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arithmetic_x86.s
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// +build amd64,blsasm amd64,blsadx
#include "textflag.h"
// addition w/ modular reduction
// a = (a + b) % p
TEXT ·addAssign(SB), NOSPLIT, $0-16
// |
MOVQ a+0(FP), DI
MOVQ b+8(FP), SI
// |
MOVQ (DI), R8
MOVQ 8(DI), R9
MOVQ 16(DI), R10
MOVQ 24(DI), R11
MOVQ 32(DI), R12
MOVQ 40(DI), R13
// |
ADDQ (SI), R8
ADCQ 8(SI), R9
ADCQ 16(SI), R10
ADCQ 24(SI), R11
ADCQ 32(SI), R12
ADCQ 40(SI), R13
// |
MOVQ R8, R14
MOVQ R9, R15
MOVQ R10, CX
MOVQ R11, DX
MOVQ R12, SI
MOVQ R13, BX
MOVQ $0xb9feffffffffaaab, AX
SUBQ AX, R14
MOVQ $0x1eabfffeb153ffff, AX
SBBQ AX, R15
MOVQ $0x6730d2a0f6b0f624, AX
SBBQ AX, CX
MOVQ $0x64774b84f38512bf, AX
SBBQ AX, DX
MOVQ $0x4b1ba7b6434bacd7, AX
SBBQ AX, SI
MOVQ $0x1a0111ea397fe69a, AX
SBBQ AX, BX
CMOVQCC R14, R8
CMOVQCC R15, R9
CMOVQCC CX, R10
CMOVQCC DX, R11
CMOVQCC SI, R12
CMOVQCC BX, R13
// |
MOVQ R8, (DI)
MOVQ R9, 8(DI)
MOVQ R10, 16(DI)
MOVQ R11, 24(DI)
MOVQ R12, 32(DI)
MOVQ R13, 40(DI)
RET
/* | end */
// addition w/ modular reduction
// c = (a + b) % p
TEXT ·add(SB), NOSPLIT, $0-24
// |
MOVQ a+8(FP), DI
MOVQ b+16(FP), SI
// |
MOVQ (DI), R8
MOVQ 8(DI), R9
MOVQ 16(DI), R10
MOVQ 24(DI), R11
MOVQ 32(DI), R12
MOVQ 40(DI), R13
// |
ADDQ (SI), R8
ADCQ 8(SI), R9
ADCQ 16(SI), R10
ADCQ 24(SI), R11
ADCQ 32(SI), R12
ADCQ 40(SI), R13
// |
MOVQ R8, R14
MOVQ R9, R15
MOVQ R10, CX
MOVQ R11, DX
MOVQ R12, SI
MOVQ R13, BX
MOVQ $0xb9feffffffffaaab, DI
SUBQ DI, R14
MOVQ $0x1eabfffeb153ffff, DI
SBBQ DI, R15
MOVQ $0x6730d2a0f6b0f624, DI
SBBQ DI, CX
MOVQ $0x64774b84f38512bf, DI
SBBQ DI, DX
MOVQ $0x4b1ba7b6434bacd7, DI
SBBQ DI, SI
MOVQ $0x1a0111ea397fe69a, DI
SBBQ DI, BX
CMOVQCC R14, R8
CMOVQCC R15, R9
CMOVQCC CX, R10
CMOVQCC DX, R11
CMOVQCC SI, R12
CMOVQCC BX, R13
// |
MOVQ c+0(FP), DI
MOVQ R8, (DI)
MOVQ R9, 8(DI)
MOVQ R10, 16(DI)
MOVQ R11, 24(DI)
MOVQ R12, 32(DI)
MOVQ R13, 40(DI)
RET
/* | end */
// addition w/o reduction check
// c = (a + b)
TEXT ·ladd(SB), NOSPLIT, $0-24
// |
MOVQ a+8(FP), DI
MOVQ b+16(FP), SI
// |
MOVQ (DI), R8
MOVQ 8(DI), R9
MOVQ 16(DI), R10
MOVQ 24(DI), R11
