| dnl Intel Pentium-4 mpn_divrem_1 -- mpn by limb division. |
| |
| dnl Copyright 1999, 2000, 2001, 2002, 2003, 2004 Free Software Foundation, |
| dnl Inc. |
| dnl |
| 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 |
| dnl modify it under the terms of the GNU Lesser General Public License as |
| dnl published by the Free Software Foundation; either version 3 of the |
| dnl License, or (at your option) any later version. |
| dnl |
| dnl The GNU MP Library is distributed in the hope that it will be useful, |
| dnl but WITHOUT ANY WARRANTY; without even the implied warranty of |
| dnl MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
| dnl Lesser General Public License for more details. |
| dnl |
| dnl You should have received a copy of the GNU Lesser General Public License |
| dnl along with the GNU MP Library. If not, see http://www.gnu.org/licenses/. |
| |
| include(`../config.m4') |
| |
| |
| C P4: 32 cycles/limb integer part, 30 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 Algorithm: |
| C |
| C The method and nomenclature follow part 8 of "Division by Invariant |
| C Integers using Multiplication" by Granlund and Montgomery, reference in |
| C gmp.texi. |
| C |
| C "m" is written for what is m' in the paper, and "d" for d_norm, which |
| C won't cause any confusion since it's only the normalized divisor that's of |
| C any use in the code. "b" is written for 2^N, the size of a limb, N being |
| C 32 here. |
| C |
| C The step "sdword dr = n - 2^N*d + (2^N-1-q1) * d" is instead done as |
| C "n-d - q1*d". This rearrangement gives the same two-limb answer but lets |
| C us have just a psubq on the dependent chain. |
| C |
| C For reference, the way the k7 code uses "n-(q1+1)*d" would not suit here, |
| C detecting an overflow of q1+1 when q1=0xFFFFFFFF would cost too much. |
| C |
| C Notes: |
| C |
| C mpn_divrem_1 and mpn_preinv_divrem_1 avoid one division if the src high |
| C limb is less than the divisor. mpn_divrem_1c doesn't check for a zero |
| C carry, since in normal circumstances that will be a very rare event. |
| C |
| C The test for skipping a division is branch free (once size>=1 is tested). |
| C The store to the destination high limb is 0 when a divide is skipped, or |
| C if it's not skipped then a copy of the src high limb is stored. The |
| C latter is in case src==dst. |
| C |
| C There's a small bias towards expecting xsize==0, by having code for |
| C xsize==0 in a straight line and xsize!=0 under forward jumps. |
| C |
| C Enhancements: |
| C |
| C The loop measures 32 cycles, but the dependent chain would suggest it |
| C could be done with 30. Not sure where to start looking for the extras. |
