diff options
author | Thomas Voss <mail@thomasvoss.com> | 2024-06-21 23:36:36 +0200 |
---|---|---|
committer | Thomas Voss <mail@thomasvoss.com> | 2024-06-21 23:42:26 +0200 |
commit | a89a14ef5da44684a16b204e7a70460cc8c4922a (patch) | |
tree | b23b4c6b155977909ef508fdae2f48d33d802813 /vendor/gmp-6.3.0/mpn/x86/p6/mmx/divrem_1.asm | |
parent | 1db63fcedab0b288820d66e100b1877b1a5a8851 (diff) |
Basic constant folding implementation
Diffstat (limited to 'vendor/gmp-6.3.0/mpn/x86/p6/mmx/divrem_1.asm')
-rw-r--r-- | vendor/gmp-6.3.0/mpn/x86/p6/mmx/divrem_1.asm | 767 |
1 files changed, 767 insertions, 0 deletions
diff --git a/vendor/gmp-6.3.0/mpn/x86/p6/mmx/divrem_1.asm b/vendor/gmp-6.3.0/mpn/x86/p6/mmx/divrem_1.asm new file mode 100644 index 0000000..5300616 --- /dev/null +++ b/vendor/gmp-6.3.0/mpn/x86/p6/mmx/divrem_1.asm @@ -0,0 +1,767 @@ +dnl Intel Pentium-II mpn_divrem_1 -- mpn by limb division. + +dnl Copyright 1999-2002 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 P6MMX: 25.0 cycles/limb integer part, 17.5 cycles/limb fraction part. + + +C mp_limb_t mpn_divrem_1 (mp_ptr dst, mp_size_t xsize, +C mp_srcptr src, mp_size_t size, +C mp_limb_t divisor); +C mp_limb_t mpn_divrem_1c (mp_ptr dst, mp_size_t xsize, +C mp_srcptr src, mp_size_t size, +C mp_limb_t divisor, mp_limb_t carry); +C mp_limb_t mpn_preinv_divrem_1 (mp_ptr dst, mp_size_t xsize, +C mp_srcptr src, mp_size_t size, +C mp_limb_t divisor, mp_limb_t inverse, +C unsigned shift); +C +C This code is a lightly reworked version of mpn/x86/k7/mmx/divrem_1.asm, +C see that file for some comments. It's possible what's here can be improved. + + +dnl MUL_THRESHOLD is the value of xsize+size at which the multiply by +dnl inverse method is used, rather than plain "divl"s. Minimum value 1. +dnl +dnl The different speeds of the integer and fraction parts means that using +dnl xsize+size isn't quite right. The threshold wants to be a bit higher +dnl for the integer part and a bit lower for the fraction part. (Or what's +dnl really wanted is to speed up the integer part!) +dnl +dnl The threshold is set to make the integer part right. At 4 limbs the +dnl div and mul are about the same there, but on the fractional part the +dnl mul is much faster. + +deflit(MUL_THRESHOLD, 4) + + +defframe(PARAM_PREINV_SHIFT, 28) dnl mpn_preinv_divrem_1 +defframe(PARAM_PREINV_INVERSE, 24) dnl mpn_preinv_divrem_1 +defframe(PARAM_CARRY, 24) dnl mpn_divrem_1c +defframe(PARAM_DIVISOR,20) +defframe(PARAM_SIZE, 16) +defframe(PARAM_SRC, 12) +defframe(PARAM_XSIZE, 8) +defframe(PARAM_DST, 4) + +defframe(SAVE_EBX, -4) +defframe(SAVE_ESI, -8) +defframe(SAVE_EDI, -12) +defframe(SAVE_EBP, -16) + +defframe(VAR_NORM, -20) +defframe(VAR_INVERSE, -24) +defframe(VAR_SRC, -28) +defframe(VAR_DST, -32) +defframe(VAR_DST_STOP,-36) + +deflit(STACK_SPACE, 36) + + TEXT + ALIGN(16) + +PROLOGUE(mpn_preinv_divrem_1) +deflit(`FRAME',0) + movl PARAM_XSIZE, %ecx + subl $STACK_SPACE, %esp FRAME_subl_esp(STACK_SPACE) + + movl %esi, SAVE_ESI + movl PARAM_SRC, %esi + + movl %ebx, SAVE_EBX + movl PARAM_SIZE, %ebx + + movl %ebp, SAVE_EBP + movl PARAM_DIVISOR, %ebp + + movl %edi, SAVE_EDI + movl PARAM_DST, %edx + + movl -4(%esi,%ebx,4), %eax C src high limb + xorl %edi, %edi C initial carry (if can't skip a div) + + C + + leal 8(%edx,%ecx,4), %edx C &dst[xsize+2] + xor %ecx, %ecx + + movl %edx, VAR_DST_STOP C &dst[xsize+2] + cmpl %ebp, %eax C high cmp divisor + + cmovc( %eax, %edi) C high is carry if high<divisor + + cmovnc( %eax, %ecx) C 0 if skip div, src high if not + C (the latter in case src==dst) + + movl %ecx, -12(%edx,%ebx,4) C dst high limb + + sbbl $0, %ebx C skip one division if high<divisor + movl PARAM_PREINV_SHIFT, %ecx + + leal -8(%edx,%ebx,4), %edx C &dst[xsize+size] + movl $32, %eax + + movl %edx, VAR_DST C &dst[xsize+size] + + shll %cl, %ebp C d normalized + subl %ecx, %eax + movl %ecx, VAR_NORM + + movd %eax, %mm7 C rshift + movl PARAM_PREINV_INVERSE, %eax + jmp L(start_preinv) + +EPILOGUE() + + + + ALIGN(16) + +PROLOGUE(mpn_divrem_1c) +deflit(`FRAME',0) + movl PARAM_CARRY, %edx + + movl PARAM_SIZE, %ecx + subl $STACK_SPACE, %esp +deflit(`FRAME',STACK_SPACE) + + movl %ebx, SAVE_EBX + movl PARAM_XSIZE, %ebx + + movl %edi, SAVE_EDI + movl PARAM_DST, %edi + + movl %ebp, SAVE_EBP + movl PARAM_DIVISOR, %ebp + + movl %esi, SAVE_ESI + movl PARAM_SRC, %esi + + leal -4(%edi,%ebx,4), %edi + jmp L(start_1c) + +EPILOGUE() + + + C offset 0x31, close enough to aligned +PROLOGUE(mpn_divrem_1) +deflit(`FRAME',0) + + movl PARAM_SIZE, %ecx + movl $0, %edx C initial carry (if can't skip a div) + subl $STACK_SPACE, %esp +deflit(`FRAME',STACK_SPACE) + + movl %ebp, SAVE_EBP + movl PARAM_DIVISOR, %ebp + + movl %ebx, SAVE_EBX + movl PARAM_XSIZE, %ebx + + movl %esi, SAVE_ESI + movl PARAM_SRC, %esi + orl %ecx, %ecx C size + + movl %edi, SAVE_EDI + movl PARAM_DST, %edi + + leal -4(%edi,%ebx,4), %edi C &dst[xsize-1] + jz L(no_skip_div) C if size==0 + + movl -4(%esi,%ecx,4), %eax C src high limb + xorl %esi, %esi + cmpl %ebp, %eax C high cmp divisor + + cmovc( %eax, %edx) C high is carry if high<divisor + + cmovnc( %eax, %esi) C 0 if skip div, src high if not + C (the latter in case src==dst) + + movl %esi, (%edi,%ecx,4) C dst high limb + + sbbl $0, %ecx C size-1 if high<divisor + movl PARAM_SRC, %esi C reload +L(no_skip_div): + + +L(start_1c): + C eax + C ebx xsize + C ecx size + C edx carry + C esi src + C edi &dst[xsize-1] + C ebp divisor + + leal (%ebx,%ecx), %eax C size+xsize + cmpl $MUL_THRESHOLD, %eax + jae L(mul_by_inverse) + + orl %ecx, %ecx + jz L(divide_no_integer) + +L(divide_integer): + C eax scratch (quotient) + C ebx xsize + C ecx counter + C edx scratch (remainder) + C esi src + C edi &dst[xsize-1] + C ebp divisor + + movl -4(%esi,%ecx,4), %eax + + divl %ebp + + movl %eax, (%edi,%ecx,4) + decl %ecx + jnz L(divide_integer) + + +L(divide_no_integer): + movl PARAM_DST, %edi + orl %ebx, %ebx + jnz L(divide_fraction) + +L(divide_done): + movl