824 lines
18 KiB
NASM
824 lines
18 KiB
NASM
dnl AMD K7 mpn_divrem_1, mpn_divrem_1c, mpn_preinv_divrem_1 -- mpn by limb
|
|
dnl division.
|
|
|
|
dnl Copyright 1999, 2000, 2001, 2002, 2004 Free Software Foundation, 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 2.1 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
|
|
dnl License along with the GNU MP Library; see the file COPYING.LIB. If
|
|
dnl not, write to the Free Software Foundation, Inc., 51 Franklin Street,
|
|
dnl Fifth Floor, Boston, MA 02110-1301, USA.
|
|
|
|
include(`../config.m4')
|
|
|
|
|
|
C K7: 17.0 cycles/limb integer part, 15.0 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 The "and"s shown in the paper are done here with "cmov"s. "m" is written
|
|
C for m', and "d" for d_norm, which won't cause any confusion since it's
|
|
C only the normalized divisor that's of any use in the code. "b" is written
|
|
C for 2^N, the size of a limb, N being 32 here.
|
|
C
|
|
C The step "sdword dr = n - 2^N*d + (2^N-1-q1) * d" is instead done as
|
|
C "n-(q1+1)*d"; this rearrangement gives the same two-limb answer. If
|
|
C q1==0xFFFFFFFF, then q1+1 would overflow. We branch to a special case
|
|
C "q1_ff" if this occurs. Since the true quotient is either q1 or q1+1 then
|
|
C if q1==0xFFFFFFFF that must be the right value.
|
|
C
|
|
C For the last and second last steps q1==0xFFFFFFFF is instead handled by an
|
|
C sbbl to go back to 0xFFFFFFFF if an overflow occurs when adding 1. This
|
|
C then goes through as normal, and finding no addback required. sbbl costs
|
|
C an extra cycle over what the main loop code does, but it keeps code size
|
|
C and complexity down.
|
|
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 used. The latter
|
|
C 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 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, in particular note that big_base for a
|
|
C decimal mpn_get_str is not normalized in a 32-bit limb.
|
|
|
|
|
|
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 50 cycles to calculate, but after that the
|
|
dnl multiply is 17 c/l versus division at 42 c/l.
|
|
dnl
|
|
dnl At 3 limbs the mul is a touch faster than div on the integer part, and
|
|
dnl even more so on the fractional part.
|
|
|
|
deflit(MUL_THRESHOLD, 3)
|
|
|
|
|
|
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)
|
|
|
|
defframe(SAVE_EBX, -4)
|
|
defframe(SAVE_ESI, -8)
|
|
defframe(SAVE_EDI, -12)
|
|
defframe(SAVE_EBP, -16)
|
|
|
|
defframe(VAR_NORM, -20)
|
|
defframe(VAR_INVERSE, -24)
|
|
defframe(VAR_SRC, -28)
|
|
defframe(VAR_DST, -32)
|
|
defframe(VAR_DST_STOP,-36)
|
|
|
|
deflit(STACK_SPACE, 36)
|
|
|
|
TEXT
|
|
ALIGN(32)
|
|
|
|
PROLOGUE(mpn_preinv_divrem_1)
|
|
deflit(`FRAME',0)
|
|
movl PARAM_XSIZE, %ecx
