641 lines
12 KiB
NASM
641 lines
12 KiB
NASM
dnl Intel P6 mpn_sqr_basecase -- square an mpn number.
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dnl Copyright 1999, 2000, 2002 Free Software Foundation, Inc.
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dnl
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dnl This file is part of the GNU MP Library.
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dnl
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dnl The GNU MP Library is free software; you can redistribute it and/or
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dnl modify it under the terms of the GNU Lesser General Public License as
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dnl published by the Free Software Foundation; either version 2.1 of the
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dnl License, or (at your option) any later version.
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dnl
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dnl The GNU MP Library is distributed in the hope that it will be useful,
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dnl but WITHOUT ANY WARRANTY; without even the implied warranty of
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dnl MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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dnl Lesser General Public License for more details.
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dnl
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dnl You should have received a copy of the GNU Lesser General Public
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dnl License along with the GNU MP Library; see the file COPYING.LIB. If
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dnl not, write to the Free Software Foundation, Inc., 51 Franklin Street,
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dnl Fifth Floor, Boston, MA 02110-1301, USA.
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include(`../config.m4')
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C P6: approx 4.0 cycles per cross product, or 7.75 cycles per triangular
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C product (measured on the speed difference between 20 and 40 limbs,
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C which is the Karatsuba recursing range).
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dnl These are the same as in mpn/x86/k6/sqr_basecase.asm, see that file for
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dnl a description. The only difference here is that UNROLL_COUNT can go up
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dnl to 64 (not 63) making SQR_KARATSUBA_THRESHOLD_MAX 67.
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deflit(SQR_KARATSUBA_THRESHOLD_MAX, 67)
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ifdef(`SQR_KARATSUBA_THRESHOLD_OVERRIDE',
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`define(`SQR_KARATSUBA_THRESHOLD',SQR_KARATSUBA_THRESHOLD_OVERRIDE)')
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m4_config_gmp_mparam(`SQR_KARATSUBA_THRESHOLD')
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deflit(UNROLL_COUNT, eval(SQR_KARATSUBA_THRESHOLD-3))
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C void mpn_sqr_basecase (mp_ptr dst, mp_srcptr src, mp_size_t size);
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C
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C The algorithm is basically the same as mpn/generic/sqr_basecase.c, but a
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C lot of function call overheads are avoided, especially when the given size
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C is small.
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C
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C The code size might look a bit excessive, but not all of it is executed so
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C it won't all get into the code cache. The 1x1, 2x2 and 3x3 special cases
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C clearly apply only to those sizes; mid sizes like 10x10 only need part of
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C the unrolled addmul; and big sizes like 40x40 that do use the full
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C unrolling will least be making good use of it, because 40x40 will take
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C something like 7000 cycles.
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defframe(PARAM_SIZE,12)
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defframe(PARAM_SRC, 8)
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defframe(PARAM_DST, 4)
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TEXT
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ALIGN(32)
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PROLOGUE(mpn_sqr_basecase)
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deflit(`FRAME',0)
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movl PARAM_SIZE, %edx
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movl PARAM_SRC, %eax
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cmpl $2, %edx
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movl PARAM_DST, %ecx
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je L(two_limbs)
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movl (%eax), %eax
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ja L(three_or_more)
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C -----------------------------------------------------------------------------
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C one limb only
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C eax src limb
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C ebx
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C ecx dst
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C edx
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mull %eax
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movl %eax, (%ecx)
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movl %edx, 4(%ecx)
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ret
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C -----------------------------------------------------------------------------
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L(two_limbs):
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C eax src
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C ebx
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C ecx dst
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C edx
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defframe(SAVE_ESI, -4)
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defframe(SAVE_EBX, -8)
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defframe(SAVE_EDI, -12)
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defframe(SAVE_EBP, -16)
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deflit(`STACK_SPACE',16)
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subl $STACK_SPACE, %esp
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deflit(`FRAME',STACK_SPACE)
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movl %esi, SAVE_ESI
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movl %eax, %esi
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movl (%eax), %eax
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mull %eax C src[0]^2
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movl %eax, (%ecx) C dst[0]
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movl 4(%esi), %eax
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movl %ebx, SAVE_EBX
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movl %edx, %ebx C dst[1]
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mull %eax C src[1]^2
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movl %edi, SAVE_EDI
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movl %eax, %edi C dst[2]
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movl (%esi), %eax
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movl %ebp, SAVE_EBP
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movl %edx, %ebp C dst[3]
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mull 4(%esi) C src[0]*src[1]
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addl %eax, %ebx
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movl SAVE_ESI, %esi
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adcl %edx, %edi
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adcl $0, %ebp
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addl %ebx, %eax
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movl SAVE_EBX, %ebx
