|
| round.sa 3.4 7/29/91
|
| handle rounding and normalization tasks
|
|
|
| Copyright (C) Motorola, Inc. 1990
| All Rights Reserved
|
| For details on the license for this file, please see the
| file, README, in this same directory.
|ROUND idnt 2,1 | Motorola 040 Floating Point Software Package
|section 8
#include "fpsp.h"
|
| round --- round result according to precision/mode
|
| a0 points to the input operand in the internal extended format
| d1(high word) contains rounding precision:
| ext = $0000xxxx
| sgl = $0001xxxx
| dbl = $0002xxxx
| d1(low word) contains rounding mode:
| RN = $xxxx0000
| RZ = $xxxx0001
| RM = $xxxx0010
| RP = $xxxx0011
| d0{31:29} contains the g,r,s bits (extended)
|
| On return the value pointed to by a0 is correctly rounded,
| a0 is preserved and the g-r-s bits in d0 are cleared.
| The result is not typed - the tag field is invalid. The
| result is still in the internal extended format.
|
| The INEX bit of USER_FPSR will be set if the rounded result was
| inexact (i.e. if any of the g-r-s bits were set).
|
.global round
round:
| If g=r=s=0 then result is exact and round is done, else set
| the inex flag in status reg and continue.
|
bsrs ext_grs |this subroutine looks at the
| :rounding precision and sets
| ;the appropriate g-r-s bits.
tstl %d0 |if grs are zero, go force
bne rnd_cont |lower bits to zero for size
swap %d1 |set up d1.w for round prec.
bra truncate
rnd_cont:
|
| Use rounding mode as an index into a jump table for these modes.
|
orl #inx2a_mask,USER_FPSR(%a6) |set inex2/ainex
lea mode_tab,%a1
movel (%a1,%d1.w*4),%a1
jmp (%a1)
|
| Jump table indexed by rounding mode in d1.w. All following assumes
| grs != 0.
|
mode_tab:
.long rnd_near
.long rnd_zero
.long rnd_mnus
.long rnd_plus
|
| ROUND PLUS INFINITY
|
| If sign of fp number = 0 (positive), then add 1 to l.
|
rnd_plus:
swap %d1 |set up d1 for round prec.
tstb LOCAL_SGN(%a0) |check for sign
bmi truncate |if positive then truncate
movel #0xffffffff,%d0 |force g,r,s to be all f's
lea add_to_l,%a1
movel (%a1,%d1.w*4),%a1
jmp (%a1)
|
| ROUND MINUS INFINITY
|
| If sign of fp number = 1 (negative), then add 1 to l.
|
rnd_mnus:
swap %d1 |set up d1 for round prec.
tstb LOCAL_SGN(%a0) |check for sign
bpl truncate |if negative then truncate
movel #0xffffffff,%d0 |force g,r,s to be all f's
lea add_to_l,%a1
movel (%a1,%d1.w*4),%a1
jmp (%a1)
|
| ROUND ZERO
|
| Always truncate.
rnd_zero:
swap %d1 |set up d1 for round prec.
bra truncate
|
|
| ROUND NEAREST
|
| If (g=1), then add 1 to l and if (r=s=0), then clear l
| Note that this will round to even in case of a tie.
|
rnd_near:
swap %d1 |set up d1 for round prec.
asll #1,%d0 |shift g-bit to c-bit
bcc truncate |if (g=1) then
lea add_to_l,%a1
movel (%a1,%d1.w*4),%a1
jmp (%a1)
|
| ext_grs --- extract guard, round and sticky bits
|
| Input: d1 = PREC:ROUND
| Output: d0{31:29}= guard, round, sticky
|
| The ext_grs extract the guard/round/sticky bits according to the
| selected rounding precision. It is called by the round subroutine
| only. All registers except d0 are kept intact. d0 becomes an
| updated guard,round,sticky in d0{31:29}
|
| Notes: the ext_grs uses the round PREC, and therefore has to swap d1
| prior to usage, and needs to restore d1 to original.
