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488 lines
8.8 KiB
488 lines
8.8 KiB
// +build !amd64_adx
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// Copyright 2020 ConsenSys Software Inc.
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//
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// Licensed under the Apache License, Version 2.0 (the "License");
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// you may not use this file except in compliance with the License.
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// You may obtain a copy of the License at
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//
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// http://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS IS" BASIS,
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// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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// See the License for the specific language governing permissions and
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// limitations under the License.
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#include "textflag.h"
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#include "funcdata.h"
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// modulus q
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DATA q<>+0(SB)/8, $0x43e1f593f0000001
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DATA q<>+8(SB)/8, $0x2833e84879b97091
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DATA q<>+16(SB)/8, $0xb85045b68181585d
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DATA q<>+24(SB)/8, $0x30644e72e131a029
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GLOBL q<>(SB), (RODATA+NOPTR), $32
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// qInv0 q'[0]
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DATA qInv0<>(SB)/8, $0xc2e1f593efffffff
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GLOBL qInv0<>(SB), (RODATA+NOPTR), $8
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#define REDUCE(ra0, ra1, ra2, ra3, rb0, rb1, rb2, rb3) \
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MOVQ ra0, rb0; \
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SUBQ q<>(SB), ra0; \
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MOVQ ra1, rb1; \
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SBBQ q<>+8(SB), ra1; \
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MOVQ ra2, rb2; \
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SBBQ q<>+16(SB), ra2; \
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MOVQ ra3, rb3; \
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SBBQ q<>+24(SB), ra3; \
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CMOVQCS rb0, ra0; \
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CMOVQCS rb1, ra1; \
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CMOVQCS rb2, ra2; \
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CMOVQCS rb3, ra3; \
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// mul(res, x, y *Element)
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TEXT ·mul(SB), $24-24
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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] + x[j]*y[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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NO_LOCAL_POINTERS
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CMPB ·supportAdx(SB), $1
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JNE l1
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MOVQ x+8(FP), SI
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// x[0] -> DI
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// x[1] -> R8
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// x[2] -> R9
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// x[3] -> R10
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MOVQ 0(SI), DI
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MOVQ 8(SI), R8
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MOVQ 16(SI), R9
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MOVQ 24(SI), R10
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MOVQ y+16(FP), R11
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// A -> BP
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// t[0] -> R14
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// t[1] -> R15
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// t[2] -> CX
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// t[3] -> BX
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// clear the flags
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XORQ AX, AX
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MOVQ 0(R11), DX
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// (A,t[0]) := x[0]*y[0] + A
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MULXQ DI, R14, R15
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// (A,t[1]) := x[1]*y[0] + A
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MULXQ R8, AX, CX
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ADOXQ AX, R15
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// (A,t[2]) := x[2]*y[0] + A
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MULXQ R9, AX, BX
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ADOXQ AX, CX
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// (A,t[3]) := x[3]*y[0] + A
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MULXQ R10, AX, BP
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ADOXQ AX, BX
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// A += carries from ADCXQ and ADOXQ
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MOVQ $0, AX
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ADOXQ AX, BP
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// m := t[0]*q'[0] mod W
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MOVQ qInv0<>(SB), DX
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IMULQ R14, DX
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// clear the flags
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XORQ AX, AX
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// C,_ := t[0] + m*q[0]
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MULXQ q<>+0(SB), AX, R12
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ADCXQ R14, AX
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MOVQ R12, R14
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// (C,t[0]) := t[1] + m*q[1] + C
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ADCXQ R15, R14
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MULXQ q<>+8(SB), AX, R15
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ADOXQ AX, R14
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// (C,t[1]) := t[2] + m*q[2] + C
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ADCXQ CX, R15
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MULXQ q<>+16(SB), AX, CX
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ADOXQ AX, R15
