// +build amd64 // +build !generic,!generic32,!generic64 // Copyright (c) 2018 xdx. All rights reserved. // Written by xdx // // SM2 256曲线amd64平台汇编实现。参考golang标准库p256曲线的实现。 // Copyright 2015 The Go Authors. All rights reserved. // Use of this source code is governed by a BSD-style // license that can be found in the LICENSE file. // This file contains constant-time, 64-bit assembly implementation of // P256. The optimizations performed here are described in detail in: // S.Gueron and V.Krasnov, "Fast prime field elliptic-curve cryptography with // 256-bit primes" // https://link.springer.com/article/10.1007%2Fs13389-014-0090-x // https://eprint.iacr.org/2013/816.pdf #include "textflag.h" #define res_ptr DI #define x_ptr SI #define y_ptr CX #define acc0 R8 #define acc1 R9 #define acc2 R10 #define acc3 R11 #define acc4 R12 #define acc5 R13 #define t0 R14 #define t1 R15 // the p DATA c256const0<>+0x00(SB)/8, $0xffffffffffffffff DATA c256const1<>+0x00(SB)/8, $0xffffffff00000000 DATA c256const2<>+0x00(SB)/8, $0xffffffffffffffff DATA c256const3<>+0x00(SB)/8, $0xfffffffeffffffff // k0 * ord[0] = -1 mod 2^{64}, k0 = -ord[0]^{-1} mod B DATA c256ordK0<>+0x00(SB)/8, $0x327f9e8872350975 // n DATA c256ord<>+0x00(SB)/8, $0x53bbf40939d54123 DATA c256ord<>+0x08(SB)/8, $0x7203df6b21c6052b DATA c256ord<>+0x10(SB)/8, $0xffffffffffffffff DATA c256ord<>+0x18(SB)/8, $0xfffffffeffffffff // 1*R mod p DATA c256one<>+0x00(SB)/8, $0x0000000000000001 DATA c256one<>+0x08(SB)/8, $0x00000000ffffffff DATA c256one<>+0x10(SB)/8, $0x0000000000000000 DATA c256one<>+0x18(SB)/8, $0x0000000100000000 GLOBL c256const0<>(SB), 8, $8 GLOBL c256const1<>(SB), 8, $8 GLOBL c256const2<>(SB), 8, $8 GLOBL c256const3<>(SB), 8, $8 GLOBL c256ordK0<>(SB), 8, $8 GLOBL c256ord<>(SB), 8, $32 GLOBL c256one<>(SB), 8, $32 // in: a = [a0,a1,a2,a3,a4,a5], a5 <= 1 // output: a0 = 0, [a1,a2,a3,a4,a5] = (a + a0*p)/B = a/B mod p // Note: // a + a0*p <= a5*B^5 + (B^5-1) + (B-1)*p // <= 2*B^5 - 1 + (B-1)*(B-dp), dp = B-p <<< B // = 2*B^5 + (p+1)*B + (dp-1) // <= 2*B^5 + (p+1)*B, for B | a + a0*p // thus, when output, a5 <= 2 #define montReduceQW(a0,a1,a2,a3,a4,a5,tmp0) \ ADDQ a0, a1 \ ADCQ $0, a2 \ ADCQ $0, a3 \ ADCQ a0, a4 \ ADCQ $0, a5 \ \ MOVQ a0, tmp0 \ SHLQ $32, a0 \ SHRQ $32, tmp0 \ \ SUBQ a0, a1 \ SBBQ tmp0, a2 \ SBBQ a0, a3 \ SBBQ tmp0, a4 \ SBBQ $0, a5 \ XORQ a0, a0 // montMulOne QuadWord // in: a = [a0,a1,a2,a3] // out: [a1,a2,a3,a0] = a*B^{-1} = a+a0*p #define montMulOneQW(a0,a1,a2,a3,tmp0,tmp1)\ MOVQ a0, tmp0 \ SHLQ $32, tmp0 \ MOVQ a0, tmp1 \ SHRQ $32, tmp1 \ ADDQ a0, a1 \ ADCQ $0, a2 \ ADCQ $0, a3 \ ADCQ $0, a0 \ SUBQ tmp0, a1 \ SBBQ tmp1, a2 \ SBBQ tmp0, a3 \ SBBQ tmp1, a0 // in: a = [a0,a1,a2,a3] // out: [a0,a1,a2,a3] = a*R^{-1} mod p = MontMul(a,1) // note: out may > p #define montMulOne(a0,a1,a2,a3,tmp0,tmp1) \ montMulOneQW(a0,a1,a2,a3,tmp0,tmp1) \ montMulOneQW(a1,a2,a3,a0,tmp0,tmp1) \ montMulOneQW(a2,a3,a0,a1,tmp0,tmp1) \ montMulOneQW(a3,a0,a1,a2,tmp0,tmp1) // sub p if [a0, a1, a2, a3, a4] >= p #define subCond(a0, a1, a2, a3, a4, t0, t1, t2, t3) \ MOVQ a0, t0 \ MOVQ a1, t1 \ MOVQ a2, t2 \ MOVQ a3, t3 \ \ SUBQ $-1, a0 \ SBBQ c256const1<>(SB), a1 \ SBBQ $-1, a2 \ SBBQ c256const3<>(SB), a3 \ SBBQ $0, a4 \ \ CMOVQCS t0, a0 \ CMOVQCS t1, a1 \ CMOVQCS t2, a2 \ CMOVQCS t3, a3 /* ---------------------------------------*/ // func c256LittleToBig(res []byte, in []uint64) TEXT ·c256LittleToBig(SB),NOSPLIT,$0 JMP ·c256BigToLittle(SB) /* ---------------------------------------*/ // func c256BigToLittle(res []uint64, in []byte) TEXT ·c256BigToLittle(SB),NOSPLIT,$0 MOVQ res+0(FP), res_ptr MOVQ in+24(FP), x_ptr MOVQ (8*0)(x_ptr), acc0 MOVQ (8*1)(x_ptr), acc1 MOVQ (8*2)(x_ptr), acc2 MOVQ (8*3)(x_ptr), acc3 BSWAPQ acc0 BSWAPQ acc1 BSWAPQ acc2 BSWAPQ acc3 MOVQ acc3, (8*0)(res_ptr) MOVQ acc2, (8*1)(res_ptr) MOVQ acc1, (8*2)(res_ptr) MOVQ acc0, (8*3)(res_ptr) RET /* ---------------------------------------*/ // func c256MovCond(res, a, b []uint64, cond int) // If cond == 0 res=b, else res=a TEXT ·c256MovCond(SB),NOSPLIT,$0 MOVQ res+0(FP), res_ptr MOVQ a+24(FP), x_ptr MOVQ b+48(FP), y_ptr MOVQ cond+72(FP), X12 PXOR X13, X13 PSHUFD $0, X12, X12 PCMPEQL X13, X12 // X12 = 0xFFFF...FF if cond = 0, otherwise X12 = 0 //X[0:5] = !X12 && a MOVOU X12, X0 MOVOU (16*0)(x_ptr), X6 PANDN X6, X0 MOVOU X12, X1 MOVOU (16*1)(x_ptr), X7 PANDN X7, X1 MOVOU X12, X2 MOVOU (16*2)(x_ptr), X8 PANDN X8, X2 MOVOU X12, X3 MOVOU (16*3)(x_ptr), X9 PANDN X9, X3 MOVOU X12, X4 MOVOU (16*4)(x_ptr), X10 PANDN X10, X4 MOVOU X12, X5 MOVOU (16*5)(x_ptr), X11 PANDN X11, X5 MOVOU (16*0)(y_ptr), X6 MOVOU (16*1)(y_ptr), X7 MOVOU (16*2)(y_ptr), X8 MOVOU (16*3)(y_ptr), X9 MOVOU (16*4)(y_ptr), X10 MOVOU (16*5)(y_ptr), X11 // X[6:11] = X12 && b PAND X12, X6 PAND X12, X7 PAND X12, X8 PAND X12, X9 PAND X12, X10 PAND X12, X11 // res = (!X12 && a) ^ (X12 && b) // cond == 0 => X12 = 0xFF..FF => res = b PXOR X6, X0 PXOR X7, X1 PXOR X8, X2 PXOR X9, X3 PXOR X10, X4 PXOR X11, X5 MOVOU X0, (16*0)(res_ptr) MOVOU X1, (16*1)(res_ptr) MOVOU X2, (16*2)(res_ptr) MOVOU X3, (16*3)(res_ptr) MOVOU X4, (16*4)(res_ptr) MOVOU X5, (16*5)(res_ptr) RET /* ---------------------------------------*/ // func c256NegCond(val []uint64, cond int) TEXT ·c256NegCond(SB),NOSPLIT,$0 MOVQ val+0(FP), res_ptr MOVQ cond+24(FP), t0 // acc = p MOVQ c256const0<>(SB), acc0 MOVQ c256const1<>(SB), acc1 MOVQ c256const2<>(SB), acc2 MOVQ c256const3<>(SB), acc3 // Load the original value MOVQ (8*0)(res_ptr), acc4 MOVQ (8*1)(res_ptr), x_ptr MOVQ (8*2)(res_ptr), y_ptr MOVQ (8*3)(res_ptr), t1 // acc = p - val SUBQ acc4, acc0 SBBQ x_ptr, acc1 SBBQ y_ptr, acc2 SBBQ t1, acc3 // If condition is 0, keep original value TESTQ t0, t0 CMOVQEQ acc4, acc0 CMOVQEQ x_ptr, acc1 CMOVQEQ y_ptr, acc2 CMOVQEQ t1, acc3 // Store result MOVQ acc0, (8*0)(res_ptr) MOVQ acc1, (8*1)(res_ptr) MOVQ acc2, (8*2)(res_ptr) MOVQ acc3, (8*3)(res_ptr) RET /* ---------------------------------------*/ // func c256Sqr(res, in []uint64, n int) TEXT ·c256Sqr(SB),NOSPLIT,$0 MOVQ res+0(FP), res_ptr MOVQ in+24(FP), x_ptr MOVQ n+48(FP), BX sqrLoop: // y[1:] * y[0] MOVQ (8*0)(x_ptr), t0 MOVQ (8*1)(x_ptr), AX MULQ t0 // implicit mul with AX: t0 * AX => DX:AX MOVQ AX, acc1 MOVQ DX, acc2 MOVQ (8*2)(x_ptr), AX MULQ t0 ADDQ AX, acc2 ADCQ $0, DX MOVQ DX, acc3 MOVQ (8*3)(x_ptr), AX MULQ t0 ADDQ AX, acc3 ADCQ $0, DX MOVQ DX, acc4 // y[2:] * y[1] MOVQ (8*1)(x_ptr), t0 MOVQ (8*2)(x_ptr), AX MULQ t0 ADDQ AX, acc3 ADCQ $0, DX MOVQ DX, t1 MOVQ (8*3)(x_ptr), AX MULQ t0 ADDQ t1, acc4 ADCQ $0, DX ADDQ AX, acc4 ADCQ $0, DX MOVQ DX, acc5 // Q: DX <= B-2, 这里可能发生进位吗？ // A: 不会。 // [0, acc1, acc2, acc3, acc4, acc5, carry] // = (y1*B + y2B^2 + y3*B^3)*y0 + (y2*B^2 + y3*B^3)*y1 // <= (B^3-1)*B*(B-1) + (B^2-1)*B^2*(B-1) // < B^6 // y[3] * y[2] MOVQ (8*2)(x_ptr), t0 MOVQ (8*3)(x_ptr), AX MULQ t0 ADDQ AX, acc5 ADCQ $0, DX MOVQ DX, y_ptr XORQ t1, t1 // [0, acc1, acc2, acc3, acc4, acc5, y_ptr] = \sum_{i!=j}yi * yj // *2 ADDQ acc1, acc1 ADCQ acc2, acc2 ADCQ acc3, acc3 ADCQ acc4, acc4 ADCQ acc5, acc5 ADCQ y_ptr, y_ptr ADCQ $0, t1 // [0, acc1, acc2, acc3, acc4, acc5, y_ptr, t1] = 2*\sum_{i!=j}yi * yj // Missing products \sum yi^2 // acc0, acc1, acc2, acc3, acc4, acc5, y_ptr, t1 //+ AX DX //----------------------------------------------- //= acc0, acc1, acc2, acc3, acc4, acc5, y_ptr, t1 //+ t0 MOVQ (8*0)(x_ptr), AX MULQ AX MOVQ AX, acc0 MOVQ DX, t0 // acc0, acc1, acc2, acc3, acc4, acc5, y_ptr, t1 //+ t0 AX DX //----------------------------------------------- //=acc0, acc1, acc2, acc3, acc4, acc5, y_ptr, t1 //+ t0 MOVQ (8*1)(x_ptr), AX MULQ AX ADDQ t0, acc1 ADCQ AX, acc2 ADCQ $0, DX MOVQ DX, t0 // acc0, acc1, acc2, acc3, acc4, acc5, y_ptr, t1 //+ t0 AX DX //----------------------------------------------- //=acc0, acc1, acc2, acc3, acc4, acc5, y_ptr, t1 //+ t0 MOVQ (8*2)(x_ptr), AX MULQ AX ADDQ t0, acc3 ADCQ AX, acc4 ADCQ $0, DX MOVQ DX, t0 // acc0, acc1, acc2, acc3, acc4, acc5, y_ptr, t1 //+ t0 AX DX //----------------------------------------------- //=acc0, acc1, acc2, acc3, acc4, acc5, y_ptr, x_ptr MOVQ (8*3)(x_ptr), AX MULQ AX ADDQ t0, acc5 ADCQ AX, y_ptr ADCQ DX, t1 MOVQ t1, x_ptr // Reduction step montMulOne(acc0,acc1,acc2,acc3, t0, t1) XORQ t0,t0 // Add bits [511:256] of the sqr result ADCQ acc4, acc0 ADCQ acc5, acc1 ADCQ y_ptr, acc2 ADCQ x_ptr, acc3 ADCQ $0, t0 subCond(acc0, acc1, acc2, acc3, t0, acc4, acc5, y_ptr, t1) // MOVQ acc0, acc4 // MOVQ acc1, acc5 // MOVQ acc2, y_ptr // MOVQ acc3, t1 // // Subtract c256 // SUBQ $-1, acc0 // SBBQ c256const1<>(SB) ,acc1 // SBBQ $-1 ,acc2 // SBBQ c256const3<>(SB), acc3 // SBBQ $0, t0 // // if borrow(CF=1) then [acc0,acc1,acc2,acc3,t0] < p // // the result is old [acc4,acc5,y_ptr,t1] // CMOVQCS acc4, acc0 //Move if below (CF=1). = AT&T CMOVBQ // CMOVQCS acc5, acc1 // CMOVQCS y_ptr, acc2 // CMOVQCS t1, acc3 MOVQ acc0, (8*0)(res_ptr) MOVQ acc1, (8*1)(res_ptr) MOVQ acc2, (8*2)(res_ptr) MOVQ acc3, (8*3)(res_ptr) MOVQ res_ptr, x_ptr DECQ BX JNE sqrLoop RET /* ---------------------------------------*/ // func c256Mul(res, in1, in2 []uint64) TEXT ·c256Mul(SB),NOSPLIT,$0 MOVQ res+0(FP), res_ptr MOVQ in1+24(FP), x_ptr MOVQ in2+48(FP), y_ptr // x * y[0] MOVQ (8*0)(y_ptr), t0 MOVQ (8*0)(x_ptr), AX MULQ t0 MOVQ AX, acc0 MOVQ DX, acc1 // acc0, acc1 //+ AX DX //----------------------------------------------- //=acc0, acc1, acc2 MOVQ (8*1)(x_ptr), AX MULQ t0 ADDQ AX, acc1 ADCQ $0, DX MOVQ DX, acc2 // acc0, acc1, acc2 //+ AX DX //----------------------------------------------- //=acc0, acc1, acc2, acc3 MOVQ (8*2)(x_ptr), AX MULQ t0 ADDQ AX, acc2 ADCQ $0, DX MOVQ DX, acc3 // acc0, acc1, acc2, acc3 //+ AX DX //----------------------------------------------- //=acc0, acc1, acc2, acc3, acc4 MOVQ (8*3)(x_ptr), AX MULQ t0 ADDQ AX, acc3 ADCQ $0, DX MOVQ DX, acc4 XORQ acc5, acc5 // [acc0, acc1, acc2, acc3, aac4, acc5(=0)] = [x0, x1, x2, x3] * y0的结果 montReduceQW(acc0,acc1,acc2,acc3,acc4, acc5, t0) // [acc1, acc2, acc3, aac4, acc5] // = ([acc0, acc1, acc2, acc3, aac4, acc5] + acc0 * p) / B // = [x0, x1, x2, x3] * y0 / B mod p // x * y[1] MOVQ (8*1)(y_ptr), t0 // B^0 B^1 B^2 B^3 B^4 // acc1, acc2, acc3, acc4, acc5 //+ AX DX //----------------------------------------------- //= acc1, acc2, acc3, acc4, acc5 //+ t1 MOVQ (8*0)(x_ptr), AX MULQ t0 ADDQ AX, acc1 ADCQ $0, DX MOVQ DX, t1 // B^0 B^1 B^2 B^3 B^4 // acc1, acc2, acc3, acc4, acc5 //+ t1 //+ AX DX //----------------------------------------------- //= acc1, acc2, acc3, acc4, acc5 //+ t1 MOVQ (8*1)(x_ptr), AX MULQ t0 ADDQ t1, acc2 ADCQ $0, DX ADDQ AX, acc2 ADCQ $0, DX MOVQ DX, t1 // B^0 B^1 B^2 B^3 B^4 // acc1, acc2, acc3, acc4, acc5 //+ t1 //+ AX DX //----------------------------------------------- //= acc1, acc2, acc3, acc4, acc5 //+ t1 MOVQ (8*2)(x_ptr), AX MULQ t0 ADDQ t1, acc3 ADCQ $0, DX ADDQ AX, acc3 ADCQ $0, DX MOVQ DX, t1 // B^0 B^1 B^2 B^3 B^4 // acc1, acc2, acc3, acc4, acc5 //+ t1 //+ AX DX //----------------------------------------------- //= acc1, acc2, acc3, acc4, acc5, acc0 MOVQ (8*3)(x_ptr), AX MULQ t0 ADDQ t1, acc4 ADCQ $0, DX ADDQ AX, acc4 ADCQ DX, acc5 ADCQ $0, acc0 // Second reduction step