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dnl Intel Pentium-4 mpn_divexact_1 -- mpn by limb exact division.
dnl Copyright 2001, 2002, 2007 Free Software Foundation, Inc.
dnl This file is part of the GNU MP Library.
dnl
dnl The GNU MP Library is free software; you can redistribute it and/or modify
dnl it under the terms of either:
dnl
dnl * the GNU Lesser General Public License as published by the Free
dnl Software Foundation; either version 3 of the License, or (at your
dnl option) any later version.
dnl
dnl or
dnl
dnl * the GNU General Public License as published by the Free Software
dnl Foundation; either version 2 of the License, or (at your option) any
dnl later version.
dnl
dnl or both in parallel, as here.
dnl
dnl The GNU MP Library is distributed in the hope that it will be useful, but
dnl WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
dnl or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
dnl for more details.
dnl
dnl You should have received copies of the GNU General Public License and the
dnl GNU Lesser General Public License along with the GNU MP Library. If not,
dnl see https://www.gnu.org/licenses/.
include(`../config.m4')
C P4: 19.0 cycles/limb
C void mpn_divexact_1 (mp_ptr dst, mp_srcptr src, mp_size_t size,
C mp_limb_t divisor);
C
C Pairs of movd's are used to avoid unaligned loads. Despite the loads not
C being on the dependent chain and there being plenty of cycles available,
C using an unaligned movq on every second iteration measured about 23 c/l.
C
C Using divl for size==1 seems a touch quicker than mul-by-inverse. The mul
C will be about 9+2*4+2*2+10*4+19+12 = 92 cycles latency, though some of
C that might be hidden by out-of-order execution, whereas divl is around 60.
C At size==2 an extra 19 for the mul versus 60 for the divl will see the mul
C faster.
defframe(PARAM_DIVISOR,16)
defframe(PARAM_SIZE, 12)
defframe(PARAM_SRC, 8)
defframe(PARAM_DST, 4)
TEXT
ALIGN(16)
PROLOGUE(mpn_divexact_1)
deflit(`FRAME',0)
movl PARAM_SIZE, %edx
movl PARAM_SRC, %eax
movl PARAM_DIVISOR, %ecx
subl $1, %edx
jnz L(two_or_more)
movl (%eax), %eax
xorl %edx, %edx
divl %ecx
movl PARAM_DST, %ecx
movl %eax, (%ecx)
ret
L(two_or_more):
C eax src
C ebx
C ecx divisor
C edx size-1
movl %ecx, %eax
bsfl %ecx, %ecx C trailing twos
shrl %cl, %eax C d = divisor without twos
movd %eax, %mm6
movd %ecx, %mm7 C shift
shrl %eax C d/2
andl $127, %eax C d/2, 7 bits
ifdef(`PIC',`
LEA( binvert_limb_table, %ecx)
movzbl (%eax,%ecx), %eax C inv 8 bits
',`
movzbl binvert_limb_table(%eax), %eax C inv 8 bits
')
C
movd %eax, %mm5 C inv
movd %eax, %mm0 C inv
pmuludq %mm5, %mm5 C inv*inv
C
pmuludq %mm6, %mm5 C inv*inv*d
paddd %mm0, %mm0 C 2*inv
C
psubd %mm5, %mm0 C inv = 2*inv - inv*inv*d
pxor %mm5, %mm5
paddd %mm0, %mm5
pmuludq %mm0, %mm0 C inv*inv
pcmpeqd %mm4, %mm4
psrlq $32, %mm4 C 0x00000000FFFFFFFF
C
pmuludq %mm6, %mm0 C inv*inv*d
paddd %mm5, %mm5 C 2*inv
movl PARAM_SRC, %eax
movl PARAM_DST, %ecx
pxor %mm1, %mm1 C initial carry limb
C
psubd %mm0, %mm5 C inv = 2*inv - inv*inv*d
ASSERT(e,` C expect d*inv == 1 mod 2^GMP_LIMB_BITS
pushl %eax FRAME_pushl()
movq %mm6, %mm0
pmuludq %mm5, %mm0
movd %mm0, %eax
cmpl $1, %eax
popl %eax FRAME_popl()')
pxor %mm0, %mm0 C initial carry bit
C The dependent chain here is as follows.
C
C latency
C psubq s = (src-cbit) - climb 2
C pmuludq q = s*inverse 8
C pmuludq prod = q*divisor 8
C psrlq climb = high(prod) 2
C --
C 20
C
C Yet the loop measures 19.0 c/l, so obviously there's something gained
C there over a straight reading of the chip documentation.
L(top):
C eax src, incrementing
C ebx
C ecx dst, incrementing
C edx counter, size-1 iterations
C
C mm0 carry bit
C mm1 carry limb
C mm4 0x00000000FFFFFFFF
C mm5 inverse
C mm6 divisor
C mm7 shift
movd (%eax), %mm2
movd 4(%eax), %mm3
addl $4, %eax
punpckldq %mm3, %mm2
psrlq %mm7, %mm2
pand %mm4, %mm2 C src
psubq %mm0, %mm2 C src - cbit
psubq %mm1, %mm2 C src - cbit - climb
movq %mm2, %mm0
psrlq $63, %mm0 C new cbit
pmuludq %mm5, %mm2 C s*inverse
movd %mm2, (%ecx) C q
addl $4, %ecx
movq %mm6, %mm1
pmuludq %mm2, %mm1 C q*divisor
psrlq $32, %mm1 C new climb
subl $1, %edx
jnz L(top)
L(done):
movd (%eax), %mm2
psrlq %mm7, %mm2 C src
psubq %mm0, %mm2 C src - cbit
psubq %mm1, %mm2 C src - cbit - climb
pmuludq %mm5, %mm2 C s*inverse
movd %mm2, (%ecx) C q
emms
ret
EPILOGUE()
ASM_END()
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