|
|
movl PARAM_DST, %edx
|
|
subl $STACK_SPACE, %esp FRAME_subl_esp(STACK_SPACE)
|
|
|
|
movl %esi, SAVE_ESI
|
|
movl PARAM_SRC, %esi
|
|
|
|
movl %ebx, SAVE_EBX
|
|
movl PARAM_SIZE, %ebx
|
|
|
|
leal 8(%edx,%ecx,4), %edx C &dst[xsize+2]
|
|
movl %ebp, SAVE_EBP
|
|
movl PARAM_DIVISOR, %ebp
|
|
|
|
movl %edx, VAR_DST_STOP C &dst[xsize+2]
|
|
movl %edi, SAVE_EDI
|
|
xorl %edi, %edi C carry
|
|
|
|
movl -4(%esi,%ebx,4), %eax C src high limb
|
|
xor %ecx, %ecx
|
|
|
|
C
|
|
|
|
C
|
|
|
|
cmpl %ebp, %eax C high cmp divisor
|
|
|
|
cmovc( %eax, %edi) C high is carry if high<divisor
|
|
cmovnc( %eax, %ecx) C 0 if skip div, src high if not
|
|
C (the latter in case src==dst)
|
|
|
|
movl %ecx, -12(%edx,%ebx,4) C dst high limb
|
|
sbbl $0, %ebx C skip one division if high<divisor
|
|
movl PARAM_PREINV_SHIFT, %ecx
|
|
|
|
leal -8(%edx,%ebx,4), %edx C &dst[xsize+size]
|
|
movl $32, %eax
|
|
|
|
movl %edx, VAR_DST C &dst[xsize+size]
|
|
|
|
shll %cl, %ebp C d normalized
|
|
subl %ecx, %eax
|
|
movl %ecx, VAR_NORM
|
|
|
|
movd %eax, %mm7 C rshift
|
|
movl PARAM_PREINV_INVERSE, %eax
|
|
jmp L(start_preinv)
|
|
|
|
EPILOGUE()
|
|
|
|
|
|
ALIGN(16)
|
|
|
|
PROLOGUE(mpn_divrem_1c)
|
|
deflit(`FRAME',0)
|
|
movl PARAM_CARRY, %edx
|
|
movl PARAM_SIZE, %ecx
|
|
subl $STACK_SPACE, %esp
|
|
deflit(`FRAME',STACK_SPACE)
|
|
|
|
movl %ebx, SAVE_EBX
|
|
movl PARAM_XSIZE, %ebx
|
|
|
|
movl %edi, SAVE_EDI
|
|
movl PARAM_DST, %edi
|
|
|
|
movl %ebp, SAVE_EBP
|
|
movl PARAM_DIVISOR, %ebp
|
|
|
|
movl %esi, SAVE_ESI
|
|
movl PARAM_SRC, %esi
|
|
|
|
leal -4(%edi,%ebx,4), %edi C &dst[xsize-1]
|
|
jmp L(start_1c)
|
|
|
|
EPILOGUE()
|
|
|
|
|
|
C offset 0xa1, close enough to aligned
|
|
PROLOGUE(mpn_divrem_1)
|
|
deflit(`FRAME',0)
|
|
|
|
movl PARAM_SIZE, %ecx
|
|
movl $0, %edx C initial carry (if can't skip a div)
|
|
subl $STACK_SPACE, %esp
|
|
deflit(`FRAME',STACK_SPACE)
|
|
|
|
movl %esi, SAVE_ESI
|
|
movl PARAM_SRC, %esi
|
|
|
|
movl %ebx, SAVE_EBX
|
|
movl PARAM_XSIZE, %ebx
|
|
|
|
movl %ebp, SAVE_EBP
|
|
movl PARAM_DIVISOR, %ebp
|
|
orl %ecx, %ecx C size
|
|
|
|
movl %edi, SAVE_EDI
|
|
movl PARAM_DST, %edi
|
|
leal -4(%edi,%ebx,4), %edi C &dst[xsize-1]
|
|
|
|
jz L(no_skip_div) C if size==0
|
|
movl -4(%esi,%ecx,4), %eax C src high limb
|
|
xorl %esi, %esi
|
|
|
|
cmpl %ebp, %eax C high cmp divisor
|
|
|
|
cmovc( %eax, %edx) C high is carry if high<divisor
|
|
cmovnc( %eax, %esi) C 0 if skip div, src high if not
|
|
|
|
movl %esi, (%edi,%ecx,4) C dst high limb
|
|
sbbl $0, %ecx C size-1 if high<divisor
|
|
movl PARAM_SRC, %esi C reload
|
|
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
|
|
cmpl $MUL_THRESHOLD, %eax
|
|
jae L(mul_by_inverse)
|
|
|
|
|
|
C With MUL_THRESHOLD set to 3, the simple loops here only do 0 to 2 limbs.
