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arith_arm64.s
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arith_arm64.s
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// Copyright 2013 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.
// +build !math_big_pure_go
#include "textflag.h"
// This file provides fast assembly versions for the elementary
// arithmetic operations on vectors implemented in arith.go.
// TODO: Consider re-implementing using Advanced SIMD
// once the assembler supports those instructions.
// func mulWW(x, y Word) (z1, z0 Word)
TEXT ·mulWW(SB),NOSPLIT,$0
MOVD x+0(FP), R0
MOVD y+8(FP), R1
MUL R0, R1, R2
UMULH R0, R1, R3
MOVD R3, z1+16(FP)
MOVD R2, z0+24(FP)
RET
// func divWW(x1, x0, y Word) (q, r Word)
TEXT ·divWW(SB),NOSPLIT,$0
B ·divWW_g(SB) // ARM64 has no multiword division
// func addVV(z, x, y []Word) (c Word)
TEXT ·addVV(SB),NOSPLIT,$0
MOVD z_len+8(FP), R0
MOVD x+24(FP), R8
MOVD y+48(FP), R9
MOVD z+0(FP), R10
ADDS $0, R0 // clear carry flag
TBZ $0, R0, two
MOVD.P 8(R8), R11
MOVD.P 8(R9), R15
ADCS R15, R11
MOVD.P R11, 8(R10)
SUB $1, R0
two:
TBZ $1, R0, loop
LDP.P 16(R8), (R11, R12)
LDP.P 16(R9), (R15, R16)
ADCS R15, R11
ADCS R16, R12
STP.P (R11, R12), 16(R10)
SUB $2, R0
loop:
CBZ R0, done // careful not to touch the carry flag
LDP.P 32(R8), (R11, R12)
LDP -16(R8), (R13, R14)
LDP.P 32(R9), (R15, R16)
LDP -16(R9), (R17, R19)
ADCS R15, R11
ADCS R16, R12
ADCS R17, R13
ADCS R19, R14
STP.P (R11, R12), 32(R10)
STP (R13, R14), -16(R10)
SUB $4, R0
B loop
done:
CSET HS, R0 // extract carry flag
MOVD R0, c+72(FP)
RET
// func subVV(z, x, y []Word) (c Word)
TEXT ·subVV(SB),NOSPLIT,$0
MOVD z_len+8(FP), R0
MOVD x+24(FP), R8
MOVD y+48(FP), R9
MOVD z+0(FP), R10
CMP R0, R0 // set carry flag
TBZ $0, R0, two
MOVD.P 8(R8), R11
MOVD.P 8(R9), R15
SBCS R15, R11
MOVD.P R11, 8(R10)
SUB $1, R0
two:
TBZ $1, R0, loop
LDP.P 16(R8), (R11, R12)
LDP.P 16(R9), (R15, R16)
SBCS R15, R11
SBCS R16, R12
STP.P (R11, R12), 16(R10)
SUB $2, R0
loop:
CBZ R0, done // careful not to touch the carry flag
LDP.P 32(R8), (R11, R12)
LDP -16(R8), (R13, R14)
LDP.P 32(R9), (R15, R16)
LDP -16(R9), (R17, R19)
SBCS R15, R11
SBCS R16, R12
SBCS R17, R13
SBCS R19, R14
STP.P (R11, R12), 32(R10)
STP (R13, R14), -16(R10)
SUB $4, R0
B loop
done:
CSET LO, R0 // extract carry flag
MOVD R0, c+72(FP)
RET
// func addVW(z, x []Word, y Word) (c Word)
TEXT ·addVW(SB),NOSPLIT,$0
MOVD z+0(FP), R3
MOVD z_len+8(FP), R0
MOVD x+24(FP), R1
MOVD y+48(FP), R2
CBZ R0, len0 // the length of z is 0
MOVD.P 8(R1), R4
ADDS R2, R4 // z[0] = x[0] + y, set carry
MOVD.P R4, 8(R3)
SUB $1, R0
CBZ R0, len1 // the length of z is 1
TBZ $0, R0, two
MOVD.P 8(R1), R4 // do it once
ADCS $0, R4
MOVD.P R4, 8(R3)
SUB $1, R0
two: // do it twice
TBZ $1, R0, loop
LDP.P 16(R1), (R4, R5)
ADCS $0, R4, R8 // c, z[i] = x[i] + c
ADCS $0, R5, R9
STP.P (R8, R9), 16(R3)
SUB $2, R0
loop: // do four times per round
CBZ R0, len1 // careful not to touch the carry flag
LDP.P 32(R1), (R4, R5)
LDP -16(R1), (R6, R7)
ADCS $0, R4, R8
ADCS $0, R5, R9
ADCS $0, R6, R10
ADCS $0, R7, R11
STP.P (R8, R9), 32(R3)
