmp_res_snan:
bsr.l res_snan
andi.b &0xf7,FPSR_CC(%a6)
rts
#
# DENORMs are a little more difficult.
# If you have a 2 DENORMs, then you can just force the j-bit to a one
# and use the fcmp_norm routine.
# If you have a DENORM and an INF or ZERO, just force the DENORM's j-bit to a one
# and use the fcmp_norm routine.
# If you have a DENORM and a NORM with opposite signs, then use fcmp_norm, also.
# But with a DENORM and a NORM of the same sign, the neg bit is set if the
# (1) signs are (+) and the DENORM is the dst or
# (2) signs are (-) and the DENORM is the src
#
fcmp_dnrm_s:
mov.w SRC_EX(%a0),FP_SCR0_EX(%a6)
mov.l SRC_HI(%a0),%d0
bset &31,%d0 # DENORM src; make into small norm
mov.l %d0,FP_SCR0_HI(%a6)
mov.l SRC_LO(%a0),FP_SCR0_LO(%a6)
lea FP_SCR0(%a6),%a0
bra.w fcmp_norm
fcmp_dnrm_d:
mov.l DST_EX(%a1),FP_SCR0_EX(%a6)
mov.l DST_HI(%a1),%d0
bset &31,%d0 # DENORM src; make into small norm
mov.l %d0,FP_SCR0_HI(%a6)
mov.l DST_LO(%a1),FP_SCR0_LO(%a6)
lea FP_SCR0(%a6),%a1
bra.w fcmp_norm
fcmp_dnrm_sd:
mov.w DST_EX(%a1),FP_SCR1_EX(%a6)
mov.w SRC_EX(%a0),FP_SCR0_EX(%a6)
mov.l DST_HI(%a1),%d0
bset &31,%d0 # DENORM dst; make into small norm
mov.l %d0,FP_SCR1_HI(%a6)
mov.l SRC_HI(%a0),%d0
bset &31,%d0 # DENORM dst; make into small norm
mov.l %d0,FP_SCR0_HI(%a6)
mov.l DST_LO(%a1),FP_SCR1_LO(%a6)
mov.l SRC_LO(%a0),FP_SCR0_LO(%a6)
lea FP_SCR1(%a6),%a1
lea FP_SCR0(%a6),%a0
bra.w fcmp_norm
fcmp_nrm_dnrm:
mov.b SRC_EX(%a0),%d0 # determine if like signs
mov.b DST_EX(%a1),%d1
eor.b %d0,%d1
bmi.w fcmp_dnrm_s
# signs are the same, so must determine the answer ourselves.
tst.b %d0 # is src op negative?
bmi.b fcmp_nrm_dnrm_m # yes
rts
fcmp_nrm_dnrm_m:
mov.b &neg_bmask,FPSR_CC(%a6) # set'Z' ccode bit
rts
fcmp_dnrm_nrm:
mov.b SRC_EX(%a0),%d0 # determine if like signs
mov.b DST_EX(%a1),%d1
eor.b %d0,%d1
bmi.w fcmp_dnrm_d
# signs are the same, so must determine the answer ourselves.
tst.b %d0 # is src op negative?
bpl.b fcmp_dnrm_nrm_m # no
rts
fcmp_dnrm_nrm_m:
mov.b &neg_bmask,FPSR_CC(%a6) # set'Z' ccode bit
rts
#########################################################################
# XDEF **************************************************************** #
# fsglmul(): emulates the fsglmul instruction #
# #
# XREF **************************************************************** #
# scale_to_zero_src() - scale src exponent to zero #
# scale_to_zero_dst() - scale dst exponent to zero #
# unf_res4() - return default underflow result for sglop #
# ovf_res() - return default overflow result #
# res_qnan() - return QNAN result #
# res_snan() - return SNAN result #
# #
# INPUT *************************************************************** #
# a0 = pointer to extended precision source operand #
# a1 = pointer to extended precision destination operand #
# d0 rnd prec,mode #
# #
# OUTPUT ************************************************************** #
# fp0 = result #
# fp1 = EXOP (if exception occurred) #
# #
# ALGORITHM *********************************************************** #
# Handle NANs, infinities, and zeroes as special cases. Divide #
# norms/denorms into ext/sgl/dbl precision. #
# For norms/denorms, scale the exponents such that a multiply #
# instruction won't cause an exception. Use the regular fsglmul to #
# compute a result. Check if the regular operands would have taken #
# an exception. If so, return the default overflow/underflow result #
# and return the EXOP if exceptions are enabled. Else, scale the #
# result operand to the proper exponent. #
# #
#########################################################################
global fsglmul
fsglmul:
mov.l %d0,L_SCR3(%a6) # store rnd info
fmov.l %fpsr,%d1 # save status
fmov.l &0x0,%fpcr # clear FPCR
or.l %d1,USER_FPSR(%a6) # save INEX2,N
mov.b FPCR_ENABLE(%a6),%d1
andi.b &0x0b,%d1 # is UNFL or INEX enabled?
bne.b fsglmul_unfl_ena # yes
fsglmul_unfl_dis:
fmovm.x &0x80,FP_SCR0(%a6) # store out result
lea FP_SCR0(%a6),%a0 # pass: result addr
mov.l L_SCR3(%a6),%d1 # pass: rnd prec,mode
bsr.l unf_res4 # calculate default result
or.b %d0,FPSR_CC(%a6) # 'Z' bit may have been set
fmovm.x FP_SCR0(%a6),&0x80 # return default result in fp0
rts
#
# UNFL is enabled.
#
fsglmul_unfl_ena:
fmovm.x FP_SCR1(%a6),&0x40 # load dst op
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fmov.l &0x0,%fpsr # clear FPSR
fmov.l %fpsr,%d1 # save status
fmov.l &0x0,%fpcr # clear FPCR
or.l %d1,USER_FPSR(%a6) # save INEX2,N
fabs.x %fp0,%fp1 # make a copy of result
fcmp.b %fp1,&0x2 # is |result| > 2.b?
fbgt.w fsglmul_normal_exit # no; no underflow occurred
fblt.w fsglmul_unfl # yes; underflow occurred
#
# we still don't know if underflow occurred. result is ~ equal to 2. but,
# we don't know if the result was an underflow that rounded up to a 2 or
# a normalized number that rounded down to a 2. so, redo the entire operation
# using RZ as the rounding mode to see what the pre-rounded result is.
# this case should be relatively rare.
#
fmovm.x FP_SCR1(%a6),&0x40 # load dst op into fp1
#
# Single Precision Multiply: inputs are not both normalized; what are they?
#
fsglmul_not_norm:
mov.w (tbl_fsglmul_op.b,%pc,%d1.w*2),%d1
jmp (tbl_fsglmul_op.b,%pc,%d1.w*1)
swbeg &48
tbl_fsglmul_op:
short fsglmul_norm - tbl_fsglmul_op # NORM x NORM
short fsglmul_zero - tbl_fsglmul_op # NORM x ZERO
short fsglmul_inf_src - tbl_fsglmul_op # NORM x INF
short fsglmul_res_qnan - tbl_fsglmul_op # NORM x QNAN
short fsglmul_norm - tbl_fsglmul_op # NORM x DENORM
short fsglmul_res_snan - tbl_fsglmul_op # NORM x SNAN
short tbl_fsglmul_op - tbl_fsglmul_op #
short tbl_fsglmul_op - tbl_fsglmul_op #
short fsglmul_zero - tbl_fsglmul_op # ZERO x NORM
short fsglmul_zero - tbl_fsglmul_op # ZERO x ZERO
short fsglmul_res_operr - tbl_fsglmul_op # ZERO x INF
short fsglmul_res_qnan - tbl_fsglmul_op # ZERO x QNAN
short fsglmul_zero - tbl_fsglmul_op # ZERO x DENORM
short fsglmul_res_snan - tbl_fsglmul_op # ZERO x SNAN
short tbl_fsglmul_op - tbl_fsglmul_op #
short tbl_fsglmul_op - tbl_fsglmul_op #
short fsglmul_inf_dst - tbl_fsglmul_op # INF x NORM
short fsglmul_res_operr - tbl_fsglmul_op # INF x ZERO
short fsglmul_inf_dst - tbl_fsglmul_op # INF x INF
short fsglmul_res_qnan - tbl_fsglmul_op # INF x QNAN
short fsglmul_inf_dst - tbl_fsglmul_op # INF x DENORM
short fsglmul_res_snan - tbl_fsglmul_op # INF x SNAN
short tbl_fsglmul_op - tbl_fsglmul_op #
short tbl_fsglmul_op - tbl_fsglmul_op #
short fsglmul_res_qnan - tbl_fsglmul_op # QNAN x NORM
short fsglmul_res_qnan - tbl_fsglmul_op # QNAN x ZERO
short fsglmul_res_qnan - tbl_fsglmul_op # QNAN x INF
short fsglmul_res_qnan - tbl_fsglmul_op # QNAN x QNAN
short fsglmul_res_qnan - tbl_fsglmul_op # QNAN x DENORM
short fsglmul_res_snan - tbl_fsglmul_op # QNAN x SNAN
short tbl_fsglmul_op - tbl_fsglmul_op #
short tbl_fsglmul_op - tbl_fsglmul_op #
short fsglmul_norm - tbl_fsglmul_op # NORM x NORM
short fsglmul_zero - tbl_fsglmul_op # NORM x ZERO
short fsglmul_inf_src - tbl_fsglmul_op # NORM x INF
short fsglmul_res_qnan - tbl_fsglmul_op # NORM x QNAN
short fsglmul_norm - tbl_fsglmul_op # NORM x DENORM
short fsglmul_res_snan - tbl_fsglmul_op # NORM x SNAN
short tbl_fsglmul_op - tbl_fsglmul_op #
short tbl_fsglmul_op - tbl_fsglmul_op #
short fsglmul_res_snan - tbl_fsglmul_op # SNAN x NORM
short fsglmul_res_snan - tbl_fsglmul_op # SNAN x ZERO
short fsglmul_res_snan - tbl_fsglmul_op # SNAN x INF
short fsglmul_res_snan - tbl_fsglmul_op # SNAN x QNAN
short fsglmul_res_snan - tbl_fsglmul_op # SNAN x DENORM
short fsglmul_res_snan - tbl_fsglmul_op # SNAN x SNAN
short tbl_fsglmul_op - tbl_fsglmul_op #
short tbl_fsglmul_op - tbl_fsglmul_op #
#########################################################################
# XDEF **************************************************************** #
# fsgldiv(): emulates the fsgldiv instruction #
# #
# XREF **************************************************************** #
# scale_to_zero_src() - scale src exponent to zero #
# scale_to_zero_dst() - scale dst exponent to zero #
# unf_res4() - return default underflow result for sglop #
# ovf_res() - return default overflow result #
# res_qnan() - return QNAN result #
# res_snan() - return SNAN result #
# #
# INPUT *************************************************************** #
# a0 = pointer to extended precision source operand #
# a1 = pointer to extended precision destination operand #
# d0 rnd prec,mode #
# #
# OUTPUT ************************************************************** #
# fp0 = result #
# fp1 = EXOP (if exception occurred) #
# #
# ALGORITHM *********************************************************** #
# Handle NANs, infinities, and zeroes as special cases. Divide #
# norms/denorms into ext/sgl/dbl precision. #
# For norms/denorms, scale the exponents such that a divide #
# instruction won't cause an exception. Use the regular fsgldiv to #
# compute a result. Check if the regular operands would have taken #
# an exception. If so, return the default overflow/underflow result #
# and return the EXOP if exceptions are enabled. Else, scale the #
# result operand to the proper exponent. #
# #
#########################################################################
global fsgldiv
fsgldiv:
mov.l %d0,L_SCR3(%a6) # store rnd info
cmpi.l %d0,&0x3fff-0x0000 # will result underflow?