|
|
C It'd be possible to write them out without the looping, but no speedup
|
|
C would be expected.
|
|
C
|
|
C Using PARAM_DIVISOR instead of %ebp measures 1 cycle/loop faster on the
|
|
C integer part, but curiously not on the fractional part, where %ebp is a
|
|
C (fixed) couple of cycles faster.
|
|
|
|
orl %ecx, %ecx
|
|
jz L(divide_no_integer)
|
|
|
|
L(divide_integer):
|
|
C eax scratch (quotient)
|
|
C ebx xsize
|
|
C ecx counter
|
|
C edx scratch (remainder)
|
|
C esi src
|
|
C edi &dst[xsize-1]
|
|
C ebp divisor
|
|
|
|
movl -4(%esi,%ecx,4), %eax
|
|
|
|
divl PARAM_DIVISOR
|
|
|
|
movl %eax, (%edi,%ecx,4)
|
|
decl %ecx
|
|
jnz L(divide_integer)
|
|
|
|
|
|
L(divide_no_integer):
|
|
movl PARAM_DST, %edi
|
|
orl %ebx, %ebx
|
|
jnz L(divide_fraction)
|
|
|
|
L(divide_done):
|
|
movl SAVE_ESI, %esi
|
|
movl SAVE_EDI, %edi
|
|
movl %edx, %eax
|
|
|
|
movl SAVE_EBX, %ebx
|
|
movl SAVE_EBP, %ebp
|
|
addl $STACK_SPACE, %esp
|
|
|
|
ret
|
|
|
|
|
|
L(divide_fraction):
|
|
C eax scratch (quotient)
|
|
C ebx counter
|
|
C ecx
|
|
C edx scratch (remainder)
|
|
C esi
|
|
C edi dst
|
|
C ebp divisor
|
|
|
|
movl $0, %eax
|
|
|
|
divl %ebp
|
|
|
|
movl %eax, -4(%edi,%ebx,4)
|
|
decl %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
|
|
C edi &dst[xsize-1]
|
|
C ebp divisor
|
|
|
|
bsrl %ebp, %eax C 31-l
|
|
|
|
leal 12(%edi), %ebx C &dst[xsize+2], loop dst stop
|
|
leal 4(%edi,%ecx,4), %edi C &dst[xsize+size]
|
|
|
|
movl %edi, VAR_DST
|
|
movl %ebx, VAR_DST_STOP
|
|
|
|
movl %ecx, %ebx C size
|
|
movl $31, %ecx
|
|
|
|
movl %edx, %edi C carry
|
|
movl $-1, %edx
|
|
|
|
C
|
|
|
|
xorl %eax, %ecx C l
|
|
incl %eax C 32-l
|
|
|
|
shll %cl, %ebp C d normalized
|
|
movl %ecx, VAR_NORM
|
|
|
|
movd %eax, %mm7
|
|
|
|
movl $-1, %eax
|
|
subl %ebp, %edx C (b-d)-1 giving edx:eax = b*(b-d)-1
|
|
|
|
divl %ebp C floor (b*(b-d)-1) / d
|
|
|
|
L(start_preinv):
|
|
C eax inverse
|
|
C ebx size
|
|
C ecx shift
|
|
C edx
|
|
C esi src
|
|
C edi carry
|
|
C ebp divisor
|
|
C
|
|
C mm7 rshift
|
|
|
|
orl %ebx, %ebx C size
|
|
movl %eax, VAR_INVERSE
|
|
leal -12(%esi,%ebx,4), %eax C &src[size-3]
|
|
|
|
jz L(start_zero)
|
|
movl %eax, VAR_SRC
|
|
cmpl $1, %ebx
|
|
|
|
movl 8(%eax), %esi C src high limb
|
|
jz L(start_one)
|
|
|
|
L(start_two_or_more):
|
|
movl 4(%eax), %edx C src second highest limb
|
|
|
|
shldl( %cl, %esi, %edi) C n2 = carry,high << l
|
|
|
|
shldl( %cl, %edx, %esi) C n10 = high,second << l
|
|
|
|
cmpl $2, %ebx
|
|
je L(integer_two_left)
|
|
jmp L(integer_top)
|
|
|
|
|
|
L(start_one):
|
|
shldl( %cl, %esi, %edi) C n2 = carry,high << l
|
|
|
|
shll %cl, %esi C n10 = high << l
|
|
movl %eax, VAR_SRC
|
|
jmp L(integer_one_left)
|
|
|
|
|
|
L(start_zero):
|
|
C Can be here with xsize==0 if mpn_preinv_divrem_1 had size==1 and
|
|
C skipped a division.