|
ext_grs:
swap %d1 |have d1.w point to round precision
cmpiw #0,%d1
bnes sgl_or_dbl
bras end_ext_grs
sgl_or_dbl:
moveml %d2/%d3,-(%a7) |make some temp registers
cmpiw #1,%d1
bnes grs_dbl
grs_sgl:
bfextu LOCAL_HI(%a0){#24:#2},%d3 |sgl prec. g-r are 2 bits right
movel #30,%d2 |of the sgl prec. limits
lsll %d2,%d3 |shift g-r bits to MSB of d3
movel LOCAL_HI(%a0),%d2 |get word 2 for s-bit test
andil #0x0000003f,%d2 |s bit is the or of all other
bnes st_stky |bits to the right of g-r
tstl LOCAL_LO(%a0) |test lower mantissa
bnes st_stky |if any are set, set sticky
tstl %d0 |test original g,r,s
bnes st_stky |if any are set, set sticky
bras end_sd |if words 3 and 4 are clr, exit
grs_dbl:
bfextu LOCAL_LO(%a0){#21:#2},%d3 |dbl-prec. g-r are 2 bits right
movel #30,%d2 |of the dbl prec. limits
lsll %d2,%d3 |shift g-r bits to the MSB of d3
movel LOCAL_LO(%a0),%d2 |get lower mantissa for s-bit test
andil #0x000001ff,%d2 |s bit is the or-ing of all
bnes st_stky |other bits to the right of g-r
tstl %d0 |test word original g,r,s
bnes st_stky |if any are set, set sticky
bras end_sd |if clear, exit
st_stky:
bset #rnd_stky_bit,%d3
end_sd:
movel %d3,%d0 |return grs to d0
moveml (%a7)+,%d2/%d3 |restore scratch registers
end_ext_grs:
swap %d1 |restore d1 to original
rts
|******************* Local Equates
.set ad_1_sgl,0x00000100 | constant to add 1 to l-bit in sgl prec
.set ad_1_dbl,0x00000800 | constant to add 1 to l-bit in dbl prec
|Jump table for adding 1 to the l-bit indexed by rnd prec
add_to_l:
.long add_ext
.long add_sgl
.long add_dbl
.long add_dbl
|
| ADD SINGLE
|
add_sgl:
addl #ad_1_sgl,LOCAL_HI(%a0)
bccs scc_clr |no mantissa overflow
roxrw LOCAL_HI(%a0) |shift v-bit back in
roxrw LOCAL_HI+2(%a0) |shift v-bit back in
addw #0x1,LOCAL_EX(%a0) |and incr exponent
scc_clr:
tstl %d0 |test for rs = 0
bnes sgl_done
andiw #0xfe00,LOCAL_HI+2(%a0) |clear the l-bit
sgl_done:
andil #0xffffff00,LOCAL_HI(%a0) |truncate bits beyond sgl limit
clrl LOCAL_LO(%a0) |clear d2
rts
|
| ADD EXTENDED
|
add_ext:
addql #1,LOCAL_LO(%a0) |add 1 to l-bit
bccs xcc_clr |test for carry out
addql #1,LOCAL_HI(%a0) |propagate carry
bccs xcc_clr
roxrw LOCAL_HI(%a0) |mant is 0 so restore v-bit
roxrw LOCAL_HI+2(%a0) |mant is 0 so restore v-bit
roxrw LOCAL_LO(%a0)
roxrw LOCAL_LO+2(%a0)
addw #0x1,LOCAL_EX(%a0) |and inc exp
xcc_clr:
tstl %d0 |test rs = 0
bnes add_ext_done
andib #0xfe,LOCAL_LO+3(%a0) |clear the l bit
add_ext_done:
rts
|
| ADD DOUBLE
|
add_dbl:
addl #ad_1_dbl,LOCAL_LO(%a0)
bccs dcc_clr
addql #1,LOCAL_HI(%a0) |propagate carry
bccs dcc_clr
roxrw LOCAL_HI(%a0) |mant is 0 so restore v-bit
roxrw LOCAL_HI+2(%a0) |mant is 0 so restore v-bit
roxrw LOCAL_LO(%a0)
roxrw LOCAL_LO+2(%a0)
addw #0x1,LOCAL_EX(%a0) |incr exponent
dcc_clr:
tstl %d0 |test for rs = 0
bnes dbl_done
andiw #0xf000,LOCAL_LO+2(%a0) |clear the l-bit
|
| NORMALIZE
|
| These routines (nrm_zero & nrm_set) normalize the unnorm. This
| is done by shifting the mantissa left while decrementing the
| exponent.
|
| NRM_SET shifts and decrements until there is a 1 set in the integer
| bit of the mantissa (msb in d1).
|
| NRM_ZERO shifts and decrements until there is a 1 set in the integer
| bit of the mantissa (msb in d1) unless this would mean the exponent
| would go less than 0. In that case the number becomes a denorm - the
| exponent (d0) is set to 0 and the mantissa (d1 & d2) is not
| normalized.