MOVQ 32(DI), R12
MOVQ 40(DI), R13
// |
ADDQ (SI), R8
ADCQ 8(SI), R9
ADCQ 16(SI), R10
ADCQ 24(SI), R11
ADCQ 32(SI), R12
ADCQ 40(SI), R13
// |
MOVQ c+0(FP), DI
MOVQ R8, (DI)
MOVQ R9, 8(DI)
MOVQ R10, 16(DI)
MOVQ R11, 24(DI)
MOVQ R12, 32(DI)
MOVQ R13, 40(DI)
RET
/* | end */
// addition w/o reduction check
// a = a + b
TEXT ·laddAssign(SB), NOSPLIT, $0-16
// |
MOVQ a+0(FP), DI
MOVQ b+8(FP), SI
// |
MOVQ (DI), R8
MOVQ 8(DI), R9
MOVQ 16(DI), R10
MOVQ 24(DI), R11
MOVQ 32(DI), R12
MOVQ 40(DI), R13
// |
ADDQ (SI), R8
ADCQ 8(SI), R9
ADCQ 16(SI), R10
ADCQ 24(SI), R11
ADCQ 32(SI), R12
ADCQ 40(SI), R13
// |
MOVQ a+0(FP), DI
MOVQ R8, (DI)
MOVQ R9, 8(DI)
MOVQ R10, 16(DI)
MOVQ R11, 24(DI)
MOVQ R12, 32(DI)
MOVQ R13, 40(DI)
RET
/* | end */
// subtraction w/ modular reduction
// c = (a - b) % p
TEXT ·sub(SB), NOSPLIT, $0-24
// |
MOVQ a+8(FP), DI
MOVQ b+16(FP), SI
XORQ AX, AX
// |
MOVQ (DI), R8
MOVQ 8(DI), R9
MOVQ 16(DI), R10
MOVQ 24(DI), R11
MOVQ 32(DI), R12
MOVQ 40(DI), R13
SUBQ (SI), R8
SBBQ 8(SI), R9
SBBQ 16(SI), R10
SBBQ 24(SI), R11
SBBQ 32(SI), R12
SBBQ 40(SI), R13
// |
MOVQ $0xb9feffffffffaaab, R14
MOVQ $0x1eabfffeb153ffff, R15
MOVQ $0x6730d2a0f6b0f624, CX
MOVQ $0x64774b84f38512bf, DX
MOVQ $0x4b1ba7b6434bacd7, SI
MOVQ $0x1a0111ea397fe69a, BX
CMOVQCC AX, R14
CMOVQCC AX, R15
CMOVQCC AX, CX
CMOVQCC AX, DX
CMOVQCC AX, SI
CMOVQCC AX, BX
ADDQ R14, R8
ADCQ R15, R9
ADCQ CX, R10
ADCQ DX, R11
ADCQ SI, R12
ADCQ BX, R13
// |
MOVQ c+0(FP), DI
MOVQ R8, (DI)
MOVQ R9, 8(DI)
MOVQ R10, 16(DI)
MOVQ R11, 24(DI)
MOVQ R12, 32(DI)
MOVQ R13, 40(DI)
RET
/* | end */
// subtraction w/ modular reduction
// a = (a - b) % p
TEXT ·subAssign(SB), NOSPLIT, $0-16
// |
MOVQ a+0(FP), DI
MOVQ b+8(FP), SI
XORQ AX, AX
// |
MOVQ (DI), R8
MOVQ 8(DI), R9
MOVQ 16(DI), R10
MOVQ 24(DI), R11
MOVQ 32(DI), R12
MOVQ 40(DI), R13
SUBQ (SI), R8
SBBQ 8(SI), R9
SBBQ 16(SI), R10
SBBQ 24(SI), R11
SBBQ 32(SI), R12
SBBQ 40(SI), R13
// |
MOVQ $0xb9feffffffffaaab, R14
MOVQ $0x1eabfffeb153ffff, R15
MOVQ $0x6730d2a0f6b0f624, CX
MOVQ $0x64774b84f38512bf, DX
MOVQ $0x4b1ba7b6434bacd7, SI
MOVQ $0x1a0111ea397fe69a, BX
CMOVQCC AX, R14
CMOVQCC AX, R15
CMOVQCC AX, CX
CMOVQCC AX, DX