beq.w fsgldiv_may_unfl # maybe
bgt.w fsgldiv_unfl # yes; go handle underflow
fsgldiv_normal:
fmovm.x FP_SCR1(%a6),&0x80 # load dst op
fmov.l L_SCR3(%a6),%fpcr # save FPCR
fmov.l &0x0,%fpsr # clear FPSR
fsgldiv.x FP_SCR0(%a6),%fp0 # perform sgl divide
fmov.l %fpsr,%d1 # save FPSR
fmov.l &0x0,%fpcr # clear FPCR
or.l %d1,USER_FPSR(%a6) # save INEX2,N
fsgldiv_normal_exit:
fmovm.x &0x80,FP_SCR0(%a6) # store result on stack
mov.l %d2,-(%sp) # save d2
mov.w FP_SCR0_EX(%a6),%d1 # load {sgn,exp}
mov.l %d1,%d2 # make a copy
andi.l &0x7fff,%d1 # strip sign
andi.w &0x8000,%d2 # keep old sign sub.l %d0,%d1 # add scale factor
or.w %d2,%d1 # concat old sign,new exp
mov.w %d1,FP_SCR0_EX(%a6) # insert new exponent
mov.l (%sp)+,%d2 # restore d2
fmovm.x FP_SCR0(%a6),&0x80 # return result in fp0
rts
fsgldiv_may_ovfl:
fmovm.x FP_SCR1(%a6),&0x80 # load dst op
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fmov.l &0x0,%fpsr # set FPSR
fsgldiv.x FP_SCR0(%a6),%fp0 # execute divide
fmov.l %fpsr,%d1
fmov.l &0x0,%fpcr
or.l %d1,USER_FPSR(%a6) # save INEX,N
fmovm.x &0x01,-(%sp) # save result to stack
mov.w (%sp),%d1 # fetch new exponent
add.l &0xc,%sp # clear result
andi.l &0x7fff,%d1 # strip sign sub.l %d0,%d1 # add scale factor
cmp.l %d1,&0x7fff # did divide overflow?
blt.b fsgldiv_normal_exit
fsgldiv_ovfl_tst:
or.w &ovfl_inx_mask,2+USER_FPSR(%a6) # set ovfl/aovfl/ainex
mov.b FPCR_ENABLE(%a6),%d1
andi.b &0x13,%d1 # is OVFL or INEX enabled?
bne.b fsgldiv_ovfl_ena # yes
fsgldiv_ovfl_dis:
btst &neg_bit,FPSR_CC(%a6) # is result negative
sne %d1 # set sign param accordingly
mov.l L_SCR3(%a6),%d0 # pass prec:rnd
andi.b &0x30,%d0 # kill precision
bsr.l ovf_res # calculate default result
or.b %d0,FPSR_CC(%a6) # set INF if applicable
fmovm.x (%a0),&0x80 # return default result in fp0
rts
fsgldiv_ovfl_ena:
fmovm.x &0x80,FP_SCR0(%a6) # move result to stack
mov.l %d2,-(%sp) # save d2
mov.w FP_SCR0_EX(%a6),%d1 # fetch {sgn,exp}
mov.l %d1,%d2 # make a copy
andi.l &0x7fff,%d1 # strip sign
andi.w &0x8000,%d2 # keep old sign sub.l %d0,%d1 # add scale factor
subi.l &0x6000,%d1 # subtract new bias
andi.w &0x7fff,%d1 # clear ms bit
or.w %d2,%d1 # concat old sign,new exp
mov.w %d1,FP_SCR0_EX(%a6) # insert new exponent
mov.l (%sp)+,%d2 # restore d2
fmovm.x FP_SCR0(%a6),&0x40 # return EXOP in fp1
bra.b fsgldiv_ovfl_dis
fsgldiv_unfl:
bset &unfl_bit,FPSR_EXCEPT(%a6) # set unfl exc bit
fmovm.x FP_SCR1(%a6),&0x80 # load dst op
fmov.l &rz_mode*0x10,%fpcr # set FPCR
fmov.l &0x0,%fpsr # clear FPSR
fsgldiv.x FP_SCR0(%a6),%fp0 # execute sgl divide
fmov.l %fpsr,%d1 # save status
fmov.l &0x0,%fpcr # clear FPCR
or.l %d1,USER_FPSR(%a6) # save INEX2,N
mov.b FPCR_ENABLE(%a6),%d1
andi.b &0x0b,%d1 # is UNFL or INEX enabled?
bne.b fsgldiv_unfl_ena # yes
fsgldiv_unfl_dis:
fmovm.x &0x80,FP_SCR0(%a6) # store out result
lea FP_SCR0(%a6),%a0 # pass: result addr
mov.l L_SCR3(%a6),%d1 # pass: rnd prec,mode
bsr.l unf_res4 # calculate default result
or.b %d0,FPSR_CC(%a6) # 'Z' bit may have been set
fmovm.x FP_SCR0(%a6),&0x80 # return default result in fp0
rts
#
# UNFL is enabled.
#
fsgldiv_unfl_ena:
fmovm.x FP_SCR1(%a6),&0x40 # load dst op
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fmov.l &0x0,%fpsr # clear FPSR
fsgldiv.x FP_SCR0(%a6),%fp1 # execute sgl divide
fmov.l &0x0,%fpcr # clear FPCR
fmovm.x &0x40,FP_SCR0(%a6) # save result to stack
mov.l %d2,-(%sp) # save d2
mov.w FP_SCR0_EX(%a6),%d1 # fetch {sgn,exp}
mov.l %d1,%d2 # make a copy
andi.l &0x7fff,%d1 # strip sign
andi.w &0x8000,%d2 # keep old sign sub.l %d0,%d1 # add scale factor
addi.l &0x6000,%d1 # add bias
andi.w &0x7fff,%d1 # clear top bit
or.w %d2,%d1 # concat old sign, new exp
mov.w %d1,FP_SCR0_EX(%a6) # insert new exponent
mov.l (%sp)+,%d2 # restore d2
fmovm.x FP_SCR0(%a6),&0x40 # return EXOP in fp1
bra.b fsgldiv_unfl_dis
#
# the divide operation MAY underflow:
#
fsgldiv_may_unfl:
fmovm.x FP_SCR1(%a6),&0x80 # load dst op
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fmov.l &0x0,%fpsr # clear FPSR
fsgldiv.x FP_SCR0(%a6),%fp0 # execute sgl divide
fmov.l %fpsr,%d1 # save status
fmov.l &0x0,%fpcr # clear FPCR
or.l %d1,USER_FPSR(%a6) # save INEX2,N
fabs.x %fp0,%fp1 # make a copy of result
fcmp.b %fp1,&0x1 # is |result| > 1.b?