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adcl %edi, %edx
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movl SAVE_EDI, %edi
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adcl $0, %ebp
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movl %eax, 4(%ecx)
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movl %ebp, 12(%ecx)
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movl SAVE_EBP, %ebp
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movl %edx, 8(%ecx)
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addl $FRAME, %esp
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ret
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C -----------------------------------------------------------------------------
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L(three_or_more):
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C eax src low limb
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C ebx
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C ecx dst
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C edx size
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deflit(`FRAME',0)
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pushl %esi defframe_pushl(`SAVE_ESI')
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cmpl $4, %edx
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movl PARAM_SRC, %esi
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jae L(four_or_more)
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C -----------------------------------------------------------------------------
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C three limbs
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C eax src low limb
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C ebx
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C ecx dst
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C edx
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C esi src
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C edi
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C ebp
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pushl %ebp defframe_pushl(`SAVE_EBP')
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pushl %edi defframe_pushl(`SAVE_EDI')
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mull %eax C src[0] ^ 2
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movl %eax, (%ecx)
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movl %edx, 4(%ecx)
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movl 4(%esi), %eax
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xorl %ebp, %ebp
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mull %eax C src[1] ^ 2
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movl %eax, 8(%ecx)
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movl %edx, 12(%ecx)
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movl 8(%esi), %eax
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pushl %ebx defframe_pushl(`SAVE_EBX')
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mull %eax C src[2] ^ 2
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movl %eax, 16(%ecx)
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movl %edx, 20(%ecx)
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movl (%esi), %eax
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mull 4(%esi) C src[0] * src[1]
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movl %eax, %ebx
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movl %edx, %edi
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movl (%esi), %eax
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mull 8(%esi) C src[0] * src[2]
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addl %eax, %edi
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movl %edx, %ebp
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adcl $0, %ebp
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movl 4(%esi), %eax
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mull 8(%esi) C src[1] * src[2]
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xorl %esi, %esi
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addl %eax, %ebp
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C eax
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C ebx dst[1]
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C ecx dst
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C edx dst[4]
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C esi zero, will be dst[5]
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C edi dst[2]
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C ebp dst[3]
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adcl $0, %edx
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addl %ebx, %ebx
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adcl %edi, %edi
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adcl %ebp, %ebp
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adcl %edx, %edx
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movl 4(%ecx), %eax
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adcl $0, %esi
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addl %ebx, %eax
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movl %eax, 4(%ecx)
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movl 8(%ecx), %eax
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adcl %edi, %eax
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movl 12(%ecx), %ebx
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adcl %ebp, %ebx
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movl 16(%ecx), %edi
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movl %eax, 8(%ecx)
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movl SAVE_EBP, %ebp
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movl %ebx, 12(%ecx)
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movl SAVE_EBX, %ebx
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adcl %edx, %edi
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movl 20(%ecx), %eax
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movl %edi, 16(%ecx)
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movl SAVE_EDI, %edi
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adcl %esi, %eax C no carry out of this
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movl SAVE_ESI, %esi
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movl %eax, 20(%ecx)
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addl $FRAME, %esp
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ret
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C -----------------------------------------------------------------------------
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defframe(VAR_COUNTER,-20)
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defframe(VAR_JMP, -24)
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deflit(`STACK_SPACE',24)
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L(four_or_more):
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C eax src low limb
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C ebx
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C ecx
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C edx size
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C esi src
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C edi
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C ebp
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deflit(`FRAME',4) dnl %esi already pushed
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C First multiply src[0]*src[1..size-1] and store at dst[1..size].
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subl $STACK_SPACE-FRAME, %esp
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deflit(`FRAME',STACK_SPACE)
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movl $1, %ecx
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movl %edi, SAVE_EDI
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movl PARAM_DST, %edi
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movl %ebx, SAVE_EBX
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subl %edx, %ecx C -(size-1)
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movl %ebp, SAVE_EBP
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movl $0, %ebx C initial carry
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leal (%esi,%edx,4), %esi C &src[size]
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movl %eax, %ebp C multiplier
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leal -4(%edi,%edx,4), %edi C &dst[size-1]
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C This loop runs at just over 6 c/l.
