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695 lines
13 KiB
695 lines
13 KiB
// Code generated by goff (v0.2.0) DO NOT EDIT
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#include "textflag.h"
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// func MulAssignElement(res,y *Element)
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// montgomery multiplication of res by y
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// stores the result in res
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TEXT ·MulAssignElement(SB), NOSPLIT, $0-16
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// dereference our parameters
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MOVQ res+0(FP), DI
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MOVQ y+8(FP), R8
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// check if we support adx and mulx
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CMPB ·supportAdx(SB), $1
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JNE no_adx
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// the algorithm is described here
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// https://hackmd.io/@zkteam/modular_multiplication
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// however, to benefit from the ADCX and ADOX carry chains
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// we split the inner loops in 2:
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// for i=0 to N-1
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// for j=0 to N-1
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// (A,t[j]) := t[j] + a[j]*b[i] + A
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// m := t[0]*q'[0] mod W
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// C,_ := t[0] + m*q[0]
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// for j=1 to N-1
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// (C,t[j-1]) := t[j] + m*q[j] + C
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// t[N-1] = C + A
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// ---------------------------------------------------------------------------------------------
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// outter loop 0
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// clear up the carry flags
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XORQ R9 , R9
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// R12 = y[0]
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MOVQ 0(R8), R12
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// for j=0 to N-1
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// (A,t[j]) := t[j] + x[j]*y[i] + A
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// DX = res[0]
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MOVQ 0(DI), DX
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MULXQ R12, CX , R9
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// DX = res[1]
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MOVQ 8(DI), DX
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MOVQ R9, BX
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MULXQ R12, AX, R9
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ADOXQ AX, BX
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// DX = res[2]
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MOVQ 16(DI), DX
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MOVQ R9, BP
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MULXQ R12, AX, R9
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ADOXQ AX, BP
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// DX = res[3]
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MOVQ 24(DI), DX
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MOVQ R9, SI
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MULXQ R12, AX, R9
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ADOXQ AX, SI
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// add the last carries to R9
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MOVQ $0, DX
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ADCXQ DX, R9
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ADOXQ DX, R9
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// m := t[0]*q'[0] mod W
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MOVQ $0xc2e1f593efffffff, DX
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MULXQ CX,R11, DX
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// clear the carry flags
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XORQ DX, DX
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// C,_ := t[0] + m*q[0]
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MOVQ $0x43e1f593f0000001, DX
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MULXQ R11, AX, R10
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ADCXQ CX ,AX
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// for j=1 to N-1
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// (C,t[j-1]) := t[j] + m*q[j] + C
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MOVQ $0x2833e84879b97091, DX
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MULXQ R11, AX, DX
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ADCXQ BX, R10
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ADOXQ AX, R10
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MOVQ R10, CX
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MOVQ DX, R10
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MOVQ $0xb85045b68181585d, DX
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MULXQ R11, AX, DX
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ADCXQ BP, R10
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ADOXQ AX, R10
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MOVQ R10, BX
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MOVQ DX, R10
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MOVQ $0x30644e72e131a029, DX
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MULXQ R11, AX, DX
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ADCXQ SI, R10
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ADOXQ AX, R10
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MOVQ R10, BP
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MOVQ $0, AX
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ADCXQ AX, DX
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ADOXQ DX, R9
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MOVQ R9, SI
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// ---------------------------------------------------------------------------------------------
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// outter loop 1
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// clear up the carry flags
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XORQ R9 , R9
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// R12 = y[1]
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MOVQ 8(R8), R12
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// for j=0 to N-1