fbgt.w fsgldiv_normal_exit # no; no underflow occurred
fblt.w fsgldiv_unfl # yes; underflow occurred
#
# we still don't know if underflow occurred. result is ~ equal to 1. but,
# we don't know if the result was an underflow that rounded up to a 1
# or a normalized number that rounded down to a 1. so, redo the entire
# operation using RZ as the rounding mode to see what the pre-rounded
# result is. this case should be relatively rare.
#
fmovm.x FP_SCR1(%a6),&0x40 # load dst op into %fp1
#
# Divide: inputs are not both normalized; what are they?
#
fsgldiv_not_norm:
mov.w (tbl_fsgldiv_op.b,%pc,%d1.w*2),%d1
jmp (tbl_fsgldiv_op.b,%pc,%d1.w*1)
swbeg &48
tbl_fsgldiv_op:
short fsgldiv_norm - tbl_fsgldiv_op # NORM / NORM
short fsgldiv_inf_load - tbl_fsgldiv_op # NORM / ZERO
short fsgldiv_zero_load - tbl_fsgldiv_op # NORM / INF
short fsgldiv_res_qnan - tbl_fsgldiv_op # NORM / QNAN
short fsgldiv_norm - tbl_fsgldiv_op # NORM / DENORM
short fsgldiv_res_snan - tbl_fsgldiv_op # NORM / SNAN
short tbl_fsgldiv_op - tbl_fsgldiv_op #
short tbl_fsgldiv_op - tbl_fsgldiv_op #
short fsgldiv_zero_load - tbl_fsgldiv_op # ZERO / NORM
short fsgldiv_res_operr - tbl_fsgldiv_op # ZERO / ZERO
short fsgldiv_zero_load - tbl_fsgldiv_op # ZERO / INF
short fsgldiv_res_qnan - tbl_fsgldiv_op # ZERO / QNAN
short fsgldiv_zero_load - tbl_fsgldiv_op # ZERO / DENORM
short fsgldiv_res_snan - tbl_fsgldiv_op # ZERO / SNAN
short tbl_fsgldiv_op - tbl_fsgldiv_op #
short tbl_fsgldiv_op - tbl_fsgldiv_op #
short fsgldiv_inf_dst - tbl_fsgldiv_op # INF / NORM
short fsgldiv_inf_dst - tbl_fsgldiv_op # INF / ZERO
short fsgldiv_res_operr - tbl_fsgldiv_op # INF / INF
short fsgldiv_res_qnan - tbl_fsgldiv_op # INF / QNAN
short fsgldiv_inf_dst - tbl_fsgldiv_op # INF / DENORM
short fsgldiv_res_snan - tbl_fsgldiv_op # INF / SNAN
short tbl_fsgldiv_op - tbl_fsgldiv_op #
short tbl_fsgldiv_op - tbl_fsgldiv_op #
short fsgldiv_res_qnan - tbl_fsgldiv_op # QNAN / NORM
short fsgldiv_res_qnan - tbl_fsgldiv_op # QNAN / ZERO
short fsgldiv_res_qnan - tbl_fsgldiv_op # QNAN / INF
short fsgldiv_res_qnan - tbl_fsgldiv_op # QNAN / QNAN
short fsgldiv_res_qnan - tbl_fsgldiv_op # QNAN / DENORM
short fsgldiv_res_snan - tbl_fsgldiv_op # QNAN / SNAN
short tbl_fsgldiv_op - tbl_fsgldiv_op #
short tbl_fsgldiv_op - tbl_fsgldiv_op #
short fsgldiv_norm - tbl_fsgldiv_op # DENORM / NORM
short fsgldiv_inf_load - tbl_fsgldiv_op # DENORM / ZERO
short fsgldiv_zero_load - tbl_fsgldiv_op # DENORM / INF
short fsgldiv_res_qnan - tbl_fsgldiv_op # DENORM / QNAN
short fsgldiv_norm - tbl_fsgldiv_op # DENORM / DENORM
short fsgldiv_res_snan - tbl_fsgldiv_op # DENORM / SNAN
short tbl_fsgldiv_op - tbl_fsgldiv_op #
short tbl_fsgldiv_op - tbl_fsgldiv_op #
short fsgldiv_res_snan - tbl_fsgldiv_op # SNAN / NORM
short fsgldiv_res_snan - tbl_fsgldiv_op # SNAN / ZERO
short fsgldiv_res_snan - tbl_fsgldiv_op # SNAN / INF
short fsgldiv_res_snan - tbl_fsgldiv_op # SNAN / QNAN
short fsgldiv_res_snan - tbl_fsgldiv_op # SNAN / DENORM
short fsgldiv_res_snan - tbl_fsgldiv_op # SNAN / SNAN
short tbl_fsgldiv_op - tbl_fsgldiv_op #
short tbl_fsgldiv_op - tbl_fsgldiv_op #
#########################################################################
# XDEF **************************************************************** #
# fadd(): emulates the fadd instruction #
# fsadd(): emulates the fadd instruction #
# fdadd(): emulates the fdadd instruction #
# #
# XREF **************************************************************** #
# addsub_scaler2() - scale the operands so they won't take exc #
# ovf_res() - return default overflow result #
# unf_res() - return default underflow result #
# res_qnan() - set QNAN result #
# res_snan() - set SNAN result #
# res_operr() - set OPERR result #
# scale_to_zero_src() - set src operand exponent equal to zero #
# scale_to_zero_dst() - set dst operand exponent equal to zero #
# #
# INPUT *************************************************************** #
# a0 = pointer to extended precision source operand #
# a1 = pointer to extended precision destination operand #
# #
# OUTPUT ************************************************************** #
# fp0 = result #
# fp1 = EXOP (if exception occurred) #
# #
# ALGORITHM *********************************************************** #
# Handle NANs, infinities, and zeroes as special cases. Divide #
# norms into extended, single, and double precision. #
# Do addition after scaling exponents such that exception won't #
# occur. Then, check result exponent to see if exception would have #
# occurred. If so, return default result and maybe EXOP. Else, insert #
# the correct result exponent and return. Set FPSR bits as appropriate. #
# #
#########################################################################
fadd_unfl:
bset &unfl_bit,FPSR_EXCEPT(%a6) # set unfl exc bit
add.l &0xc,%sp
fmovm.x FP_SCR1(%a6),&0x80 # load dst op
fmov.l &rz_mode*0x10,%fpcr # set FPCR
fmov.l &0x0,%fpsr # clear FPSR
fadd.x FP_SCR0(%a6),%fp0 # execute add
fmov.l &0x0,%fpcr # clear FPCR
fmov.l %fpsr,%d1 # save status
or.l %d1,USER_FPSR(%a6) # save INEX,N
mov.b FPCR_ENABLE(%a6),%d1
andi.b &0x0b,%d1 # is UNFL or INEX enabled?
bne.b fadd_unfl_ena # yes
fadd_unfl_dis:
fmovm.x &0x80,FP_SCR0(%a6) # store out result
lea FP_SCR0(%a6),%a0 # pass: result addr
mov.l L_SCR3(%a6),%d1 # pass: rnd prec,mode
bsr.l unf_res # calculate default result
or.b %d0,FPSR_CC(%a6) # 'Z' bit may have been set
fmovm.x FP_SCR0(%a6),&0x80 # return default result in fp0
mov.l (%sp)+,%d2 # restore d2
rts
fadd_unfl_ena:
fmovm.x FP_SCR1(%a6),&0x40 # load dst op
mov.l L_SCR3(%a6),%d1
andi.b &0xc0,%d1 # is precision extended?
bne.b fadd_unfl_ena_sd # no; sgl or dbl
fmovm.x &0x40,FP_SCR0(%a6) # save result to stack
mov.w FP_SCR0_EX(%a6),%d1 # fetch {sgn,exp}
mov.l %d1,%d2 # make a copy
andi.l &0x7fff,%d1 # strip sign
andi.w &0x8000,%d2 # keep old sign sub.l %d0,%d1 # add scale factor
addi.l &0x6000,%d1 # add new bias
andi.w &0x7fff,%d1 # clear top bit
or.w %d2,%d1 # concat sign,new exp
mov.w %d1,FP_SCR0_EX(%a6) # insert new exponent
fmovm.x FP_SCR0(%a6),&0x40 # return EXOP in fp1
bra.w fadd_unfl_dis
fadd_unfl_ena_sd:
mov.l L_SCR3(%a6),%d1
andi.b &0x30,%d1 # use only rnd mode
fmov.l %d1,%fpcr # set FPCR
bra.b fadd_unfl_ena_cont
#
# result is equal to the smallest normalized number in the selected precision
# if the precision is extended, this result could not have come from an
# underflow that rounded up.
#
fadd_may_unfl:
mov.l L_SCR3(%a6),%d1
andi.b &0xc0,%d1
beq.w fadd_normal # yes; no underflow occurred
mov.l 0x4(%sp),%d1 # extract hi(man)
cmpi.l %d1,&0x80000000 # is hi(man) = 0x80000000?
bne.w fadd_normal # no; no underflow occurred
tst.l 0x8(%sp) # is lo(man) = 0x0?
bne.w fadd_normal # no; no underflow occurred
btst &inex2_bit,FPSR_EXCEPT(%a6) # is INEX2 set?
