dnl AMD K6 mpn_addmul_1/mpn_submul_1 --
add or subtract mpn multiple.
dnl Copyright 1999-2003, 2005 Free Software Foundation,
Inc.
dnl
This file is part of the GNU MP Library.
dnl
dnl The GNU MP Library is free software
; you can redistribute it and/or modify
dnl it under the terms of either:
dnl
dnl * the GNU Lesser General
Public License as published by the Free
dnl Software Foundation
; either version 3 of the License, or (at your
dnl
option) any later
version.
dnl
dnl
or
dnl
dnl * the GNU General
Public License as published by the Free Software
dnl Foundation
; either version 2 of the License, or (at your option) any
dnl later
version.
dnl
dnl
or both in parallel, as here.
dnl
dnl The GNU MP Library is distributed in the hope that it will be useful, but
dnl WITHOUT ANY WARRANTY
; without even the implied warranty of MERCHANTABILITY
dnl
or FITNESS
FOR A PARTICULAR PURPOSE. See the GNU General
Public License
dnl
for more details.
dnl
dnl You should have received copies of the GNU General
Public License
and the
dnl GNU Lesser General
Public License along with the GNU MP Library.
If not,
dnl see
https://www.gnu.org/licenses/.
include(`../config.m4
')
C cycles/limb
C P5
C P6
model 0-8,10-12 5.94
C P6
model 9 (Banias) 5.51
C P6
model 13 (Dothan) 5.57
C P4
model 0 (Willamette)
C P4
model 1 (?)
C P4
model 2 (Northwood)
C P4
model 3 (Prescott)
C P4
model 4 (Nocona)
C AMD K6 7.65-8.5 (
data dependent)
C AMD K7
C AMD K8
dnl K6: large multipliers small multipliers
dnl UNROLL_COUNT cycles/limb cycles/limb
dnl 4 9.5 7.78
dnl 8 9.0 7.78
dnl 16 8.4 7.65
dnl 32 8.4 8.2
dnl
dnl Maximum possible unrolling with the current
code is 32.
dnl
dnl Unrolling to 16 limbs/loop makes the unrolled loop fit exactly in a 256
dnl
byte block, which might explain the good speed at that unrolling.
deflit(UNROLL_COUNT, 16)
ifdef(`OPERATION_addmul_1
', `
define(M4_inst, addl)
define(M4_function_1, mpn_addmul_1)
define(M4_function_1c, mpn_addmul_1c)
',`ifdef(`OPERATION_submul_1', `
define(M4_inst, subl)
define(M4_function_1, mpn_submul_1)
define(M4_function_1c, mpn_submul_1c)
',`m4_error(`Need OPERATION_addmul_1 or OPERATION_submul_1
')')
')
MULFUNC_PROLOGUE(mpn_addmul_1 mpn_addmul_1c mpn_submul_1 mpn_submul_1c)
C mp_limb_t mpn_addmul_1 (mp_ptr dst, mp_srcptr src, mp_size_t size,
C mp_limb_t mult)
;
C mp_limb_t mpn_addmul_1c (mp_ptr dst, mp_srcptr src, mp_size_t size,
C mp_limb_t mult, mp_limb_t
carry)
;
C mp_limb_t mpn_submul_1 (mp_ptr dst, mp_srcptr src, mp_size_t size,
C mp_limb_t mult)
;
C mp_limb_t mpn_submul_1c (mp_ptr dst, mp_srcptr src, mp_size_t size,
C mp_limb_t mult, mp_limb_t
carry)
;
C
C The jadcl0()s in the unrolled loop makes the speed
data dependent. Small
C multipliers (most significant few bits clear) result in few
carry bits
and
C speeds up to 7.65 cycles/limb are attained. Large multipliers (most
C significant few bits set) make the
carry bits 50/50
and lead to something
C more like 8.4 c/l. With adcl
's both of these would be 9.3 c/l.
C
C It
's important that the gains for jadcl0 on small multipliers don't come
C at the cost of slowing down other
data. Tests on uniformly distributed
C random
data, designed to confound branch prediction, show about a 7%
C speed-up using jadcl0 over adcl (8.93 versus 9.57 cycles/limb, with all
C overheads included).