|
| Note that both routines have been optimized (for the worst case) and
| therefore do not have the easy to follow decrement/shift loop.
|
| NRM_ZERO
|
| Distance to first 1 bit in mantissa = X
| Distance to 0 from exponent = Y
| If X < Y
| Then
| nrm_set
| Else
| shift mantissa by Y
| set exponent = 0
|
|input:
| FP_SCR1 = exponent, ms mantissa part, ls mantissa part
|output:
| L_SCR1{4} = fpte15 or ete15 bit
|
.global nrm_zero
nrm_zero:
movew LOCAL_EX(%a0),%d0
cmpw #64,%d0 |see if exp > 64
bmis d0_less
bsr nrm_set |exp > 64 so exp won't exceed 0
rts
d0_less:
moveml %d2/%d3/%d5/%d6,-(%a7)
movel LOCAL_HI(%a0),%d1
movel LOCAL_LO(%a0),%d2
bfffo %d1{#0:#32},%d3 |get the distance to the first 1
| ;in ms mant
beqs ms_clr |branch if no bits were set
cmpw %d3,%d0 |of X>Y
bmis greater |then exp will go past 0 (neg) if
| ;it is just shifted
bsr nrm_set |else exp won't go past 0
moveml (%a7)+,%d2/%d3/%d5/%d6
rts
greater:
movel %d2,%d6 |save ls mant in d6
lsll %d0,%d2 |shift ls mant by count
lsll %d0,%d1 |shift ms mant by count
movel #32,%d5
subl %d0,%d5 |make op a denorm by shifting bits
lsrl %d5,%d6 |by the number in the exp, then
| ;set exp = 0.
orl %d6,%d1 |shift the ls mant bits into the ms mant
movel #0,%d0 |same as if decremented exp to 0
| ;while shifting
movew %d0,LOCAL_EX(%a0)
movel %d1,LOCAL_HI(%a0)
movel %d2,LOCAL_LO(%a0)
moveml (%a7)+,%d2/%d3/%d5/%d6
rts
ms_clr:
bfffo %d2{#0:#32},%d3 |check if any bits set in ls mant
beqs all_clr |branch if none set
addw #32,%d3
cmpw %d3,%d0 |if X>Y
bmis greater |then branch
bsr nrm_set |else exp won't go past 0
moveml (%a7)+,%d2/%d3/%d5/%d6
rts
all_clr:
movew #0,LOCAL_EX(%a0) |no mantissa bits set. Set exp = 0.
moveml (%a7)+,%d2/%d3/%d5/%d6
rts
|
| NRM_SET
|
.global nrm_set
nrm_set:
movel %d7,-(%a7)
bfffo LOCAL_HI(%a0){#0:#32},%d7 |find first 1 in ms mant to d7)
beqs lower |branch if ms mant is all 0's
movel %d6,-(%a7)
subw %d7,LOCAL_EX(%a0) |sub exponent by count
movel LOCAL_HI(%a0),%d0 |d0 has ms mant
movel LOCAL_LO(%a0),%d1 |d1 has ls mant
lsll %d7,%d0 |shift first 1 to j bit position
movel %d1,%d6 |copy ls mant into d6
lsll %d7,%d6 |shift ls mant by count
movel %d6,LOCAL_LO(%a0) |store ls mant into memory
moveql #32,%d6
subl %d7,%d6 |continue shift
lsrl %d6,%d1 |shift off all bits but those that will
| ;be shifted into ms mant
orl %d1,%d0 |shift the ls mant bits into the ms mant
movel %d0,LOCAL_HI(%a0) |store ms mant into memory
moveml (%a7)+,%d7/%d6 |restore registers
rts
|
| We get here if ms mant was = 0, and we assume ls mant has bits
| set (otherwise this would have been tagged a zero not a denorm).
|
lower:
movew LOCAL_EX(%a0),%d0 |d0 has exponent
movel LOCAL_LO(%a0),%d1 |d1 has ls mant
subw #32,%d0 |account for ms mant being all zeros
bfffo %d1{#0:#32},%d7 |find first 1 in ls mant to d7)
subw %d7,%d0 |subtract shift count from exp
lsll %d7,%d1 |shift first 1 to integer bit in ms mant
movew %d0,LOCAL_EX(%a0) |store ms mant
movel %d1,LOCAL_HI(%a0) |store exp
clrl LOCAL_LO(%a0) |clear ls mant
movel (%a7)+,%d7
rts
|
| denorm --- denormalize an intermediate result
|
| Used by underflow.