beq.w fadd_normal # no; no underflow occurred
#
# ok, so now the result has a exponent equal to the smallest normalized
# exponent for the selected precision. also, the mantissa is equal to
# 0x8000000000000000 and this mantissa is the result of rounding non-zero
# g,r,s.
# now, we must determine whether the pre-rounded result was an underflow
# rounded "up" or a normalized number rounded "down".
# so, we do this be re-executing the add using RZ as the rounding mode and
# seeing if the new result is smaller or equal to the current result.
#
fmovm.x FP_SCR1(%a6),&0x40 # load dst op into fp1
#
# Add: inputs are not both normalized; what are they?
#
fadd_not_norm:
mov.w (tbl_fadd_op.b,%pc,%d1.w*2),%d1
jmp (tbl_fadd_op.b,%pc,%d1.w*1)
swbeg &48
tbl_fadd_op:
short fadd_norm - tbl_fadd_op # NORM + NORM
short fadd_zero_src - tbl_fadd_op # NORM + ZERO
short fadd_inf_src - tbl_fadd_op # NORM + INF
short fadd_res_qnan - tbl_fadd_op # NORM + QNAN
short fadd_norm - tbl_fadd_op # NORM + DENORM
short fadd_res_snan - tbl_fadd_op # NORM + SNAN
short tbl_fadd_op - tbl_fadd_op #
short tbl_fadd_op - tbl_fadd_op #
short fadd_zero_dst - tbl_fadd_op # ZERO + NORM
short fadd_zero_2 - tbl_fadd_op # ZERO + ZERO
short fadd_inf_src - tbl_fadd_op # ZERO + INF
short fadd_res_qnan - tbl_fadd_op # NORM + QNAN
short fadd_zero_dst - tbl_fadd_op # ZERO + DENORM
short fadd_res_snan - tbl_fadd_op # NORM + SNAN
short tbl_fadd_op - tbl_fadd_op #
short tbl_fadd_op - tbl_fadd_op #
short fadd_inf_dst - tbl_fadd_op # INF + NORM
short fadd_inf_dst - tbl_fadd_op # INF + ZERO
short fadd_inf_2 - tbl_fadd_op # INF + INF
short fadd_res_qnan - tbl_fadd_op # NORM + QNAN
short fadd_inf_dst - tbl_fadd_op # INF + DENORM
short fadd_res_snan - tbl_fadd_op # NORM + SNAN
short tbl_fadd_op - tbl_fadd_op #
short tbl_fadd_op - tbl_fadd_op #
short fadd_res_qnan - tbl_fadd_op # QNAN + NORM
short fadd_res_qnan - tbl_fadd_op # QNAN + ZERO
short fadd_res_qnan - tbl_fadd_op # QNAN + INF
short fadd_res_qnan - tbl_fadd_op # QNAN + QNAN
short fadd_res_qnan - tbl_fadd_op # QNAN + DENORM
short fadd_res_snan - tbl_fadd_op # QNAN + SNAN
short tbl_fadd_op - tbl_fadd_op #
short tbl_fadd_op - tbl_fadd_op #
short fadd_norm - tbl_fadd_op # DENORM + NORM
short fadd_zero_src - tbl_fadd_op # DENORM + ZERO
short fadd_inf_src - tbl_fadd_op # DENORM + INF
short fadd_res_qnan - tbl_fadd_op # NORM + QNAN
short fadd_norm - tbl_fadd_op # DENORM + DENORM
short fadd_res_snan - tbl_fadd_op # NORM + SNAN
short tbl_fadd_op - tbl_fadd_op #
short tbl_fadd_op - tbl_fadd_op #
short fadd_res_snan - tbl_fadd_op # SNAN + NORM
short fadd_res_snan - tbl_fadd_op # SNAN + ZERO
short fadd_res_snan - tbl_fadd_op # SNAN + INF
short fadd_res_snan - tbl_fadd_op # SNAN + QNAN
short fadd_res_snan - tbl_fadd_op # SNAN + DENORM
short fadd_res_snan - tbl_fadd_op # SNAN + SNAN
short tbl_fadd_op - tbl_fadd_op #
short tbl_fadd_op - tbl_fadd_op #
#
# both operands are ZEROes
#
fadd_zero_2:
mov.b SRC_EX(%a0),%d0 # are the signs opposite
mov.b DST_EX(%a1),%d1
eor.b %d0,%d1
bmi.w fadd_zero_2_chk_rm # weed out (-ZERO)+(+ZERO)
# the signs are the same. so determine whether they are positive or negative
# and return the appropriately signed zero.
tst.b %d0 # are ZEROes positive or negative?
bmi.b fadd_zero_rm # negative
fmov.s &0x00000000,%fp0 # return +ZERO
mov.b &z_bmask,FPSR_CC(%a6) # set Z
rts
#
# the ZEROes have opposite signs:
# - Therefore, we return +ZERO if the rounding modes are RN,RZ, or RP.
# - -ZERO is returned in the case of RM.
#
fadd_zero_2_chk_rm:
mov.b 3+L_SCR3(%a6),%d1
andi.b &0x30,%d1 # extract rnd mode
cmpi.b %d1,&rm_mode*0x10 # is rnd mode == RM?
beq.b fadd_zero_rm # yes
fmov.s &0x00000000,%fp0 # return +ZERO
mov.b &z_bmask,FPSR_CC(%a6) # set Z
rts
#
# one operand is a ZERO and the other is a DENORM or NORM. scale
# the DENORM or NORM and jump to the regular fadd routine.
#
fadd_zero_dst:
mov.w SRC_EX(%a0),FP_SCR0_EX(%a6)
mov.l SRC_HI(%a0),FP_SCR0_HI(%a6)
mov.l SRC_LO(%a0),FP_SCR0_LO(%a6)
bsr.l scale_to_zero_src # scale the operand clr.w FP_SCR1_EX(%a6) clr.l FP_SCR1_HI(%a6) clr.l FP_SCR1_LO(%a6)
bra.w fadd_zero_entry # go execute fadd
#
# both operands are INFs. an OPERR will result if the INFs have
# different signs. else, an INF of the same sign is returned
#
fadd_inf_2:
mov.b SRC_EX(%a0),%d0 # exclusive or the signs
mov.b DST_EX(%a1),%d1
eor.b %d1,%d0
bmi.l res_operr # weed out (-INF)+(+INF)
# ok, so it's not an OPERR. but, we do have to remember to return the
# src INF since that's where the 881/882 gets the j-bit from...
#
# operands are INF and one of {ZERO, INF, DENORM, NORM}
#
fadd_inf_src:
fmovm.x SRC(%a0),&0x80 # return src INF
tst.b SRC_EX(%a0) # is INF positive?
bpl.b fadd_inf_done # yes; we're done
mov.b &neg_bmask+inf_bmask,FPSR_CC(%a6) # set INF/NEG
rts
#
# operands are INF and one of {ZERO, INF, DENORM, NORM}
#
fadd_inf_dst:
fmovm.x DST(%a1),&0x80 # return dst INF
tst.b DST_EX(%a1) # is INF positive?
bpl.b fadd_inf_done # yes; we're done
mov.b &neg_bmask+inf_bmask,FPSR_CC(%a6) # set INF/NEG
rts
fadd_inf_done:
mov.b &inf_bmask,FPSR_CC(%a6) # set INF
rts
#########################################################################
# XDEF **************************************************************** #
# fsub(): emulates the fsub instruction #
# fssub(): emulates the fssub instruction #
# fdsub(): emulates the fdsub instruction #
# #
# XREF **************************************************************** #
# addsub_scaler2() - scale the operands so they won't take exc #
# ovf_res() - return default overflow result #
# unf_res() - return default underflow result #
# res_qnan() - set QNAN result #
# res_snan() - set SNAN result #
# res_operr() - set OPERR result #
# scale_to_zero_src() - set src operand exponent equal to zero #
# scale_to_zero_dst() - set dst operand exponent equal to zero #
# #
# INPUT *************************************************************** #
# a0 = pointer to extended precision source operand #
# a1 = pointer to extended precision destination operand #
# #
# OUTPUT ************************************************************** #
# fp0 = result #
# fp1 = EXOP (if exception occurred) #
# #
# ALGORITHM *********************************************************** #
# Handle NANs, infinities, and zeroes as special cases. Divide #
# norms into extended, single, and double precision. #
# Do subtraction after scaling exponents such that exception won't#
# occur. Then, check result exponent to see if exception would have #
# occurred. If so, return default result and maybe EXOP. Else, insert #
# the correct result exponent and return. Set FPSR bits as appropriate. #
# #
#########################################################################
fsub_unfl:
bset &unfl_bit,FPSR_EXCEPT(%a6) # set unfl exc bit
add.l &0xc,%sp
fmovm.x FP_SCR1(%a6),&0x80 # load dst op
fmov.l &rz_mode*0x10,%fpcr # set FPCR
fmov.l &0x0,%fpsr # clear FPSR
fsub.x FP_SCR0(%a6),%fp0 # execute subtract
fmov.l &0x0,%fpcr # clear FPCR
fmov.l %fpsr,%d1 # save status
or.l %d1,USER_FPSR(%a6)
mov.b FPCR_ENABLE(%a6),%d1
andi.b &0x0b,%d1 # is UNFL or INEX enabled?
bne.b fsub_unfl_ena # yes
fsub_unfl_dis:
fmovm.x &0x80,FP_SCR0(%a6) # store out result
lea FP_SCR0(%a6),%a0 # pass: result addr
mov.l L_SCR3(%a6),%d1 # pass: rnd prec,mode
bsr.l unf_res # calculate default result
or.b %d0,FPSR_CC(%a6) # 'Z' may have been set
fmovm.x FP_SCR0(%a6),&0x80 # return default result in fp0
mov.l (%sp)+,%d2 # restore d2
rts
fsub_unfl_ena:
fmovm.x FP_SCR1(%a6),&0x40
mov.l L_SCR3(%a6),%d1
andi.b &0xc0,%d1 # is precision extended?
bne.b fsub_unfl_ena_sd # no
#
# result is equal to the smallest normalized number in the selected precision
# if the precision is extended, this result could not have come from an
# underflow that rounded up.
#
fsub_may_unfl:
mov.l L_SCR3(%a6),%d1
andi.b &0xc0,%d1 # fetch rnd prec
beq.w fsub_normal # yes; no underflow occurred
mov.l 0x4(%sp),%d1
cmpi.l %d1,&0x80000000 # is hi(man) = 0x80000000?
bne.w fsub_normal # no; no underflow occurred
tst.l 0x8(%sp) # is lo(man) = 0x0?
bne.w fsub_normal # no; no underflow occurred
btst &inex2_bit,FPSR_EXCEPT(%a6) # is INEX2 set?