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L(mul_1):
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C eax scratch
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C ebx carry
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C ecx counter, limbs, negative, -(size-1) to -1
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C edx scratch
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C esi &src[size]
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C edi &dst[size-1]
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C ebp multiplier
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movl %ebp, %eax
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mull (%esi,%ecx,4)
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addl %ebx, %eax
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movl $0, %ebx
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adcl %edx, %ebx
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movl %eax, 4(%edi,%ecx,4)
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incl %ecx
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jnz L(mul_1)
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movl %ebx, 4(%edi)
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C Addmul src[n]*src[n+1..size-1] at dst[2*n-1...], for each n=1..size-2.
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C
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C The last two addmuls, which are the bottom right corner of the product
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C triangle, are left to the end. These are src[size-3]*src[size-2,size-1]
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C and src[size-2]*src[size-1]. If size is 4 then it's only these corner
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C cases that need to be done.
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C
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C The unrolled code is the same as mpn_addmul_1(), see that routine for some
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C comments.
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C
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C VAR_COUNTER is the outer loop, running from -(size-4) to -1, inclusive.
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C
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C VAR_JMP is the computed jump into the unrolled code, stepped by one code
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C chunk each outer loop.
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dnl This is also hard-coded in the address calculation below.
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deflit(CODE_BYTES_PER_LIMB, 15)
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dnl With &src[size] and &dst[size-1] pointers, the displacements in the
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dnl unrolled code fit in a byte for UNROLL_COUNT values up to 32, but above
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dnl that an offset must be added to them.
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deflit(OFFSET,
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ifelse(eval(UNROLL_COUNT>32),1,
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eval((UNROLL_COUNT-32)*4),
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0))
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C eax
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C ebx carry
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C ecx
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C edx
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C esi &src[size]
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C edi &dst[size-1]
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C ebp
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movl PARAM_SIZE, %ecx
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subl $4, %ecx
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jz L(corner)
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movl %ecx, %edx
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negl %ecx
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shll $4, %ecx
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ifelse(OFFSET,0,,`subl $OFFSET, %esi')
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ifdef(`PIC',`
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call L(pic_calc)
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L(here):
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',`
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leal L(unroll_inner_end)-eval(2*CODE_BYTES_PER_LIMB)(%ecx,%edx), %ecx
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')
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negl %edx
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ifelse(OFFSET,0,,`subl $OFFSET, %edi')
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C The calculated jump mustn't be before the start of the available
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C code. This is the limit that UNROLL_COUNT puts on the src operand
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C size, but checked here using the jump address directly.
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ASSERT(ae,
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`movl_text_address( L(unroll_inner_start), %eax)
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cmpl %eax, %ecx')
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C -----------------------------------------------------------------------------
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ALIGN(16)
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L(unroll_outer_top):
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C eax
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C ebx high limb to store
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C ecx VAR_JMP
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C edx VAR_COUNTER, limbs, negative
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C esi &src[size], constant
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C edi dst ptr, second highest limb of last addmul
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C ebp
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movl -12+OFFSET(%esi,%edx,4), %ebp C multiplier
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movl %edx, VAR_COUNTER
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movl -8+OFFSET(%esi,%edx,4), %eax C first limb of multiplicand
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mull %ebp
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define(cmovX,`ifelse(eval(UNROLL_COUNT%2),1,`cmovz($@)',`cmovnz($@)')')
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testb $1, %cl
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movl %edx, %ebx C high carry
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leal 4(%edi), %edi
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movl %ecx, %edx C jump
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movl %eax, %ecx C low carry
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leal CODE_BYTES_PER_LIMB(%edx), %edx
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cmovX( %ebx, %ecx) C high carry reverse
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cmovX( %eax, %ebx) C low carry reverse
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movl %edx, VAR_JMP
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jmp *%edx
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C Must be on an even address here so the low bit of the jump address
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C will indicate which way around ecx/ebx should start.