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// (A,t[j]) := t[j] + x[j]*y[i] + A
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// DX = res[0]
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MOVQ 0(DI), DX
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MULXQ R12, AX, R9
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ADOXQ AX, CX
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// DX = res[1]
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MOVQ 8(DI), DX
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ADCXQ R9, BX
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MULXQ R12, AX, R9
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ADOXQ AX, BX
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// DX = res[2]
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MOVQ 16(DI), DX
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ADCXQ R9, BP
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MULXQ R12, AX, R9
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ADOXQ AX, BP
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// DX = res[3]
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MOVQ 24(DI), DX
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ADCXQ R9, SI
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MULXQ R12, AX, R9
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ADOXQ AX, SI
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// add the last carries to R9
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MOVQ $0, DX
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ADCXQ DX, R9
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ADOXQ DX, R9
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// m := t[0]*q'[0] mod W
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MOVQ $0xc2e1f593efffffff, DX
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MULXQ CX,R11, DX
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// clear the carry flags
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XORQ DX, DX
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// C,_ := t[0] + m*q[0]
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MOVQ $0x43e1f593f0000001, DX
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MULXQ R11, AX, R10
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ADCXQ CX ,AX
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// for j=1 to N-1
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// (C,t[j-1]) := t[j] + m*q[j] + C
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MOVQ $0x2833e84879b97091, DX
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MULXQ R11, AX, DX
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ADCXQ BX, R10
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ADOXQ AX, R10
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MOVQ R10, CX
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MOVQ DX, R10
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MOVQ $0xb85045b68181585d, DX
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MULXQ R11, AX, DX
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ADCXQ BP, R10
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ADOXQ AX, R10
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MOVQ R10, BX
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MOVQ DX, R10
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MOVQ $0x30644e72e131a029, DX
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MULXQ R11, AX, DX
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ADCXQ SI, R10
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ADOXQ AX, R10
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MOVQ R10, BP
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MOVQ $0, AX
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ADCXQ AX, DX
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ADOXQ DX, R9
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MOVQ R9, SI
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// ---------------------------------------------------------------------------------------------
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// outter loop 2
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// clear up the carry flags
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XORQ R9 , R9
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// R12 = y[2]
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MOVQ 16(R8), R12
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// for j=0 to N-1
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// (A,t[j]) := t[j] + x[j]*y[i] + A
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// DX = res[0]
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MOVQ 0(DI), DX
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MULXQ R12, AX, R9
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ADOXQ AX, CX
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// DX = res[1]
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MOVQ 8(DI), DX
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ADCXQ R9, BX
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MULXQ R12, AX, R9
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ADOXQ AX, BX
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// DX = res[2]
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MOVQ 16(DI), DX
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ADCXQ R9, BP
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MULXQ R12, AX, R9
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ADOXQ AX, BP
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// DX = res[3]
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MOVQ 24(DI), DX
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ADCXQ R9, SI
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MULXQ R12, AX, R9
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ADOXQ AX, SI
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// add the last carries to R9
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MOVQ $0, DX
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ADCXQ DX, R9
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ADOXQ DX, R9
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// m := t[0]*q'[0] mod W
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MOVQ $0xc2e1f593efffffff, DX
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MULXQ CX,R11, DX
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// clear the carry flags
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XORQ DX, DX
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// C,_ := t[0] + m*q[0]
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MOVQ $0x43e1f593f0000001, DX
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MULXQ R11, AX, R10
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ADCXQ CX ,AX
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// for j=1 to N-1
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// (C,t[j-1]) := t[j] + m*q[j] + C
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MOVQ $0x2833e84879b97091, DX
