dnl AMD K6 mpn_addmul_1/mpn_submul_1 -- add or subtract mpn multiple. dnl Copyright 1999, 2000, 2001, 2002, 2003, 2005 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 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 cycles/limb C P5: C P6 model 0-8,10-12) 5.94 C P6 model 9 (Banias) C P6 model 13 (Dothan) 5.57 C P4 model 0 (Willamette) C P4 model 1 (?) C P4 model 2 (Northwood) C P4 model 3 (Prescott) C P4 model 4 (Nocona) C K6: 7.65-8.5 (data dependent) C K7: C K8: dnl K6: large multpliers small multpliers dnl UNROLL_COUNT cycles/limb cycles/limb dnl 4 9.5 7.78 dnl 8 9.0 7.78 dnl 16 8.4 7.65 dnl 32 8.4 8.2 dnl dnl Maximum possible unrolling with the current code is 32. dnl dnl Unrolling to 16 limbs/loop makes the unrolled loop fit exactly in a 256 dnl byte block, which might explain the good speed at that unrolling. deflit(UNROLL_COUNT, 16) ifdef(`OPERATION_addmul_1', ` define(M4_inst, addl) define(M4_function_1, mpn_addmul_1) define(M4_function_1c, mpn_addmul_1c) ',`ifdef(`OPERATION_submul_1', ` define(M4_inst, subl) define(M4_function_1, mpn_submul_1) define(M4_function_1c, mpn_submul_1c) ',`m4_error(`Need OPERATION_addmul_1 or OPERATION_submul_1 ')')') MULFUNC_PROLOGUE(mpn_addmul_1 mpn_addmul_1c mpn_submul_1 mpn_submul_1c) C mp_limb_t mpn_addmul_1 (mp_ptr dst, mp_srcptr src, mp_size_t size, C mp_limb_t mult); C mp_limb_t mpn_addmul_1c (mp_ptr dst, mp_srcptr src, mp_size_t size, C mp_limb_t mult, mp_limb_t carry); C mp_limb_t mpn_submul_1 (mp_ptr dst, mp_srcptr src, mp_size_t size, C mp_limb_t mult); C mp_limb_t mpn_submul_1c (mp_ptr dst, mp_srcptr src, mp_size_t size, C mp_limb_t mult, mp_limb_t carry); C C The jadcl0()s in the unrolled loop makes the speed data dependent. Small C multipliers (most significant few bits clear) result in few carry bits and C speeds up to 7.65 cycles/limb are attained. Large multipliers (most C significant few bits set) make the carry bits 50/50 and lead to something C more like 8.4 c/l. With adcl's both of these would be 9.3 c/l. C C It's important that the gains for jadcl0 on small multipliers don't come C at the cost of slowing down other data. Tests on uniformly distributed C random data, designed to confound branch prediction, show about a 7% C speed-up using jadcl0 over adcl (8.93 versus 9.57 cycles/limb, with all C overheads included). C C In the simple loop, jadcl0() measures slower than adcl (11.9-14.7 versus C 11.0 cycles/limb), and hence isn't used. C C In the simple loop, note that running ecx from negative to zero and using C it as an index in the two movs wouldn't help. It would save one C instruction (2*addl+loop becoming incl+jnz), but there's nothing unpaired C that would be collapsed by this. C C Attempts at a simpler main loop, with less unrolling, haven't yielded much C success, generally running over 9 c/l. C C C jadcl0 C ------ C C jadcl0() being faster than adcl $0 seems to be an artifact of two things, C firstly the instruction decoding and secondly the fact that there's a C carry bit for the jadcl0 only on average about 1/4 of the time. C C The code in the unrolled loop decodes something like the following. C C decode cycles C mull %ebp 2 C M4_inst %esi, disp(%edi) 1 C adcl %eax, %ecx 2 C movl %edx, %esi \ 1 C jnc 1f / C incl %esi \ 1 C 1: movl disp(%ebx), %eax / C --- C 7 C C In a back-to-back style test this measures 7 with the jnc not taken, or 8 C with it taken (both when correctly predicted). This is opposite to the C measurements showing small multipliers running faster than large ones. C Don't really know why. C C It's not clear how much branch misprediction might be costing. The K6 C doco says it will be 1 to 4 cycles, but presumably it's near the low end C of that range to get the measured results. C C C In the code the two carries are more or less the preceding mul product and C the calculation is roughly C C x*y + u*b+v C C where b=2^32 is the size of a limb, x*y is the two carry limbs, and u and C v are the two limbs it's added to (being the low of the next mul, and a C