--- /dev/null
+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()
projects / msp430-gcc.git / blobdiff