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// (C,t[2]) := t[3] + m*q[3] + C
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ADCXQ BX, CX
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MULXQ q<>+24(SB), AX, BX
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ADOXQ AX, CX
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// t[3] = C + A
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MOVQ $0, AX
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ADCXQ AX, BX
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ADOXQ BP, BX
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// clear the flags
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XORQ AX, AX
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MOVQ 8(R11), DX
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// (A,t[0]) := t[0] + x[0]*y[1] + A
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MULXQ DI, AX, BP
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ADOXQ AX, R14
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// (A,t[1]) := t[1] + x[1]*y[1] + A
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ADCXQ BP, R15
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MULXQ R8, AX, BP
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ADOXQ AX, R15
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// (A,t[2]) := t[2] + x[2]*y[1] + A
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ADCXQ BP, CX
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MULXQ R9, AX, BP
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ADOXQ AX, CX
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// (A,t[3]) := t[3] + x[3]*y[1] + A
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ADCXQ BP, BX
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MULXQ R10, AX, BP
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ADOXQ AX, BX
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// A += carries from ADCXQ and ADOXQ
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MOVQ $0, AX
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ADCXQ AX, BP
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ADOXQ AX, BP
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// m := t[0]*q'[0] mod W
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MOVQ qInv0<>(SB), DX
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IMULQ R14, DX
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// clear the flags
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XORQ AX, AX
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// C,_ := t[0] + m*q[0]
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MULXQ q<>+0(SB), AX, R12
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ADCXQ R14, AX
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MOVQ R12, R14
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// (C,t[0]) := t[1] + m*q[1] + C
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ADCXQ R15, R14
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MULXQ q<>+8(SB), AX, R15
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ADOXQ AX, R14
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// (C,t[1]) := t[2] + m*q[2] + C
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ADCXQ CX, R15
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MULXQ q<>+16(SB), AX, CX
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ADOXQ AX, R15
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// (C,t[2]) := t[3] + m*q[3] + C
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ADCXQ BX, CX
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MULXQ q<>+24(SB), AX, BX
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ADOXQ AX, CX
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// t[3] = C + A
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MOVQ $0, AX
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ADCXQ AX, BX
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ADOXQ BP, BX
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// clear the flags
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XORQ AX, AX
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MOVQ 16(R11), DX
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// (A,t[0]) := t[0] + x[0]*y[2] + A
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MULXQ DI, AX, BP
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ADOXQ AX, R14
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// (A,t[1]) := t[1] + x[1]*y[2] + A
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ADCXQ BP, R15
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MULXQ R8, AX, BP
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ADOXQ AX, R15
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// (A,t[2]) := t[2] + x[2]*y[2] + A
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ADCXQ BP, CX
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MULXQ R9, AX, BP
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ADOXQ AX, CX
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// (A,t[3]) := t[3] + x[3]*y[2] + A
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ADCXQ BP, BX
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MULXQ R10, AX, BP
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ADOXQ AX, BX
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// A += carries from ADCXQ and ADOXQ
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MOVQ $0, AX
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ADCXQ AX, BP
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ADOXQ AX, BP
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// m := t[0]*q'[0] mod W
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MOVQ qInv0<>(SB), DX
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IMULQ R14, DX
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// clear the flags
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XORQ AX, AX
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// C,_ := t[0] + m*q[0]
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MULXQ q<>+0(SB), AX, R12
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ADCXQ R14, AX
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MOVQ R12, R14
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// (C,t[0]) := t[1] + m*q[1] + C
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ADCXQ R15, R14
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MULXQ q<>+8(SB), AX, R15
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ADOXQ AX, R14
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// (C,t[1]) := t[2] + m*q[2] + C
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ADCXQ CX, R15
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MULXQ q<>+16(SB), AX, CX
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ADOXQ AX, R15
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// (C,t[2]) := t[3] + m*q[3] + C
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ADCXQ BX, CX
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MULXQ q<>+24(SB), AX, BX
