520 lines
14 KiB
NASM
520 lines
14 KiB
NASM
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; Copyright 1999, 2000, 2001, 2002 Free Software Foundation, Inc.
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;
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; This file is part of the GNU MP Library.
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;
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; The GNU MP Library is free software; you can redistribute it and/or
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; modify it under the terms of the GNU Lesser General Public License as
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; published by the Free Software Foundation; either version 2.1 of the
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; License, or (at your option) any later version.
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;
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; The GNU MP Library is distributed in the hope that it will be useful,
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; but WITHOUT ANY WARRANTY; without even the implied warranty of
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; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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; Lesser General Public License for more details.
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;
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; You should have received a copy of the GNU Lesser General Public
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; License along with the GNU MP Library; see the file COPYING.LIB. If
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; not, write to the Free Software Foundation, Inc., 59 Temple Place -
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; Suite 330, Boston, MA 02111-1307, USA.
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;
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; Translation of AT&T syntax code by Brian Gladman
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%include "..\..\x86i.inc"
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global ___gmpn_preinv_divrem_1
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global ___gmpn_divrem_1c
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global ___gmpn_divrem_1
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%ifdef DLL
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export ___gmpn_divrem_1c
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export ___gmpn_divrem_1
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%endif
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%define MUL_THRESHOLD 4
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%define PARAM_PREINV_SHIFT esp+frame+28
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%define PARAM_PREINV_INVERSE esp+frame+24
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%define PARAM_CARRY esp+frame+24
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%define PARAM_DIVISOR esp+frame+20
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%define PARAM_SIZE esp+frame+16
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%define PARAM_SRC esp+frame+12
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%define PARAM_XSIZE esp+frame+8
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%define PARAM_DST esp+frame+4
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%define SAVE_EBX esp+frame-4
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%define SAVE_ESI esp+frame-8
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%define SAVE_EDI esp+frame-12
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%define SAVE_EBP esp+frame-16
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%define VAR_NORM esp+frame-20
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%define VAR_INVERSE esp+frame-24
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%define VAR_SRC esp+frame-28
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%define VAR_DST esp+frame-32
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%define VAR_DST_STOP esp+frame-36
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%define STACK_SPACE 36
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%define frame 0
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section .text
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align 16
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___gmpn_preinv_divrem_1:
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mov ecx,[PARAM_XSIZE]
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sub esp,STACK_SPACE
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FR_sesp STACK_SPACE
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mov [SAVE_ESI],esi
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mov esi,[PARAM_SRC]
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mov [SAVE_EBX],ebx
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mov ebx,[PARAM_SIZE]
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mov [SAVE_EBP],ebp
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mov ebp,[PARAM_DIVISOR]
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mov [SAVE_EDI],edi
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mov edx,[PARAM_DST]
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mov eax,[-4+esi+ebx*4] ; src high limb
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xor edi,edi ; initial carry (if can't skip a div)
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lea edx,[8+edx+ecx*4] ; &dst[xsize+2]
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xor ecx,ecx
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mov [VAR_DST_STOP],edx ; &dst[xsize+2]
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cmp eax,ebp ; high cmp divisor
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cmovc edi,eax
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cmovnc ecx,eax ; (the latter in case src==dst)
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mov [-12+edx+ebx*4],ecx ; dst high limb
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sbb ebx,0 ; skip one division if high<divisor
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mov ecx,[PARAM_PREINV_SHIFT]
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lea edx,[-8+edx+ebx*4] ; &dst[xsize+size]
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mov eax,32
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mov [VAR_DST],edx ; &dst[xsize+size]
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shl ebp,cl ; d normalized
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sub eax,ecx
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mov [VAR_NORM],ecx
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movd mm7,eax ; rshift
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mov eax,[PARAM_PREINV_INVERSE]
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jmp Lstart_preinv
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align 16
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%define frame 0
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___gmpn_divrem_1c:
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mov edx,[PARAM_CARRY]
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mov ecx,[PARAM_SIZE]
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sub esp,STACK_SPACE
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%define frame STACK_SPACE
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mov [SAVE_EBX],ebx
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mov ebx,[PARAM_XSIZE]
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mov [SAVE_EDI],edi
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mov edi,[PARAM_DST]
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mov [SAVE_EBP],ebp
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mov ebp,[PARAM_DIVISOR]
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mov [SAVE_ESI],esi
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mov esi,[PARAM_SRC]
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lea edi,[-4+edi+ebx*4]
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jmp Lstart_1c
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; offset 0x31,close enough to aligned
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%define frame 0
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___gmpn_divrem_1:
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mov ecx,[PARAM_SIZE]
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mov edx,0 ; initial carry (if can't skip a div)
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sub esp,STACK_SPACE
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%define frame STACK_SPACE
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mov [SAVE_EBP],ebp
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mov ebp,[PARAM_DIVISOR]
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mov [SAVE_EBX],ebx