|
|
|
|
shll %cl, %edi C n2 = carry << l
|
|
movl %edi, %eax C return value for zero_done
|
|
cmpl $0, PARAM_XSIZE
|
|
|
|
je L(zero_done)
|
|
jmp L(fraction_some)
|
|
|
|
|
|
|
|
C -----------------------------------------------------------------------------
|
|
C
|
|
C The multiply by inverse loop is 17 cycles, and relies on some out-of-order
|
|
C execution. The instruction scheduling is important, with various
|
|
C apparently equivalent forms running 1 to 5 cycles slower.
|
|
C
|
|
C A lower bound for the time would seem to be 16 cycles, based on the
|
|
C following successive dependencies.
|
|
C
|
|
C cycles
|
|
C n2+n1 1
|
|
C mul 6
|
|
C q1+1 1
|
|
C mul 6
|
|
C sub 1
|
|
C addback 1
|
|
C ---
|
|
C 16
|
|
C
|
|
C This chain is what the loop has already, but 16 cycles isn't achieved.
|
|
C K7 has enough decode, and probably enough execute (depending maybe on what
|
|
C a mul actually consumes), but nothing running under 17 has been found.
|
|
C
|
|
C In theory n2+n1 could be done in the sub and addback stages (by
|
|
C calculating both n2 and n2+n1 there), but lack of registers makes this an
|
|
C unlikely proposition.
|
|
C
|
|
C The jz in the loop keeps the q1+1 stage to 1 cycle. Handling an overflow
|
|
C from q1+1 with an "sbbl $0, %ebx" would add a cycle to the dependent
|
|
C chain, and nothing better than 18 cycles has been found when using it.
|
|
C The jump is taken only when q1 is 0xFFFFFFFF, and on random data this will
|
|
C be an extremely rare event.
|
|
C
|
|
C Branch mispredictions will hit random occurrances of q1==0xFFFFFFFF, but
|
|
C if some special data is coming out with this always, the q1_ff special
|
|
C case actually runs at 15 c/l. 0x2FFF...FFFD divided by 3 is a good way to
|
|
C induce the q1_ff case, for speed measurements or testing. Note that
|
|
C 0xFFF...FFF divided by 1 or 2 doesn't induce it.
|
|
C
|
|
C The instruction groupings and empty comments show the cycles for a naive
|
|
C in-order view of the code (conveniently ignoring the load latency on
|
|
C VAR_INVERSE). This shows some of where the time is going, but is nonsense
|
|
C to the extent that out-of-order execution rearranges it. In this case
|
|
C there's 19 cycles shown, but it executes at 17.