montReduceQW(acc1, acc2, acc3, acc4, acc5, acc0, t0) // x * y[2] MOVQ (8*2)(y_ptr), t0 MOVQ (8*0)(x_ptr), AX MULQ t0 ADDQ AX, acc2 ADCQ $0, DX MOVQ DX, t1 MOVQ (8*1)(x_ptr), AX MULQ t0 ADDQ t1, acc3 ADCQ $0, DX ADDQ AX, acc3 ADCQ $0, DX MOVQ DX, t1 MOVQ (8*2)(x_ptr), AX MULQ t0 ADDQ t1, acc4 ADCQ $0, DX ADDQ AX, acc4 ADCQ $0, DX MOVQ DX, t1 MOVQ (8*3)(x_ptr), AX MULQ t0 ADDQ t1, acc5 ADCQ $0, DX ADDQ AX, acc5 ADCQ DX, acc0 ADCQ $0, acc1 // Third reduction step montReduceQW(acc2, acc3, acc4, acc5, acc0, acc1, t0) // x * y[3] MOVQ (8*3)(y_ptr), t0 MOVQ (8*0)(x_ptr), AX MULQ t0 ADDQ AX, acc3 ADCQ $0, DX MOVQ DX, t1 MOVQ (8*1)(x_ptr), AX MULQ t0 ADDQ t1, acc4 ADCQ $0, DX ADDQ AX, acc4 ADCQ $0, DX MOVQ DX, t1 MOVQ (8*2)(x_ptr), AX MULQ t0 ADDQ t1, acc5 ADCQ $0, DX ADDQ AX, acc5 ADCQ $0, DX MOVQ DX, t1 MOVQ (8*3)(x_ptr), AX MULQ t0 ADDQ t1, acc0 ADCQ $0, DX ADDQ AX, acc0 ADCQ DX, acc1 ADCQ $0, acc2 // Last reduction step montReduceQW(acc3, acc4, acc5, acc0, acc1, acc2, t0) // Note: // [acc4, acc5, acc0, acc1, acc2] = (((x*y0)/B + (x*y1))/B + (x*y2)/B) + (x*y3)/B // = x*y0 + u0*p // ------------- + x*y1 + u1*p // B // ---------------------------- + x*y2 + u2*p // B // ------------------------------------------- + x*y3 + u3*p // B // ----------------------------------------------------------- // B // = (x*y + u*p)/R // < (p*p + R*p)/R, if x,y < p // < 2p. // // if let x, y < R, then // (x*y + u*p)/R <= ((R-1)^2+(R-1)*p)/R = (R-1)/R * (R-1 + p) < R-1+p // thus substruct p, the result is less then R. subCond(acc4, acc5, acc0, acc1, acc2, x_ptr, acc3, t0, t1) // MOVQ acc4, x_ptr // MOVQ acc5, acc3 // MOVQ acc0, t0 // MOVQ acc1, t1 // // Subtract c256 // SUBQ $-1, acc4 // SBBQ c256const1<>(SB) ,acc5 // SBBQ $-1, acc0 // SBBQ c256const3<>(SB), acc1 // SBBQ $0, acc2 // CMOVQCS x_ptr, acc4 // CMOVQCS acc3, acc5 // CMOVQCS t0, acc0 // CMOVQCS t1, acc1 MOVQ acc4, (8*0)(res_ptr) MOVQ acc5, (8*1)(res_ptr) MOVQ acc0, (8*2)(res_ptr) MOVQ acc1, (8*3)(res_ptr) RET /* ---------------------------------------*/ // func c256FromMont(res, in []uint64) TEXT ·c256FromMont(SB),NOSPLIT,$0 MOVQ res+0(FP), res_ptr MOVQ in+24(FP), x_ptr MOVQ (8*0)(x_ptr), acc0 MOVQ (8*1)(x_ptr), acc1 MOVQ (8*2)(x_ptr), acc2 MOVQ (8*3)(x_ptr), acc3 montMulOne(acc0, acc1, acc2, acc3, t0, t1) MOVQ acc0, x_ptr MOVQ acc1, acc4 MOVQ acc2, t0 MOVQ acc3, t1 SUBQ $-1, acc0 SBBQ c256const1<>(SB), acc1 SBBQ $-1, acc2 SBBQ c256const3<>(SB), acc3 CMOVQCS x_ptr, acc0 CMOVQCS acc4, acc1 CMOVQCS t0, acc2 CMOVQCS t1, acc3 MOVQ acc0, (8*0)(res_ptr) MOVQ acc1, (8*1)(res_ptr) MOVQ acc2, (8*2)(res_ptr) MOVQ acc3, (8*3)(res_ptr) RET /* ---------------------------------------*/ // Constant time point access to arbitrary point table. // Indexed from 1 to 15, with -1 offset // (index 0 is implicitly point at infinity) // func c256Select(point, table []uint64, idx int) TEXT ·c256Select(SB),NOSPLIT,$0 MOVQ idx+48(FP),AX MOVQ table+24(FP),DI MOVQ point+0(FP),DX PXOR X15, X15 // X15 = 0 PCMPEQL X14, X14 // X14 = -1 PSUBL X14, X15 // X15 = 1 MOVL AX, X14 PSHUFD $0, X14, X14 PXOR X0, X0 PXOR X1, X1 PXOR X2, X2 PXOR X3, X3 PXOR X4, X4 PXOR X5, X5 MOVQ $16, AX MOVOU X15, X13 loop_select: MOVOU X13, X12 PADDL X15, X13 PCMPEQL X14, X12 MOVOU (16*0)(DI), X6 MOVOU (16*1)(DI), X7 MOVOU (16*2)(DI), X8 MOVOU (16*3)(DI), X9 MOVOU (16*4)(DI), X10 MOVOU (16*5)(DI), X11 ADDQ $(16*6), DI PAND X12, X6 PAND X12, X7 PAND X12, X8 PAND X12, X9 PAND X12, X10 PAND X12, X11 PXOR X6, X0 PXOR X7, X1 PXOR X8, X2 PXOR X9, X3 PXOR X10, X4 PXOR X11, X5 DECQ AX JNE loop_select MOVOU X0, (16*0)(DX) MOVOU X1, (16*1)(DX) MOVOU X2, (16*2)(DX) MOVOU X3, (16*3)(DX) MOVOU X4, (16*4)(DX) MOVOU X5, (16*5)(DX) RET /* ---------------------------------------*/ // Constant time point access to base point table. // func c256SelectBase(point, table []uint64, idx int) TEXT ·c256SelectBase(SB),NOSPLIT,$0 MOVQ idx+48(FP),AX MOVQ table+24(FP),DI MOVQ point+0(FP),DX PXOR X15, X15 // X15 = 0 PCMPEQL X14, X14 // X14 = -1 PSUBL X14, X15 // X15 = 1 MOVL AX, X14 PSHUFD $0, X14, X14 PXOR X0, X0 PXOR X1, X1 PXOR X2, X2 PXOR X3, X3 MOVQ $16, AX MOVOU X15, X13 loop_select_base: MOVOU X13, X12 PADDL X15, X13 PCMPEQL X14, X12 MOVOU (16*0)(DI), X4 MOVOU (16*1)(DI), X5 MOVOU (16*2)(DI), X6 MOVOU (16*3)(DI), X7 MOVOU (16*4)(DI), X8 MOVOU (16*5)(DI), X9 MOVOU (16*6)(DI), X10 MOVOU (16*7)(DI), X11 ADDQ $(16*8), DI PAND X12, X4 PAND X12, X5 PAND X12, X6 PAND X12, X7 MOVOU X13, X12 PADDL X15, X13 PCMPEQL X14, X12 PAND X12, X8 PAND X12, X9 PAND X12, X10 PAND X12, X11 PXOR X4, X0 PXOR X5, X1 PXOR X6, X2 PXOR X7, X3 PXOR X8, X0 PXOR X9, X1 PXOR X10, X2 PXOR X11, X3 DECQ AX JNE loop_select_base MOVOU X0, (16*0)(DX) MOVOU X1, (16*1)(DX) MOVOU X2, (16*2)(DX) MOVOU X3, (16*3)(DX) RET /* ---------------------------------------*/ // func c256OrdMul(res, in1, in2 []uint64) // The general mothod of montgomery mul of N and R=2^{64} TEXT ·c256OrdMul(SB),NOSPLIT,$0 MOVQ res+0(FP), res_ptr MOVQ in1+24(FP), x_ptr MOVQ in2+48(FP), y_ptr // x * y[0] MOVQ (8*0)(y_ptr), t0 MOVQ (8*0)(x_ptr), AX MULQ t0 MOVQ AX, acc0 MOVQ DX, acc1 MOVQ (8*1)(x_ptr), AX MULQ t0 ADDQ AX, acc1 ADCQ $0, DX MOVQ DX, acc2 MOVQ (8*2)(x_ptr), AX MULQ t0 ADDQ AX, acc2 ADCQ $0, DX MOVQ DX, acc3 MOVQ (8*3)(x_ptr), AX MULQ t0 ADDQ AX, acc3 ADCQ $0, DX MOVQ DX, acc4 XORQ acc5, acc5 MOVQ c256ordK0<>(SB), BX // First reduction step // t0 = acc0 * k0 mod B MOVQ acc0, AX MULQ BX MOVQ AX, t0 // acc0, acc1, acc2, acc3, acc4, acc5 //+ AX DX //----------------------------------------------- //= acc0, acc1, acc2, acc3, acc4, acc5 //+ t1 MOVQ c256ord<>+0x00(SB), AX MULQ t0 ADDQ AX, acc0 ADCQ $0, DX MOVQ DX, t1 // acc0, acc1, acc2, acc3, acc4, acc5 //+ AX DX //----------------------------------------------- //= acc0, acc1, acc2, acc3, acc4, acc5 //+ t1 MOVQ c256ord<>+0x08(SB), AX MULQ t0 ADDQ t1, acc1 ADCQ $0, DX ADDQ AX, acc1 ADCQ $0, DX MOVQ DX, t1 // acc0, acc1, acc2, acc3, acc4, acc5 //+ AX DX //----------------------------------------------- //= acc0, acc1, acc2, acc3, acc4, acc5 //+ t1 MOVQ c256ord<>+0x10(SB), AX MULQ t0 ADDQ t1, acc2 ADCQ $0, DX ADDQ AX, acc2 ADCQ $0, DX MOVQ DX, t1 // acc0, acc1, acc2, acc3, acc4, acc5 //+ AX DX //----------------------------------------------- //= acc0, acc1, acc2, acc3, acc4, acc5 MOVQ c256ord<>+0x18(SB), AX MULQ t0 ADDQ t1, acc3 ADCQ $0, DX ADDQ AX, acc3 ADCQ DX, acc4 ADCQ $0, acc5 // x * y[1] // [acc1, acc2, acc3, acc4, acc5] + (x * y1) MOVQ (8*1)(y_ptr), t0 MOVQ (8*0)(x_ptr), AX MULQ t0 ADDQ AX, acc1 ADCQ $0, DX MOVQ DX, t1 MOVQ (8*1)(x_ptr), AX MULQ t0 ADDQ t1, acc2 ADCQ $0, DX ADDQ AX, acc2 ADCQ $0, DX MOVQ DX, t1 MOVQ (8*2)(x_ptr), AX MULQ t0 ADDQ t1, acc3 ADCQ $0, DX ADDQ AX, acc3 ADCQ $0, DX MOVQ DX, t1 MOVQ (8*3)(x_ptr), AX MULQ t0 ADDQ t1, acc4 ADCQ $0, DX ADDQ AX, acc4 ADCQ DX, acc5 ADCQ $0, acc0 // Second reduction step MOVQ acc1, AX MULQ BX MOVQ AX, t0 MOVQ c256ord<>+0x00(SB), AX MULQ t0 ADDQ AX, acc1 ADCQ $0, DX MOVQ DX, t1 MOVQ c256ord<>+0x08(SB), AX MULQ t0 ADDQ t1, acc2 ADCQ $0, DX ADDQ AX, acc2 ADCQ $0, DX MOVQ DX, t1 MOVQ c256ord<>+0x10(SB), AX MULQ t0 ADDQ t1, acc3 ADCQ $0, DX ADDQ AX, acc3 ADCQ $0, DX MOVQ DX, t1 MOVQ c256ord<>+0x18(SB), AX MULQ t0 ADDQ t1, acc4 ADCQ $0, DX ADDQ AX, acc4 ADCQ DX, acc5 ADCQ $0, acc0 // x * y[2] MOVQ (8*2)(y_ptr), t0 MOVQ (8*0)(x_ptr), AX MULQ t0 ADDQ AX, acc2 ADCQ $0, DX MOVQ DX, t1 MOVQ (8*1)(x_ptr), AX MULQ t0 ADDQ t1, acc3 ADCQ $0, DX ADDQ AX, acc3 ADCQ $0, DX MOVQ DX, t1 MOVQ (8*2)(x_ptr), AX MULQ t0 ADDQ t1, acc4 ADCQ $0, DX ADDQ AX, acc4 ADCQ $0, DX MOVQ DX, t1 MOVQ (8*3)(x_ptr), AX MULQ t0 ADDQ t1, acc5 ADCQ $0, DX ADDQ AX, acc5 ADCQ DX, acc0 ADCQ $0, acc1 // Third reduction step MOVQ acc2, AX MULQ BX MOVQ AX, t0 MOVQ c256ord<>+0x00(SB), AX MULQ t0 ADDQ AX, acc2 ADCQ $0, DX MOVQ DX, t1 MOVQ c256ord<>+0x08(SB), AX MULQ t0 ADDQ t1, acc3 ADCQ $0, DX ADDQ AX, acc3 ADCQ $0, DX MOVQ DX, t1 MOVQ c256ord<>+0x10(SB), AX MULQ t0 ADDQ t1, acc4 ADCQ $0, DX ADDQ AX, acc4 ADCQ $0, DX MOVQ DX, t1 MOVQ c256ord<>+0x18(SB), AX MULQ t0 ADDQ t1, acc5 ADCQ $0, DX ADDQ AX, acc5 ADCQ DX, acc0 ADCQ $0, acc1 // x * y[3] MOVQ (8*3)(y_ptr), t0 MOVQ (8*0)(x_ptr), AX MULQ t0 ADDQ AX, acc3 ADCQ $0, DX MOVQ DX, t1 MOVQ (8*1)(x_ptr), AX MULQ t0 ADDQ t1, acc4 ADCQ $0, DX ADDQ AX, acc4 ADCQ $0, DX MOVQ DX, t1 MOVQ (8*2)(x_ptr), AX MULQ t0 ADDQ t1, acc5 ADCQ $0, DX ADDQ AX, acc5 ADCQ $0, DX MOVQ DX, t1 MOVQ (8*3)(x_ptr), AX MULQ t0 ADDQ t1, acc0 ADCQ $0, DX ADDQ AX, acc0 ADCQ DX, acc1 ADCQ $0, acc2 // Last reduction step MOVQ acc3, AX MULQ BX MOVQ AX, t0 MOVQ c256ord<>+0x00(SB), AX MULQ t0 ADDQ AX, acc3 ADCQ $0, DX MOVQ DX, t1 MOVQ c256ord<>+0x08(SB), AX MULQ t0 ADDQ t1, acc4 ADCQ $0, DX ADDQ AX, acc4 ADCQ $0, DX MOVQ DX, t1 MOVQ c256ord<>+0x10(SB), AX MULQ t0 ADDQ t1, acc5 ADCQ $0, DX ADDQ AX, acc5 ADCQ $0, DX MOVQ DX, t1 MOVQ c256ord<>+0x18(SB), AX MULQ t0 ADDQ t1, acc0 ADCQ $0, DX ADDQ AX, acc0 ADCQ DX, acc1 ADCQ $0, acc2 // Copy result [255:0] MOVQ acc4, x_ptr MOVQ acc5, acc3 MOVQ acc0, t0 MOVQ acc1, t1 // Subtract c256 SUBQ c256ord<>+0x00(SB), acc4 SBBQ c256ord<>+0x08(SB) ,acc5 SBBQ c256ord<>+0x10(SB), acc0 SBBQ c256ord<>+0x18(SB), acc1 SBBQ $0, acc2 CMOVQCS x_ptr, acc4 CMOVQCS acc3, acc5 CMOVQCS t0, acc0 CMOVQCS t1, acc1 MOVQ acc4, (8*0)(res_ptr) MOVQ acc5, (8*1)(res_ptr) MOVQ acc0, (8*2)(res_ptr) MOVQ acc1, (8*3)(res_ptr) RET /* ---------------------------------------*/ // func c256OrdSqr(res, in []uint64, n int) TEXT ·c256OrdSqr(SB),NOSPLIT,$0 MOVQ res+0(FP), res_ptr MOVQ in+24(FP), x_ptr MOVQ n+48(FP), BX ordSqrLoop: // y[1:] * y[0] MOVQ (8*0)(x_ptr), t0 MOVQ (8*1)(x_ptr), AX MULQ t0 MOVQ AX, acc1 MOVQ DX, acc2 MOVQ (8*2)(x_ptr), AX MULQ t0 ADDQ AX, acc2 ADCQ $0, DX MOVQ DX, acc3 MOVQ (8*3)(x_ptr), AX MULQ t0 ADDQ AX, acc3 ADCQ $0, DX MOVQ DX, acc4 // y[2:] * y[1] MOVQ (8*1)(x_ptr), t0 MOVQ (8*2)(x_ptr), AX MULQ t0 ADDQ AX, acc3 ADCQ $0, DX MOVQ DX, t1 MOVQ (8*3)(x_ptr), AX MULQ t0 ADDQ t1, acc4 ADCQ $0, DX ADDQ AX, acc4 ADCQ $0, DX MOVQ DX, acc5 // y[3] * y[2] MOVQ (8*2)(x_ptr), t0 MOVQ (8*3)(x_ptr), AX MULQ t0 ADDQ AX, acc5 ADCQ $0, DX MOVQ DX, y_ptr XORQ t1, t1 // *2 ADDQ acc1, acc1 ADCQ acc2, acc2 ADCQ acc3, acc3 ADCQ acc4, acc4 ADCQ acc5, acc5 ADCQ y_ptr, y_ptr ADCQ $0, t1 // Missing products MOVQ (8*0)(x_ptr), AX MULQ AX MOVQ AX, acc0 MOVQ DX, t0 MOVQ (8*1)(x_ptr), AX MULQ AX ADDQ t0, acc1 ADCQ AX, acc2 ADCQ $0, DX MOVQ DX, t0 MOVQ (8*2)(x_ptr), AX MULQ AX ADDQ t0, acc3 ADCQ AX, acc4 ADCQ $0, DX MOVQ DX, t0 MOVQ (8*3)(x_ptr), AX MULQ AX ADDQ t0, acc5 ADCQ AX, y_ptr ADCQ DX, t1 MOVQ t1, x_ptr // in*in = [acc0, acc1, acc2, acc3, acc4, acc5, y_ptr, x_ptr] // in * in / R mod p = [acc0, acc1, acc2, acc3] / R mod p + [acc4, acc5, y_ptr, x_ptr] // First reduction step // [acc1, acc2, acc3, acc0] = [acc0, acc1, acc2, acc3] + (acc0*k0 mod B) * N // where k0 = -N^-1 mod B constant MOVQ acc0, AX MULQ c256ordK0<>(SB) MOVQ AX, t0 // t0 = acc0*k0 mod B // [acc0, acc1, acc2, acc3] + t0 * N // acc0, acc1, acc2, acc3 //+ AX DX //----------------------------------------------- //= acc0, acc1, acc2, acc3 //+ t1 MOVQ c256ord<>+0x00(SB), AX MULQ t0 ADDQ AX, acc0 ADCQ $0, DX MOVQ DX, t1 // acc0, acc1, acc2, acc3 //+ t1 //+ AX DX //----------------------------------------------- //= acc0, acc1, acc2, acc3 //+ DX //+ CF MOVQ c256ord<>+0x08(SB), AX MULQ t0 ADDQ t1, acc1 ADCQ $0, DX ADDQ AX, acc1 // note N2 = B - 1 // acc0, acc1, acc2, acc3 //+ DX //+ CF //+ t0 //- t0 //----------------------------------------------- //= acc0, acc1, acc2, acc3 //+ t1 // Note that no carry for B^4 here: // [acc0, acc1, acc2, t1] = [acc0, acc1, acc2] + t0 * [N0, N1, N2] // < B^3 - 1 + t0 * (B^3 - 1) // < (t0 + 1)(B^3 - 1) // <= B(B^3-1) // < B^4 MOVQ t0, t1 ADCQ DX, acc2 ADCQ $0, t1 SUBQ t0, acc2 SBBQ $0, t1 // Note N3 = B - 2^{32} - 1 // 0, acc1, acc2, acc3, acc0(=t0) //+ t1 //- t0 //- t0<<32 t0>>32 //----------------------------------------------- //= 0, acc1, acc2, acc3, acc0 MOVQ t0, AX MOVQ t0, DX MOVQ t0, acc0 SHLQ $32, AX SHRQ $32, DX ADDQ t1, acc3 ADCQ $0, acc0 SUBQ AX, acc3 SBBQ DX, acc0 SUBQ t0, acc3 SBBQ $0, acc0 // Second reduction step MOVQ acc1, AX MULQ c256ordK0<>(SB) MOVQ AX, t0 MOVQ c256ord<>+0x00(SB), AX MULQ t0 ADDQ AX, acc1 ADCQ $0, DX MOVQ DX, t1 MOVQ c256ord<>+0x08(SB), AX MULQ t0 ADDQ t1, acc2 ADCQ $0, DX ADDQ AX, acc2 MOVQ t0, t1 ADCQ DX, acc3 ADCQ $0, t1 SUBQ t0, acc3 SBBQ $0, t1 MOVQ t0, AX MOVQ t0, DX MOVQ t0, acc1 SHLQ $32, AX SHRQ $32, DX ADDQ t1, acc0 ADCQ $0, acc1 SUBQ AX, acc0 SBBQ DX, acc1 SUBQ t0, acc0 SBBQ $0, acc1 // Third reduction step MOVQ acc2, AX MULQ c256ordK0<>(SB) MOVQ AX, t0 MOVQ c256ord<>+0x00(SB), AX MULQ t0 ADDQ AX, acc2 ADCQ $0, DX MOVQ DX, t1 MOVQ c256ord<>+0x08(SB), AX MULQ t0 ADDQ t1, acc3 ADCQ $0, DX ADDQ AX, acc3 MOVQ t0, t1 ADCQ DX, acc0 ADCQ $0, t1 SUBQ t0, acc0 SBBQ $0, t1 MOVQ t0, AX MOVQ t0, DX MOVQ t0, acc2 SHLQ $32, AX SHRQ $32, DX ADDQ t1, acc1 ADCQ $0, acc2 SUBQ AX, acc1 SBBQ DX, acc2 SUBQ t0, acc1 SBBQ $0, acc2 // Last reduction step MOVQ acc3, AX MULQ c256ordK0<>(SB) MOVQ AX, t0 MOVQ c256ord<>+0x00(SB), AX MULQ t0 ADDQ AX, acc3 ADCQ $0, DX MOVQ DX, t1 MOVQ c256ord<>+0x08(SB), AX MULQ t0 ADDQ t1, acc0 ADCQ $0, DX ADDQ AX, acc0 ADCQ $0, DX MOVQ DX, t1 MOVQ t0, t1 ADCQ DX, acc1 ADCQ $0, t1 SUBQ t0, acc1 SBBQ $0, t1 MOVQ t0, AX MOVQ t0, DX MOVQ t0, acc3 SHLQ $32, AX SHRQ $32, DX ADDQ t1, acc2 ADCQ $0, acc3 SUBQ AX, acc2 SBBQ DX, acc3 SUBQ t0, acc2 SBBQ $0, acc3 // Sub N from [acc0, acc1, acc2, acc3] if necessary. XORQ t0, t0 ADCQ acc4, acc0 ADCQ acc5, acc1 ADCQ y_ptr, acc2 ADCQ x_ptr, acc3 ADCQ $0, t0 MOVQ acc0, acc4 MOVQ acc1, acc5 MOVQ acc2, y_ptr MOVQ acc3, t1 SUBQ c256ord<>+0x00(SB), acc0 SBBQ c256ord<>+0x08(SB) ,acc1 SBBQ c256ord<>+0x10(SB), acc2 SBBQ c256ord<>+0x18(SB), acc3 SBBQ $0, t0 CMOVQCS acc4, acc0 CMOVQCS acc5, acc1 CMOVQCS y_ptr, acc2 CMOVQCS t1, acc3 MOVQ acc0, (8*0)(res_ptr) MOVQ acc1, (8*1)(res_ptr) MOVQ acc2, (8*2)(res_ptr) MOVQ acc3, (8*3)(res_ptr) MOVQ res_ptr, x_ptr DECQ BX JNE ordSqrLoop RET /* ---------------------------------------*/ // arithmetic for Fp and Fn complete. #undef res_ptr #undef x_ptr #undef y_ptr #undef acc0 #undef acc1 #undef acc2 #undef acc3 #undef acc4 #undef acc5 #undef t0 #undef t1 /* ---------------------------------------*/ #define mul0 AX #define mul1 DX #define acc0 BX #define acc1 CX #define acc2 R8 #define acc3 R9 #define acc4 R10 #define acc5 R11 #define acc6 R12 #define acc7 R13 #define t0 R14 #define t1 R15 #define t2 DI #define t3 SI #define hlp BP /* ---------------------------------------*/ // For internal call only, no register saving and loading // acc[4:8] = acc[4:8] - t0:t3 TEXT c256SubInternal(SB),NOSPLIT,$0 XORQ mul0, mul0 SUBQ t0, acc4 SBBQ t1, acc5 SBBQ t2, acc6 SBBQ t3, acc7 SBBQ $0, mul0 MOVQ acc4, acc0 MOVQ acc5, acc1 MOVQ acc6, acc2 MOVQ acc7, acc3 ADDQ $-1, acc4 ADCQ c256const1<>(SB), acc5 ADCQ $-1, acc6 ADCQ c256const3<>(SB), acc7 ANDQ $1, mul0 CMOVQEQ acc0, acc4 CMOVQEQ acc1, acc5 CMOVQEQ acc2, acc6 CMOVQEQ acc3, acc7 RET /* ---------------------------------------*/ // in: a = [acc4,acc5,acc6,acc7], t = [t0,t1,t2,t3] // out: [acc4,acc5,acc6,acc7] = a * t mod p TEXT c256MulInternal(SB),NOSPLIT,$0 // acc4 * t[0:4] -> acc0:acc4 MOVQ acc4, mul0 MULQ t0 MOVQ mul0, acc0 MOVQ mul1, acc1 MOVQ acc4, mul0 MULQ t1 ADDQ mul0, acc1 ADCQ $0, mul1 MOVQ mul1, acc2 MOVQ acc4, mul0 MULQ t2 ADDQ mul0, acc2 ADCQ $0, mul1 MOVQ mul1, acc3 MOVQ acc4, mul0 MULQ t3 ADDQ mul0, acc3 ADCQ $0, mul1 MOVQ mul1, acc4 // add acc5 * t[0:4] to acc1:acc5 MOVQ acc5, mul0 MULQ t0 ADDQ mul0, acc1 ADCQ $0, mul1 MOVQ mul1, hlp MOVQ acc5, mul0 MULQ t1 ADDQ hlp, acc2 ADCQ $0, mul1 ADDQ mul0, acc2 ADCQ $0, mul1 MOVQ mul1, hlp MOVQ acc5, mul0 MULQ t2 ADDQ hlp, acc3 ADCQ $0, mul1 ADDQ mul0, acc3 ADCQ $0, mul1 MOVQ mul1, hlp MOVQ acc5, mul0 MULQ t3 ADDQ hlp, acc4 ADCQ $0, mul1 ADDQ mul0, acc4 ADCQ $0, mul1 MOVQ mul1, acc5 // add acc6 * t[0:4] to acc2:acc6 MOVQ acc6, mul0 MULQ t0 ADDQ mul0, acc2 ADCQ $0, mul1 MOVQ mul1, hlp MOVQ acc6, mul0 MULQ t1 ADDQ hlp, acc3 ADCQ $0, mul1 ADDQ mul0, acc3 ADCQ $0, mul1 MOVQ mul1, hlp MOVQ acc6, mul0 MULQ t2 ADDQ hlp, acc4 ADCQ $0, mul1 ADDQ mul0, acc4 ADCQ $0, mul1 MOVQ mul1, hlp MOVQ acc6, mul0 MULQ t3 ADDQ hlp, acc5 ADCQ $0, mul1 ADDQ mul0, acc5 ADCQ $0, mul1 MOVQ mul1, acc6 // add acc7 * t[0:4] to acc3:acc7 MOVQ acc7, mul0 MULQ t0 ADDQ mul0, acc3 ADCQ $0, mul1 MOVQ mul1, hlp MOVQ acc7, mul0 MULQ t1 ADDQ hlp, acc4 ADCQ $0, mul1 ADDQ mul0, acc4 ADCQ $0, mul1 MOVQ mul1, hlp MOVQ acc7, mul0 MULQ t2 ADDQ hlp, acc5 ADCQ $0, mul1 ADDQ mul0, acc5 ADCQ $0, mul1 MOVQ mul1, hlp MOVQ acc7, mul0 MULQ t3 ADDQ hlp, acc6 ADCQ $0, mul1 ADDQ mul0, acc6 ADCQ $0, mul1 MOVQ mul1, acc7 // The result in [acc0, acc1,···, acc7] // Calculate [acc0, acc1, acc2, acc3]*R^{-1} + [acc4,acc5,acc6,acc7] // reduce acc0-acc3 montMulOne(acc0,acc1,acc2,acc3, mul0, hlp) XORQ hlp,hlp // Add bits [511:256] of the result ADCQ acc0, acc4 ADCQ acc1, acc5 ADCQ acc2, acc6 ADCQ acc3, acc7 ADCQ $0, hlp // Copy result MOVQ acc4, acc0 MOVQ acc5, acc1 MOVQ acc6, acc2 MOVQ acc7, acc3 // Subtract c256 SUBQ $-1, acc4 SBBQ c256const1<>(SB) ,acc5 SBBQ $-1, acc6 SBBQ c256const3<>(SB), acc7 SBBQ $0, hlp // If the result of the subtraction is negative, restore the previous result CMOVQCS acc0, acc4 CMOVQCS acc1, acc5 CMOVQCS acc2, acc6 CMOVQCS acc3, acc7 RET /* ---------------------------------------*/ // in: a = [acc4,acc5,acc6,acc7] // out: [acc4,acc5,acc6,acc7] = a ^ 2 TEXT c256SqrInternal(SB),NOSPLIT,$0 MOVQ acc4, mul0 MULQ acc5 MOVQ mul0, acc1 MOVQ mul1, acc2 MOVQ acc4, mul0 MULQ acc6 ADDQ mul0, acc2 ADCQ $0, mul1 MOVQ mul1, acc3 MOVQ acc4, mul0 MULQ acc7 ADDQ mul0, acc3 ADCQ $0, mul1 MOVQ mul1, t0 MOVQ acc5, mul0 MULQ acc6 ADDQ mul0, acc3 ADCQ $0, mul1 MOVQ mul1, hlp MOVQ acc5, mul0 MULQ acc7 ADDQ hlp, t0 ADCQ $0, mul1 ADDQ mul0, t0 ADCQ $0, mul1 MOVQ mul1, t1 MOVQ acc6, mul0 MULQ acc7 ADDQ mul0, t1 ADCQ $0, mul1 MOVQ mul1, t2 XORQ t3, t3 // *2 ADDQ acc1, acc1 ADCQ acc2, acc2 ADCQ acc3, acc3 ADCQ t0, t0 ADCQ t1, t1 ADCQ t2, t2 ADCQ $0, t3 // Missing products MOVQ acc4, mul0 MULQ mul0 MOVQ mul0, acc0 MOVQ DX, acc4 MOVQ acc5, mul0 MULQ mul0 ADDQ acc4, acc1 ADCQ mul0, acc2 ADCQ $0, DX MOVQ DX, acc4 MOVQ acc6, mul0 MULQ mul0 ADDQ acc4, acc3 ADCQ mul0, t0 ADCQ $0, DX MOVQ DX, acc4 MOVQ acc7, mul0 MULQ mul0 ADDQ acc4, t1 ADCQ mul0, t2 ADCQ DX, t3 // acc0-acc4 t0-t3 // reduction montMulOne(acc0,acc1,acc2,acc3, mul0, hlp) // MOVQ $0, BP XORQ hlp,hlp // Add bits [511:256] of the result ADCQ acc0, t0 ADCQ acc1, t1 ADCQ acc2, t2 ADCQ acc3, t3 ADCQ $0, hlp // Copy result MOVQ t0, acc4 MOVQ t1, acc5 MOVQ t2, acc6 MOVQ t3, acc7 // Subtract c256 SUBQ $-1, acc4 SBBQ c256const1<>(SB) ,acc5 SBBQ $-1 ,acc6 SBBQ c256const3<>(SB), acc7 SBBQ $0, hlp // If the result of the subtraction is negative, restore the previous result CMOVQCS t0, acc4 CMOVQCS t1, acc5 CMOVQCS t2, acc6 CMOVQCS t3, acc7 RET /* ---------------------------------------*/ // acc[4:8] = 2 * acc[4:8] mod p // done #define c256MulBy2Inline\ XORQ mul0, mul0;\ ADDQ acc4, acc4;\ ADCQ acc5, acc5;\ ADCQ acc6, acc6;\ ADCQ acc7, acc7;\ ADCQ $0, mul0;\ MOVQ acc4, t0;\ MOVQ acc5, t1;\ MOVQ acc6, t2;\ MOVQ acc7, t3;\ SUBQ $-1, t0;\ SBBQ c256const1<>(SB), t1;\ SBBQ $-1, t2;\ SBBQ c256const3<>(SB), t3;\ SBBQ $0, mul0;\ CMOVQCS acc4, t0;\ CMOVQCS acc5, t1;\ CMOVQCS acc6, t2;\ CMOVQCS acc7, t3; /* ---------------------------------------*/ // acc[4:8] = t0:t3 + acc[4:8] mod p // done #define c256AddInline \ XORQ mul0, mul0;\ ADDQ t0, acc4;\ ADCQ t1, acc5;\ ADCQ t2, acc6;\ ADCQ t3, acc7;\ ADCQ $0, mul0;\ MOVQ acc4, t0;\ MOVQ acc5, t1;\ MOVQ acc6, t2;\ MOVQ acc7, t3;\ SUBQ $-1, t0;\ SBBQ c256const1<>(SB), t1;\ SBBQ $-1, t2;\ SBBQ c256const3<>(SB), t3;\ SBBQ $0, mul0;\ CMOVQCS acc4, t0;\ CMOVQCS acc5, t1;\ CMOVQCS acc6, t2;\ CMOVQCS acc7, t3; /* ---------------------------------------*/ #define LDacc(src) MOVQ src(8*0), acc4; MOVQ src(8*1), acc5; MOVQ src(8*2), acc6; MOVQ src(8*3), acc7 #define LDt(src) MOVQ src(8*0), t0; MOVQ src(8*1), t1; MOVQ src(8*2), t2; MOVQ src(8*3), t3 #define ST(dst) MOVQ acc4, dst(8*0); MOVQ acc5, dst(8*1); MOVQ acc6, dst(8*2); MOVQ acc7, dst(8*3) #define STt(dst) MOVQ t0, dst(8*0); MOVQ t1, dst(8*1); MOVQ t2, dst(8*2); MOVQ t3, dst(8*3) #define acc2t MOVQ acc4, t0; MOVQ acc5, t1; MOVQ acc6, t2; MOVQ acc7, t3 #define t2acc MOVQ t0, acc4; MOVQ t1, acc5; MOVQ t2, acc6; MOVQ t3, acc7 /* ---------------------------------------*/ // Temp vars in ·c256PointAddAffineAsm, 32*16 = 512 bytes #define x1in(off) (32*0 + off)(SP) #define y1in(off) (32*1 + off)(SP) #define z1in(off) (32*2 + off)(SP) #define x2in(off) (32*3 + off)(SP) #define y2in(off) (32*4 + off)(SP) #define xout(off) (32*5 + off)(SP) #define yout(off) (32*6 + off)(SP) #define zout(off) (32*7 + off)(SP) #define s2(off) (32*8 + off)(SP) #define z1sqr(off) (32*9 + off)(SP) #define h(off) (32*10 + off)(SP) #define r(off) (32*11 + off)(SP) #define hsqr(off) (32*12 + off)(SP) #define rsqr(off) (32*13 + off)(SP) #define hcub(off) (32*14 + off)(SP) #define rptr (32*15)(SP) #define sel_save (32*15 + 8)(SP) #define zero_save (32*15 + 8 + 4)(SP) // func c256PointAddAffineAsm(res, in1, in2 []uint64, sign, sel, zero int) TEXT ·c256PointAddAffineAsm(SB),0,$512-96 // Special case of https://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-add-2007-bl (with Z2 = 1 in Montgomery domain) // Z1Z1 = Z1^2 // Z2Z2 = Z2^2 // U1 = X1*Z2Z2 // U2 = X2*Z1Z1 // S1 = Y1*Z2*Z2Z2 // S2 = Y2*Z1*Z1Z1 // H = U2-U1 // I = (2*H)^2 // J = H*I // r = 2*(S2-S1) // V = U1*I // X3 = r^2-J-2*V // Y3 = r*(V-X3)-2*S1*J // Z3 = ((Z1+Z2)^2-Z1Z1-Z2Z2)*H // with Z2 = 1: // X3 = r^2-J-2*V = 4 * ((S2-S1)^2 - H^3 - 2*U1*H^2) // Y3 = r*(V-X3)-2*S1*J = 8 * ((S2-S1)(U1*H^2-X3/4) - S1*H^3) // Z3 = ((Z1+1)^2-Z1Z1-1)*H/2 = 2 * Z1 * H. // Thus let: // Z1Z1 = Z1^2 // U1 = X1 // U2 = X2*Z1Z1 // S1 = Y1 // S2 = Y2*Z1*Z1Z1 // H = U2 - X1 // r = S2-S1 // X3 = (S2-S1)^2 - H^3 - 2*U1*H^2 = r^2 - H^3 - 2*X1*H^2 // Y3 = (S2-S1)(U1*H^2-X3) - S1*H^3 = r*(U1*H^2-X3) - Y1*H^3 // Z3 = ((Z1+1)^2-Z1Z1-1)*H/2 = Z1 * H // Move input to stack in order to free registers MOVQ res+0(FP), AX MOVQ in1+24(FP), BX MOVQ in2+48(FP), CX MOVQ sign+72(FP), DX MOVQ sel+80(FP), t1 MOVQ zero+88(FP), t2 // a point is [x,y,z] = [12]uint64 = [6]uint128 // Xi is 128bits // move in