| C |
| C Alternatives: |
| C |
| C If the divisor is normalized (high bit set) then a division step can |
| C always be skipped, since the high destination limb is always 0 or 1 in |
| C that case. It doesn't seem worth checking for this though, since it |
| C probably occurs infrequently. |
| |
| |
| 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 inverse takes about 80-90 cycles to calculate, but after that the |
| dnl multiply is 32 c/l versus division at about 58 c/l. |
| dnl |
| dnl At 4 limbs the div is a touch faster than the mul (and of course |
| dnl simpler), so start the mul from 5 limbs. |
| |
| deflit(MUL_THRESHOLD, 5) |
| |
| |
| 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) |
| |
| dnl re-use parameter space |
| define(SAVE_ESI,`PARAM_SIZE') |
| define(SAVE_EBP,`PARAM_SRC') |
| define(SAVE_EDI,`PARAM_DIVISOR') |
| define(SAVE_EBX,`PARAM_DST') |
| |
| TEXT |
| |
| ALIGN(16) |
| PROLOGUE(mpn_preinv_divrem_1) |
| deflit(`FRAME',0) |
| |
| movl PARAM_SIZE, %ecx |
| xorl %edx, %edx C carry if can't skip a div |
| |
| movl %esi, SAVE_ESI |
| movl PARAM_SRC, %esi |
| |
| movl %ebp, SAVE_EBP |
| movl PARAM_DIVISOR, %ebp |
| |
| movl %edi, SAVE_EDI |
| movl PARAM_DST, %edi |
| |
| movl -4(%esi,%ecx,4), %eax C src high limb |
| |
| movl %ebx, SAVE_EBX |
| movl PARAM_XSIZE, %ebx |
| |
| movd PARAM_PREINV_INVERSE, %mm4 |
| |
| movd PARAM_PREINV_SHIFT, %mm7 C l |
| cmpl %ebp, %eax C high cmp divisor |
| |
| cmovc( %eax, %edx) C high is carry if high<divisor |
| movd %edx, %mm0 C carry |
| |
| movd %edx, %mm1 C carry |
| movl $0, %edx |
| |
| movd %ebp, %mm5 C d |
| cmovnc( %eax, %edx) C 0 if skip div, src high if not |
| C (the latter in case src==dst) |
| leal -4(%edi,%ebx,4), %edi C &dst[xsize-1] |
| |
| movl %edx, (%edi,%ecx,4) C dst high limb |
| sbbl $0, %ecx C skip one division if high<divisor |
| movl $32, %eax |
| |
| subl PARAM_PREINV_SHIFT, %eax |
| psllq %mm7, %mm5 C d normalized |
| leal (%edi,%ecx,4), %edi C &dst[xsize+size-1] |
| leal -4(%esi,%ecx,4), %esi C &src[size-1] |
| |
| movd %eax, %mm6 C 32-l |
| jmp L(start_preinv) |
| |
| EPILOGUE() |
| |
| |
| ALIGN(16) |
| PROLOGUE(mpn_divrem_1c) |
| deflit(`FRAME',0) |
| |
| movl PARAM_CARRY, %edx |
| |
| movl PARAM_SIZE, %ecx |
| |
| movl %esi, SAVE_ESI |
| movl PARAM_SRC, %esi |
| |
| movl %ebp, SAVE_EBP |
| movl PARAM_DIVISOR, %ebp |
| |
| movl %edi, SAVE_EDI |
| movl PARAM_DST, %edi |
| |
| movl %ebx, SAVE_EBX |
| movl PARAM_XSIZE, %ebx |
| |
| leal -4(%edi,%ebx,4), %edi C &dst[xsize-1] |
| jmp L(start_1c) |
| |
| EPILOGUE() |
| |
| |
| ALIGN(16) |
| PROLOGUE(mpn_divrem_1) |
| deflit(`FRAME',0) |
| |
| movl PARAM_SIZE, %ecx |
| xorl %edx, %edx C initial carry (if can't skip a div) |
| |
| movl %esi, SAVE_ESI |
| movl PARAM_SRC, %esi |
| |
| movl %ebp, SAVE_EBP |
| movl PARAM_DIVISOR, %ebp |
| |
| movl %edi, SAVE_EDI |
| movl PARAM_DST, %edi |
| |
| movl %ebx, SAVE_EBX |
| movl PARAM_XSIZE, %ebx |
| leal -4(%edi,%ebx,4), %edi C &dst[xsize-1] |
| |
| orl %ecx, %ecx C size |
| jz L(no_skip_div) C if size==0 |
| movl -4(%esi,%ecx,4), %eax C src high limb |
| |
| cmpl %ebp, %eax C high cmp divisor |
| |
| cmovnc( %eax, %edx) C 0 if skip div, src high if not |
| movl %edx, (%edi,%ecx,4) C dst high limb |
| |
| movl $0, %edx |
| cmovc( %eax, %edx) C high is carry if high<divisor |
| |
| sbbl $0, %ecx C size-1 if high<divisor |
| 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 |
| leal -4(%esi,%ecx,4), %esi C &src[size-1] |
| leal (%edi,%ecx,4), %edi C &dst[size+xsize-1] |
| |
| cmpl $MUL_THRESHOLD, %eax |
| jae L(mul_by_inverse) |
| |
| |
| orl %ecx, %ecx |
| jz L(divide_no_integer) C if size==0 |
| |
| L(divide_integer): |
| C eax scratch (quotient) |
| C ebx xsize |
| C ecx counter |
| C edx carry |
| C esi src, decrementing |
| C edi dst, decrementing |
| C ebp divisor |
| |
| movl (%esi), %eax |
| subl $4, %esi |
| |
| divl %ebp |
| |
| movl %eax, (%edi) |
| subl $4, %edi |
| |
| subl $1, %ecx |
| jnz L(divide_integer) |
| |
| |
| L(divide_no_integer): |
| orl %ebx, %ebx |
| jnz L(divide_fraction) C if xsize!=0 |
| |
| L(divide_done): |
| movl SAVE_ESI, %esi |
| movl SAVE_EDI, %edi |
| movl SAVE_EBX, %ebx |
| movl SAVE_EBP, %ebp |
| movl %edx, %eax |
| ret |
| |
| |
| L(divide_fraction): |
| C eax scratch (quotient) |
| C ebx counter |
| C ecx |
| C edx carry |
| C esi |
| C edi dst, decrementing |
| C ebp divisor |
| |
| movl $0, %eax |
| |
| divl %ebp |
| |
| movl %eax, (%edi) |
| subl $4, %edi |
| |
| subl $1, %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[size-1] |
| C edi &dst[size+xsize-1] |
| C ebp divisor |
| |
| bsrl %ebp, %eax C 31-l |
| movd %edx, %mm0 C carry |
| movd %edx, %mm1 C carry |
| movl %ecx, %edx C size |
| movl $31, %ecx |
| |
| C |
| |
| xorl %eax, %ecx C l = leading zeros on d |
| addl $1, %eax |
| |
| shll %cl, %ebp C d normalized |
| movd %ecx, %mm7 C l |
| movl %edx, %ecx C size |
| |
| movd %eax, %mm6 C 32-l |
| movl $-1, %edx |
| movl $-1, %eax |
| |
| C |
| |
| subl %ebp, %edx C (b-d)-1 so edx:eax = b*(b-d)-1 |
| |
| divl %ebp C floor (b*(b-d)-1 / d) |
| movd %ebp, %mm5 C d |
| |
| C |
| |
| movd %eax, %mm4 C m |
| |
| |
| L(start_preinv): |
| C eax inverse |
| C ebx xsize |
| C ecx size |
| C edx |
| C esi &src[size-1] |
| C edi &dst[size+xsize-1] |
| C ebp |