|
| Input:
| a0 points to the operand to be denormalized
| (in the internal extended format)
|
| d0: rounding precision
| Output:
| a0 points to the denormalized result
| (in the internal extended format)
|
| d0 is guard,round,sticky
|
| d0 comes into this routine with the rounding precision. It
| is then loaded with the denormalized exponent threshold for the
| rounding precision.
|
.global denorm
denorm:
btstb #6,LOCAL_EX(%a0) |check for exponents between $7fff-$4000
beqs no_sgn_ext
bsetb #7,LOCAL_EX(%a0) |sign extend if it is so
no_sgn_ext:
clrl %d1 |load d1 with ext threshold
clrl %d0 |clear the sticky flag
bsr dnrm_lp |denormalize the number
tstb %d1 |check for inex
beq no_inex |if clr, no inex
bras dnrm_inex |if set, set inex
not_ext:
cmpil #1,%d0 |if 1 then single precision
beqs load_sgl |else must be 2, double prec
load_dbl:
movew #dbl_thresh,%d1 |put copy of threshold in d1
movel %d1,%d0 |copy d1 into d0
subw LOCAL_EX(%a0),%d0 |diff = threshold - exp
cmpw #67,%d0 |if diff > 67 (mant + grs bits)
bpls chk_stky |then branch (all bits would be
| ; shifted off in denorm routine)
clrl %d0 |else clear the sticky flag
bsr dnrm_lp |denormalize the number
tstb %d1 |check flag
beqs no_inex |if clr, no inex
bras dnrm_inex |if set, set inex
load_sgl:
movew #sgl_thresh,%d1 |put copy of threshold in d1
movel %d1,%d0 |copy d1 into d0
subw LOCAL_EX(%a0),%d0 |diff = threshold - exp
cmpw #67,%d0 |if diff > 67 (mant + grs bits)
bpls chk_stky |then branch (all bits would be
| ; shifted off in denorm routine)
clrl %d0 |else clear the sticky flag
bsr dnrm_lp |denormalize the number
tstb %d1 |check flag
beqs no_inex |if clr, no inex
bras dnrm_inex |if set, set inex
chk_stky:
tstl LOCAL_HI(%a0) |check for any bits set
bnes set_stky
tstl LOCAL_LO(%a0) |check for any bits set
bnes set_stky
bras clr_mant
set_stky:
orl #inx2a_mask,USER_FPSR(%a6) |set inex2/ainex
movel #0x20000000,%d0 |set sticky bit in return value
clr_mant:
movew %d1,LOCAL_EX(%a0) |load exp with threshold
movel #0,LOCAL_HI(%a0) |set d1 = 0 (ms mantissa)
movel #0,LOCAL_LO(%a0) |set d2 = 0 (ms mantissa)
rts
dnrm_inex:
orl #inx2a_mask,USER_FPSR(%a6) |set inex2/ainex
no_inex:
rts
|
| dnrm_lp --- normalize exponent/mantissa to specified threshold
|
| Input:
| a0 points to the operand to be denormalized
| d0{31:29} initial guard,round,sticky
| d1{15:0} denormalization threshold
| Output:
| a0 points to the denormalized operand
| d0{31:29} final guard,round,sticky
| d1.b inexact flag: all ones means inexact result
|
| The LOCAL_LO and LOCAL_GRS parts of the value are copied to FP_SCR2
| so that bfext can be used to extract the new low part of the mantissa.
| Dnrm_lp can be called with a0 pointing to ETEMP or WBTEMP and there
| is no LOCAL_GRS scratch word following it on the fsave frame.