STP (R10, R11), -16(R3)
SUB $4, R0
B loop
len1:
CSET HS, R2 // extract carry flag
len0:
MOVD R2, c+56(FP)
RET
// func subVW(z, x []Word, y Word) (c Word)
TEXT ·subVW(SB),NOSPLIT,$0
MOVD z+0(FP), R3
MOVD z_len+8(FP), R0
MOVD x+24(FP), R1
MOVD y+48(FP), R2
CBZ R0, len0 // the length of z is 0
MOVD.P 8(R1), R4
SUBS R2, R4 // z[0] = x[0] - y, set carry
MOVD.P R4, 8(R3)
SUB $1, R0
CBZ R0, len1 // the length of z is 1
TBZ $0, R0, two // do it once
MOVD.P 8(R1), R4
SBCS $0, R4
MOVD.P R4, 8(R3)
SUB $1, R0
two: // do it twice
TBZ $1, R0, loop
LDP.P 16(R1), (R4, R5)
SBCS $0, R4, R8 // c, z[i] = x[i] + c
SBCS $0, R5, R9
STP.P (R8, R9), 16(R3)
SUB $2, R0
loop: // do four times per round
CBZ R0, len1 // careful not to touch the carry flag
LDP.P 32(R1), (R4, R5)
LDP -16(R1), (R6, R7)
SBCS $0, R4, R8
SBCS $0, R5, R9
SBCS $0, R6, R10
SBCS $0, R7, R11
STP.P (R8, R9), 32(R3)
STP (R10, R11), -16(R3)
SUB $4, R0
B loop
len1:
CSET LO, R2 // extract carry flag
len0:
MOVD R2, c+56(FP)
RET
// func shlVU(z, x []Word, s uint) (c Word)
// This implementation handles the shift operation from the high word to the low word,
// which may be an error for the case where the low word of x overlaps with the high
// word of z. When calling this function directly, you need to pay attention to this
// situation.
TEXT ·shlVU(SB),NOSPLIT,$0
LDP z+0(FP), (R0, R1) // R0 = z.ptr, R1 = len(z)
MOVD x+24(FP), R2
MOVD s+48(FP), R3
ADD R1<<3, R0 // R0 = &z[n]
ADD R1<<3, R2 // R2 = &x[n]
CBZ R1, len0
CBZ R3, copy // if the number of shift is 0, just copy x to z
MOVD $64, R4
SUB R3, R4
// handling the most significant element x[n-1]
MOVD.W -8(R2), R6
LSR R4, R6, R5 // return value
LSL R3, R6, R8 // x[i] << s
SUB $1, R1
one: TBZ $0, R1, two
MOVD.W -8(R2), R6
LSR R4, R6, R7
ORR R8, R7
LSL R3, R6, R8
SUB $1, R1
MOVD.W R7, -8(R0)
two:
TBZ $1, R1, loop
LDP.W -16(R2), (R6, R7)
LSR R4, R7, R10
ORR R8, R10
LSL R3, R7
LSR R4, R6, R9
ORR R7, R9
LSL R3, R6, R8
SUB $2, R1
STP.W (R9, R10), -16(R0)
loop:
CBZ R1, done
LDP.W -32(R2), (R10, R11)
LDP 16(R2), (R12, R13)
LSR R4, R13, R23
ORR R8, R23 // z[i] = (x[i] << s) | (x[i-1] >> (64 - s))
LSL R3, R13
LSR R4, R12, R22
ORR R13, R22
LSL R3, R12
LSR R4, R11, R21
ORR R12, R21
LSL R3, R11
LSR R4, R10, R20
ORR R11, R20
LSL R3, R10, R8
STP.W (R20, R21), -32(R0)
STP (R22, R23), 16(R0)
SUB $4, R1
B loop
done:
MOVD.W R8, -8(R0) // the first element x[0]
MOVD R5, c+56(FP) // the part moved out from x[n-1]
RET
copy:
CMP R0, R2
BEQ len0
TBZ $0, R1, ctwo
MOVD.W -8(R2), R4
MOVD.W R4, -8(R0)
SUB $1, R1
ctwo:
TBZ $1, R1, cloop
LDP.W -16(R2), (R4, R5)
STP.W (R4, R5), -16(R0)
SUB $2, R1
cloop:
CBZ R1, len0
LDP.W -32(R2), (R4, R5)
LDP 16(R2), (R6, R7)
STP.W (R4, R5), -32(R0)
STP (R6, R7), 16(R0)
SUB $4, R1
B cloop
len0:
MOVD $0, c+56(FP)
RET
// func shrVU(z, x []Word, s uint) (c Word)
// This implementation handles the shift operation from the low word to the high word,
// which may be an error for the case where the high word of x overlaps with the low
// word of z. When calling this function directly, you need to pay attention to this
// situation.