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MULXQ R11, AX, DX
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ADCXQ BX, R10
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ADOXQ AX, R10
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MOVQ R10, CX
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MOVQ DX, R10
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MOVQ $0xb85045b68181585d, DX
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MULXQ R11, AX, DX
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ADCXQ BP, R10
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ADOXQ AX, R10
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MOVQ R10, BX
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MOVQ DX, R10
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MOVQ $0x30644e72e131a029, DX
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MULXQ R11, AX, DX
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ADCXQ SI, R10
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ADOXQ AX, R10
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MOVQ R10, BP
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MOVQ $0, AX
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ADCXQ AX, DX
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ADOXQ DX, R9
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MOVQ R9, SI
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// ---------------------------------------------------------------------------------------------
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// outter loop 3
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// clear up the carry flags
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XORQ R9 , R9
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// R12 = y[3]
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MOVQ 24(R8), R12
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// for j=0 to N-1
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// (A,t[j]) := t[j] + x[j]*y[i] + A
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// DX = res[0]
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MOVQ 0(DI), DX
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MULXQ R12, AX, R9
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ADOXQ AX, CX
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// DX = res[1]
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MOVQ 8(DI), DX
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ADCXQ R9, BX
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MULXQ R12, AX, R9
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ADOXQ AX, BX
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// DX = res[2]
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MOVQ 16(DI), DX
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ADCXQ R9, BP
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MULXQ R12, AX, R9
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ADOXQ AX, BP
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// DX = res[3]
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MOVQ 24(DI), DX
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ADCXQ R9, SI
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MULXQ R12, AX, R9
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ADOXQ AX, SI
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// add the last carries to R9
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MOVQ $0, DX
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ADCXQ DX, R9
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ADOXQ DX, R9
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// m := t[0]*q'[0] mod W
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MOVQ $0xc2e1f593efffffff, DX
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MULXQ CX,R11, DX
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// clear the carry flags
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XORQ DX, DX
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// C,_ := t[0] + m*q[0]
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MOVQ $0x43e1f593f0000001, DX
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MULXQ R11, AX, R10
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ADCXQ CX ,AX
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// for j=1 to N-1
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// (C,t[j-1]) := t[j] + m*q[j] + C
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MOVQ $0x2833e84879b97091, DX
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MULXQ R11, AX, DX
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ADCXQ BX, R10
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ADOXQ AX, R10
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MOVQ R10, CX
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MOVQ DX, R10
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MOVQ $0xb85045b68181585d, DX
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MULXQ R11, AX, DX
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ADCXQ BP, R10
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ADOXQ AX, R10
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MOVQ R10, BX
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MOVQ DX, R10
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MOVQ $0x30644e72e131a029, DX
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MULXQ R11, AX, DX
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ADCXQ SI, R10
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ADOXQ AX, R10
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MOVQ R10, BP
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MOVQ $0, AX
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ADCXQ AX, DX
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ADOXQ DX, R9
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MOVQ R9, SI
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reduce:
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// reduce, constant time version
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// first we copy registers storing t in a separate set of registers
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// as SUBQ modifies the 2nd operand
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MOVQ CX, DX
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MOVQ BX, R8
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MOVQ BP, R9
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MOVQ SI, R10
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MOVQ $0x43e1f593f0000001, R11
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SUBQ R11, DX
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MOVQ $0x2833e84879b97091, R11
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SBBQ R11, R8
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MOVQ $0xb85045b68181585d, R11
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SBBQ R11, R9
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MOVQ $0x30644e72e131a029, R11
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SBBQ R11, R10