point to stack MOVOU (16*0)(BX), X0 // x MOVOU (16*1)(BX), X1 MOVOU (16*2)(BX), X2 // y MOVOU (16*3)(BX), X3 MOVOU (16*4)(BX), X4 // z MOVOU (16*5)(BX), X5 MOVOU X0, x1in(16*0) MOVOU X1, x1in(16*1) MOVOU X2, y1in(16*0) MOVOU X3, y1in(16*1) MOVOU X4, z1in(16*0) MOVOU X5, z1in(16*1) MOVOU (16*0)(CX), X0 MOVOU (16*1)(CX), X1 MOVOU X0, x2in(16*0) MOVOU X1, x2in(16*1) // Store pointer to result MOVQ mul0, rptr MOVL t1, sel_save MOVL t2, zero_save // Negate y2in based on sign MOVQ (16*2 + 8*0)(CX), acc4 MOVQ (16*2 + 8*1)(CX), acc5 MOVQ (16*2 + 8*2)(CX), acc6 MOVQ (16*2 + 8*3)(CX), acc7 MOVQ $-1, acc0 MOVQ c256const1<>(SB), acc1 MOVQ $-1, acc2 MOVQ c256const3<>(SB), acc3 XORQ mul0, mul0 // Speculatively subtract SUBQ acc4, acc0 SBBQ acc5, acc1 SBBQ acc6, acc2 SBBQ acc7, acc3 SBBQ $0, mul0 MOVQ acc0, t0 MOVQ acc1, t1 MOVQ acc2, t2 MOVQ acc3, t3 // acc[0:4] = t0:t3 = -yin, acc[4:8] = yin // Add in case the operand was > c256 ADDQ $-1, acc0 ADCQ c256const1<>(SB), acc1 ADCQ $-1, acc2 ADCQ c256const3<>(SB), acc3 // The go stdlib implementation. // when p > y2in > p - (R-p), then [acc0, acc1, acc2, acc3] = 2p-y2in > p // for example: y2in = p-1, then [acc0, acc1, acc2, acc3] = p+1 // but it is ok. ADCQ $0, mul0 CMOVQNE t0, acc0 CMOVQNE t1, acc1 CMOVQNE t2, acc2 CMOVQNE t3, acc3 // TODO: it can be replaced by the following. // CMPQ mul0, $0 // CMOVQEQ t0, acc0 // CMOVQEQ t1, acc1 // CMOVQEQ t2, acc2 // CMOVQEQ t3, acc3 // If condition is 0, keep original value TESTQ DX, DX CMOVQEQ acc4, acc0 CMOVQEQ acc5, acc1 CMOVQEQ acc6, acc2 CMOVQEQ acc7, acc3 // Store result MOVQ acc0, y2in(8*0) MOVQ acc1, y2in(8*1) MOVQ acc2, y2in(8*2) MOVQ acc3, y2in(8*3) // y2in = sign*yin // Begin point add LDacc (z1in) CALL c256SqrInternal(SB) // z1ˆ2 ST (z1sqr) LDt (x2in) CALL c256MulInternal(SB) // x2 * z1ˆ2 LDt (x1in) CALL c256SubInternal(SB) // h = u2 - u1 ST (h) LDt (z1in) CALL c256MulInternal(SB) // z3 = h * z1 ST (zout) LDacc (z1sqr) CALL c256MulInternal(SB) // z1ˆ3 LDt (y2in) CALL c256MulInternal(SB) // s2 = y2 * z1ˆ3 ST (s2) LDt (y1in) CALL c256SubInternal(SB) // r = s2 - s1 ST (r) CALL c256SqrInternal(SB) // rsqr = rˆ2 ST (rsqr) LDacc (h) CALL c256SqrInternal(SB) // hsqr = hˆ2 ST (hsqr) LDt (h) CALL c256MulInternal(SB) // hcub = hˆ3 ST (hcub) LDt (y1in) CALL c256MulInternal(SB) // y1 * hˆ3 ST (s2) LDacc (x1in) LDt (hsqr) CALL c256MulInternal(SB) // u1 * hˆ2 ST (h) c256MulBy2Inline // u1 * hˆ2 * 2, inline LDacc (rsqr) CALL c256SubInternal(SB) // rˆ2 - u1 * hˆ2 * 2 LDt (hcub) CALL c256SubInternal(SB) // ST (xout) MOVQ acc4, t0 MOVQ acc5, t1 MOVQ acc6, t2 MOVQ acc7, t3 LDacc (h) CALL c256SubInternal(SB) // u1*h^2 - x3 LDt (r) CALL c256MulInternal(SB) // r*(u1*h^2 - x3) LDt (s2) CALL c256SubInternal(SB) //r*(u1*h^2 - x3) - y1*H3 ST (yout) // Load stored values from stack MOVQ rptr, AX MOVL sel_save, BX MOVL zero_save, CX // The result is not valid if (sel == 0), conditional choose MOVOU xout(16*0), X0 MOVOU xout(16*1), X1 MOVOU yout(16*0), X2 MOVOU yout(16*1), X3 MOVOU zout(16*0), X4 MOVOU zout(16*1), X5 MOVL BX, X6 MOVL CX, X7 PXOR X8, X8 PCMPEQL X9, X9 PSHUFD $0, X6, X6 PSHUFD $0, X7, X7 PCMPEQL X8, X6 PCMPEQL X8, X7 MOVOU X6, X15 PANDN X9, X15 MOVOU x1in(16*0), X9 MOVOU x1in(16*1), X10 MOVOU y1in(16*0), X11 MOVOU y1in(16*1), X12 MOVOU z1in(16*0), X13 MOVOU z1in(16*1), X14 PAND X15, X0 PAND X15, X1 PAND X15, X2 PAND X15, X3 PAND X15, X4 PAND X15, X5 PAND X6, X9 PAND X6, X10 PAND X6, X11 PAND X6, X12 PAND X6, X13 PAND X6, X14 PXOR X9, X0 PXOR X10, X1 PXOR X11, X2 PXOR X12, X3 PXOR X13, X4 PXOR X14, X5 // Similarly if zero == 0 PCMPEQL X9, X9 MOVOU X7, X15 PANDN X9, X15 MOVOU x2in(16*0), X9 MOVOU x2in(16*1), X10 MOVOU y2in(16*0), X11 MOVOU y2in(16*1), X12 MOVOU c256one<>+0x00(SB), X13 MOVOU c256one<>+0x10(SB), X14 PAND X15, X0 PAND X15, X1 PAND X15, X2 PAND X15, X3 PAND X15, X4 PAND X15, X5 PAND X7, X9 PAND X7, X10 PAND X7, X11 PAND X7, X12 PAND X7, X13 PAND X7, X14 PXOR X9, X0 PXOR X10, X1 PXOR X11, X2 PXOR X12, X3 PXOR X13, X4 PXOR X14, X5 // Finally output the result MOVOU X0, (16*0)(AX) MOVOU X1, (16*1)(AX) MOVOU X2, (16*2)(AX) MOVOU X3, (16*3)(AX) MOVOU X4, (16*4)(AX) MOVOU X5, (16*5)(AX) MOVQ $0, rptr RET #undef x1in #undef y1in #undef z1in #undef x2in #undef y2in #undef xout #undef yout #undef zout #undef s2 #undef z1sqr #undef h #undef r #undef hsqr #undef rsqr #undef hcub #undef rptr #undef sel_save #undef zero_save // c256IsZero returns 1 in AX if [acc4..acc7] represents zero and zero // otherwise. It writes to [acc4..acc7], t0 and t1. // done TEXT c256IsZero(SB),NOSPLIT,$0 // AX contains a flag that is set if the input is zero. XORQ AX, AX MOVQ $1, t1 // Check whether [acc4..acc7] are all zero. MOVQ acc4, t0 ORQ acc5, t0 ORQ acc6, t0 ORQ acc7, t0 // Set the zero flag if so. (CMOV of a constant to a register doesn't // appear to be supported in Go. Thus t1 = 1.) CMOVQEQ t1, AX // XOR [acc4..acc7] with P and compare with zero again. XORQ $-1, acc4 XORQ c256const1<>(SB), acc5 XORQ $-1, acc6 XORQ c256const3<>(SB), acc7 ORQ acc5, acc4 ORQ acc6, acc4 ORQ acc7, acc4 // Set the zero flag if so. CMOVQEQ t1, AX RET /* ---------------------------------------*/ #define x1in(off) (32*0 + off)(SP) #define y1in(off) (32*1 + off)(SP) #define z1in(off) (32*2 + off)(SP) #define x2in(off) (32*3 + off)(SP) #define y2in(off) (32*4 + off)(SP) #define z2in(off) (32*5 + off)(SP) #define xout(off) (32*6 + off)(SP) #define yout(off) (32*7 + off)(SP) #define zout(off) (32*8 + off)(SP) #define u1(off) (32*9 + off)(SP) #define u2(off) (32*10 + off)(SP) #define s1(off) (32*11 + off)(SP) #define s2(off) (32*12 + off)(SP) #define z1sqr(off) (32*13 + off)(SP) #define z2sqr(off) (32*14 + off)(SP) #define h(off) (32*15 + off)(SP) #define r(off) (32*16 + off)(SP) #define hsqr(off) (32*17 + off)(SP) #define rsqr(off) (32*18 + off)(SP) #define hcub(off) (32*19 + off)(SP) #define rptr (32*20)(SP) #define points_eq (32*20+8)(SP) //func c256PointAddAsm(res, in1, in2 []uint64) int TEXT ·c256PointAddAsm(SB),0,$680-80 // See https://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-add-2007-bl // Move input to stack in order to free registers MOVQ res+0(FP), AX MOVQ in1+24(FP), BX MOVQ in2+48(FP), CX MOVOU (16*0)(BX), X0 MOVOU (16*1)(BX), X1 MOVOU (16*2)(BX), X2 MOVOU (16*3)(BX), X3 MOVOU (16*4)(BX), X4 MOVOU (16*5)(BX), X5 MOVOU X0, x1in(16*0) MOVOU X1, x1in(16*1) MOVOU X2, y1in(16*0) MOVOU X3, y1in(16*1) MOVOU X4, z1in(16*0) MOVOU X5, z1in(16*1) MOVOU (16*0)(CX), X0 MOVOU (16*1)(CX), X1 MOVOU (16*2)(CX), X2 MOVOU (16*3)(CX), X3 MOVOU (16*4)(CX), X4 MOVOU (16*5)(CX), X5 MOVOU X0, x2in(16*0) MOVOU X1, x2in(16*1) MOVOU X2, y2in(16*0) MOVOU X3, y2in(16*1) MOVOU X4, z2in(16*0) MOVOU X5, z2in(16*1) // Store pointer to result MOVQ AX, rptr // Begin point add LDacc (z2in) CALL c256SqrInternal(SB) // z2ˆ2 ST (z2sqr) LDt (z2in) CALL c256MulInternal(SB) // z2ˆ3 LDt (y1in) CALL c256MulInternal(SB) // s1 = z2ˆ3*y1 ST (s1) LDacc (z1in) CALL c256SqrInternal(SB) // z1ˆ2 ST (z1sqr) LDt (z1in) CALL c256MulInternal(SB) // z1ˆ3 LDt (y2in) CALL c256MulInternal(SB) // s2 = z1ˆ3*y2 ST (s2) LDt (s1) CALL c256SubInternal(SB) // r = s2 - s1 ST (r) CALL c256IsZero(SB) MOVQ AX, points_eq LDacc (z2sqr) LDt (x1in) CALL c256MulInternal(SB) // u1 = x1 * z2ˆ2 ST (u1) LDacc (z1sqr) LDt (x2in) CALL c256MulInternal(SB) // u2 = x2 * z1ˆ2 ST (u2) LDt (u1) CALL c256SubInternal(SB) // h = u2 - u1 ST (h) CALL c256IsZero(SB) ANDQ points_eq, AX MOVQ AX, points_eq LDacc (r) CALL c256SqrInternal(SB) // rsqr = rˆ2 ST (rsqr) LDacc (h) CALL c256SqrInternal(SB) // hsqr = hˆ2 ST (hsqr) LDt (h) CALL c256MulInternal(SB) // hcub = hˆ3 ST (hcub) LDt (s1) CALL c256MulInternal(SB) ST (s2) LDacc (z1in) LDt (z2in) CALL c256MulInternal(SB) // z1 * z2 LDt (h) CALL c256MulInternal(SB) // z1 * z2 * h ST (zout) LDacc (hsqr) LDt (u1) CALL c256MulInternal(SB) // hˆ2 * u1 ST (u2) c256MulBy2Inline // u1 * hˆ2 * 2, inline LDacc (rsqr) CALL c256SubInternal(SB) // rˆ2 - u1 * hˆ2 * 2 LDt (hcub) CALL c256SubInternal(SB) ST (xout) MOVQ acc4, t0 MOVQ acc5, t1 MOVQ acc6, t2 MOVQ acc7, t3 LDacc (u2) CALL c256SubInternal(SB) LDt (r) CALL c256MulInternal(SB) LDt (s2) CALL c256SubInternal(SB) ST (yout) MOVOU xout(16*0), X0 MOVOU xout(16*1), X1 MOVOU yout(16*0), X2 MOVOU yout(16*1), X3 MOVOU zout(16*0), X4 MOVOU zout(16*1), X5 // Finally output the result MOVQ rptr, AX MOVQ $0, rptr MOVOU X0, (16*0)(AX) MOVOU X1, (16*1)(AX) MOVOU X2, (16*2)(AX) MOVOU X3, (16*3)(AX) MOVOU X4, (16*4)(AX) MOVOU X5, (16*5)(AX) MOVQ points_eq, AX MOVQ AX, ret+72(FP) RET #undef x1in #undef y1in #undef z1in #undef x2in #undef y2in #undef z2in #undef xout #undef yout #undef zout #undef s1 #undef s2 #undef u1 #undef u2 #undef z1sqr #undef z2sqr #undef h #undef r #undef hsqr #undef rsqr #undef hcub #undef rptr /* ---------------------------------------*/ #define x(off) (32*0 + off)(SP) #define y(off) (32*1 + off)(SP) #define z(off) (32*2 + off)(SP) #define s(off) (32*3 + off)(SP) #define m(off) (32*4 + off)(SP) #define zsqr(off) (32*5 + off)(SP) #define tmp(off) (32*6 + off)(SP) #define rptr (32*7)(SP) //func c256PointDoubleAsm(res, in []uint64) // done TODO - check once more TEXT ·c256PointDoubleAsm(SB),NOSPLIT,$256-48 // Move input to stack in order to free registers MOVQ res+0(FP), AX MOVQ in+24(FP), BX MOVOU (16*0)(BX), X0 MOVOU (16*1)(BX), X1 MOVOU (16*2)(BX), X2 MOVOU (16*3)(BX), X3 MOVOU (16*4)(BX), X4 MOVOU (16*5)(BX), X5 MOVOU X0, x(16*0) MOVOU X1, x(16*1) MOVOU X2, y(16*0) MOVOU X3, y(16*1) MOVOU X4, z(16*0) MOVOU X5, z(16*1) // Store pointer to result MOVQ AX, rptr // Begin point double LDacc (z) CALL c256SqrInternal(SB) ST (zsqr) LDt (x) c256AddInline STt (m) LDacc (z) LDt (y) CALL c256MulInternal(SB) c256MulBy2Inline MOVQ rptr, AX // Store z MOVQ t0, (16*4 + 8*0)(AX) MOVQ t1, (16*4 + 8*1)(AX) MOVQ t2, (16*4 + 8*2)(AX) MOVQ t3, (16*4 + 8*3)(AX) LDacc (x) LDt (zsqr) CALL c256SubInternal(SB) LDt (m) CALL c256MulInternal(SB) ST (m) // Multiply by 3 c256MulBy2Inline LDacc (m) c256AddInline STt (m) //////////////////////// LDacc (y) c256MulBy2Inline t2acc CALL c256SqrInternal(SB) ST (s) CALL c256SqrInternal(SB) // Divide by 2 XORQ mul0, mul0 MOVQ acc4, t0 MOVQ acc5, t1 MOVQ acc6, t2 MOVQ acc7, t3 ADDQ $-1, acc4 ADCQ c256const1<>(SB), acc5 ADCQ $-1, acc6 ADCQ c256const3<>(SB), acc7 ADCQ $0, mul0 TESTQ $1, t0 CMOVQEQ t0, acc4 CMOVQEQ t1, acc5 CMOVQEQ t2, acc6 CMOVQEQ t3, acc7 ANDQ t0, mul0 SHRQ $1, acc5, acc4 SHRQ $1, acc6, acc5 SHRQ $1, acc7, acc6 SHRQ $1, mul0, acc7 ST (y) ///////////////////////// LDacc (x) LDt (s) CALL c256MulInternal(SB) ST (s) c256MulBy2Inline STt (tmp) LDacc (m) CALL c256SqrInternal(SB) LDt (tmp) CALL c256SubInternal(SB) MOVQ rptr, AX // Store x MOVQ acc4, (16*0 + 8*0)(AX) MOVQ acc5, (16*0 + 8*1)(AX) MOVQ acc6, (16*0 + 8*2)(AX) MOVQ acc7, (16*0 + 8*3)(AX) acc2t LDacc (s) CALL c256SubInternal(SB) LDt (m) CALL c256MulInternal(SB) LDt (y) CALL c256SubInternal(SB) MOVQ rptr, AX // Store y MOVQ acc4, (16*2 + 8*0)(AX) MOVQ acc5, (16*2 + 8*1)(AX) MOVQ acc6, (16*2 + 8*2)(AX) MOVQ acc7, (16*2 + 8*3)(AX) /////////////////////// MOVQ $0, rptr RET /* ---------------------------------------*/