CMOVQCC AX, SI
CMOVQCC AX, BX
ADDQ R14, R8
ADCQ R15, R9
ADCQ CX, R10
ADCQ DX, R11
ADCQ SI, R12
ADCQ BX, R13
// |
MOVQ a+0(FP), DI
MOVQ R8, (DI)
MOVQ R9, 8(DI)
MOVQ R10, 16(DI)
MOVQ R11, 24(DI)
MOVQ R12, 32(DI)
MOVQ R13, 40(DI)
RET
/* | end */
// subtraction w/o reduction check
// a = (a - b)
TEXT ·lsubAssign(SB), NOSPLIT, $0-16
// |
MOVQ a+0(FP), DI
MOVQ b+8(FP), SI
// |
MOVQ (DI), R8
MOVQ 8(DI), R9
MOVQ 16(DI), R10
MOVQ 24(DI), R11
MOVQ 32(DI), R12
MOVQ 40(DI), R13
SUBQ (SI), R8
SBBQ 8(SI), R9
SBBQ 16(SI), R10
SBBQ 24(SI), R11
SBBQ 32(SI), R12
SBBQ 40(SI), R13
// |
MOVQ a+0(FP), DI
MOVQ R8, (DI)
MOVQ R9, 8(DI)
MOVQ R10, 16(DI)
MOVQ R11, 24(DI)
MOVQ R12, 32(DI)
MOVQ R13, 40(DI)
RET
/* | end */
// doubling w/ reduction
// c = (2 * a) % p
TEXT ·double(SB), NOSPLIT, $0-16
// |
MOVQ a+8(FP), DI
MOVQ (DI), R8
MOVQ 8(DI), R9
MOVQ 16(DI), R10
MOVQ 24(DI), R11
MOVQ 32(DI), R12
MOVQ 40(DI), R13
ADDQ R8, R8
ADCQ R9, R9
ADCQ R10, R10
ADCQ R11, R11
ADCQ R12, R12
ADCQ R13, R13
// |
MOVQ R8, R14
MOVQ R9, R15
MOVQ R10, CX
MOVQ R11, DX
MOVQ R12, SI
MOVQ R13, BX
MOVQ $0xb9feffffffffaaab, DI
SUBQ DI, R14
MOVQ $0x1eabfffeb153ffff, DI
SBBQ DI, R15
MOVQ $0x6730d2a0f6b0f624, DI
SBBQ DI, CX
MOVQ $0x64774b84f38512bf, DI
SBBQ DI, DX
MOVQ $0x4b1ba7b6434bacd7, DI
SBBQ DI, SI
MOVQ $0x1a0111ea397fe69a, DI
SBBQ DI, BX
CMOVQCC R14, R8
CMOVQCC R15, R9
CMOVQCC CX, R10
CMOVQCC DX, R11
CMOVQCC SI, R12
CMOVQCC BX, R13
// |
MOVQ c+0(FP), DI
MOVQ R8, (DI)
MOVQ R9, 8(DI)
MOVQ R10, 16(DI)
MOVQ R11, 24(DI)
MOVQ R12, 32(DI)
MOVQ R13, 40(DI)
RET
/* | end */
// doubling w/ reduction
// a = (2 * a) % p
TEXT ·doubleAssign(SB), NOSPLIT, $0-8
// |
MOVQ a+0(FP), DI
MOVQ (DI), R8
MOVQ 8(DI), R9
MOVQ 16(DI), R10
MOVQ 24(DI), R11
MOVQ 32(DI), R12
MOVQ 40(DI), R13
ADDQ R8, R8
ADCQ R9, R9
ADCQ R10, R10
ADCQ R11, R11
ADCQ R12, R12
ADCQ R13, R13
// |
MOVQ R8, R14
MOVQ R9, R15
MOVQ R10, CX
MOVQ R11, DX
MOVQ R12, SI
MOVQ R13, BX
MOVQ $0xb9feffffffffaaab, AX
SUBQ AX, R14
MOVQ $0x1eabfffeb153ffff, AX
SBBQ AX, R15
MOVQ $0x6730d2a0f6b0f624, AX
SBBQ AX, CX
MOVQ $0x64774b84f38512bf, AX
SBBQ AX, DX
MOVQ $0x4b1ba7b6434bacd7, AX
SBBQ AX, SI
MOVQ $0x1a0111ea397fe69a, AX
