; mpn_karasub ; ; Copyright 2011 The Code Cavern ; ; Windows Conversion Copyright 2008 Brian Gladman ; ; This file is part of the MPIR Library. ; ; The MPIR 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 MPIR 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 MPIR Library; see the file COPYING.LIB. If not, write ; to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, ; Boston, MA 02110-1301, USA. ; ; void mpn_karasub(mp_ptr, mp_ptr, mp_size_t) ; rax rdi rsi rdx ; rax rcx rdx r8 ; ; Karasuba Multiplication ; ; Let x = xh.B + xl and y = yh.B + yl ; ; x.y = xh.yh.B^2 + (xh.yl + xl.yh).B + xl.yl ; = xh.yh.B^2 + (xh.yh + xl.yl - {xh - xl}.{yh - yl}).B + xl.yl ; ; If the length of the elements is m, the output length is 4 * m as shown ; below. The middle two blocks ; ; -------------------- rp ; | |--> ; | A:xl.yl[lo] | | ; | | | (xh - xl).(yh - yl) ; -------------------- | -------------------- tp ; <-- | |<--< <-- | | ; | | B:xl.yl[hi] | | | E:[lo] | ; | | | | | | ; | -------------------- | -------------------- ; >--> | |--> <-- | | ; | | C:xh.yh[lo] | | F:[hi] | ; | | | | | ; | -------------------- -------------------- ; <-- | | ; | D:xh.yh[hi] | ; | | ; -------------------- ; ; To avoid overwriting B before it is used, we need to do two ; operations in parallel: ; ; (1) B = B + C + A - E = (B + C) + A - E ; (2) C = C + B + D - F = (B + C) + D - F ; ; The final carry from (1) has to be propagated into C and D, and ; the final carry from (2) has to be propagated into D. %include "yasm_mac.inc" %define reg_save_list rbx, rbp, rsi, rdi, r12, r13, r14, r15 BITS 64 TEXT ; requires n >= 8 FRAME_PROC mpn_karasub, 1, reg_save_list mov rdi, rcx mov rsi, rdx mov rdx, r8 mov [rsp], rdx ;rp is rdi ;tp is rsi ;n is rdx and put it on the stack shr rdx, 1 ;n2 is rdx lea rcx, [rdx+rdx*1] ; 2*n2 is rcx ; L is rdi ; H is rbp ; tp is rsi lea rbp, [rdi+rcx*8] xor rax, rax xor rbx, rbx ; rax rbx are the carrys lea rdi, [rdi+rdx*8-24] lea rsi, [rsi+rdx*8-24] lea rbp, [rbp+rdx*8-24] mov ecx, 3 sub rcx, rdx mov edx, 3 align 16 .1: bt rbx, 2 mov r8, [rdi+rdx*8] adc r8, [rbp+rcx*8] mov r12, r8 mov r9, [rdi+rdx*8+8] adc r9, [rbp+rcx*8+8] mov r10, [rdi+rdx*8+16] adc r10, [rbp+rcx*8+16] mov r11, [rdi+rdx*8+24] adc r11, [rbp+rcx*8+24] rcl rbx, 1 bt rax, 1 mov r15, r11 adc r8, [rdi+rcx*8] mov r13, r9 adc r9, [rdi+rcx*8+8] mov r14, r10 adc r10, [rdi+rcx*8+16] adc r11, [rdi+rcx*8+24] rcl rax, 1 bt rbx, 2 adc r12, [rbp+rdx*8] adc r13, [rbp+rdx*8+8] adc r14, [rbp+rdx*8+16] adc r15, [rbp+rdx*8+24] rcl rbx, 1 bt rax, 1 sbb r8, [rsi+rcx*8] sbb r9, [rsi+rcx*8+8] sbb r10, [rsi+rcx*8+16] sbb r11, [rsi+rcx*8+24] mov [rdi+rdx*8+16], r10 mov [rdi+rdx*8+24], r11 rcl rax, 1 bt rbx, 2 mov [rdi+rdx*8], r8 mov [rdi+rdx*8+8], r9 sbb