|
.global dnrm_lp
dnrm_lp:
movel %d2,-(%sp) |save d2 for temp use
btstb #E3,E_BYTE(%a6) |test for type E3 exception
beqs not_E3 |not type E3 exception
bfextu WBTEMP_GRS(%a6){#6:#3},%d2 |extract guard,round, sticky bit
movel #29,%d0
lsll %d0,%d2 |shift g,r,s to their positions
movel %d2,%d0
not_E3:
movel (%sp)+,%d2 |restore d2
movel LOCAL_LO(%a0),FP_SCR2+LOCAL_LO(%a6)
movel %d0,FP_SCR2+LOCAL_GRS(%a6)
movel %d1,%d0 |copy the denorm threshold
subw LOCAL_EX(%a0),%d1 |d1 = threshold - uns exponent
bles no_lp |d1 <= 0
cmpw #32,%d1
blts case_1 |0 = d1 < 32
cmpw #64,%d1
blts case_2 |32 <= d1 < 64
bra case_3 |d1 >= 64
|
| No normalization necessary
|
no_lp:
clrb %d1 |set no inex2 reported
movel FP_SCR2+LOCAL_GRS(%a6),%d0 |restore original g,r,s
rts
|
| case (0<d1<32)
|
case_1:
movel %d2,-(%sp)
movew %d0,LOCAL_EX(%a0) |exponent = denorm threshold
movel #32,%d0
subw %d1,%d0 |d0 = 32 - d1
bfextu LOCAL_EX(%a0){%d0:#32},%d2
bfextu %d2{%d1:%d0},%d2 |d2 = new LOCAL_HI
bfextu LOCAL_HI(%a0){%d0:#32},%d1 |d1 = new LOCAL_LO
bfextu FP_SCR2+LOCAL_LO(%a6){%d0:#32},%d0 |d0 = new G,R,S
movel %d2,LOCAL_HI(%a0) |store new LOCAL_HI
movel %d1,LOCAL_LO(%a0) |store new LOCAL_LO
clrb %d1
bftst %d0{#2:#30}
beqs c1nstky
bsetl #rnd_stky_bit,%d0 st %d1
c1nstky:
movel FP_SCR2+LOCAL_GRS(%a6),%d2 |restore original g,r,s
andil #0xe0000000,%d2 |clear all but G,R,S
tstl %d2 |test if original G,R,S are clear
beqs grs_clear
orl #0x20000000,%d0 |set sticky bit in d0
grs_clear:
andil #0xe0000000,%d0 |clear all but G,R,S
movel (%sp)+,%d2
rts
|
| case (32<=d1<64)
|
case_2:
movel %d2,-(%sp)
movew %d0,LOCAL_EX(%a0) |unsigned exponent = threshold
subw #32,%d1 |d1 now between 0 and 32
movel #32,%d0
subw %d1,%d0 |d0 = 32 - d1
bfextu LOCAL_EX(%a0){%d0:#32},%d2
bfextu %d2{%d1:%d0},%d2 |d2 = new LOCAL_LO
bfextu LOCAL_HI(%a0){%d0:#32},%d1 |d1 = new G,R,S
bftst %d1{#2:#30}
bnes c2_sstky |bra if sticky bit to be set
bftst FP_SCR2+LOCAL_LO(%a6){%d0:#32}
bnes c2_sstky |bra if sticky bit to be set
movel %d1,%d0
clrb %d1
bras end_c2
c2_sstky:
movel %d1,%d0
bsetl #rnd_stky_bit,%d0 st %d1
end_c2:
clrl LOCAL_HI(%a0) |store LOCAL_HI = 0
movel %d2,LOCAL_LO(%a0) |store LOCAL_LO
movel FP_SCR2+LOCAL_GRS(%a6),%d2 |restore original g,r,s
andil #0xe0000000,%d2 |clear all but G,R,S
tstl %d2 |test if original G,R,S are clear
beqs clear_grs
orl #0x20000000,%d0 |set sticky bit in d0
clear_grs:
andil #0xe0000000,%d0 |get rid of all but G,R,S
movel (%sp)+,%d2
rts
|
| d1 >= 64 Force the exponent to be the denorm threshold with the
| correct sign.
|
case_3:
movew %d0,LOCAL_EX(%a0)
tstw LOCAL_SGN(%a0)
bges c3con
c3neg:
orl #0x80000000,LOCAL_EX(%a0)
c3con:
cmpw #64,%d1
beqs sixty_four
cmpw #65,%d1
beqs sixty_five
|
| Shift value is out of range. Set d1 for inex2 flag and
| return a zero with the given threshold.
|
clrl LOCAL_HI(%a0)
clrl LOCAL_LO(%a0)
movel #0x20000000,%d0 st %d1
rts
sixty_four:
movel LOCAL_HI(%a0),%d0
bfextu %d0{#2:#30},%d1
andil #0xc0000000,%d0
bras c3com
sixty_five:
movel LOCAL_HI(%a0),%d0
bfextu %d0{#1:#31},%d1
andil #0x80000000,%d0
lsrl #1,%d0 |shift high bit into R bit
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