SAVE_ESI, %esi + + movl SAVE_EDI, %edi + + movl SAVE_EBX, %ebx + movl %edx, %eax + + movl SAVE_EBP, %ebp + addl $STACK_SPACE, %esp + + ret + + +L(divide_fraction): + C eax scratch (quotient) + C ebx counter + C ecx + C edx scratch (remainder) + C esi + C edi dst + C ebp divisor + + movl $0, %eax + + divl %ebp + + movl %eax, -4(%edi,%ebx,4) + decl %ebx + jnz L(divide_fraction) + + jmp L(divide_done) + + + +C ----------------------------------------------------------------------------- + +L(mul_by_inverse): + C eax + C ebx xsize + C ecx size + C edx carry + C esi src + C edi &dst[xsize-1] + C ebp divisor + + leal 12(%edi), %ebx C &dst[xsize+2], loop dst stop + + movl %ebx, VAR_DST_STOP + leal 4(%edi,%ecx,4), %edi C &dst[xsize+size] + + movl %edi, VAR_DST + movl %ecx, %ebx C size + + bsrl %ebp, %ecx C 31-l + movl %edx, %edi C carry + + leal 1(%ecx), %eax C 32-l + xorl $31, %ecx C l + + movl %ecx, VAR_NORM + movl $-1, %edx + + shll %cl, %ebp C d normalized + movd %eax, %mm7 + + movl $-1, %eax + subl %ebp, %edx C (b-d)-1 giving edx:eax = b*(b-d)-1 + + divl %ebp C floor (b*(b-d)-1) / d + +L(start_preinv): + C eax inverse + C ebx size + C ecx shift + C edx + C esi src + C edi carry + C ebp divisor + C + C mm7 rshift + + movl %eax, VAR_INVERSE + orl %ebx, %ebx C size + leal -12(%esi,%ebx,4), %eax C &src[size-3] + + movl %eax, VAR_SRC + jz L(start_zero) + + movl 8(%eax), %esi C src high limb + cmpl $1, %ebx + jz L(start_one) + +L(start_two_or_more): + movl 4(%eax), %edx C src second highest limb + + shldl( %cl, %esi, %edi) C n2 = carry,high << l + + shldl( %cl, %edx, %esi) C n10 = high,second << l + + cmpl $2, %ebx + je L(integer_two_left) + jmp L(integer_top) + + +L(start_one): + shldl( %cl, %esi, %edi) C n2 = carry,high << l + + shll %cl, %esi C n10 = high << l + jmp L(integer_one_left) + + +L(start_zero): + C Can be here with xsize==0 if mpn_preinv_divrem_1 had size==1 and + C skipped a division. + + shll %cl, %edi C n2 = carry << l + movl %edi, %eax C return value for zero_done + cmpl $0, PARAM_XSIZE + + je L(zero_done) + jmp L(fraction_some) + + + +C ----------------------------------------------------------------------------- +C +C This loop runs at about 25 cycles, which is probably sub-optimal, and +C certainly more than the dependent chain would suggest. A better loop, or +C a better rough analysis of what's possible, would be welcomed. +C +C In the current implementation, the following successively dependent +C micro-ops seem to exist. +C +C uops +C n2+n1 1 (addl) +C mul 5 +C q1+1 3 (addl/adcl) +C mul 5 +C sub 3 (subl/sbbl) +C addback 2 (cmov) +C --- +C 19 +C +C Lack of registers hinders explicit scheduling and it might be that the +C normal out of order execution isn't able to hide enough under the mul +C latencies. +C +C Using sarl/negl to pick out n1 for the n2+n1 stage is a touch faster than +C cmov (and takes one uop off the dependent chain). A sarl/andl/addl +C combination was tried for the addback (despite the fact it would lengthen +C the dependent chain) but found to be no faster. + + + ALIGN(16) +L(integer_top): + C eax scratch + C ebx scratch (nadj, q1) + C ecx scratch (src, dst) + C edx scratch + C esi n10 + C edi n2 + C ebp d + C + C mm0 scratch (src qword) + C mm7 rshift for normalization + + movl %esi, %eax + movl %ebp, %ebx + + sarl $31, %eax C -n1 + movl VAR_SRC, %ecx + + andl %eax, %ebx C -n1 & d + negl %eax C n1 + + addl %esi, %ebx C nadj = n10 + (-n1 & d), ignoring overflow + addl %edi, %eax C n2+n1 + movq (%ecx), %mm0 C next src limb and the one below it + + mull VAR_INVERSE C m*(n2+n1) + + subl $4, %ecx + + movl %ecx, VAR_SRC + + C + + C + + addl %ebx, %eax C m*(n2+n1) + nadj, low giving carry flag + movl %ebp, %eax C d + leal 1(%edi), %ebx C n2+1 + + adcl %edx, %ebx C 1 + high(n2<<32 + m*(n2+n1) + nadj) = q1+1 + jz L(q1_ff) + + mull %ebx C (q1+1)*d + + movl VAR_DST, %ecx + psrlq %mm7, %mm0 + + C + + C + + C + + subl %eax, %esi + movl VAR_DST_STOP, %eax + + sbbl %edx, %edi C n - (q1+1)*d + movl %esi, %edi C remainder -> n2 + leal (%ebp,%esi), %edx + + cmovc( %edx, %edi) C n - q1*d if underflow from using q1+1 + movd %mm0, %esi + + sbbl $0, %ebx C q + subl $4, %ecx + + movl %ebx, (%ecx) + cmpl %eax, %ecx + + movl %ecx, VAR_DST + jne L(integer_top) + + +L(integer_loop_done): + + +C ----------------------------------------------------------------------------- +C +C Here, and in integer_one_left below, an sbbl $0 is used rather than a jz +C q1_ff special case. This make the code a bit smaller and simpler, and +C costs only 2 cycles (each). + +L(integer_two_left): + C eax scratch + C ebx scratch (nadj, q1) + C ecx scratch (src, dst) + C edx scratch + C esi n10 + C edi n2 + C ebp divisor + C + C mm7 rshift + + + movl %esi, %eax + movl %ebp, %ebx + + sarl $31, %eax C -n1 + movl PARAM_SRC, %ecx + + andl %eax, %ebx C -n1 & d + negl %eax C n1 + + addl %esi, %ebx C nadj = n10 + (-n1 & d), ignoring overflow + addl %edi, %eax C n2+n1 + + mull VAR_INVERSE C m*(n2+n1) + + movd (%ecx), %mm0 C src low limb + + movl VAR_DST_STOP, %ecx + + C + + C + + addl %ebx, %eax C m*(n2+n1) + nadj, low giving carry flag + leal 1(%edi), %ebx C n2+1 + movl %ebp, %eax C d + + adcl %edx, %ebx C 1 + high(n2<<32 + m*(n2+n1) + nadj) = q1+1 + + sbbl $0, %ebx + + mull %ebx C (q1+1)*d + + psllq $32, %mm0 + + psrlq %mm7, %mm0 + + C + + C + + subl %eax, %esi + + sbbl %edx, %edi C n - (q1+1)*d + movl %esi, %edi C remainder -> n2 + leal (%ebp,%esi), %edx + + cmovc( %edx, %edi) C n - q1*d if underflow from using q1+1 + movd %mm0, %esi + + sbbl $0, %ebx C q + + movl %ebx, -4(%ecx) + + +C ----------------------------------------------------------------------------- +L(integer_one_left): + C eax scratch + C ebx scratch (nadj, q1) + C ecx scratch (dst) + C edx scratch + C esi n10 + C edi n2 + C ebp divisor + C + C mm7 rshift + + + movl %esi, %eax + movl %ebp, %ebx + + sarl $31, %eax C -n1 + movl VAR_DST_STOP, %ecx + + andl %eax, %ebx C -n1 & d + negl %eax C n1 + + addl %esi, %ebx C nadj = n10 + (-n1 & d), ignoring overflow + addl %edi, %eax C n2+n1 + + mull VAR_INVERSE C m*(n2+n1) + + C + + C + + C + + addl %ebx, %eax C m*(n2+n1) + nadj, low giving carry flag + leal 1(%edi), %ebx C n2+1 + movl %ebp, %eax C d + + C + + adcl %edx, %ebx C 1 + high(n2<<32 + m*(n2+n1) + nadj) = q1+1 + + sbbl $0, %ebx C q1 if q1+1 overflowed + + mull %ebx + + C + + C + + C + + C + + subl %eax, %esi + movl PARAM_XSIZE, %eax + + sbbl %edx, %edi C n - (q1+1)*d + movl %esi, %edi C remainder -> n2 + leal (%ebp,%esi), %edx + + cmovc( %edx, %edi) C n - q1*d if underflow from using q1+1 + + sbbl $0, %ebx C q + + movl %ebx, -8(%ecx) + subl $8, %ecx + + + + orl %eax, %eax C xsize + jnz L(fraction_some) + + movl %edi, %eax +L(fraction_done): + movl VAR_NORM, %ecx +L(zero_done): + movl SAVE_EBP, %ebp + + movl SAVE_EDI, %edi + + movl SAVE_ESI, %esi + + movl SAVE_EBX, %ebx + addl $STACK_SPACE, %esp + + shrl %cl, %eax + emms + + ret + + +C ----------------------------------------------------------------------------- +C +C Special case for q1=0xFFFFFFFF, giving q=0xFFFFFFFF meaning the low dword +C of q*d is simply -d and the remainder n-q*d = n10+d + +L(q1_ff): + C eax (divisor) + C ebx (q1+1 == 0) + C ecx + C edx + C esi n10 + C edi n2 + C ebp divisor + + movl VAR_DST, %ecx + movl VAR_DST_STOP, %edx + subl $4, %ecx + + movl %ecx, VAR_DST + psrlq %mm7, %mm0 + leal (%ebp,%esi), %edi C n-q*d remainder -> next n2 + + movl $-1, (%ecx) + movd %mm0, %esi C next n10 + + cmpl %ecx, %edx + jne L(integer_top) + + jmp L(integer_loop_done) + + + +C ----------------------------------------------------------------------------- +C +C In the current implementation, the following successively dependent +C micro-ops seem to exist. +C +C uops +C mul 5 +C q1+1 1 (addl) +C mul 5 +C sub 3 (negl/sbbl) +C addback 2 (cmov) +C --- +C 16 +C +C The loop in fact runs at about 17.5 cycles. Using a sarl/andl/addl for +C the addback was found to be a touch slower. + + + ALIGN(16) +L(fraction_some): + C eax + C ebx + C ecx + C edx + C esi + C edi carry + C ebp divisor + + movl PARAM_DST, %esi + movl VAR_DST_STOP, %ecx C &dst[xsize+2] + movl %edi, %eax + + subl $8, %ecx C &dst[xsize] + + + ALIGN(16) +L(fraction_top): + C eax n2, then scratch + C ebx scratch (nadj, q1) + C ecx dst, decrementing + C edx scratch + C esi dst stop point + C edi n2 + C ebp divisor + + mull VAR_INVERSE C m*n2 + + movl %ebp, %eax C d + subl $4, %ecx C dst + leal 1(%edi), %ebx + + C + + C + + C + + addl %edx, %ebx C 1 + high(n2<<32 + m*n2) = q1+1 + + mull %ebx C (q1+1)*d + + C + + C + + C + + C + + negl %eax C low of n - (q1+1)*d + + sbbl %edx, %edi C high of n - (q1+1)*d, caring only about carry + leal (%ebp,%eax), %edx + + cmovc( %edx, %eax) C n - q1*d if underflow from using q1+1 + + sbbl $0, %ebx C q + movl %eax, %edi C remainder->n2 + cmpl %esi, %ecx + + movl %ebx, (%ecx) C previous q + jne L(fraction_top) + + + jmp L(fraction_done) + +EPILOGUE() |