mpir/mpn/x86w/p3/divrem_1.asm
2012-11-25 22:33:07 +00:00

520 lines
14 KiB
NASM

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