SBBQ AX, BX
CMOVQCC R14, R8
CMOVQCC R15, R9
CMOVQCC CX, R10
CMOVQCC DX, R11
CMOVQCC SI, R12
CMOVQCC BX, R13
MOVQ R8, (DI)
MOVQ R9, 8(DI)
MOVQ R10, 16(DI)
MOVQ R11, 24(DI)
MOVQ R12, 32(DI)
MOVQ R13, 40(DI)
RET
/* | end */
// doubling w/o reduction
// c = 2 * a
TEXT ·ldouble(SB), NOSPLIT, $0-16
// |
MOVQ a+8(FP), DI
MOVQ (DI), R8
MOVQ 8(DI), R9
MOVQ 16(DI), R10
MOVQ 24(DI), R11
MOVQ 32(DI), R12
MOVQ 40(DI), R13
// |
ADDQ R8, R8
ADCQ R9, R9
ADCQ R10, R10
ADCQ R11, R11
ADCQ R12, R12
ADCQ R13, R13
// |
MOVQ c+0(FP), DI
MOVQ R8, (DI)
MOVQ R9, 8(DI)
MOVQ R10, 16(DI)
MOVQ R11, 24(DI)
MOVQ R12, 32(DI)
MOVQ R13, 40(DI)
RET
/* | end */
TEXT ·_neg(SB), NOSPLIT, $0-16
// |
MOVQ a+8(FP), DI
// |
MOVQ $0xb9feffffffffaaab, R8
MOVQ $0x1eabfffeb153ffff, R9
MOVQ $0x6730d2a0f6b0f624, R10
MOVQ $0x64774b84f38512bf, R11
MOVQ $0x4b1ba7b6434bacd7, R12
MOVQ $0x1a0111ea397fe69a, R13
SUBQ (DI), R8
SBBQ 8(DI), R9
SBBQ 16(DI), R10
SBBQ 24(DI), R11
SBBQ 32(DI), R12
SBBQ 40(DI), R13
// |
MOVQ c+0(FP), DI
MOVQ R8, (DI)
MOVQ R9, 8(DI)
MOVQ R10, 16(DI)
MOVQ R11, 24(DI)
MOVQ R12, 32(DI)
MOVQ R13, 40(DI)
RET
/* | end */
// multiplication without using MULX/ADX
// c = a * b % p
TEXT ·mulNoADX(SB), NOSPLIT, $24-24
// |
/* inputs */
MOVQ a+8(FP), DI
MOVQ b+16(FP), SI
MOVQ $0x00, R9
MOVQ $0x00, R10
MOVQ $0x00, R11
MOVQ $0x00, R12
MOVQ $0x00, R13
MOVQ $0x00, R14
MOVQ $0x00, R15
// |
/* i0 */
// | a0 @ CX
MOVQ (DI), CX
// | a0 * b0
MOVQ (SI), AX
MULQ CX
MOVQ AX, (SP)
MOVQ DX, R8
// | a0 * b1
MOVQ 8(SI), AX
MULQ CX
ADDQ AX, R8
ADCQ DX, R9
// | a0 * b2
MOVQ 16(SI), AX
MULQ CX
ADDQ AX, R9
ADCQ DX, R10
// | a0 * b3
MOVQ 24(SI), AX
MULQ CX
ADDQ AX, R10
ADCQ DX, R11
// | a0 * b4
MOVQ 32(SI), AX
MULQ CX
ADDQ AX, R11
ADCQ DX, R12
// | a0 * b5
MOVQ 40(SI), AX
MULQ CX
ADDQ AX, R12
ADCQ DX, R13
// |
/* i1 */
// | a1 @ CX
MOVQ 8(DI), CX
MOVQ $0x00, BX
// | a1 * b0
MOVQ (SI), AX
MULQ CX
ADDQ AX, R8
ADCQ DX, R9
ADCQ $0x00, R10
ADCQ $0x00, BX
MOVQ R8, 8(SP)
MOVQ $0x00, R8
// | a1 * b1
MOVQ 8(SI), AX
MULQ CX
ADDQ AX, R9
ADCQ DX, R10
ADCQ BX, R11
MOVQ $0x00, BX
ADCQ $0x00, BX
// | a1 * b2
MOVQ 16(SI), AX
MULQ CX
ADDQ AX, R10
ADCQ DX, R11
ADCQ BX, R12