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ADOXQ AX, CX
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// t[3] = C + A
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MOVQ $0, AX
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ADCXQ AX, BX
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ADOXQ BP, BX
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// clear the flags
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XORQ AX, AX
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MOVQ 24(R11), DX
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// (A,t[0]) := t[0] + x[0]*y[3] + A
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MULXQ DI, AX, BP
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ADOXQ AX, R14
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// (A,t[1]) := t[1] + x[1]*y[3] + A
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ADCXQ BP, R15
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MULXQ R8, AX, BP
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ADOXQ AX, R15
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// (A,t[2]) := t[2] + x[2]*y[3] + A
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ADCXQ BP, CX
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MULXQ R9, AX, BP
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ADOXQ AX, CX
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// (A,t[3]) := t[3] + x[3]*y[3] + A
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ADCXQ BP, BX
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MULXQ R10, AX, BP
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ADOXQ AX, BX
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// A += carries from ADCXQ and ADOXQ
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MOVQ $0, AX
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ADCXQ AX, BP
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ADOXQ AX, BP
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// m := t[0]*q'[0] mod W
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MOVQ qInv0<>(SB), DX
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IMULQ R14, DX
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// clear the flags
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XORQ AX, AX
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// C,_ := t[0] + m*q[0]
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MULXQ q<>+0(SB), AX, R12
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ADCXQ R14, AX
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MOVQ R12, R14
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// (C,t[0]) := t[1] + m*q[1] + C
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ADCXQ R15, R14
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MULXQ q<>+8(SB), AX, R15
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ADOXQ AX, R14
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// (C,t[1]) := t[2] + m*q[2] + C
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ADCXQ CX, R15
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MULXQ q<>+16(SB), AX, CX
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ADOXQ AX, R15
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// (C,t[2]) := t[3] + m*q[3] + C
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ADCXQ BX, CX
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MULXQ q<>+24(SB), AX, BX
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ADOXQ AX, CX
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// t[3] = C + A
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MOVQ $0, AX
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ADCXQ AX, BX
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ADOXQ BP, BX
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// reduce element(R14,R15,CX,BX) using temp registers (R13,SI,R12,R11)
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REDUCE(R14,R15,CX,BX,R13,SI,R12,R11)
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MOVQ res+0(FP), AX
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MOVQ R14, 0(AX)
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MOVQ R15, 8(AX)
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MOVQ CX, 16(AX)
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MOVQ BX, 24(AX)
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RET
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l1:
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MOVQ res+0(FP), AX
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MOVQ AX, (SP)
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MOVQ x+8(FP), AX
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MOVQ AX, 8(SP)
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MOVQ y+16(FP), AX
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MOVQ AX, 16(SP)
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CALL ·_mulGeneric(SB)
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RET
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TEXT ·fromMont(SB), $8-8
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NO_LOCAL_POINTERS
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// the algorithm is described here
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// https://hackmd.io/@zkteam/modular_multiplication
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// when y = 1 we have:
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// for i=0 to N-1
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// t[i] = x[i]
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// for i=0 to N-1
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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
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CMPB ·supportAdx(SB), $1
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JNE l2
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MOVQ res+0(FP), DX
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MOVQ 0(DX), R14
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MOVQ 8(DX), R15
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MOVQ 16(DX), CX
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MOVQ 24(DX), BX
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XORQ DX, DX
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// m := t[0]*q'[0] mod W
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MOVQ qInv0<>(SB), DX
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IMULQ R14, DX
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XORQ AX, AX
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// C,_ := t[0] + m*q[0]
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MULXQ q<>+0(SB), AX, BP
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ADCXQ R14, AX
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MOVQ BP, R14
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// (C,t[0]) := t[1] + m*q[1] + C
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ADCXQ R15, R14
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MULXQ q<>+8(SB), AX, R15
