dnl AMD K6 mpn_mul_basecase -- multiply two mpn numbers.
dnl Copyright 1999-2003 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 K6: approx 9.0 cycles per cross product on 30x30 limbs (with 16 limbs/loop
C unrolling).
dnl K6: UNROLL_COUNT cycles/product (approx)
dnl 8 9.75
dnl 16 9.3
dnl 32 9.3
dnl Maximum possible with the current code is 32.
dnl
dnl With 16 the inner unrolled loop fits exactly in a 256 byte block, which
dnl might explain it's good performance.
deflit(UNROLL_COUNT, 16)
C void mpn_mul_basecase (mp_ptr wp,
C mp_srcptr xp, mp_size_t xsize,
C mp_srcptr yp, mp_size_t ysize);
C
C Calculate xp,xsize multiplied by yp,ysize, storing the result in
C wp,xsize+ysize.
C
C This routine is essentially the same as mpn/generic/mul_basecase.c, but
C it's faster because it does most of the mpn_addmul_1() entry code only
C once. The saving is about 10-20% on typical sizes coming from the
C Karatsuba multiply code.
C
C Enhancements:
C
C The mul_1 loop is about 8.5 c/l, which is slower than mpn_mul_1 at 6.25
C c/l. Could call mpn_mul_1 when ysize is big enough to make it worthwhile.
C
C The main unrolled addmul loop could be shared by mpn_addmul_1, using some
C extra stack setups and maybe 2 or 3 wasted cycles at the end. Code saving
C would be 256 bytes.
ifdef(`PIC',`
deflit(UNROLL_THRESHOLD, 8)
',`
deflit(UNROLL_THRESHOLD, 8)
')
defframe(PARAM_YSIZE,20)
defframe(PARAM_YP, 16)
defframe(PARAM_XSIZE,12)
defframe(PARAM_XP, 8)
defframe(PARAM_WP, 4)
TEXT
ALIGN(32)
PROLOGUE(mpn_mul_basecase)
deflit(`FRAME',0)
movl PARAM_XSIZE, %ecx
movl PARAM_YP, %eax
movl PARAM_XP, %edx
movl (%eax), %eax C yp low limb
cmpl $2, %ecx
ja L(xsize_more_than_two_limbs)
je L(two_by_something)
C one limb by one limb
movl (%edx), %edx C xp low limb
movl PARAM_WP, %ecx
mull %edx
movl %eax, (%ecx)
movl %edx, 4(%ecx)
ret
C -----------------------------------------------------------------------------
L(two_by_something):
decl PARAM_YSIZE
pushl %ebx
deflit(`FRAME',4)
movl PARAM_WP, %ebx
pushl %esi
deflit(`FRAME',8)
movl %eax, %ecx C yp low limb
movl (%edx), %eax C xp low limb
movl %edx, %esi C xp
jnz L(two_by_two)
C two limbs by one limb
mull %ecx
movl %eax, (%ebx)
movl 4(%esi), %eax
movl %edx, %esi C carry
mull %ecx
addl %eax, %esi
movl %esi, 4(%ebx)
adcl $0, %edx
movl %edx, 8(%ebx)
popl %esi
popl %ebx
ret
C -----------------------------------------------------------------------------
ALIGN(16)
L(two_by_two):
C eax xp low limb
C ebx wp
C ecx yp low limb
C edx
C esi xp
C edi
C ebp
deflit(`FRAME',8)
mull %ecx C xp[0] * yp[0]
push %edi
deflit(`FRAME',12)
movl %eax, (%ebx)
movl 4(%esi), %eax
movl %edx, %edi C carry, for wp[1]
mull %ecx C xp[1] * yp[0]
addl %eax, %edi
movl PARAM_YP, %ecx
adcl $0, %edx
movl %edi, 4(%ebx)
movl 4(%ecx), %ecx C yp[1]
movl 4(%esi), %eax C xp[1]
movl %edx, %edi C carry, for wp[2]
mull %ecx C xp[1] * yp[1]
addl %eax, %edi
adcl $0, %edx
movl (%esi), %eax C xp[0]
movl %edx, %esi C carry, for wp[3]
mull %ecx C xp[0] * yp[1]
addl %eax, 4(%ebx)
adcl %edx, %edi
adcl $0, %esi
movl %edi, 8(%ebx)
popl %edi
movl %esi, 12(%ebx)
popl %esi
popl %ebx
ret
C -----------------------------------------------------------------------------
ALIGN(16)
L(xsize_more_than_two_limbs):
C The first limb of yp is processed with a simple mpn_mul_1 style loop
C inline. Unrolling this doesn't seem worthwhile since it's only run once
C (whereas the addmul below is run ysize-1 many times). A call to the
C actual mpn_mul_1 will be slowed down by the call and parameter pushing and
C popping, and doesn't seem likely to be worthwhile on the typical 10-20
C limb operations the Karatsuba code calls here with.