MOVQ $0x00, BX
ADCQ $0x00, BX
// | a1 * b3
MOVQ 24(SI), AX
MULQ CX
ADDQ AX, R11
ADCQ DX, R12
ADCQ BX, R13
MOVQ $0x00, BX
ADCQ $0x00, BX
// | a1 * b4
MOVQ 32(SI), AX
MULQ CX
ADDQ AX, R12
ADCQ DX, R13
ADCQ BX, R14
// | a1 * b5
MOVQ 40(SI), AX
MULQ CX
ADDQ AX, R13
ADCQ DX, R14
// |
/* i2 */
// | a2 @ CX
MOVQ 16(DI), CX
MOVQ $0x00, BX
// | a2 * b0
MOVQ (SI), AX
MULQ CX
ADDQ AX, R9
ADCQ DX, R10
ADCQ $0x00, R11
ADCQ $0x00, BX
MOVQ R9, 16(SP)
MOVQ $0x00, R9
// | a2 * b1
MOVQ 8(SI), AX
MULQ CX
ADDQ AX, R10
ADCQ DX, R11
ADCQ BX, R12
MOVQ $0x00, BX
ADCQ $0x00, BX
// | a2 * b2
MOVQ 16(SI), AX
MULQ CX
ADDQ AX, R11
ADCQ DX, R12
ADCQ BX, R13
MOVQ $0x00, BX
ADCQ $0x00, BX
// | a2 * b3
MOVQ 24(SI), AX
MULQ CX
ADDQ AX, R12
ADCQ DX, R13
ADCQ BX, R14
MOVQ $0x00, BX
ADCQ $0x00, BX
// | a2 * b4
MOVQ 32(SI), AX
MULQ CX
ADDQ AX, R13
ADCQ DX, R14
ADCQ BX, R15
// | a2 * b5
MOVQ 40(SI), AX
MULQ CX
ADDQ AX, R14
ADCQ DX, R15
// |
/* i3 */
// | a3 @ CX
MOVQ 24(DI), CX
MOVQ $0x00, BX
// | a3 * b0
MOVQ (SI), AX
MULQ CX
ADDQ AX, R10
ADCQ DX, R11
ADCQ $0x00, R12
ADCQ $0x00, BX
// | a3 * b1
MOVQ 8(SI), AX
MULQ CX
ADDQ AX, R11
ADCQ DX, R12
ADCQ BX, R13
MOVQ $0x00, BX
ADCQ $0x00, BX
// | a3 * b2
MOVQ 16(SI), AX
MULQ CX
ADDQ AX, R12
ADCQ DX, R13
ADCQ BX, R14
MOVQ $0x00, BX
ADCQ $0x00, BX
// | a3 * b3
MOVQ 24(SI), AX
MULQ CX
ADDQ AX, R13
ADCQ DX, R14
ADCQ BX, R15
MOVQ $0x00, BX
ADCQ $0x00, BX
// | a3 * b4
MOVQ 32(SI), AX
MULQ CX
ADDQ AX, R14
ADCQ DX, R15
ADCQ BX, R8
// | a3 * b5
MOVQ 40(SI), AX
MULQ CX
ADDQ AX, R15
ADCQ DX, R8
// |
/* i4 */
// | a4 @ CX
MOVQ 32(DI), CX
MOVQ $0x00, BX
// | a4 * b0
MOVQ (SI), AX
MULQ CX
ADDQ AX, R11
ADCQ DX, R12
ADCQ $0x00, R13
ADCQ $0x00, BX
// | a4 * b1
MOVQ 8(SI), AX
MULQ CX
ADDQ AX, R12
ADCQ DX, R13
ADCQ BX, R14
MOVQ $0x00, BX
ADCQ $0x00, BX
// | a4 * b2
MOVQ 16(SI), AX
MULQ CX
ADDQ AX, R13
ADCQ DX, R14
ADCQ BX, R15
MOVQ $0x00, BX
ADCQ $0x00, BX
// | a4 * b3
MOVQ 24(SI), AX
MULQ CX
ADDQ AX, R14
ADCQ DX, R15
ADCQ BX, R8
MOVQ $0x00, BX
ADCQ $0x00, BX
// | a4 * b4
MOVQ 32(SI), AX
MULQ CX
ADDQ AX, R15
ADCQ DX, R8
ADCQ BX, R9
// | a4 * b5
MOVQ 40(SI), AX
MULQ CX
ADDQ AX, R8
ADCQ DX, R9
// |
/* i5 */
// | a5 @ CX