r12, [rsi+rdx*8] sbb r13, [rsi+rdx*8+8] sbb r14, [rsi+rdx*8+16] sbb r15, [rsi+rdx*8+24] rcl rbx, 1 add rdx, 4 mov [rbp+rcx*8], r12 mov [rbp+rcx*8+8], r13 mov [rbp+rcx*8+16], r14 mov [rbp+rcx*8+24], r15 add rcx, 4 jnc .1 cmp rcx, 2 jg .6 jz .4 jp .3 .2: bt rbx, 2 mov r8, [rdi+rdx*8] adc r8, [rbp] mov r12, r8 mov r9, [rdi+rdx*8+8] adc r9, [rbp+8] mov r10, [rdi+rdx*8+16] adc r10, [rbp+16] rcl rbx, 1 bt rax, 1 adc r8, [rdi] mov r13, r9 adc r9, [rdi+8] mov r14, r10 adc r10, [rdi+16] rcl rax, 1 bt rbx, 2 adc r12, [rbp+rdx*8] adc r13, [rbp+rdx*8+8] adc r14, [rbp+rdx*8+16] rcl rbx, 1 bt rax, 1 sbb r8, [rsi] sbb r9, [rsi+8] sbb r10, [rsi+16] mov [rdi+rdx*8+16], r10 rcl rax, 1 bt rbx, 2 mov [rdi+rdx*8], r8 mov [rdi+rdx*8+8], r9 sbb r12, [rsi+rdx*8] sbb r13, [rsi+rdx*8+8] sbb r14, [rsi+rdx*8+16] rcl rbx, 1 add rdx, 3 mov [rbp], r12 mov [rbp+8], r13 mov [rbp+16], r14 jmp .5 .3: bt rbx, 2 mov r8, [rdi+rdx*8] adc r8, [rbp+8] mov r12, r8 mov r9, [rdi+rdx*8+8] adc r9, [rbp+16] rcl rbx, 1 bt rax, 1 adc r8, [rdi+8] mov r13, r9 adc r9, [rdi+16] rcl rax, 1 bt rbx, 2 adc r12, [rbp+rdx*8] adc r13, [rbp+rdx*8+8] rcl rbx, 1 bt rax, 1 sbb r8, [rsi+8] sbb r9, [rsi+16] rcl rax, 1 bt rbx, 2 mov [rdi+rdx*8], r8 mov [rdi+rdx*8+8], r9 sbb r12, [rsi+rdx*8] sbb r13, [rsi+rdx*8+8] rcl rbx, 1 add rdx, 2 mov [rbp+8], r12 mov [rbp+16], r13 jmp .5 .4: bt rbx, 2 mov r8, [rdi+rdx*8] adc r8, [rbp+16] mov r12, r8 rcl rbx, 1 bt rax, 1 adc r8, [rdi+16] rcl rax, 1 bt rbx, 2 adc r12, [rbp+rdx*8] rcl rbx, 1 bt rax, 1 sbb r8, [rsi+16] rcl rax, 1 bt rbx, 2 mov [rdi+rdx*8], r8 sbb r12, [rsi+rdx*8] rcl rbx, 1 inc rdx mov [rbp+rcx*8], r12 .5: mov rcx, 3 .6: ; if odd the do next two mov r8, [rsp] bt r8, 0 jnc .9 xor r10, r10 mov r8, [rbp+rdx*8] mov r9, [rbp+rdx*8+8] sub r8, [rsi+rdx*8] sbb r9, [rsi+rdx*8+8] rcl r10, 1 add [rbp+24], r8 adc [rbp+32], r9 .7: adc qword[rbp+rcx*8+16], 0 inc rcx jc .7 mov rcx, 3 bt r10, 0 .8: sbb qword[rbp+rcx*8+16], 0 inc rcx jc .8 mov rcx, 3 ; add in any carryies and/or borrows ; ; carries from low half to upper half: ; rbx{2} is the carry in (B + C) ; rbx{1} is the carry in (B + C) + A ; rbx{0} is the borrow in (B + C + A) - E ; carries from the third to the fourth quarter ; rbx{2} is the carry in (B + C) ; rax{1} is the carry in (B + C) + D ; rax{0} is the borrow in (B + C + D) - F .9: xor r8, r8 bt rbx, 2 adc r8, r8 bt rax, 1 adc r8, 0 bt rax, 0 sbb r8, 0 jz .13 jnc .11 .10: sbb qword[rdi+rdx*8], 0 inc rdx jc .10 jmp .13 .11: add [rdi+rdx*8], r8 .12: adc qword[rdi+rdx*8+8], 0 inc rdx jc .12 .13: mov rax, 6 and rax, rbx popcnt r8, rax bt rbx, 0 sbb r8, 0 jz .17 jnc .15 .14: sbb qword[rbp+rcx*8], 0 inc rcx jc .14 jmp .17 .15: add [rbp+rcx*8], r8 .16: adc qword[rbp+rcx*8+8], 0 inc rcx jc .16 .17: END_PROC reg_save_list end