|
|
|
|
ALIGN(16)
|
|
L(integer_top):
|
|
C eax scratch
|
|
C ebx scratch (nadj, q1)
|
|
C ecx scratch (src, dst)
|
|
C edx scratch
|
|
C esi n10
|
|
C edi n2
|
|
C ebp divisor
|
|
C
|
|
C mm0 scratch (src qword)
|
|
C mm7 rshift for normalization
|
|
|
|
cmpl $0x80000000, %esi C n1 as 0=c, 1=nc
|
|
movl %edi, %eax C n2
|
|
movl VAR_SRC, %ecx
|
|
|
|
leal (%ebp,%esi), %ebx
|
|
cmovc( %esi, %ebx) C nadj = n10 + (-n1 & d), ignoring overflow
|
|
sbbl $-1, %eax C n2+n1
|
|
|
|
mull VAR_INVERSE C m*(n2+n1)
|
|
|
|
movq (%ecx), %mm0 C next limb and the one below it
|
|
subl $4, %ecx
|
|
|
|
movl %ecx, VAR_SRC
|
|
|
|
C
|
|
|
|
addl %ebx, %eax C m*(n2+n1) + nadj, low giving carry flag
|
|
leal 1(%edi), %ebx C n2+1
|
|
movl %ebp, %eax C d
|
|
|
|
C
|
|
|
|
adcl %edx, %ebx C 1 + high(n2<<32 + m*(n2+n1) + nadj) = q1+1
|
|
jz L(q1_ff)
|
|
movl VAR_DST, %ecx
|
|
|
|
mull %ebx C (q1+1)*d
|
|
|
|
psrlq %mm7, %mm0
|
|
|
|
leal -4(%ecx), %ecx
|
|
|
|
C
|
|
|
|
subl %eax, %esi
|
|
movl VAR_DST_STOP, %eax
|
|
|
|
C
|
|
|
|
sbbl %edx, %edi C n - (q1+1)*d
|
|
movl %esi, %edi C remainder -> n2
|
|
leal (%ebp,%esi), %edx
|
|
|
|
movd %mm0, %esi
|
|
|
|
cmovc( %edx, %edi) C n - q1*d if underflow from using q1+1
|
|
sbbl $0, %ebx C q
|
|
cmpl %eax, %ecx
|
|
|
|
movl %ebx, (%ecx)
|
|
movl %ecx, VAR_DST
|
|
jne L(integer_top)
|
|
|
|
|
|
L(integer_loop_done):
|
|
|
|
|
|
C -----------------------------------------------------------------------------
|
|
C
|
|
C Here, and in integer_one_left below, an sbbl $0 is used rather than a jz
|
|
C q1_ff special case. This make the code a bit smaller and simpler, and
|
|
C costs only 1 cycle (each).
|
|
|
|
L(integer_two_left):
|
|
C eax scratch
|
|
C ebx scratch (nadj, q1)
|
|
C ecx scratch (src, dst)
|
|
C edx scratch
|
|
C esi n10
|
|
C edi n2
|
|
C ebp divisor
|
|
C
|
|
C mm7 rshift
|
|
|
|
cmpl $0x80000000, %esi C n1 as 0=c, 1=nc
|
|
movl %edi, %eax C n2
|
|
movl PARAM_SRC, %ecx
|
|
|
|
leal (%ebp,%esi), %ebx
|
|
cmovc( %esi, %ebx) C nadj = n10 + (-n1 & d), ignoring overflow
|
|
sbbl $-1, %eax C n2+n1
|
|
|
|
mull VAR_INVERSE C m*(n2+n1)
|
|
|
|
movd (%ecx), %mm0 C src low limb
|
|
|
|
movl VAR_DST_STOP, %ecx
|
|
|
|
C
|
|
|
|
addl %ebx, %eax C m*(n2+n1) + nadj, low giving carry flag
|
|
leal 1(%edi), %ebx C n2+1
|
|
movl %ebp, %eax C d
|
|
|
|
adcl %edx, %ebx C 1 + high(n2<<32 + m*(n2+n1) + nadj) = q1+1
|
|
|
|
sbbl $0, %ebx
|
|
|
|
mull %ebx C (q1+1)*d
|
|
|
|
psllq $32, %mm0
|
|
|
|
psrlq %mm7, %mm0
|
|
|
|
C
|
|
|
|
subl %eax, %esi
|
|
|
|
C
|
|
|
|
sbbl %edx, %edi C n - (q1+1)*d
|
|
movl %esi, %edi C remainder -> n2