C eax yp[0]
C ebx
C ecx xsize
C edx xp
C esi
C edi
C ebp
deflit(`FRAME',0)
pushl %edi defframe_pushl(SAVE_EDI)
pushl %ebp defframe_pushl(SAVE_EBP)
movl PARAM_WP, %edi
pushl %esi defframe_pushl(SAVE_ESI)
movl %eax, %ebp
pushl %ebx defframe_pushl(SAVE_EBX)
leal (%edx,%ecx,4), %ebx C xp end
xorl %esi, %esi
leal (%edi,%ecx,4), %edi C wp end of mul1
negl %ecx
L(mul1):
C eax scratch
C ebx xp end
C ecx counter, negative
C edx scratch
C esi carry
C edi wp end of mul1
C ebp multiplier
movl (%ebx,%ecx,4), %eax
mull %ebp
addl %esi, %eax
movl $0, %esi
adcl %edx, %esi
movl %eax, (%edi,%ecx,4)
incl %ecx
jnz L(mul1)
movl PARAM_YSIZE, %edx
movl %esi, (%edi) C final carry
movl PARAM_XSIZE, %ecx
decl %edx
jnz L(ysize_more_than_one_limb)
popl %ebx
popl %esi
popl %ebp
popl %edi
ret
L(ysize_more_than_one_limb):
cmpl $UNROLL_THRESHOLD, %ecx
movl PARAM_YP, %eax
jae L(unroll)
C -----------------------------------------------------------------------------
C Simple addmul loop.
C
C Using ebx and edi pointing at the ends of their respective locations saves
C a couple of instructions in the outer loop. The inner loop is still 11
C cycles, the same as the simple loop in aorsmul_1.asm.
C eax yp
C ebx xp end
C ecx xsize
C edx ysize-1
C esi
C edi wp end of mul1
C ebp
movl 4(%eax), %ebp C multiplier
negl %ecx
movl %ecx, PARAM_XSIZE C -xsize
xorl %esi, %esi C initial carry
leal 4(%eax,%edx,4), %eax C yp end
negl %edx
movl %eax, PARAM_YP
movl %edx, PARAM_YSIZE
jmp L(simple_outer_entry)
C aligning here saves a couple of cycles
ALIGN(16)
L(simple_outer_top):
C edx ysize counter, negative
movl PARAM_YP, %eax C yp end
xorl %esi, %esi C carry
movl PARAM_XSIZE, %ecx C -xsize
movl %edx, PARAM_YSIZE
movl (%eax,%edx,4), %ebp C yp limb multiplier
L(simple_outer_entry):
addl $4, %edi
L(simple_inner):
C eax scratch
C ebx xp end
C ecx counter, negative
C edx scratch
C esi carry
C edi wp end of this addmul
C ebp multiplier
movl (%ebx,%ecx,4), %eax
mull %ebp
addl %esi, %eax
movl $0, %esi
adcl $0, %edx
addl %eax, (%edi,%ecx,4)
adcl %edx, %esi
incl %ecx
jnz L(simple_inner)
movl PARAM_YSIZE, %edx
movl %esi, (%edi)
incl %edx
jnz L(simple_outer_top)
popl %ebx
popl %esi
popl %ebp
popl %edi
ret
C -----------------------------------------------------------------------------
C Unrolled loop.
C
C The unrolled inner loop is the same as in aorsmul_1.asm, see that code for
C some comments.
C
C VAR_COUNTER is for the inner loop, running from VAR_COUNTER_INIT down to
C 0, inclusive.
C
C VAR_JMP is the computed jump into the unrolled loop.
C
C PARAM_XP and PARAM_WP get offset appropriately for where the unrolled loop
C is entered.
C
C VAR_XP_LOW is the least significant limb of xp, which is needed at the
C start of the unrolled loop. This can't just be fetched through the xp
C pointer because of the offset applied to it.
C
C PARAM_YSIZE is the outer loop counter, going from -(ysize-1) up to -1,
C inclusive.
C
C PARAM_YP is offset appropriately so that the PARAM_YSIZE counter can be
C added to give the location of the next limb of yp, which is the multiplier
C in the unrolled loop.
C
C PARAM_WP is similarly offset so that the PARAM_YSIZE counter can be added
C to give the starting point in the destination for each unrolled loop (this
C point is one limb upwards for each limb of yp processed).