C
C In the simple loop, jadcl0() measures slower than adcl (11.9-14.7 versus
C 11.0 cycles/limb),
and hence isn
't used.
C
C In the simple loop, note that running
ecx from negative to
zero and using
C it as an index in the two movs wouldn
't help. It would save one
C instruction (2*addl+loop becoming incl+
jnz), but there
's nothing unpaired
C that would be collapsed by
this.
C
C Attempts at a simpler main loop, with less unrolling, haven
't yielded much
C success, generally running over 9 c/l.
C
C
C jadcl0
C ------
C
C jadcl0() being faster than adcl $0 seems to be an artifact of two things,
C firstly the instruction decoding
and secondly the fact that there
's a
C
carry bit
for the jadcl0 only on average about 1/4 of the
time.
C
C The
code in the unrolled loop decodes something like the following.
C
C decode cycles
C mull %
ebp 2
C M4_inst %
esi, disp(%
edi) 1
C adcl %
eax, %
ecx 2
C movl %
edx, %
esi \ 1
C jnc 1f /
C incl %
esi \ 1
C 1: movl disp(%ebx), %
eax /
C ---
C 7
C
C In a back-to-back style test
this measures 7 with the jnc not taken,
or 8
C with it taken (both when correctly predicted).
This is opposite to the
C measurements showing small multipliers running faster than large ones.
C Don
't really know why.
C
C It
's not clear how much branch misprediction might be costing. The K6
C doco says it will be 1 to 4 cycles, but presumably it
's near the low end
C of that range to get the measured results.
C
C
C In the
code the two carries are more
or less the preceding
mul product
and
C the calculation is roughly
C
C x*y + u*b+v
C
C where b=2^32 is the size of a limb, x*y is the two
carry limbs,
and u
and
C v are the two limbs it
's added to (being the low of the next mul, and a
C limb from the destination).
C
C To get a
carry requires x*y+u*b+v >= b^2, which is u*b+v >= b^2-x*y,
and
C there are b^2-(b^2-x*y) = x*y many such values, giving a probability of
C x*y/b^2.
If x, y, u
and v are random
and uniformly distributed between 0
C
and b-1, then the total probability can be summed over x
and y,
C
C 1 b-1 b-1 x*y 1 b*(b-1) b*(b-1)
C --- * sum sum --- = --- * ------- * ------- = 1/4
C b^2 x=0 y=1 b^2 b^4 2 2
C
C Actually it
's a very tiny bit less than 1/4 of course. If y is fixed,
C then the probability is 1/2*y/b thus varying linearly between 0
and 1/2.
ifdef(`PIC
',`
deflit(UNROLL_THRESHOLD, 9)
',`
deflit(UNROLL_THRESHOLD, 6)
')
defframe(PARAM_CARRY, 20)
defframe(PARAM_MULTIPLIER,16)
defframe(PARAM_SIZE, 12)
defframe(PARAM_SRC, 8)
defframe(PARAM_DST, 4)
TEXT
ALIGN(32)
PROLOGUE(M4_function_1c)
pushl %
esi
deflit(`FRAME
',4)
movl PARAM_CARRY, %
esi
jmp L(start_nc)
EPILOGUE()
PROLOGUE(M4_function_1)
push %
esi
deflit(`FRAME
',4)
xorl %
esi, %
esi C initial
carry
L(start_nc):
movl PARAM_SIZE, %
ecx
pushl %ebx
deflit(`FRAME
',8)
movl PARAM_SRC, %ebx
pushl %
edi
deflit(`FRAME
',12)
cmpl $UNROLL_THRESHOLD, %
ecx
movl PARAM_DST, %
edi
pushl %
ebp
deflit(`FRAME
',16)
jae L(unroll)
C simple loop
movl PARAM_MULTIPLIER, %
ebp
L(simple):
C
eax scratch
C ebx src
C
ecx counter
C
edx scratch
C
esi carry
C
edi dst
C
ebp multiplier
movl (%ebx), %
eax
addl $4, %ebx
mull %
ebp
addl $4, %
edi
addl %
esi, %
eax
adcl $0, %
edx
M4_inst %
eax, -4(%
edi)
adcl $0, %
edx
movl %
edx, %
esi
loop L(simple)
popl %
ebp
popl %
edi
popl %ebx
movl %
esi, %
eax
popl %
esi
ret
C -----------------------------------------------------------------------------
C The unrolled loop uses a
"two carry limbs" scheme. At the top of the loop
C the carries are
ecx=lo,
esi=hi, then they swap
for each limb processed.