beq.w fsub_normal # no; no underflow occurred
#
# ok, so now the result has a exponent equal to the smallest normalized
# exponent for the selected precision. also, the mantissa is equal to
# 0x8000000000000000 and this mantissa is the result of rounding non-zero
# g,r,s.
# now, we must determine whether the pre-rounded result was an underflow
# rounded "up" or a normalized number rounded "down".
# so, we do this be re-executing the add using RZ as the rounding mode and
# seeing if the new result is smaller or equal to the current result.
#
fmovm.x FP_SCR1(%a6),&0x40 # load dst op into fp1
#
# Sub: inputs are not both normalized; what are they?
#
fsub_not_norm:
mov.w (tbl_fsub_op.b,%pc,%d1.w*2),%d1
jmp (tbl_fsub_op.b,%pc,%d1.w*1)
swbeg &48
tbl_fsub_op:
short fsub_norm - tbl_fsub_op # NORM - NORM
short fsub_zero_src - tbl_fsub_op # NORM - ZERO
short fsub_inf_src - tbl_fsub_op # NORM - INF
short fsub_res_qnan - tbl_fsub_op # NORM - QNAN
short fsub_norm - tbl_fsub_op # NORM - DENORM
short fsub_res_snan - tbl_fsub_op # NORM - SNAN
short tbl_fsub_op - tbl_fsub_op #
short tbl_fsub_op - tbl_fsub_op #
short fsub_zero_dst - tbl_fsub_op # ZERO - NORM
short fsub_zero_2 - tbl_fsub_op # ZERO - ZERO
short fsub_inf_src - tbl_fsub_op # ZERO - INF
short fsub_res_qnan - tbl_fsub_op # NORM - QNAN
short fsub_zero_dst - tbl_fsub_op # ZERO - DENORM
short fsub_res_snan - tbl_fsub_op # NORM - SNAN
short tbl_fsub_op - tbl_fsub_op #
short tbl_fsub_op - tbl_fsub_op #
short fsub_inf_dst - tbl_fsub_op # INF - NORM
short fsub_inf_dst - tbl_fsub_op # INF - ZERO
short fsub_inf_2 - tbl_fsub_op # INF - INF
short fsub_res_qnan - tbl_fsub_op # NORM - QNAN
short fsub_inf_dst - tbl_fsub_op # INF - DENORM
short fsub_res_snan - tbl_fsub_op # NORM - SNAN
short tbl_fsub_op - tbl_fsub_op #
short tbl_fsub_op - tbl_fsub_op #
short fsub_res_qnan - tbl_fsub_op # QNAN - NORM
short fsub_res_qnan - tbl_fsub_op # QNAN - ZERO
short fsub_res_qnan - tbl_fsub_op # QNAN - INF
short fsub_res_qnan - tbl_fsub_op # QNAN - QNAN
short fsub_res_qnan - tbl_fsub_op # QNAN - DENORM
short fsub_res_snan - tbl_fsub_op # QNAN - SNAN
short tbl_fsub_op - tbl_fsub_op #
short tbl_fsub_op - tbl_fsub_op #
short fsub_norm - tbl_fsub_op # DENORM - NORM
short fsub_zero_src - tbl_fsub_op # DENORM - ZERO
short fsub_inf_src - tbl_fsub_op # DENORM - INF
short fsub_res_qnan - tbl_fsub_op # NORM - QNAN
short fsub_norm - tbl_fsub_op # DENORM - DENORM
short fsub_res_snan - tbl_fsub_op # NORM - SNAN
short tbl_fsub_op - tbl_fsub_op #
short tbl_fsub_op - tbl_fsub_op #
short fsub_res_snan - tbl_fsub_op # SNAN - NORM
short fsub_res_snan - tbl_fsub_op # SNAN - ZERO
short fsub_res_snan - tbl_fsub_op # SNAN - INF
short fsub_res_snan - tbl_fsub_op # SNAN - QNAN
short fsub_res_snan - tbl_fsub_op # SNAN - DENORM
short fsub_res_snan - tbl_fsub_op # SNAN - SNAN
short tbl_fsub_op - tbl_fsub_op #
short tbl_fsub_op - tbl_fsub_op #
#
# both operands are ZEROes
#
fsub_zero_2:
mov.b SRC_EX(%a0),%d0
mov.b DST_EX(%a1),%d1
eor.b %d1,%d0
bpl.b fsub_zero_2_chk_rm
# the signs are opposite, so, return a ZERO w/ the sign of the dst ZERO
tst.b %d0 # is dst negative?
bmi.b fsub_zero_2_rm # yes
fmov.s &0x00000000,%fp0 # no; return +ZERO
mov.b &z_bmask,FPSR_CC(%a6) # set Z
rts
#
# the ZEROes have the same signs:
# - Therefore, we return +ZERO if the rounding mode is RN,RZ, or RP
# - -ZERO is returned in the case of RM.
#
fsub_zero_2_chk_rm:
mov.b 3+L_SCR3(%a6),%d1
andi.b &0x30,%d1 # extract rnd mode
cmpi.b %d1,&rm_mode*0x10 # is rnd mode = RM?
beq.b fsub_zero_2_rm # yes
fmov.s &0x00000000,%fp0 # no; return +ZERO
mov.b &z_bmask,FPSR_CC(%a6) # set Z
rts
#
# one operand is a ZERO and the other is a DENORM or a NORM.
# scale the DENORM or NORM and jump to the regular fsub routine.
#
fsub_zero_dst:
mov.w SRC_EX(%a0),FP_SCR0_EX(%a6)
mov.l SRC_HI(%a0),FP_SCR0_HI(%a6)
mov.l SRC_LO(%a0),FP_SCR0_LO(%a6)
bsr.l scale_to_zero_src # scale the operand clr.w FP_SCR1_EX(%a6) clr.l FP_SCR1_HI(%a6) clr.l FP_SCR1_LO(%a6)
bra.w fsub_zero_entry # go execute fsub
#
# both operands are INFs. an OPERR will result if the INFs have the
# same signs. else,
#
fsub_inf_2:
mov.b SRC_EX(%a0),%d0 # exclusive or the signs
mov.b DST_EX(%a1),%d1
eor.b %d1,%d0
bpl.l res_operr # weed out (-INF)+(+INF)
# ok, so it's not an OPERR. but we do have to remember to return
# the src INF since that's where the 881/882 gets the j-bit.
fsub_inf_src:
fmovm.x SRC(%a0),&0x80 # return src INF
fneg.x %fp0 # invert sign
fbge.w fsub_inf_done # sign is now positive
mov.b &neg_bmask+inf_bmask,FPSR_CC(%a6) # set INF/NEG
rts
fsub_inf_dst:
fmovm.x DST(%a1),&0x80 # return dst INF
tst.b DST_EX(%a1) # is INF negative?
bpl.b fsub_inf_done # no
mov.b &neg_bmask+inf_bmask,FPSR_CC(%a6) # set INF/NEG
rts
fsub_inf_done:
mov.b &inf_bmask,FPSR_CC(%a6) # set INF
rts
#########################################################################
# XDEF **************************************************************** #
# fsqrt(): emulates the fsqrt instruction #
# fssqrt(): emulates the fssqrt instruction #
# fdsqrt(): emulates the fdsqrt instruction #
# #
# XREF **************************************************************** #
# scale_sqrt() - scale the source operand #
# unf_res() - return default underflow result #
# ovf_res() - return default overflow result #
# res_qnan_1op() - return QNAN result #
# res_snan_1op() - return SNAN result #
# #
# INPUT *************************************************************** #
# a0 = pointer to extended precision source operand #
# d0 rnd prec,mode #
# #
# OUTPUT ************************************************************** #
# fp0 = result #
# fp1 = EXOP (if exception occurred) #
# #
# ALGORITHM *********************************************************** #
# Handle NANs, infinities, and zeroes as special cases. Divide #
# norms/denorms into ext/sgl/dbl precision. #
# For norms/denorms, scale the exponents such that a sqrt #
# instruction won't cause an exception. Use the regular fsqrt to #
# compute a result. Check if the regular operands would have taken #
# an exception. If so, return the default overflow/underflow result #
# and return the EXOP if exceptions are enabled. Else, scale the #
# result operand to the proper exponent. #
# #
#########################################################################
#
# operand is either single or double
#
fsqrt_not_ext:
cmpi.b %d0,&s_mode*0x10 # separate sgl/dbl prec
bne.w fsqrt_dbl
#
# operand is to be rounded to single precision
#
fsqrt_sgl:
mov.w SRC_EX(%a0),FP_SCR0_EX(%a6)
mov.l SRC_HI(%a0),FP_SCR0_HI(%a6)
mov.l SRC_LO(%a0),FP_SCR0_LO(%a6)
bsr.l scale_sqrt # calculate scale factor
cmpi.l %d0,&0x3fff-0x3f81 # will move in underflow?
beq.w fsqrt_sd_may_unfl
bgt.w fsqrt_sd_unfl # yes; go handle underflow
cmpi.l %d0,&0x3fff-0x407f # will move in overflow?
beq.w fsqrt_sd_may_ovfl # maybe; go check
blt.w fsqrt_sd_ovfl # yes; go handle overflow
#
# operand will NOT overflow or underflow when moved in to the fp reg file
#
fsqrt_sd_normal:
fmov.l &0x0,%fpsr # clear FPSR
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fsqrt.x FP_SCR0(%a6),%fp0 # perform absolute
fmov.l %fpsr,%d1 # save FPSR
fmov.l &0x0,%fpcr # clear FPCR
or.l %d1,USER_FPSR(%a6) # save INEX2,N
fsqrt_sd_normal_exit:
mov.l %d2,-(%sp) # save d2
fmovm.x &0x80,FP_SCR0(%a6) # store out result
mov.w FP_SCR0_EX(%a6),%d1 # load sgn,exp
mov.l %d1,%d2 # make a copy
andi.l &0x7fff,%d1 # strip sign sub.l %d0,%d1 # add scale factor
andi.w &0x8000,%d2 # keep old sign
or.w %d1,%d2 # concat old sign,new exp
mov.w %d2,FP_SCR0_EX(%a6) # insert new exponent
mov.l (%sp)+,%d2 # restore d2
fmovm.x FP_SCR0(%a6),&0x80 # return result in fp0
rts
#
# operand is to be rounded to double precision
#
fsqrt_dbl:
mov.w SRC_EX(%a0),FP_SCR0_EX(%a6)
mov.l SRC_HI(%a0),FP_SCR0_HI(%a6)
mov.l SRC_LO(%a0),FP_SCR0_LO(%a6)
bsr.l scale_sqrt # calculate scale factor
cmpi.l %d0,&0x3fff-0x3c01 # will move in underflow?