|
|
leal (%ebp,%esi), %edx
|
|
|
|
movd %mm0, %esi
|
|
|
|
cmovc( %edx, %edi) C n - q1*d if underflow from using q1+1
|
|
sbbl $0, %ebx C q
|
|
|
|
movl %ebx, -4(%ecx)
|
|
|
|
|
|
C -----------------------------------------------------------------------------
|
|
L(integer_one_left):
|
|
C eax scratch
|
|
C ebx scratch (nadj, q1)
|
|
C ecx dst
|
|
C edx scratch
|
|
C esi n10
|
|
C edi n2
|
|
C ebp divisor
|
|
C
|
|
C mm7 rshift
|
|
|
|
movl VAR_DST_STOP, %ecx
|
|
cmpl $0x80000000, %esi C n1 as 0=c, 1=nc
|
|
movl %edi, %eax C n2
|
|
|
|
leal (%ebp,%esi), %ebx
|
|
cmovc( %esi, %ebx) C nadj = n10 + (-n1 & d), ignoring overflow
|
|
sbbl $-1, %eax C n2+n1
|
|
|
|
mull VAR_INVERSE C m*(n2+n1)
|
|
|
|
C
|
|
|
|
C
|
|
|
|
C
|
|
|
|
addl %ebx, %eax C m*(n2+n1) + nadj, low giving carry flag
|
|
leal 1(%edi), %ebx C n2+1
|
|
movl %ebp, %eax C d
|
|
|
|
C
|
|
|
|
adcl %edx, %ebx C 1 + high(n2<<32 + m*(n2+n1) + nadj) = q1+1
|
|
|
|
sbbl $0, %ebx C q1 if q1+1 overflowed
|
|
|
|
mull %ebx
|
|
|
|
C
|
|
|
|
C
|
|
|
|
C
|
|
|
|
subl %eax, %esi
|
|
|
|
C
|
|
|
|
sbbl %edx, %edi C n - (q1+1)*d
|
|
movl %esi, %edi C remainder -> n2
|
|
leal (%ebp,%esi), %edx
|
|
|
|
cmovc( %edx, %edi) C n - q1*d if underflow from using q1+1
|
|
sbbl $0, %ebx C q
|
|
|
|
movl %ebx, -8(%ecx)
|
|
subl $8, %ecx
|
|
|
|
|
|
|
|
L(integer_none):
|
|
cmpl $0, PARAM_XSIZE
|
|
jne L(fraction_some)
|
|
|
|
movl %edi, %eax
|
|
L(fraction_done):
|
|
movl VAR_NORM, %ecx
|
|
L(zero_done):
|
|
movl SAVE_EBP, %ebp
|
|
|
|
movl SAVE_EDI, %edi
|
|
movl SAVE_ESI, %esi
|
|
|
|
movl SAVE_EBX, %ebx
|
|
addl $STACK_SPACE, %esp
|
|
|
|
shrl %cl, %eax
|
|
emms
|
|
|
|
ret
|
|
|
|
|
|
C -----------------------------------------------------------------------------
|
|
C
|
|
C Special case for q1=0xFFFFFFFF, giving q=0xFFFFFFFF meaning the low dword
|
|
C of q*d is simply -d and the remainder n-q*d = n10+d
|
|
|
|
L(q1_ff):
|
|
C eax (divisor)
|
|
C ebx (q1+1 == 0)
|
|
C ecx
|
|
C edx
|
|
C esi n10
|
|
C edi n2
|
|
C ebp divisor
|
|
|
|
movl VAR_DST, %ecx
|
|
movl VAR_DST_STOP, %edx
|
|
subl $4, %ecx
|
|
|
|
psrlq %mm7, %mm0
|
|
leal (%ebp,%esi), %edi C n-q*d remainder -> next n2
|
|
movl %ecx, VAR_DST
|
|
|
|
movd %mm0, %esi C next n10
|
|
|
|
movl $-1, (%ecx)
|
|
cmpl %ecx, %edx
|
|
jne L(integer_top)
|
|
|
|
jmp L(integer_loop_done)
|
|
|
|
|
|
|
|
C -----------------------------------------------------------------------------
|
|
C
|
|
C Being the fractional part, the "source" limbs are all zero, meaning
|
|
C n10=0, n1=0, and hence nadj=0, leading to many instructions eliminated.