| C |
| C mm0 carry |
| C mm1 carry |
| C mm2 |
| C mm4 m |
| C mm5 d |
| C mm6 31-l |
| C mm7 l |
| |
| psllq %mm7, %mm0 C n2 = carry << l, for size==0 |
| |
| subl $1, %ecx |
| jb L(integer_none) |
| |
| movd (%esi), %mm0 C src high limb |
| punpckldq %mm1, %mm0 |
| psrlq %mm6, %mm0 C n2 = high (carry:srchigh << l) |
| jz L(integer_last) |
| |
| |
| C The dependent chain here consists of |
| C |
| C 2 paddd n1+n2 |
| C 8 pmuludq m*(n1+n2) |
| C 2 paddq n2:nadj + m*(n1+n2) |
| C 2 psrlq q1 |
| C 8 pmuludq d*q1 |
| C 2 psubq (n-d)-q1*d |
| C 2 psrlq high n-(q1+1)*d mask |
| C 2 pand d masked |
| C 2 paddd n2+d addback |
| C -- |
| C 30 |
| C |
| C But it seems to run at 32 cycles, so presumably there's something else |
| C going on. |
| |
| ALIGN(16) |
| L(integer_top): |
| C eax |
| C ebx |
| C ecx counter, size-1 to 0 |
| C edx |
| C esi src, decrementing |
| C edi dst, decrementing |
| C |
| C mm0 n2 |
| C mm4 m |
| C mm5 d |
| C mm6 32-l |
| C mm7 l |
| |
| ASSERT(b,`C n2<d |
| movd %mm0, %eax |
| movd %mm5, %edx |
| cmpl %edx, %eax') |
| |
| movd -4(%esi), %mm1 C next src limbs |
| movd (%esi), %mm2 |
| leal -4(%esi), %esi |
| |
| punpckldq %mm2, %mm1 |
| psrlq %mm6, %mm1 C n10 |
| |
| movq %mm1, %mm2 C n10 |
| movq %mm1, %mm3 C n10 |
| psrad $31, %mm1 C -n1 |
| pand %mm5, %mm1 C -n1 & d |
| paddd %mm2, %mm1 C nadj = n10+(-n1&d), ignore overflow |
| |
| psrld $31, %mm2 C n1 |
| paddd %mm0, %mm2 C n2+n1 |
| punpckldq %mm0, %mm1 C n2:nadj |
| |
| pmuludq %mm4, %mm2 C m*(n2+n1) |
| |
| C |
| |
| paddq %mm2, %mm1 C n2:nadj + m*(n2+n1) |
| pxor %mm2, %mm2 C break dependency, saves 4 cycles |
| pcmpeqd %mm2, %mm2 C FF...FF |
| psrlq $63, %mm2 C 1 |
| |
| psrlq $32, %mm1 C q1 = high(n2:nadj + m*(n2+n1)) |
| |
| paddd %mm1, %mm2 C q1+1 |
| pmuludq %mm5, %mm1 C q1*d |
| |
| punpckldq %mm0, %mm3 C n = n2:n10 |
| pxor %mm0, %mm0 |
| |
| psubq %mm5, %mm3 C n - d |
| |
| C |
| |
| psubq %mm1, %mm3 C n - (q1+1)*d |
| |
| por %mm3, %mm0 C copy remainder -> new n2 |
| psrlq $32, %mm3 C high n - (q1+1)*d, 0 or -1 |
| |
| ASSERT(be,`C 0 or -1 |
| movd %mm3, %eax |
| addl $1, %eax |
| cmpl $1, %eax') |
| |
| paddd %mm3, %mm2 C q |
| pand %mm5, %mm3 C mask & d |
| |
| paddd %mm3, %mm0 C addback if necessary |
| movd %mm2, (%edi) |
| leal -4(%edi), %edi |
| |
| subl $1, %ecx |
| ja L(integer_top) |
| |
| |
| L(integer_last): |
| C eax |
| C ebx xsize |
| C ecx |
| C edx |
| C esi &src[0] |
| C edi &dst[xsize] |
| C |
| C mm0 n2 |
| C mm4 m |
| C mm5 d |
| C mm6 |
| C mm7 l |
| |
| ASSERT(b,`C n2<d |
| movd %mm0, %eax |
| movd %mm5, %edx |
| cmpl %edx, %eax') |
| |
| movd (%esi), %mm1 C src[0] |
| psllq %mm7, %mm1 C n10 |
| |