beq.w fsqrt_sd_may_unfl
bgt.b fsqrt_sd_unfl # yes; go handle underflow
cmpi.l %d0,&0x3fff-0x43ff # will move in overflow?
beq.w fsqrt_sd_may_ovfl # maybe; go check
blt.w fsqrt_sd_ovfl # yes; go handle overflow
bra.w fsqrt_sd_normal # no; ho handle normalized op
# we're on the line here and the distinguising characteristic is whether
# the exponent is 3fff or 3ffe. if it's 3ffe, then it's a safe number
# elsewise fall through to underflow.
fsqrt_sd_may_unfl:
btst &0x0,1+FP_SCR0_EX(%a6) # is exponent 0x3fff?
bne.w fsqrt_sd_normal # yes, so no underflow
#
# operand WILL underflow when moved in to the fp register file
#
fsqrt_sd_unfl:
bset &unfl_bit,FPSR_EXCEPT(%a6) # set unfl exc bit
fmov.l &rz_mode*0x10,%fpcr # set FPCR
fmov.l &0x0,%fpsr # clear FPSR
fsqrt.x FP_SCR0(%a6),%fp0 # execute square root
fmov.l %fpsr,%d1 # save status
fmov.l &0x0,%fpcr # clear FPCR
or.l %d1,USER_FPSR(%a6) # save INEX2,N
# if underflow or inexact is enabled, go calculate EXOP first.
mov.b FPCR_ENABLE(%a6),%d1
andi.b &0x0b,%d1 # is UNFL or INEX enabled?
bne.b fsqrt_sd_unfl_ena # yes
fsqrt_sd_unfl_dis:
fmovm.x &0x80,FP_SCR0(%a6) # store out result
lea FP_SCR0(%a6),%a0 # pass: result addr
mov.l L_SCR3(%a6),%d1 # pass: rnd prec,mode
bsr.l unf_res # calculate default result
or.b %d0,FPSR_CC(%a6) # set possible 'Z' ccode
fmovm.x FP_SCR0(%a6),&0x80 # return default result in fp0
rts
#
# operand will underflow AND underflow is enabled.
# Therefore, we must return the result rounded to extended precision.
#
fsqrt_sd_unfl_ena:
mov.l FP_SCR0_HI(%a6),FP_SCR1_HI(%a6)
mov.l FP_SCR0_LO(%a6),FP_SCR1_LO(%a6)
mov.w FP_SCR0_EX(%a6),%d1 # load current exponent
mov.l %d2,-(%sp) # save d2
mov.l %d1,%d2 # make a copy
andi.l &0x7fff,%d1 # strip sign
andi.w &0x8000,%d2 # keep old sign sub.l %d0,%d1 # subtract scale factor
addi.l &0x6000,%d1 # add new bias
andi.w &0x7fff,%d1
or.w %d2,%d1 # concat new sign,new exp
mov.w %d1,FP_SCR1_EX(%a6) # insert new exp
fmovm.x FP_SCR1(%a6),&0x40 # return EXOP in fp1
mov.l (%sp)+,%d2 # restore d2
bra.b fsqrt_sd_unfl_dis
#
# operand WILL overflow.
#
fsqrt_sd_ovfl:
fmov.l &0x0,%fpsr # clear FPSR
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fsqrt.x FP_SCR0(%a6),%fp0 # perform square root
fmov.l &0x0,%fpcr # clear FPCR
fmov.l %fpsr,%d1 # save FPSR
or.l %d1,USER_FPSR(%a6) # save INEX2,N
fsqrt_sd_ovfl_tst:
or.l &ovfl_inx_mask,USER_FPSR(%a6) # set ovfl/aovfl/ainex
mov.b FPCR_ENABLE(%a6),%d1
andi.b &0x13,%d1 # is OVFL or INEX enabled?
bne.b fsqrt_sd_ovfl_ena # yes
#
# OVFL is not enabled; therefore, we must create the default result by
# calling ovf_res().
#
fsqrt_sd_ovfl_dis:
btst &neg_bit,FPSR_CC(%a6) # is result negative?
sne %d1 # set sign param accordingly
mov.l L_SCR3(%a6),%d0 # pass: prec,mode
bsr.l ovf_res # calculate default result
or.b %d0,FPSR_CC(%a6) # set INF,N if applicable
fmovm.x (%a0),&0x80 # return default result in fp0
rts
#
# OVFL is enabled.
# the INEX2 bit has already been updated by the round to the correct precision.
# now, round to extended(and don't alter the FPSR).
#
fsqrt_sd_ovfl_ena:
mov.l %d2,-(%sp) # save d2
mov.w FP_SCR0_EX(%a6),%d1 # fetch {sgn,exp}
mov.l %d1,%d2 # make a copy
andi.l &0x7fff,%d1 # strip sign
andi.w &0x8000,%d2 # keep old sign sub.l %d0,%d1 # add scale factor
subi.l &0x6000,%d1 # subtract bias
andi.w &0x7fff,%d1
or.w %d2,%d1 # concat sign,exp
mov.w %d1,FP_SCR0_EX(%a6) # insert new exponent
fmovm.x FP_SCR0(%a6),&0x40 # return EXOP in fp1
mov.l (%sp)+,%d2 # restore d2
bra.b fsqrt_sd_ovfl_dis
#
# the move in MAY underflow. so...
#
fsqrt_sd_may_ovfl:
btst &0x0,1+FP_SCR0_EX(%a6) # is exponent 0x3fff?
bne.w fsqrt_sd_ovfl # yes, so overflow
fmov.l &0x0,%fpsr # clear FPSR
fmov.l L_SCR3(%a6),%fpcr # set FPCR
fsqrt.x FP_SCR0(%a6),%fp0 # perform absolute
fmov.l %fpsr,%d1 # save status
fmov.l &0x0,%fpcr # clear FPCR
or.l %d1,USER_FPSR(%a6) # save INEX2,N
fmov.x %fp0,%fp1 # make a copy of result
fcmp.b %fp1,&0x1 # is |result| >= 1.b?
fbge.w fsqrt_sd_ovfl_tst # yes; overflow has occurred
# no, it didn't overflow; we have correct result
bra.w fsqrt_sd_normal_exit
#
# input is not normalized; what is it?
#
fsqrt_not_norm:
cmpi.b %d1,&DENORM # weed out DENORM
beq.w fsqrt_denorm
cmpi.b %d1,&ZERO # weed out ZERO
beq.b fsqrt_zero
cmpi.b %d1,&INF # weed out INF
beq.b fsqrt_inf
cmpi.b %d1,&SNAN # weed out SNAN
beq.l res_snan_1op
bra.l res_qnan_1op
#########################################################################
# XDEF **************************************************************** #
# addsub_scaler2(): scale inputs to fadd/fsub such that no #
# OVFL/UNFL exceptions will result #
# #
# XREF **************************************************************** #
# norm() - normalize mantissa after adjusting exponent #
# #
# INPUT *************************************************************** #
# FP_SRC(a6) = fp op1(src) #
# FP_DST(a6) = fp op2(dst) #
# #
# OUTPUT ************************************************************** #
# FP_SRC(a6) = fp op1 scaled(src) #
# FP_DST(a6) = fp op2 scaled(dst) #
# d0 = scale amount #
# #
# ALGORITHM *********************************************************** #
# If the DST exponent is > the SRC exponent, set the DST exponent #
# equal to 0x3fff and scale the SRC exponent by the value that the #
# DST exponent was scaled by. If the SRC exponent is greater or equal, #
# do the opposite. Return this scale factor in d0. #
# If the two exponents differ by > the number of mantissa bits #
# plus two, then set the smallest exponent to a very small value as a #
# quick shortcut. #
# #
#########################################################################
quick_scale12:
andi.w &0x8000,FP_SCR0_EX(%a6) # zero src exponent
bset &0x0,1+FP_SCR0_EX(%a6) # set exp = 1
mov.l (%sp)+,%d0 # return SCALE factor
rts
# src exp is >= dst exp; scale src to exp = 0x3fff
src_exp_ge2:
bsr.l scale_to_zero_src
mov.l %d0,-(%sp) # save scale factor
cmpi.b DTAG(%a6),&DENORM # is dst denormalized?
bne.b cmpexp22
lea FP_SCR1(%a6),%a0
bsr.l norm # normalize the denorm; result is new exp
neg.w %d0 # new exp = -(shft val)
mov.w %d0,2+L_SCR1(%a6) # inset new exp
#########################################################################
# XDEF **************************************************************** #
# scale_to_zero_src(): scale the exponent of extended precision #
# value at FP_SCR0(a6). #
# #
# XREF **************************************************************** #
# norm() - normalize the mantissa if the operand was a DENORM #
# #
# INPUT *************************************************************** #
# FP_SCR0(a6) = extended precision operand to be scaled #
# #
# OUTPUT ************************************************************** #
# FP_SCR0(a6) = scaled extended precision operand #
# d0 = scale value #
# #
# ALGORITHM *********************************************************** #
# Set the exponent of the input operand to 0x3fff. Save the value #
# of the difference between the original and new exponent. Then, #
# normalize the operand if it was a DENORM. Add this normalization #
# value to the previous value. Return the result. #
# #
#########################################################################
global scale_to_zero_src
scale_to_zero_src:
mov.w FP_SCR0_EX(%a6),%d1 # extract operand's {sgn,exp}
mov.w %d1,%d0 # make a copy
stzs_denorm:
lea FP_SCR0(%a6),%a0 # pass ptr to src op
bsr.l norm # normalize denorm
neg.l %d0 # new exponent = -(shft val)
mov.l %d0,%d1 # prepare for op_norm call
bra.b stzs_norm # finish scaling
###
#########################################################################
# XDEF **************************************************************** #
# scale_sqrt(): scale the input operand exponent so a subsequent #
# fsqrt operation won't take an exception. #
# #
# XREF **************************************************************** #
# norm() - normalize the mantissa if the operand was a DENORM #
# #
# INPUT *************************************************************** #
# FP_SCR0(a6) = extended precision operand to be scaled #
# #
# OUTPUT ************************************************************** #
# FP_SCR0(a6) = scaled extended precision operand #
# d0 = scale value #
# #
# ALGORITHM *********************************************************** #
# If the input operand is a DENORM, normalize it. #
# If the exponent of the input operand is even, set the exponent #
# to 0x3ffe and return a scale factor of "(exp-0x3ffe)/2". If the #
# exponent of the input operand is off, set the exponent to ox3fff and #
# return a scale factor of "(exp-0x3fff)/2". #
# #
#########################################################################
global scale_sqrt
scale_sqrt:
cmpi.b STAG(%a6),&DENORM # is operand normalized?