MOVQ 40(DI), CX
MOVQ $0x00, BX
// | a5 * b0
MOVQ (SI), AX
MULQ CX
ADDQ AX, R12
ADCQ DX, R13
ADCQ $0x00, R14
ADCQ $0x00, BX
// | a5 * b1
MOVQ 8(SI), AX
MULQ CX
ADDQ AX, R13
ADCQ DX, R14
ADCQ BX, R15
MOVQ $0x00, BX
ADCQ $0x00, BX
// | a5 * b2
MOVQ 16(SI), AX
MULQ CX
ADDQ AX, R14
ADCQ DX, R15
ADCQ BX, R8
MOVQ $0x00, BX
ADCQ $0x00, BX
// | a5 * b3
MOVQ 24(SI), AX
MULQ CX
ADDQ AX, R15
ADCQ DX, R8
ADCQ BX, R9
MOVQ $0x00, BX
ADCQ $0x00, BX
// | a5 * b4
MOVQ 32(SI), AX
MULQ CX
ADDQ AX, R8
ADCQ DX, R9
ADCQ $0x00, BX
// | a5 * b5
MOVQ 40(SI), AX
MULQ CX
ADDQ AX, R9
ADCQ DX, BX
// |
/* */
// |
// | W
// | 0 (SP) | 1 8(SP) | 2 16(SP) | 3 R10 | 4 R11 | 5 R12
// | 6 R13 | 7 R14 | 8 R15 | 9 R8 | 10 R9 | 11 BX
MOVQ (SP), CX
MOVQ 8(SP), DI
MOVQ 16(SP), SI
MOVQ BX, (SP)
MOVQ R9, 8(SP)
// |
/* montgomery reduction */
// |
/* i0 */
// |
// | W
// | 0 CX | 1 DI | 2 SI | 3 R10 | 4 R11 | 5 R12
// | 6 R13 | 7 R14 | 8 R15 | 9 R8 | 10 8(SP) | 11 (SP)
// | | u0 = w0 * inp
MOVQ CX, AX
MULQ ·inp+0(SB)
MOVQ AX, R9
MOVQ $0x00, BX
// |
/* */
// | j0
// | w0 @ CX
MOVQ ·modulus+0(SB), AX
MULQ R9
ADDQ AX, CX
ADCQ DX, BX
// | j1
// | w1 @ DI
MOVQ ·modulus+8(SB), AX
MULQ R9
ADDQ AX, DI
ADCQ $0x00, DX
ADDQ BX, DI
MOVQ $0x00, BX
ADCQ DX, BX
// | j2
// | w2 @ SI
MOVQ ·modulus+16(SB), AX
MULQ R9
ADDQ AX, SI
ADCQ $0x00, DX
ADDQ BX, SI
MOVQ $0x00, BX
ADCQ DX, BX
// | j3
// | w3 @ R10
MOVQ ·modulus+24(SB), AX
MULQ R9
ADDQ AX, R10
ADCQ $0x00, DX
ADDQ BX, R10
MOVQ $0x00, BX
ADCQ DX, BX
// | j4
// | w4 @ R11
MOVQ ·modulus+32(SB), AX
MULQ R9
ADDQ AX, R11
ADCQ $0x00, DX
ADDQ BX, R11
MOVQ $0x00, BX
ADCQ DX, BX
// | j5
// | w5 @ R12
MOVQ ·modulus+40(SB), AX
MULQ R9
ADDQ AX, R12
ADCQ $0x00, DX
ADDQ BX, R12
// | w6 @ R13
ADCQ DX, R13
ADCQ $0x00, CX
// |
/* i1 */
// |
// | W
// | 0 - | 1 DI | 2 SI | 3 R10 | 4 R11 | 5 R12
// | 6 R13 | 7 R14 | 8 R15 | 9 R8 | 10 8(SP) | 11 (SP)
// | | u1 = w1 * inp
MOVQ DI, AX
MULQ ·inp+0(SB)
MOVQ AX, R9
MOVQ $0x00, BX
// |
/* */
// | j0
// | w1 @ DI
MOVQ ·modulus+0(SB), AX
MULQ R9
ADDQ AX, DI
ADCQ DX, BX
// | j1
// | w2 @ SI
MOVQ ·modulus+8(SB), AX
MULQ R9
ADDQ AX, SI
ADCQ $0x00, DX
ADDQ BX, SI
MOVQ $0x00, BX
ADCQ DX, BX