C
For the computed jump an odd size means they start one way around, an
even
C size the other.
C
C VAR_JUMP holds the computed jump temporarily because there
's not enough
C registers at the point of doing the
mul for the initial two
carry limbs.
C
C The
add/
adc for the initial
carry in %
esi is necessary only
for the
C mpn_addmul/submul_1c entry points. Duplicating the startup
code to
C eliminate
this for the plain mpn_add/submul_1 doesn
't seem like a good
C idea.
dnl overlapping with parameters already fetched
define(VAR_COUNTER, `PARAM_SIZE
')
define(VAR_JUMP, `PARAM_DST
')
L(unroll):
C
eax
C ebx src
C
ecx size
C
edx
C
esi initial
carry
C
edi dst
C
ebp
movl %
ecx, %
edx
decl %
ecx
subl $2, %
edx
negl %
ecx
shrl $UNROLL_LOG2, %
edx
andl $UNROLL_MASK, %
ecx
movl %
edx, VAR_COUNTER
movl %
ecx, %
edx
shll $4, %
edx
negl %
ecx
C 15
code bytes per limb
ifdef(`PIC
',`
call L(pic_calc)
L(here):
',`
leal L(entry) (%
edx,%
ecx,1), %
edx
')
movl (%ebx), %
eax C src low limb
movl PARAM_MULTIPLIER, %
ebp
movl %
edx, VAR_JUMP
mull %
ebp
addl %
esi, %
eax C initial
carry (from _1c)
jadcl0( %
edx)
leal 4(%ebx,%
ecx,4), %ebx
movl %
edx, %
esi C high
carry
movl VAR_JUMP, %
edx
leal (%
edi,%
ecx,4), %
edi
testl $1, %
ecx
movl %
eax, %
ecx C low
carry
jz L(noswap)
movl %
esi, %
ecx C high,low
carry other way around
movl %
eax, %
esi
L(noswap):
jmp *%
edx
ifdef(`PIC
',`
L(pic_calc):
C See mpn/x86/README about old gas bugs
leal (%
edx,%
ecx,1), %
edx
addl $L(entry)-L(here), %
edx
addl (%
esp), %
edx
ret_internal
')
C -----------------------------------------------------------
ALIGN(32)
L(top):
deflit(`FRAME
',16)
C
eax scratch
C ebx src
C
ecx carry lo
C
edx scratch
C
esi carry hi
C
edi dst
C
ebp multiplier
C
C 15
code bytes per limb
leal UNROLL_BYTES(%
edi), %
edi
L(entry):
forloop(`i
', 0, UNROLL_COUNT/2-1, `
deflit(`disp0
', eval(2*i*4))
deflit(`disp1
', eval(disp0 + 4))
Zdisp( movl, disp0,(%ebx), %
eax)
mull %
ebp
Zdisp( M4_inst,%
ecx, disp0,(%
edi))
adcl %
eax, %
esi
movl %
edx, %
ecx
jadcl0( %
ecx)
movl disp1(%ebx), %
eax
mull %
ebp
M4_inst %
esi, disp1(%
edi)
adcl %
eax, %
ecx
movl %
edx, %
esi
jadcl0( %
esi)
')
decl VAR_COUNTER
leal UNROLL_BYTES(%ebx), %ebx
jns L(top)
popl %
ebp
M4_inst %
ecx, UNROLL_BYTES(%
edi)
popl %
edi
movl %
esi, %
eax
popl %ebx
jadcl0( %
eax)
popl %
esi
ret
EPILOGUE()