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mov ebx,[PARAM_XSIZE]
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mov [SAVE_ESI],esi
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mov esi,[PARAM_SRC]
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or ecx,ecx ; size
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mov [SAVE_EDI],edi
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mov edi,[PARAM_DST]
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lea edi,[-4+edi+ebx*4] ; &dst[xsize-1]
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jz Lno_skip_div ; if size==0
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mov eax,[-4+esi+ecx*4] ; src high limb
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xor esi,esi
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cmp eax,ebp ; high cmp divisor
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cmovc edx,eax
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cmovnc esi,eax ; (the latter in case src==dst)
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mov [edi+ecx*4],esi ; dst high limb
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sbb ecx,0 ; size-1 if high<divisor
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mov esi,[PARAM_SRC] ; reload
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Lno_skip_div:
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; eax
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; ebx xsize
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; ecx size
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; edx carry
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; esi src
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; edi &dst[xsize-1]
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; ebp divisor
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Lstart_1c:
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lea eax,[ebx+ecx] ; size+xsize
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cmp eax,MUL_THRESHOLD
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jae Lmul_by_inverse
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or ecx,ecx
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jz Ldivide_no_integer
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; eax scratch (quotient)
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; ebx xsize
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; ecx counter
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; edx scratch (remainder)
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; esi src
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; edi &dst[xsize-1]
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; ebp divisor
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Ldivide_integer:
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mov eax,[-4+esi+ecx*4]
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div ebp
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mov [edi+ecx*4],eax
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dec ecx
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jnz Ldivide_integer
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Ldivide_no_integer:
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mov edi,[PARAM_DST]
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or ebx,ebx
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jnz Ldivide_fraction
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Ldivide_done:
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mov esi,[SAVE_ESI]
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mov edi,[SAVE_EDI]
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mov ebx,[SAVE_EBX]
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mov eax,edx
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mov ebp,[SAVE_EBP]
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add esp,STACK_SPACE
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ret
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; eax scratch (quotient)
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; ebx counter
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; ecx
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; edx scratch (remainder)
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; esi
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; edi dst
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; ebp divisor
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Ldivide_fraction:
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mov eax,0
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div ebp
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mov [-4+edi+ebx*4],eax
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dec ebx
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jnz Ldivide_fraction
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jmp Ldivide_done
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; eax
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; ebx xsize
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; ecx size
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; edx carry
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; esi src
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; edi &dst[xsize-1]
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; ebp divisor
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Lmul_by_inverse:
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lea ebx,[12+edi] ; &dst[xsize+2],loop dst stop
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mov [VAR_DST_STOP],ebx
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lea edi,[4+edi+ecx*4] ; &dst[xsize+size]
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mov [VAR_DST],edi
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mov ebx,ecx ; size
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bsr ecx,ebp ; 31-l
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mov edi,edx ; carry
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lea eax,[1+ecx] ; 32-l
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xor ecx,31 ; l
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mov [VAR_NORM],ecx
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mov edx,-1
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shl ebp,cl ; d normalized
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movd mm7,eax
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mov eax,-1
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sub edx,ebp ; (b-d)-1 giving edx:eax = b*(b-d)-1
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div ebp ; floor (b*(b-d)-1) / d
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; eax inverse
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; ebx size
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; ecx shift
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; edx
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; esi src
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; edi carry
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; ebp divisor
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;
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; mm7 rshift
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Lstart_preinv:
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mov [VAR_INVERSE],eax
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or ebx,ebx ; size
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lea eax,[-12+esi+ebx*4] ; &src[size-3]
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mov [VAR_SRC],eax
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jz Lstart_zero
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mov esi,[8+eax] ; src high limb
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cmp ebx,1
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jz Lstart_one
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Lstart_two_or_more:
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mov edx,[4+eax] ; src second highest limb
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shld edi,esi,cl
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shld esi,edx,cl
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cmp ebx,2
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je Linteger_two_left
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jmp Linteger_top
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Lstart_one:
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shld edi,esi,cl
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shl esi,cl ; n10 = high << l
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jmp Linteger_one_left
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Lstart_zero:
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; Can be here with xsize==0 if mpn_preinv_divrem_1 had size==1 and
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; skipped a division.