beq.b ss_denorm # normalize the DENORM
#########################################################################
# XDEF **************************************************************** #
# scale_to_zero_dst(): scale the exponent of extended precision #
# value at FP_SCR1(a6). #
# #
# XREF **************************************************************** #
# norm() - normalize the mantissa if the operand was a DENORM #
# #
# INPUT *************************************************************** #
# FP_SCR1(a6) = extended precision operand to be scaled #
# #
# OUTPUT ************************************************************** #
# FP_SCR1(a6) = scaled extended precision operand #
# d0 = scale value #
# #
# ALGORITHM *********************************************************** #
# Set the exponent of the input operand to 0x3fff. Save the value #
# of the difference between the original and new exponent. Then, #
# normalize the operand if it was a DENORM. Add this normalization #
# value to the previous value. Return the result. #
# #
#########################################################################
global scale_to_zero_dst
scale_to_zero_dst:
mov.w FP_SCR1_EX(%a6),%d1 # extract operand's {sgn,exp}
mov.w %d1,%d0 # make a copy
#########################################################################
# XDEF **************************************************************** #
# res_qnan(): return default result w/ QNAN operand for dyadic #
# res_snan(): return default result w/ SNAN operand for dyadic #
# res_qnan_1op(): return dflt result w/ QNAN operand for monadic #
# res_snan_1op(): return dflt result w/ SNAN operand for monadic #
# #
# XREF **************************************************************** #
# None #
# #
# INPUT *************************************************************** #
# FP_SRC(a6) = pointer to extended precision src operand #
# FP_DST(a6) = pointer to extended precision dst operand #
# #
# OUTPUT ************************************************************** #
# fp0 = default result #
# #
# ALGORITHM *********************************************************** #
# If either operand (but not both operands) of an operation is a #
# nonsignalling NAN, then that NAN is returned as the result. If both #
# operands are nonsignalling NANs, then the destination operand #
# nonsignalling NAN is returned as the result. #
# If either operand to an operation is a signalling NAN (SNAN), #
# then, the SNAN bit is set in the FPSR EXC byte. If the SNAN trap #
# enable bit is set in the FPCR, then the trap is taken and the #
# destination is not modified. If the SNAN trap enable bit is not set, #
# then the SNAN is converted to a nonsignalling NAN (by setting the #
# SNAN bit in the operand to one), and the operation continues as #
# described in the preceding paragraph, for nonsignalling NANs. #
# Make sure the appropriate FPSR bits are set before exiting. #
# #
#########################################################################
global res_qnan global res_snan
res_qnan:
res_snan:
cmp.b DTAG(%a6), &SNAN # is the dst an SNAN?
beq.b dst_snan2
cmp.b DTAG(%a6), &QNAN # is the dst a QNAN?
beq.b dst_qnan2
src_nan:
cmp.b STAG(%a6), &QNAN
beq.b src_qnan2 global res_snan_1op
res_snan_1op:
src_snan2:
bset &0x6, FP_SRC_HI(%a6) # set SNAN bit
or.l &nan_mask+aiop_mask+snan_mask, USER_FPSR(%a6)
lea FP_SRC(%a6), %a0
bra.b nan_comp global res_qnan_1op
res_qnan_1op:
src_qnan2:
or.l &nan_mask, USER_FPSR(%a6)
lea FP_SRC(%a6), %a0
bra.b nan_comp
dst_snan2:
or.l &nan_mask+aiop_mask+snan_mask, USER_FPSR(%a6)
bset &0x6, FP_DST_HI(%a6) # set SNAN bit
lea FP_DST(%a6), %a0
bra.b nan_comp
dst_qnan2:
lea FP_DST(%a6), %a0
cmp.b STAG(%a6), &SNAN
bne nan_done
or.l &aiop_mask+snan_mask, USER_FPSR(%a6)
nan_done:
or.l &nan_mask, USER_FPSR(%a6)
nan_comp:
btst &0x7, FTEMP_EX(%a0) # is NAN neg?
beq.b nan_not_neg
or.l &neg_mask, USER_FPSR(%a6)
nan_not_neg:
fmovm.x (%a0), &0x80
rts
#########################################################################
# XDEF **************************************************************** #
# res_operr(): return default result during operand error #
# #
# XREF **************************************************************** #
# None #
# #
# INPUT *************************************************************** #
# None #
# #
# OUTPUT ************************************************************** #
# fp0 = default operand error result #
# #
# ALGORITHM *********************************************************** #
# An nonsignalling NAN is returned as the default result when #
# an operand error occurs for the following cases: #
# #
# Multiply: (Infinity x Zero) #
# Divide : (Zero / Zero) || (Infinity / Infinity) #
# #
#########################################################################
global res_operr
res_operr:
or.l &nan_mask+operr_mask+aiop_mask, USER_FPSR(%a6)
fmovm.x nan_return(%pc), &0x80
rts
nan_return:
long 0x7fff0000, 0xffffffff, 0xffffffff
#########################################################################
# fdbcc(): routine to emulate the fdbcc instruction #
# #
# XDEF **************************************************************** #
# _fdbcc() #
# #
# XREF **************************************************************** #
# fetch_dreg() - fetch Dn value #
# store_dreg_l() - store updated Dn value #
# #
# INPUT *************************************************************** #
# d0 = displacement #
# #
# OUTPUT ************************************************************** #
# none #
# #
# ALGORITHM *********************************************************** #
# This routine checks which conditional predicate is specified by #
# the stacked fdbcc instruction opcode and then branches to a routine #
# for that predicate. The corresponding fbcc instruction is then used #
# to see whether the condition (specified by the stacked FPSR) is true #
# or false. #
# If a BSUN exception should be indicated, the BSUN and ABSUN #
# bits are set in the stacked FPSR. If the BSUN exception is enabled, #
# the fbsun_flg is set in the SPCOND_FLG location on the stack. If an #
# enabled BSUN should not be flagged and the predicate is true, then #
# Dn is fetched and decremented by one. If Dn is not equal to -1, add #
# the displacement value to the stacked PC so that when an "rte" is #
# finally executed, the branch occurs. #
# #
######################################################################### global _fdbcc
_fdbcc:
mov.l %d0,L_SCR1(%a6) # save displacement
mov.w EXC_CMDREG(%a6),%d0 # fetch predicate
clr.l %d1 # clear scratch reg
mov.b FPSR_CC(%a6),%d1 # fetch fp ccodes
ror.l &0x8,%d1 # rotate to top byte
fmov.l %d1,%fpsr # insert into FPSR
tbl_fdbcc:
short fdbcc_f - tbl_fdbcc # 00
short fdbcc_eq - tbl_fdbcc # 01
short fdbcc_ogt - tbl_fdbcc # 02
short fdbcc_oge - tbl_fdbcc # 03
short fdbcc_olt - tbl_fdbcc # 04
short fdbcc_ole - tbl_fdbcc # 05
short fdbcc_ogl - tbl_fdbcc # 06
short fdbcc_or - tbl_fdbcc # 07
short fdbcc_un - tbl_fdbcc # 08
short fdbcc_ueq - tbl_fdbcc # 09
short fdbcc_ugt - tbl_fdbcc # 10
short fdbcc_uge - tbl_fdbcc # 11
short fdbcc_ult - tbl_fdbcc # 12
short fdbcc_ule - tbl_fdbcc # 13
short fdbcc_neq - tbl_fdbcc # 14
short fdbcc_t - tbl_fdbcc # 15
short fdbcc_sf - tbl_fdbcc # 16
short fdbcc_seq - tbl_fdbcc # 17
short fdbcc_gt - tbl_fdbcc # 18
short fdbcc_ge - tbl_fdbcc # 19
short fdbcc_lt - tbl_fdbcc # 20
short fdbcc_le - tbl_fdbcc # 21
short fdbcc_gl - tbl_fdbcc # 22
short fdbcc_gle - tbl_fdbcc # 23
short fdbcc_ngle - tbl_fdbcc # 24
short fdbcc_ngl - tbl_fdbcc # 25
short fdbcc_nle - tbl_fdbcc # 26
short fdbcc_nlt - tbl_fdbcc # 27
short fdbcc_nge - tbl_fdbcc # 28
short fdbcc_ngt - tbl_fdbcc # 29
short fdbcc_sneq - tbl_fdbcc # 30
short fdbcc_st - tbl_fdbcc # 31
#########################################################################
# #
# IEEE Nonaware tests #
# #
# For the IEEE nonaware tests, only the false branch changes the #
# counter. However, the true branch may set bsun so we check to see #
# if the NAN bit is set, in which case BSUN and AIOP will be set. #
# #
# The cases EQ and NE are shared by the Aware and Nonaware groups #
# and are incapable of setting the BSUN exception bit. #
# #
# Typically, only one of the two possible branch directions could #
# have the NAN bit set. #
# (This is assuming the mutual exclusiveness of FPSR cc bit groupings #
# is preserved.) #
# #
#########################################################################
#
# not equal:
# _
# Z
#
fdbcc_neq:
fbneq.w fdbcc_neq_yes # not equal?