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ALIGN(2)
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L(unroll_inner_start):
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C eax scratch
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C ebx carry high
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C ecx carry low
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C edx scratch
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C esi src pointer
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C edi dst pointer
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C ebp multiplier
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C
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C 15 code bytes each limb
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C ecx/ebx reversed on each chunk
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forloop(`i', UNROLL_COUNT, 1, `
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deflit(`disp_src', eval(-i*4 + OFFSET))
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deflit(`disp_dst', eval(disp_src))
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m4_assert(`disp_src>=-128 && disp_src<128')
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m4_assert(`disp_dst>=-128 && disp_dst<128')
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ifelse(eval(i%2),0,`
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Zdisp( movl, disp_src,(%esi), %eax)
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mull %ebp
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Zdisp( addl, %ebx, disp_dst,(%edi))
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adcl %eax, %ecx
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movl %edx, %ebx
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adcl $0, %ebx
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',`
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dnl this one comes out last
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Zdisp( movl, disp_src,(%esi), %eax)
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mull %ebp
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Zdisp( addl, %ecx, disp_dst,(%edi))
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adcl %eax, %ebx
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movl %edx, %ecx
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adcl $0, %ecx
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')
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')
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L(unroll_inner_end):
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addl %ebx, m4_empty_if_zero(OFFSET)(%edi)
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movl VAR_COUNTER, %edx
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adcl $0, %ecx
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movl %ecx, m4_empty_if_zero(OFFSET+4)(%edi)
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movl VAR_JMP, %ecx
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incl %edx
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jnz L(unroll_outer_top)
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ifelse(OFFSET,0,,`
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addl $OFFSET, %esi
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addl $OFFSET, %edi
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')
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C -----------------------------------------------------------------------------
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ALIGN(16)
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L(corner):
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C eax
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C ebx
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C ecx
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C edx
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C esi &src[size]
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C edi &dst[2*size-5]
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C ebp
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movl -12(%esi), %eax
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mull -8(%esi)
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addl %eax, (%edi)
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movl -12(%esi), %eax
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movl $0, %ebx
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adcl %edx, %ebx
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mull -4(%esi)
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addl %eax, %ebx
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movl -8(%esi), %eax
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adcl $0, %edx
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addl %ebx, 4(%edi)
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movl $0, %ebx
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adcl %edx, %ebx
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mull -4(%esi)
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movl PARAM_SIZE, %ecx
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addl %ebx, %eax
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adcl $0, %edx
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movl %eax, 8(%edi)
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movl %edx, 12(%edi)
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movl PARAM_DST, %edi
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C Left shift of dst[1..2*size-2], the bit shifted out becomes dst[2*size-1].
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subl $1, %ecx C size-1
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xorl %eax, %eax C ready for final adcl, and clear carry
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movl %ecx, %edx
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movl PARAM_SRC, %esi
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L(lshift):
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C eax
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C ebx
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C ecx counter, size-1 to 1
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C edx size-1 (for later use)
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C esi src (for later use)
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C edi dst, incrementing
|
|
C ebp
|
|
|
|
rcll 4(%edi)
|
|
rcll 8(%edi)
|
|
|
|
leal 8(%edi), %edi
|
|
decl %ecx
|
|
jnz L(lshift)
|
|
|
|
|
|
adcl %eax, %eax
|
|
|
|
movl %eax, 4(%edi) C dst most significant limb
|
|
movl (%esi), %eax C src[0]
|
|
|
|
leal 4(%esi,%edx,4), %esi C &src[size]
|
|
subl %edx, %ecx C -(size-1)
|
|
|
|
|
|
C Now add in the squares on the diagonal, src[0]^2, src[1]^2, ...,
|
|
C src[size-1]^2. dst[0] hasn't yet been set at all yet, and just gets the
|
|
C low limb of src[0]^2.
|
|
|
|
|
|
mull %eax
|
|
|
|
movl %eax, (%edi,%ecx,8) C dst[0]
|
|
|
|
|
|
L(diag):
|
|
C eax scratch
|
|
C ebx scratch
|
|
C ecx counter, negative
|
|
C edx carry
|
|
C esi &src[size]
|
|
C edi dst[2*size-2]
|
|
C ebp
|
|
|
|
movl (%esi,%ecx,4), %eax
|
|
movl %edx, %ebx
|
|
|
|
mull %eax
|
|
|
|
addl %ebx, 4(%edi,%ecx,8)
|
|
adcl %eax, 8(%edi,%ecx,8)
|
|
adcl $0, %edx
|
|
|
|
incl %ecx
|
|
jnz L(diag)
|
|
|
|
|
|
movl SAVE_ESI, %esi
|
|
movl SAVE_EBX, %ebx
|
|
|
|
addl %edx, 4(%edi) C dst most significant limb
|
|
|
|
movl SAVE_EDI, %edi
|
|
movl SAVE_EBP, %ebp
|
|
addl $FRAME, %esp
|
|
ret
|
|
|
|
|
|
|
|
C -----------------------------------------------------------------------------
|
|
ifdef(`PIC',`
|
|
L(pic_calc):
|
|
addl (%esp), %ecx
|
|
addl $L(unroll_inner_end)-L(here)-eval(2*CODE_BYTES_PER_LIMB), %ecx
|
|
addl %edx, %ecx
|
|
ret_internal
|
|
')
|
|
|
|
|
|
EPILOGUE()
|