| movq %mm1, %mm2 C n10 |
| movq %mm1, %mm3 C n10 |
| psrad $31, %mm1 C -n1 |
| pand %mm5, %mm1 C -n1 & d |
| paddd %mm2, %mm1 C nadj = n10+(-n1&d), ignore overflow |
| |
| psrld $31, %mm2 C n1 |
| paddd %mm0, %mm2 C n2+n1 |
| punpckldq %mm0, %mm1 C n2:nadj |
| |
| pmuludq %mm4, %mm2 C m*(n2+n1) |
| |
| C |
| |
| paddq %mm2, %mm1 C n2:nadj + m*(n2+n1) |
| pcmpeqd %mm2, %mm2 C FF...FF |
| psrlq $63, %mm2 C 1 |
| |
| psrlq $32, %mm1 C q1 = high(n2:nadj + m*(n2+n1)) |
| paddd %mm1, %mm2 C q1 |
| |
| pmuludq %mm5, %mm1 C q1*d |
| punpckldq %mm0, %mm3 C n |
| psubq %mm5, %mm3 C n - d |
| pxor %mm0, %mm0 |
| |
| C |
| |
| psubq %mm1, %mm3 C n - (q1+1)*d |
| |
| por %mm3, %mm0 C remainder -> n2 |
| psrlq $32, %mm3 C high n - (q1+1)*d, 0 or -1 |
| |
| ASSERT(be,`C 0 or -1 |
| movd %mm3, %eax |
| addl $1, %eax |
| cmpl $1, %eax') |
| |
| paddd %mm3, %mm2 C q |
| pand %mm5, %mm3 C mask & d |
| |
| paddd %mm3, %mm0 C addback if necessary |
| movd %mm2, (%edi) |
| leal -4(%edi), %edi |
| |
| |
| L(integer_none): |
| C eax |
| C ebx xsize |
| |
| orl %ebx, %ebx |
| jnz L(fraction_some) C if xsize!=0 |
| |
| |
| L(fraction_done): |
| movl SAVE_EBP, %ebp |
| psrld %mm7, %mm0 C remainder |
| |
| movl SAVE_EDI, %edi |
| movd %mm0, %eax |
| |
| movl SAVE_ESI, %esi |
| movl SAVE_EBX, %ebx |
| emms |
| ret |
| |
| |
| |
| C ----------------------------------------------------------------------------- |
| C |
| |
| L(fraction_some): |
| C eax |
| C ebx xsize |
| C ecx |
| C edx |
| C esi |
| C edi &dst[xsize-1] |
| C ebp |
| |
| |
| L(fraction_top): |
| C eax |
| C ebx counter, xsize iterations |
| C ecx |
| C edx |
| C esi src, decrementing |
| C edi dst, decrementing |
| C |
| C mm0 n2 |
| C mm4 m |
| C mm5 d |
| C mm6 32-l |
| C mm7 l |
| |
| ASSERT(b,`C n2<d |
| movd %mm0, %eax |
| movd %mm5, %edx |
| cmpl %edx, %eax') |
| |
| movq %mm0, %mm1 C n2 |
| pmuludq %mm4, %mm0 C m*n2 |
| |
| pcmpeqd %mm2, %mm2 |
| psrlq $63, %mm2 |
| |
| C |
| |
| psrlq $32, %mm0 C high(m*n2) |
| |
| paddd %mm1, %mm0 C q1 = high(n2:0 + m*n2) |
| |
| paddd %mm0, %mm2 C q1+1 |
| pmuludq %mm5, %mm0 C q1*d |
| |
| psllq $32, %mm1 C n = n2:0 |
| psubq %mm5, %mm1 C n - d |
| |
| C |
| |
| psubq %mm0, %mm1 C r = n - (q1+1)*d |
| pxor %mm0, %mm0 |
| |
| por %mm1, %mm0 C r -> n2 |
| psrlq $32, %mm1 C high n - (q1+1)*d, 0 or -1 |
| |
| ASSERT(be,`C 0 or -1 |
| movd %mm1, %eax |
| addl $1, %eax |
| cmpl $1, %eax') |
| |
| paddd %mm1, %mm2 C q |
| pand %mm5, %mm1 C mask & d |
| |
| paddd %mm1, %mm0 C addback if necessary |
| movd %mm2, (%edi) |
| leal -4(%edi), %edi |
| |
| subl $1, %ebx |
| jne L(fraction_top) |
| |
| |
| jmp L(fraction_done) |
| |
| EPILOGUE() |