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shl edi,cl ; n2 = carry << l
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mov eax,edi ; return value for zero_done
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cmp [PARAM_XSIZE],dword 0
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je Lzero_done
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jmp Lfraction_some
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; This loop runs at about 25 cycles,which is probably sub-optimal,and
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; certainly more than the dependent chain would suggest. A better loop,or
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; a better rough analysis of what's possible,would be welcomed.
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;
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; In the current implementation,the following successively dependent
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; micro-ops seem to exist.
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;
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; uops
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; n2+n1 1 (addl)
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; mul 5
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; q1+1 3 (addl/adcl)
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; mul 5
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; sub 3 (subl/sbbl)
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; addback 2 (cmov)
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; ---
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; 19
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;
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; Lack of registers hinders explicit scheduling and it might be that the
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; normal out of order execution isn't able to hide enough under the mul
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; latencies.
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;
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; Using sarl/negl to pick out n1 for the n2+n1 stage is a touch faster than
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; cmov (and takes one uop off the dependent chain). A sarl/andl/addl
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; combination was tried for the addback (despite the fact it would lengthen
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; the dependent chain) but found to be no faster.
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; eax scratch
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; ebx scratch (nadj,q1)
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; ecx scratch (src,dst)
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; edx scratch
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; esi n10
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; edi n2
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; ebp d
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;
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; mm0 scratch (src qword)
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; mm7 rshift for normalization
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align 16
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Linteger_top:
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mov eax,esi
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mov ebx,ebp
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sar eax,31 ; -n1
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mov ecx,[VAR_SRC]
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and ebx,eax ; -n1 & d
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neg eax ; n1
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add ebx,esi ; nadj = n10 + (-n1 & d),ignoring overflow
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add eax,edi ; n2+n1
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movq mm0,[ecx] ; next src limb and the one below it
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mul dword [VAR_INVERSE] ; m*(n2+n1)
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sub ecx,4
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mov [VAR_SRC],ecx
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add eax,ebx ; m*(n2+n1) + nadj,low giving carry flag
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mov eax,ebp ; d
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lea ebx,[1+edi] ; n2+1
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adc ebx,edx ; 1 + high(n2<<32 + m*(n2+n1) + nadj) = q1+1
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jz Lq1_ff
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mul ebx ; (q1+1)*d
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mov ecx,[VAR_DST]
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psrlq mm0,mm7
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sub esi,eax
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mov eax,[VAR_DST_STOP]
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sbb edi,edx ; n - (q1+1)*d
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mov edi,esi ; remainder -> n2
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lea edx,[ebp+esi]
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cmovc edi,edx
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movd esi,mm0
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sbb ebx,0 ; q
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sub ecx,4
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mov [ecx],ebx
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cmp ecx,eax
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mov [VAR_DST],ecx
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jne Linteger_top
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Linteger_loop_done:
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; Here,and in integer_one_left below,an sbbl $0 is used rather than a jz
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; q1_ff special case. This make the code a bit smaller and simpler,and
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; costs only 2 cycles (each).