fdbcc_neq_no:
bra.w fdbcc_false # no; go handle counter
fdbcc_neq_yes:
rts
#
# greater than:
# _______
# NANvZvN
#
fdbcc_gt:
fbgt.w fdbcc_gt_yes # greater than?
btst &nan_bit, FPSR_CC(%a6) # is NAN set in cc?
beq.w fdbcc_false # no;go handle counter
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # is BSUN enabled?
bne.w fdbcc_bsun # yes; we have an exception
bra.w fdbcc_false # no; go handle counter
fdbcc_gt_yes:
rts # do nothing
#
# not greater than:
#
# NANvZvN
#
fdbcc_ngt:
fbngt.w fdbcc_ngt_yes # not greater than?
fdbcc_ngt_no:
bra.w fdbcc_false # no; go handle counter
fdbcc_ngt_yes:
btst &nan_bit, FPSR_CC(%a6) # is NAN set in cc?
beq.b fdbcc_ngt_done # no;go finish
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # is BSUN enabled?
bne.w fdbcc_bsun # yes; we have an exception
fdbcc_ngt_done:
rts # no; do nothing
#
# greater than or equal:
# _____
# Zv(NANvN)
#
fdbcc_ge:
fbge.w fdbcc_ge_yes # greater than or equal?
fdbcc_ge_no:
btst &nan_bit, FPSR_CC(%a6) # is NAN set in cc?
beq.w fdbcc_false # no;go handle counter
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # is BSUN enabled?
bne.w fdbcc_bsun # yes; we have an exception
bra.w fdbcc_false # no; go handle counter
fdbcc_ge_yes:
btst &nan_bit, FPSR_CC(%a6) # is NAN set in cc?
beq.b fdbcc_ge_yes_done # no;go do nothing
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # is BSUN enabled?
bne.w fdbcc_bsun # yes; we have an exception
fdbcc_ge_yes_done:
rts # do nothing
#
# not (greater than or equal):
# _
# NANv(N^Z)
#
fdbcc_nge:
fbnge.w fdbcc_nge_yes # not (greater than or equal)?
fdbcc_nge_no:
bra.w fdbcc_false # no; go handle counter
fdbcc_nge_yes:
btst &nan_bit, FPSR_CC(%a6) # is NAN set in cc?
beq.b fdbcc_nge_done # no;go finish
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # is BSUN enabled?
bne.w fdbcc_bsun # yes; we have an exception
fdbcc_nge_done:
rts # no; do nothing
#
# less than:
# _____
# N^(NANvZ)
#
fdbcc_lt:
fblt.w fdbcc_lt_yes # less than?
fdbcc_lt_no:
btst &nan_bit, FPSR_CC(%a6) # is NAN set in cc?
beq.w fdbcc_false # no; go handle counter
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # is BSUN enabled?
bne.w fdbcc_bsun # yes; we have an exception
bra.w fdbcc_false # no; go handle counter
fdbcc_lt_yes:
rts # do nothing
#
# not less than:
# _
# NANv(ZvN)
#
fdbcc_nlt:
fbnlt.w fdbcc_nlt_yes # not less than?
fdbcc_nlt_no:
bra.w fdbcc_false # no; go handle counter
fdbcc_nlt_yes:
btst &nan_bit, FPSR_CC(%a6) # is NAN set in cc?
beq.b fdbcc_nlt_done # no;go finish
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # is BSUN enabled?
bne.w fdbcc_bsun # yes; we have an exception
fdbcc_nlt_done:
rts # no; do nothing
#
# less than or equal:
# ___
# Zv(N^NAN)
#
fdbcc_le:
fble.w fdbcc_le_yes # less than or equal?
fdbcc_le_no:
btst &nan_bit, FPSR_CC(%a6) # is NAN set in cc?
beq.w fdbcc_false # no; go handle counter
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # is BSUN enabled?
bne.w fdbcc_bsun # yes; we have an exception
bra.w fdbcc_false # no; go handle counter
fdbcc_le_yes:
btst &nan_bit, FPSR_CC(%a6) # is NAN set in cc?
beq.b fdbcc_le_yes_done # no; go do nothing
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # is BSUN enabled?
bne.w fdbcc_bsun # yes; we have an exception
fdbcc_le_yes_done:
rts # do nothing
#
# not (less than or equal):
# ___
# NANv(NvZ)
#
fdbcc_nle:
fbnle.w fdbcc_nle_yes # not (less than or equal)?
fdbcc_nle_no:
bra.w fdbcc_false # no; go handle counter
fdbcc_nle_yes:
btst &nan_bit, FPSR_CC(%a6) # is NAN set in cc?
beq.w fdbcc_nle_done # no; go finish
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # is BSUN enabled?
bne.w fdbcc_bsun # yes; we have an exception
fdbcc_nle_done:
rts # no; do nothing
#
# greater or less than:
# _____
# NANvZ
#
fdbcc_gl:
fbgl.w fdbcc_gl_yes # greater or less than?
fdbcc_gl_no:
btst &nan_bit, FPSR_CC(%a6) # is NAN set in cc?
beq.w fdbcc_false # no; handle counter
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # is BSUN enabled?
bne.w fdbcc_bsun # yes; we have an exception
bra.w fdbcc_false # no; go handle counter
fdbcc_gl_yes:
rts # do nothing
#
# not (greater or less than):
#
# NANvZ
#
fdbcc_ngl:
fbngl.w fdbcc_ngl_yes # not (greater or less than)?
fdbcc_ngl_no:
bra.w fdbcc_false # no; go handle counter
fdbcc_ngl_yes:
btst &nan_bit, FPSR_CC(%a6) # is NAN set in cc?
beq.b fdbcc_ngl_done # no; go finish
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # is BSUN enabled?
bne.w fdbcc_bsun # yes; we have an exception
fdbcc_ngl_done:
rts # no; do nothing
#
# greater, less, or equal:
# ___
# NAN
#
fdbcc_gle:
fbgle.w fdbcc_gle_yes # greater, less, or equal?
fdbcc_gle_no:
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # is BSUN enabled?
bne.w fdbcc_bsun # yes; we have an exception
bra.w fdbcc_false # no; go handle counter
fdbcc_gle_yes:
rts # do nothing
#
# not (greater, less, or equal):
#
# NAN
#
fdbcc_ngle:
fbngle.w fdbcc_ngle_yes # not (greater, less, or equal)?
fdbcc_ngle_no:
bra.w fdbcc_false # no; go handle counter
fdbcc_ngle_yes:
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # is BSUN enabled?
bne.w fdbcc_bsun # yes; we have an exception
rts # no; do nothing
#########################################################################
# #
# Miscellaneous tests #
# #
# For the IEEE miscellaneous tests, all but fdbf and fdbt can set bsun. #
# #
#########################################################################
#
# false:
#
# False
#
fdbcc_f: # no bsun possible
bra.w fdbcc_false # go handle counter
#
# true:
#
# True
#
fdbcc_t: # no bsun possible
rts # do nothing
#
# signalling false:
#
# False
#
fdbcc_sf:
btst &nan_bit, FPSR_CC(%a6) # is NAN set?
beq.w fdbcc_false # no;go handle counter
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # is BSUN enabled?
bne.w fdbcc_bsun # yes; we have an exception
bra.w fdbcc_false # go handle counter
#
# signalling true:
#
# True
#
fdbcc_st:
btst &nan_bit, FPSR_CC(%a6) # is NAN set?
beq.b fdbcc_st_done # no;go finish
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # is BSUN enabled?
bne.w fdbcc_bsun # yes; we have an exception
fdbcc_st_done:
rts
#
# signalling equal:
#
# Z
#
fdbcc_seq:
fbseq.w fdbcc_seq_yes # signalling equal?
fdbcc_seq_no:
btst &nan_bit, FPSR_CC(%a6) # is NAN set?
beq.w fdbcc_false # no;go handle counter
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # is BSUN enabled?
bne.w fdbcc_bsun # yes; we have an exception
bra.w fdbcc_false # go handle counter
fdbcc_seq_yes:
btst &nan_bit, FPSR_CC(%a6) # is NAN set?
beq.b fdbcc_seq_yes_done # no;go do nothing
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # is BSUN enabled?
bne.w fdbcc_bsun # yes; we have an exception
fdbcc_seq_yes_done:
rts # yes; do nothing
#
# signalling not equal:
# _
# Z
#
fdbcc_sneq:
fbsneq.w fdbcc_sneq_yes # signalling not equal?
fdbcc_sneq_no:
btst &nan_bit, FPSR_CC(%a6) # is NAN set?
beq.w fdbcc_false # no;go handle counter
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # is BSUN enabled?
bne.w fdbcc_bsun # yes; we have an exception
bra.w fdbcc_false # go handle counter
fdbcc_sneq_yes:
btst &nan_bit, FPSR_CC(%a6) # set BSUN exc bit
beq.w fdbcc_sneq_done # no;go finish
ori.l &bsun_mask+aiop_mask, USER_FPSR(%a6) # set BSUN exc bit
btst &bsun_bit, FPCR_ENABLE(%a6) # is BSUN enabled?
bne.w fdbcc_bsun # yes; we have an exception
fdbcc_sneq_done:
rts
#########################################################################
# #
# IEEE Aware tests #
# #
# For the IEEE aware tests, action is only taken if the result is false.#
--> --------------------
--> maximum size reached
--> --------------------
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