limb from the destination). C C To get a carry requires x*y+u*b+v >= b^2, which is u*b+v >= b^2-x*y, and C there are b^2-(b^2-x*y) = x*y many such values, giving a probability of C x*y/b^2. If x, y, u and v are random and uniformly distributed between 0 C and b-1, then the total probability can be summed over x and y, C C 1 b-1 b-1 x*y 1 b*(b-1) b*(b-1) C --- * sum sum --- = --- * ------- * ------- = 1/4 C b^2 x=0 y=1 b^2 b^4 2 2 C C Actually it's a very tiny bit less than 1/4 of course. If y is fixed, C then the probability is 1/2*y/b thus varying linearly between 0 and 1/2. ifdef(`PIC',` deflit(UNROLL_THRESHOLD, 9) ',` deflit(UNROLL_THRESHOLD, 6) ') defframe(PARAM_CARRY, 20) defframe(PARAM_MULTIPLIER,16) defframe(PARAM_SIZE, 12) defframe(PARAM_SRC, 8) defframe(PARAM_DST, 4) TEXT ALIGN(32) PROLOGUE(M4_function_1c) pushl %esi deflit(`FRAME',4) movl PARAM_CARRY, %esi jmp L(start_nc) EPILOGUE() PROLOGUE(M4_function_1) push %esi deflit(`FRAME',4) xorl %esi, %esi C initial carry L(start_nc): movl PARAM_SIZE, %ecx pushl %ebx deflit(`FRAME',8) movl PARAM_SRC, %ebx pushl %edi deflit(`FRAME',12) cmpl $UNROLL_THRESHOLD, %ecx movl PARAM_DST, %edi pushl %ebp deflit(`FRAME',16) jae L(unroll) C simple loop movl PARAM_MULTIPLIER, %ebp L(simple): C eax scratch C ebx src C ecx counter C edx scratch C esi carry C edi dst C ebp multiplier movl (%ebx), %eax addl $4, %ebx mull %ebp addl $4, %edi addl %esi, %eax adcl $0, %edx M4_inst %eax, -4(%edi) adcl $0, %edx movl %edx, %esi loop L(simple) popl %ebp popl %edi popl %ebx movl %esi, %eax popl %esi ret C ----------------------------------------------------------------------------- C The unrolled loop uses a "two carry limbs" scheme. At the top of the loop C the carries are ecx=lo, esi=hi, then they swap for each limb processed. C For the computed jump an odd size means they start one way around, an even C size the other. C C VAR_JUMP holds the computed jump temporarily because there's not enough C registers at the point of doing the mul for the initial two carry limbs. C C The add/adc for the initial carry in %esi is necessary only for the C mpn_addmul/submul_1c entry points. Duplicating the startup code to C eliminiate this for the plain mpn_add/submul_1 doesn't seem like a good C idea. dnl overlapping with parameters already fetched define(VAR_COUNTER, `PARAM_SIZE') define(VAR_JUMP, `PARAM_DST') L(unroll): C eax C ebx src C ecx size C edx C esi initial carry C edi dst C ebp movl %ecx, %edx decl %ecx subl $2, %edx negl %ecx shrl $UNROLL_LOG2, %edx andl $UNROLL_MASK, %ecx movl %edx, VAR_COUNTER movl %ecx, %edx shll $4, %edx negl %ecx C 15 code bytes per limb ifdef(`PIC',` call L(pic_calc) L(here): ',` leal L(entry) (%edx,%ecx,1), %edx ') movl (%ebx), %eax C src low limb movl PARAM_MULTIPLIER, %ebp movl %edx, VAR_JUMP mull %ebp addl %esi, %eax C initial carry (from _1c) jadcl0( %edx) leal 4(%ebx,%ecx,4), %ebx movl %edx, %esi C high carry movl VAR_JUMP, %edx leal (%edi,%ecx,4), %edi testl $1, %ecx movl %eax, %ecx C low carry jz L(noswap) movl %esi, %ecx C high,low carry other way around movl %eax, %esi L(noswap): jmp *%edx ifdef(`PIC',` L(pic_calc): C See mpn/x86/README about old gas bugs leal (%edx,%ecx,1), %edx addl $L(entry)-L(here), %edx addl (%esp), %edx ret_internal ') C ----------------------------------------------------------- ALIGN(32) L(top): deflit(`FRAME',16) C eax scratch C ebx src C ecx carry lo C edx scratch C esi carry hi C edi dst C ebp multiplier C C 15 code bytes per limb leal UNROLL_BYTES(%edi), %edi L(entry): forloop(`i', 0, UNROLL_COUNT/2-1, ` deflit(`disp0', eval(2*i*4)) deflit(`disp1', eval(disp0 + 4)) Zdisp( movl, disp0,(%ebx), %eax) mull %ebp Zdisp( M4_inst,%ecx, disp0,(%edi)) adcl %eax, %esi movl %edx, %ecx jadcl0( %ecx) movl disp1(%ebx), %eax mull %ebp M4_inst %esi, disp1(%edi) adcl %eax, %ecx movl %edx, %esi jadcl0( %esi) ') decl VAR_COUNTER leal UNROLL_BYTES(%ebx), %ebx jns L(top) popl %ebp M4_inst %ecx, UNROLL_BYTES(%edi) popl %edi movl %esi, %eax popl %ebx jadcl0( %eax) popl %esi ret EPILOGUE()