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JCS t_is_smaller // no borrow, we return t
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// borrow is set, we return u
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MOVQ DX, (DI)
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MOVQ R8, 8(DI)
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MOVQ R9, 16(DI)
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MOVQ R10, 24(DI)
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RET
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t_is_smaller:
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MOVQ CX, 0(DI)
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MOVQ BX, 8(DI)
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MOVQ BP, 16(DI)
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MOVQ SI, 24(DI)
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RET
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no_adx:
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// ---------------------------------------------------------------------------------------------
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// outter loop 0
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// (A,t[0]) := t[0] + x[0]*y[0]
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MOVQ (DI), AX // x[0]
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MOVQ 0(R8), R12
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MULQ R12 // x[0] * y[0]
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MOVQ DX, R9
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MOVQ AX, CX
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// m := t[0]*q'[0] mod W
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MOVQ $0xc2e1f593efffffff, R11
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IMULQ CX , R11
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// C,_ := t[0] + m*q[0]
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MOVQ $0x43e1f593f0000001, AX
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MULQ R11
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ADDQ CX ,AX
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ADCQ $0, DX
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MOVQ DX, R10
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// for j=1 to N-1
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// (A,t[j]) := t[j] + x[j]*y[i] + A
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// (C,t[j-1]) := t[j] + m*q[j] + C
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MOVQ 8(DI), AX
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MULQ R12 // x[1] * y[0]
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MOVQ R9, BX
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ADDQ AX, BX
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ADCQ $0, DX
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MOVQ DX, R9
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MOVQ $0x2833e84879b97091, AX
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MULQ R11
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ADDQ BX, R10
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ADCQ $0, DX
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ADDQ AX, R10
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ADCQ $0, DX
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MOVQ R10, CX
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MOVQ DX, R10
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MOVQ 16(DI), AX
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MULQ R12 // x[2] * y[0]
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MOVQ R9, BP
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ADDQ AX, BP
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ADCQ $0, DX
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MOVQ DX, R9
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MOVQ $0xb85045b68181585d, AX
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MULQ R11
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ADDQ BP, R10
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ADCQ $0, DX
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ADDQ AX, R10
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ADCQ $0, DX
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MOVQ R10, BX
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MOVQ DX, R10
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MOVQ 24(DI), AX
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MULQ R12 // x[3] * y[0]
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MOVQ R9, SI
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ADDQ AX, SI
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ADCQ $0, DX
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MOVQ DX, R9
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MOVQ $0x30644e72e131a029, AX
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MULQ R11
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ADDQ SI, R10
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ADCQ $0, DX
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ADDQ AX, R10
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ADCQ $0, DX
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MOVQ R10, BP
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MOVQ DX, R10
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ADDQ R10, R9
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MOVQ R9, SI
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// ---------------------------------------------------------------------------------------------
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// outter loop 1
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// (A,t[0]) := t[0] + x[0]*y[1]
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MOVQ (DI), AX // x[0]
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MOVQ 8(R8), R12
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MULQ R12 // x[0] * y[1]
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ADDQ AX, CX
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ADCQ $0, DX
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MOVQ DX, R9
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// m := t[0]*q'[0] mod W
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MOVQ $0xc2e1f593efffffff, R11
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IMULQ CX , R11
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// C,_ := t[0] + m*q[0]
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MOVQ $0x43e1f593f0000001, AX
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MULQ R11
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ADDQ CX ,AX
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ADCQ $0, DX
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MOVQ DX, R10
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// for j=1 to N-1
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// (A,t[j]) := t[j] + x[j]*y[i] + A