C
C Having PARAM_YSIZE count negative to zero means it's not necessary to
C store new values of PARAM_YP and PARAM_WP on each loop. Those values on
C the stack remain constant and on each loop an leal adjusts them with the
C PARAM_YSIZE counter value.
defframe(VAR_COUNTER, -20)
defframe(VAR_COUNTER_INIT, -24)
defframe(VAR_JMP, -28)
defframe(VAR_XP_LOW, -32)
deflit(VAR_STACK_SPACE, 16)
dnl For some strange reason using (%esp) instead of 0(%esp) is a touch
dnl slower in this code, hence the defframe empty-if-zero feature is
dnl disabled.
dnl
dnl If VAR_COUNTER is at (%esp), the effect is worse. In this case the
dnl unrolled loop is 255 instead of 256 bytes, but quite how this affects
dnl anything isn't clear.
dnl
define(`defframe_empty_if_zero_disabled',1)
L(unroll):
C eax yp (not used)
C ebx xp end (not used)
C ecx xsize
C edx ysize-1
C esi
C edi wp end of mul1 (not used)
C ebp
deflit(`FRAME', 16)
leal -2(%ecx), %ebp C one limb processed at start,
decl %ecx C and ebp is one less
shrl $UNROLL_LOG2, %ebp
negl %ecx
subl $VAR_STACK_SPACE, %esp
deflit(`FRAME', 16+VAR_STACK_SPACE)
andl $UNROLL_MASK, %ecx
movl %ecx, %esi
shll $4, %ecx
movl %ebp, VAR_COUNTER_INIT
negl %esi
C 15 code bytes per limb
ifdef(`PIC',`
call L(pic_calc)
L(unroll_here):
',`
leal L(unroll_entry) (%ecx,%esi,1), %ecx
')
movl PARAM_XP, %ebx
movl %ebp, VAR_COUNTER
movl PARAM_WP, %edi
movl %ecx, VAR_JMP
movl (%ebx), %eax
leal 4(%edi,%esi,4), %edi C wp adjust for unrolling and mul1
leal (%ebx,%esi,4), %ebx C xp adjust for unrolling
movl %eax, VAR_XP_LOW
movl %ebx, PARAM_XP
movl PARAM_YP, %ebx
leal (%edi,%edx,4), %ecx C wp adjust for ysize indexing
movl 4(%ebx), %ebp C multiplier (yp second limb)
leal 4(%ebx,%edx,4), %ebx C yp adjust for ysize indexing
movl %ecx, PARAM_WP
leal 1(%esi), %ecx C adjust parity for decl %ecx above
movl %ebx, PARAM_YP
negl %edx
movl %edx, PARAM_YSIZE
jmp L(unroll_outer_entry)
ifdef(`PIC',`
L(pic_calc):
C See mpn/x86/README about old gas bugs
leal (%ecx,%esi,1), %ecx
addl $L(unroll_entry)-L(unroll_here), %ecx
addl (%esp), %ecx
ret_internal
')
C -----------------------------------------------------------------------------
C Aligning here saves a couple of cycles per loop. Using 32 doesn't
C cost any extra space, since the inner unrolled loop below is
C aligned to 32.
ALIGN(32)
L(unroll_outer_top):
C edx ysize
movl PARAM_YP, %eax
movl %edx, PARAM_YSIZE C incremented ysize counter
movl PARAM_WP, %edi
movl VAR_COUNTER_INIT, %ebx
movl (%eax,%edx,4), %ebp C next multiplier
movl PARAM_XSIZE, %ecx
leal (%edi,%edx,4), %edi C adjust wp for where we are in yp
movl VAR_XP_LOW, %eax
movl %ebx, VAR_COUNTER
L(unroll_outer_entry):
mull %ebp
C using testb is a tiny bit faster than testl
testb $1, %cl
movl %eax, %ecx C low carry
movl VAR_JMP, %eax
movl %edx, %esi C high carry
movl PARAM_XP, %ebx
jnz L(unroll_noswap)
movl %ecx, %esi C high,low carry other way around
movl %edx, %ecx
L(unroll_noswap):
jmp *%eax
C -----------------------------------------------------------------------------
ALIGN(32)
L(unroll_top):
C eax scratch
C ebx xp
C ecx carry low
C edx scratch
C esi carry high
C edi wp
C ebp multiplier
C VAR_COUNTER loop counter
C
C 15 code bytes each limb
leal UNROLL_BYTES(%edi), %edi
L(unroll_entry):
deflit(CHUNK_COUNT,2)
forloop(`i', 0, UNROLL_COUNT/CHUNK_COUNT-1, `
deflit(`disp0', eval(i*CHUNK_COUNT*4))
deflit(`disp1', eval(disp0 + 4))
deflit(`disp2', eval(disp1 + 4))
movl disp1(%ebx), %eax
mull %ebp
Zdisp( addl, %ecx, disp0,(%edi))
adcl %eax, %esi
movl %edx, %ecx
jadcl0( %ecx)
movl disp2(%ebx), %eax
mull %ebp
addl %esi, disp1(%edi)
adcl %eax, %ecx
movl %edx, %esi
jadcl0( %esi)
')
decl VAR_COUNTER
leal UNROLL_BYTES(%ebx), %ebx
jns L(unroll_top)
movl PARAM_YSIZE, %edx
addl %ecx, UNROLL_BYTES(%edi)
adcl $0, %esi
incl %edx
movl %esi, UNROLL_BYTES+4(%edi)
jnz L(unroll_outer_top)
movl SAVE_ESI, %esi
movl SAVE_EBP, %ebp
movl SAVE_EDI, %edi
movl SAVE_EBX, %ebx
addl $FRAME, %esp
ret
EPILOGUE()