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ADOXQ AX, R14
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// (C,t[1]) := t[2] + m*q[2] + C
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ADCXQ CX, R15
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MULXQ q<>+16(SB), AX, CX
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ADOXQ AX, R15
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// (C,t[2]) := t[3] + m*q[3] + C
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ADCXQ BX, CX
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MULXQ q<>+24(SB), AX, BX
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ADOXQ AX, CX
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MOVQ $0, AX
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ADCXQ AX, BX
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ADOXQ AX, BX
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XORQ DX, DX
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// m := t[0]*q'[0] mod W
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MOVQ qInv0<>(SB), DX
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IMULQ R14, DX
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XORQ AX, AX
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// C,_ := t[0] + m*q[0]
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MULXQ q<>+0(SB), AX, BP
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ADCXQ R14, AX
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MOVQ BP, R14
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// (C,t[0]) := t[1] + m*q[1] + C
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ADCXQ R15, R14
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MULXQ q<>+8(SB), AX, R15
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ADOXQ AX, R14
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// (C,t[1]) := t[2] + m*q[2] + C
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ADCXQ CX, R15
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MULXQ q<>+16(SB), AX, CX
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ADOXQ AX, R15
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// (C,t[2]) := t[3] + m*q[3] + C
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ADCXQ BX, CX
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MULXQ q<>+24(SB), AX, BX
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ADOXQ AX, CX
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MOVQ $0, AX
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ADCXQ AX, BX
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ADOXQ AX, BX
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XORQ DX, DX
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// m := t[0]*q'[0] mod W
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MOVQ qInv0<>(SB), DX
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IMULQ R14, DX
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XORQ AX, AX
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// C,_ := t[0] + m*q[0]
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MULXQ q<>+0(SB), AX, BP
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ADCXQ R14, AX
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MOVQ BP, R14
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// (C,t[0]) := t[1] + m*q[1] + C
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ADCXQ R15, R14
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MULXQ q<>+8(SB), AX, R15
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ADOXQ AX, R14
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// (C,t[1]) := t[2] + m*q[2] + C
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ADCXQ CX, R15
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MULXQ q<>+16(SB), AX, CX
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ADOXQ AX, R15
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// (C,t[2]) := t[3] + m*q[3] + C
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ADCXQ BX, CX
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MULXQ q<>+24(SB), AX, BX
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ADOXQ AX, CX
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MOVQ $0, AX
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ADCXQ AX, BX
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ADOXQ AX, BX
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XORQ DX, DX
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// m := t[0]*q'[0] mod W
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MOVQ qInv0<>(SB), DX
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IMULQ R14, DX
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XORQ AX, AX
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// C,_ := t[0] + m*q[0]
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MULXQ q<>+0(SB), AX, BP
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ADCXQ R14, AX
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MOVQ BP, R14
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// (C,t[0]) := t[1] + m*q[1] + C
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ADCXQ R15, R14
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MULXQ q<>+8(SB), AX, R15
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ADOXQ AX, R14
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// (C,t[1]) := t[2] + m*q[2] + C
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ADCXQ CX, R15
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MULXQ q<>+16(SB), AX, CX
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ADOXQ AX, R15
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// (C,t[2]) := t[3] + m*q[3] + C
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ADCXQ BX, CX
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MULXQ q<>+24(SB), AX, BX
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ADOXQ AX, CX
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MOVQ $0, AX
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ADCXQ AX, BX
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ADOXQ AX, BX
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// reduce element(R14,R15,CX,BX) using temp registers (SI,DI,R8,R9)
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REDUCE(R14,R15,CX,BX,SI,DI,R8,R9)
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MOVQ res+0(FP), AX
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MOVQ R14, 0(AX)
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MOVQ R15, 8(AX)
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MOVQ CX, 16(AX)
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MOVQ BX, 24(AX)
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RET
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l2:
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MOVQ res+0(FP), AX
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MOVQ AX, (SP)
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CALL ·_fromMontGeneric(SB)
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RET
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