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// (C,t[j-1]) := t[j] + m*q[j] + C
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MOVQ 8(DI), AX
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MULQ R12 // x[1] * y[1]
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ADDQ R9, BX
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ADCQ $0, DX
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ADDQ AX, BX
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ADCQ $0, DX
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MOVQ DX, R9
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MOVQ $0x2833e84879b97091, AX
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MULQ R11
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ADDQ BX, R10
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ADCQ $0, DX
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ADDQ AX, R10
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ADCQ $0, DX
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MOVQ R10, CX
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MOVQ DX, R10
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MOVQ 16(DI), AX
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MULQ R12 // x[2] * y[1]
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ADDQ R9, BP
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ADCQ $0, DX
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ADDQ AX, BP
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ADCQ $0, DX
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MOVQ DX, R9
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MOVQ $0xb85045b68181585d, AX
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MULQ R11
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ADDQ BP, R10
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ADCQ $0, DX
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ADDQ AX, R10
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ADCQ $0, DX
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MOVQ R10, BX
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MOVQ DX, R10
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MOVQ 24(DI), AX
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MULQ R12 // x[3] * y[1]
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ADDQ R9, SI
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ADCQ $0, DX
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ADDQ AX, SI
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ADCQ $0, DX
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MOVQ DX, R9
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MOVQ $0x30644e72e131a029, AX
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MULQ R11
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ADDQ SI, R10
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ADCQ $0, DX
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ADDQ AX, R10
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ADCQ $0, DX
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MOVQ R10, BP
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MOVQ DX, R10
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ADDQ R10, R9
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MOVQ R9, SI
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// ---------------------------------------------------------------------------------------------
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// outter loop 2
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// (A,t[0]) := t[0] + x[0]*y[2]
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MOVQ (DI), AX // x[0]
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MOVQ 16(R8), R12
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MULQ R12 // x[0] * y[2]
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ADDQ AX, CX
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ADCQ $0, DX
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MOVQ DX, R9
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// m := t[0]*q'[0] mod W
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MOVQ $0xc2e1f593efffffff, R11
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IMULQ CX , R11
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// C,_ := t[0] + m*q[0]
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|
MOVQ $0x43e1f593f0000001, AX
|
|
MULQ R11
|
|
ADDQ CX ,AX
|
|
ADCQ $0, DX
|
|
MOVQ DX, R10
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|
|
|
// for j=1 to N-1
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// (A,t[j]) := t[j] + x[j]*y[i] + A
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// (C,t[j-1]) := t[j] + m*q[j] + C
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|
MOVQ 8(DI), AX
|
|
MULQ R12 // x[1] * y[2]
|
|
ADDQ R9, BX
|
|
ADCQ $0, DX
|
|
ADDQ AX, BX
|
|
ADCQ $0, DX
|
|
MOVQ DX, R9
|
|
|
|
MOVQ $0x2833e84879b97091, AX
|
|
MULQ R11
|
|
ADDQ BX, R10
|
|
ADCQ $0, DX
|
|
ADDQ AX, R10
|
|
ADCQ $0, DX
|
|
|
|
MOVQ R10, CX
|
|
MOVQ DX, R10
|
|
MOVQ 16(DI), AX
|
|
MULQ R12 // x[2] * y[2]
|
|
ADDQ R9, BP
|
|
ADCQ $0, DX
|
|
ADDQ AX, BP
|
|
ADCQ $0, DX
|
|
MOVQ DX, R9
|
|
|
|
MOVQ $0xb85045b68181585d, AX
|
|
MULQ R11
|
|
ADDQ BP, R10
|
|
ADCQ $0, DX
|
|
ADDQ AX, R10
|
|
ADCQ $0, DX
|
|
|
|
MOVQ R10, BX
|
|
MOVQ DX, R10
|
|
MOVQ 24(DI), AX
|
|
MULQ R12 // x[3] * y[2]
|
|
ADDQ R9, SI
|
|
ADCQ $0, DX
|
|
ADDQ AX, SI
|
|
ADCQ $0, DX
|
|
MOVQ DX, R9
|
|
|
|
MOVQ $0x30644e72e131a029, AX
|
|
MULQ R11
|
|
ADDQ SI, R10
|
|
ADCQ $0, DX
|
|
ADDQ AX, R10
|
|
ADCQ $0, DX
|
|
|
|
MOVQ R10, BP
|
|
MOVQ DX, R10
|
|
|
|
ADDQ R10, R9
|
|
MOVQ R9, SI
|
|
|
|
// ---------------------------------------------------------------------------------------------
|
|
// outter loop 3
|
|
|
|
// (A,t[0]) := t[0] + x[0]*y[3]
|
|
MOVQ (DI), AX // x[0]
|
|
MOVQ 24(R8), R12
|
|
MULQ R12 // x[0] * y[3]
|
|
ADDQ AX, CX
|
|
ADCQ $0, DX
|
|
MOVQ DX, R9
|
|
|
|
// m := t[0]*q'[0] mod W
|
|
MOVQ $0xc2e1f593efffffff, R11
|
|
IMULQ CX , R11
|
|
|
|
// C,_ := t[0] + m*q[0]
|
|
MOVQ $0x43e1f593f0000001, AX
|
|
MULQ R11
|
|
ADDQ CX ,AX
|
|
ADCQ $0, DX
|
|
MOVQ DX, R10
|
|
|
|
// for j=1 to N-1
|
|
// (A,t[j]) := t[j] + x[j]*y[i] + A
|
|
// (C,t[j-1]) := t[j] + m*q[j] + C
|
|
MOVQ 8(DI), AX
|
|
MULQ R12 // x[1] * y[3]
|
|
ADDQ R9, BX
|
|
ADCQ $0, DX
|
|
ADDQ AX, BX
|
|
ADCQ $0, DX
|
|
MOVQ DX, R9
|
|
|
|
MOVQ $0x2833e84879b97091, AX
|
|
MULQ R11
|
|
ADDQ BX, R10
|
|
ADCQ $0, DX
|
|
ADDQ AX, R10
|
|
ADCQ $0, DX
|
|
|
|
MOVQ R10, CX
|
|
MOVQ DX, R10
|
|
MOVQ 16(DI), AX
|
|
MULQ R12 // x[2] * y[3]
|
|
ADDQ R9, BP
|
|
ADCQ $0, DX
|
|
ADDQ AX, BP
|
|
ADCQ $0, DX
|
|
MOVQ DX, R9
|
|
|
|
MOVQ $0xb85045b68181585d, AX
|
|
MULQ R11
|
|
ADDQ BP, R10
|
|
ADCQ $0, DX
|
|
ADDQ AX, R10
|
|
ADCQ $0, DX
|
|
|
|
MOVQ R10, BX
|
|
MOVQ DX, R10
|
|
MOVQ 24(DI), AX
|
|
MULQ R12 // x[3] * y[3]
|
|
ADDQ R9, SI
|
|
ADCQ $0, DX
|
|
ADDQ AX, SI
|
|
ADCQ $0, DX
|
|
MOVQ DX, R9
|
|
|
|
MOVQ $0x30644e72e131a029, AX
|
|
MULQ R11
|
|
ADDQ SI, R10
|
|
ADCQ $0, DX
|
|
ADDQ AX, R10
|
|
ADCQ $0, DX
|
|
|
|
MOVQ R10, BP
|
|
MOVQ DX, R10
|
|
|
|
ADDQ R10, R9
|
|
MOVQ R9, SI
|
|
|
|
JMP reduce
|