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; eax scratch
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; ebx scratch (nadj,q1)
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; ecx scratch (src,dst)
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; edx scratch
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; esi n10
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; edi n2
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; ebp divisor
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;
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; mm7 rshift
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Linteger_two_left:
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mov eax,esi
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mov ebx,ebp
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sar eax,31 ; -n1
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mov ecx,[PARAM_SRC]
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and ebx,eax ; -n1 & d
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neg eax ; n1
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add ebx,esi ; nadj = n10 + (-n1 & d),ignoring overflow
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add eax,edi ; n2+n1
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mul dword [VAR_INVERSE] ; m*(n2+n1)
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movd mm0,[ecx] ; src low limb
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mov ecx,[VAR_DST_STOP]
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add eax,ebx ; m*(n2+n1) + nadj,low giving carry flag
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lea ebx,[1+edi] ; n2+1
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mov eax,ebp ; d
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adc ebx,edx ; 1 + high(n2<<32 + m*(n2+n1) + nadj) = q1+1
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sbb ebx,0
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mul ebx ; (q1+1)*d
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psllq mm0,32
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psrlq mm0,mm7
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sub esi,eax
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sbb edi,edx ; n - (q1+1)*d
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mov edi,esi ; remainder -> n2
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lea edx,[ebp+esi]
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cmovc edi,edx
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movd esi,mm0
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sbb ebx,0 ; q
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mov [-4+ecx],ebx
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; eax scratch
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; ebx scratch (nadj,q1)
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; ecx scratch (dst)
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; edx scratch
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; esi n10
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; edi n2
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; ebp divisor
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;
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; mm7 rshift
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Linteger_one_left:
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mov eax,esi
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mov ebx,ebp
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sar eax,31 ; -n1
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mov ecx,[VAR_DST_STOP]
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and ebx,eax ; -n1 & d
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neg eax ; n1
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add ebx,esi ; nadj = n10 + (-n1 & d),ignoring overflow
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add eax,edi ; n2+n1
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mul dword [VAR_INVERSE] ; m*(n2+n1)
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add eax,ebx ; m*(n2+n1) + nadj,low giving carry flag
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lea ebx,[1+edi] ; n2+1
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mov eax,ebp ; d
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adc ebx,edx ; 1 + high(n2<<32 + m*(n2+n1) + nadj) = q1+1
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sbb ebx,0 ; q1 if q1+1 overflowed
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mul ebx
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sub esi,eax
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mov eax,[PARAM_XSIZE]
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sbb edi,edx ; n - (q1+1)*d
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mov edi,esi ; remainder -> n2
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lea edx,[ebp+esi]
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cmovc edi,edx
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sbb ebx,0 ; q
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mov [-8+ecx],ebx
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sub ecx,8
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or eax,eax ; xsize
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jnz Lfraction_some
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mov eax,edi
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Lfraction_done:
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mov ecx,[VAR_NORM]
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Lzero_done:
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mov ebp,[SAVE_EBP]
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mov edi,[SAVE_EDI]
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mov esi,[SAVE_ESI]
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mov ebx,[SAVE_EBX]
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add esp,STACK_SPACE
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shr eax,cl
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emms
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ret
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; Special case for q1=0xFFFFFFFF,giving q=0xFFFFFFFF meaning the low dword
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; of q*d is simply -d and the remainder n-q*d = n10+d
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;
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; eax (divisor)
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; ebx (q1+1 == 0)
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; ecx
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; edx
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; esi n10
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; edi n2
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; ebp divisor
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Lq1_ff:
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mov ecx,[VAR_DST]
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mov edx,[VAR_DST_STOP]
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sub ecx,4
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mov [VAR_DST],ecx
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psrlq mm0,mm7
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lea edi,[ebp+esi] ; n-q*d remainder -> next n2
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mov [ecx],dword -1
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movd esi,mm0 ; next n10
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cmp edx,ecx
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jne Linteger_top
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jmp Linteger_loop_done
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;
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; In the current implementation,the following successively dependent
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; micro-ops seem to exist.
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;
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; uops
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; mul 5
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; q1+1 1 (addl)
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; mul 5
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; sub 3 (negl/sbbl)
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; addback 2 (cmov)
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; ---
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; 16
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;
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; The loop in fact runs at about 17.5 cycles. Using a sarl/andl/addl for
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; the addback was found to be a touch slower.
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; eax
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; ebx
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; ecx
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; edx
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; esi
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; edi carry
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; ebp divisor
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align 16
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Lfraction_some:
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mov esi,[PARAM_DST]
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mov ecx,[VAR_DST_STOP] ; &dst[xsize+2]
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mov eax,edi
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sub ecx,8 ; &dst[xsize]
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; eax n2,then scratch
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; ebx scratch (nadj,q1)
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; ecx dst,decrementing
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; edx scratch
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; esi dst stop point
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; edi n2
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; ebp divisor
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align 16
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Lfraction_top:
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mul dword [VAR_INVERSE] ; m*n2
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mov eax,ebp ; d
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sub ecx,4 ; dst
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lea ebx,[edi+1]
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add ebx,edx ; 1 + high(n2<<32 + m*n2) = q1+1
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mul ebx ; (q1+1)*d
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neg eax ; low of n - (q1+1)*d
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|
sbb edi,edx ; high of n - (q1+1)*d,caring only about carry
|
|
lea edx,[ebp+eax]
|
|
cmovc eax,edx
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|
sbb ebx,0 ; q
|
|
mov edi,eax ; remainder->n2
|
|
cmp ecx,esi
|
|
mov [ecx],ebx ; previous q
|
|
jne Lfraction_top
|
|
jmp Lfraction_done
|
|
|
|
end
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