|
|
C
|
|
C The loop runs at 15 cycles. The dependent chain is the same as the
|
|
C general case above, but without the n2+n1 stage (due to n1==0), so 15
|
|
C would seem to be the lower bound.
|
|
C
|
|
C A not entirely obvious simplification is that q1+1 never overflows a limb,
|
|
C and so there's no need for the sbbl $0 or jz q1_ff from the general case.
|
|
C q1 is the high word of m*n2+b*n2 and the following shows q1<=b-2 always.
|
|
C rnd() means rounding down to a multiple of d.
|
|
C
|
|
C m*n2 + b*n2 <= m*(d-1) + b*(d-1)
|
|
C = m*d + b*d - m - b
|
|
C = floor((b(b-d)-1)/d)*d + b*d - m - b
|
|
C = rnd(b(b-d)-1) + b*d - m - b
|
|
C = rnd(b(b-d)-1 + b*d) - m - b
|
|
C = rnd(b*b-1) - m - b
|
|
C <= (b-2)*b
|
|
C
|
|
C Unchanged from the general case is that the final quotient limb q can be
|
|
C either q1 or q1+1, and the q1+1 case occurs often. This can be seen from
|
|
C equation 8.4 of the paper which simplifies as follows when n1==0 and
|
|
C n0==0.
|
|
C
|
|
C n-q1*d = (n2*k+q0*d)/b <= d + (d*d-2d)/b
|
|
C
|
|
C As before, the instruction groupings and empty comments show a naive
|
|
C in-order view of the code, which is made a nonsense by out of order
|
|
C execution. There's 17 cycles shown, but it executes at 15.
|
|
C
|
|
C Rotating the store q and remainder->n2 instructions up to the top of the
|
|
C loop gets the run time down from 16 to 15.
|
|
|
|
ALIGN(16)
|
|
L(fraction_some):
|
|
C eax
|
|
C ebx
|
|
C ecx
|
|
C edx
|
|
C esi
|
|
C edi carry
|
|
C ebp divisor
|
|
|
|
movl PARAM_DST, %esi
|
|
movl VAR_DST_STOP, %ecx C &dst[xsize+2]
|
|
movl %edi, %eax
|
|
|
|
subl $8, %ecx C &dst[xsize]
|
|
jmp L(fraction_entry)
|
|
|
|
|
|
ALIGN(16)
|
|
L(fraction_top):
|
|
C eax n2 carry, then scratch
|
|
C ebx scratch (nadj, q1)
|
|
C ecx dst, decrementing
|
|
C edx scratch
|
|
C esi dst stop point
|
|
C edi (will be n2)
|
|
C ebp divisor
|
|
|
|
movl %ebx, (%ecx) C previous q
|
|
movl %eax, %edi C remainder->n2
|
|
|
|
L(fraction_entry):
|
|
mull VAR_INVERSE C m*n2
|
|
|
|
movl %ebp, %eax C d
|
|
subl $4, %ecx C dst
|
|
leal 1(%edi), %ebx
|
|
|
|
C
|
|
|
|
C
|
|
|
|
C
|
|
|
|
C
|
|
|
|
addl %edx, %ebx C 1 + high(n2<<32 + m*n2) = q1+1
|
|
|
|
mull %ebx C (q1+1)*d
|
|
|
|
C
|
|
|
|
C
|
|
|
|
C
|
|
|
|
negl %eax C low of n - (q1+1)*d
|
|
|
|
C
|
|
|
|
sbbl %edx, %edi C high of n - (q1+1)*d, caring only about carry
|
|
leal (%ebp,%eax), %edx
|
|
|
|
cmovc( %edx, %eax) C n - q1*d if underflow from using q1+1
|
|
sbbl $0, %ebx C q
|
|
cmpl %esi, %ecx
|
|
|
|
jne L(fraction_top)
|
|
|
|
|
|
movl %ebx, (%ecx)
|
|
jmp L(fraction_done)
|
|
|
|
EPILOGUE()
|