TEXT ·shrVU(SB),NOSPLIT,$0
MOVD z+0(FP), R0
MOVD z_len+8(FP), R1
MOVD x+24(FP), R2
MOVD s+48(FP), R3
MOVD $0, R8
MOVD $64, R4
SUB R3, R4
CBZ R1, len0
CBZ R3, copy // if the number of shift is 0, just copy x to z
MOVD.P 8(R2), R20
LSR R3, R20, R8
LSL R4, R20
MOVD R20, c+56(FP) // deal with the first element
SUB $1, R1
TBZ $0, R1, two
MOVD.P 8(R2), R6
LSL R4, R6, R20
ORR R8, R20
LSR R3, R6, R8
MOVD.P R20, 8(R0)
SUB $1, R1
two:
TBZ $1, R1, loop
LDP.P 16(R2), (R6, R7)
LSL R4, R6, R20
LSR R3, R6
ORR R8, R20
LSL R4, R7, R21
LSR R3, R7, R8
ORR R6, R21
STP.P (R20, R21), 16(R0)
SUB $2, R1
loop:
CBZ R1, done
LDP.P 32(R2), (R10, R11)
LDP -16(R2), (R12, R13)
LSL R4, R10, R20
LSR R3, R10
ORR R8, R20 // z[i] = (x[i] >> s) | (x[i+1] << (64 - s))
LSL R4, R11, R21
LSR R3, R11
ORR R10, R21
LSL R4, R12, R22
LSR R3, R12
ORR R11, R22
LSL R4, R13, R23
LSR R3, R13, R8
ORR R12, R23
STP.P (R20, R21), 32(R0)
STP (R22, R23), -16(R0)
SUB $4, R1
B loop
done:
MOVD R8, (R0) // deal with the last element
RET
copy:
CMP R0, R2
BEQ len0
TBZ $0, R1, ctwo
MOVD.P 8(R2), R3
MOVD.P R3, 8(R0)
SUB $1, R1
ctwo:
TBZ $1, R1, cloop
LDP.P 16(R2), (R4, R5)
STP.P (R4, R5), 16(R0)
SUB $2, R1
cloop:
CBZ R1, len0
LDP.P 32(R2), (R4, R5)
LDP -16(R2), (R6, R7)
STP.P (R4, R5), 32(R0)
STP (R6, R7), -16(R0)
SUB $4, R1
B cloop
len0:
MOVD $0, c+56(FP)
RET
// func mulAddVWW(z, x []Word, y, r Word) (c Word)
TEXT ·mulAddVWW(SB),NOSPLIT,$0
MOVD z+0(FP), R1
MOVD z_len+8(FP), R0
MOVD x+24(FP), R2
MOVD y+48(FP), R3
MOVD r+56(FP), R4
// c, z = x * y + r
TBZ $0, R0, two
MOVD.P 8(R2), R5
MUL R3, R5, R7
UMULH R3, R5, R8
ADDS R4, R7
ADC $0, R8, R4 // c, z[i] = x[i] * y + r
MOVD.P R7, 8(R1)
SUB $1, R0
two:
TBZ $1, R0, loop
LDP.P 16(R2), (R5, R6)
MUL R3, R5, R10
UMULH R3, R5, R11
ADDS R4, R10
MUL R3, R6, R12
UMULH R3, R6, R13
ADCS R12, R11
ADC $0, R13, R4
STP.P (R10, R11), 16(R1)
SUB $2, R0
loop:
CBZ R0, done
LDP.P 32(R2), (R5, R6)
LDP -16(R2), (R7, R8)
MUL R3, R5, R10
UMULH R3, R5, R11
ADDS R4, R10
MUL R3, R6, R12
UMULH R3, R6, R13
ADCS R11, R12
MUL R3, R7, R14
UMULH R3, R7, R15
ADCS R13, R14
MUL R3, R8, R16
UMULH R3, R8, R17
ADCS R15, R16
ADC $0, R17, R4
STP.P (R10, R12), 32(R1)
STP (R14, R16), -16(R1)
SUB $4, R0
B loop
done:
MOVD R4, c+64(FP)
RET
// func addMulVVW(z, x []Word, y Word) (c Word)
TEXT ·addMulVVW(SB),NOSPLIT,$0
MOVD z+0(FP), R1
MOVD z_len+8(FP), R0
MOVD x+24(FP), R2
MOVD y+48(FP), R3
MOVD $0, R4
TBZ $0, R0, two
MOVD.P 8(R2), R5
MOVD (R1), R6
MUL R5, R3, R7
UMULH R5, R3, R8
ADDS R7, R6
ADC $0, R8, R4
MOVD.P R6, 8(R1)
SUB $1, R0
two:
TBZ $1, R0, loop
LDP.P 16(R2), (R5, R10)
LDP (R1), (R6, R11)
MUL R10, R3, R13
UMULH R10, R3, R12
MUL R5, R3, R7
UMULH R5, R3, R8
ADDS R4, R6
ADCS R13, R11
ADC $0, R12
ADDS R7, R6
ADCS R8, R11
ADC $0, R12, R4
STP.P (R6, R11), 16(R1)
SUB $2, R0
// The main loop of this code operates on a block of 4 words every iteration
// performing [R4:R12:R11:R10:R9] = R4 + R3 * [R8:R7:R6:R5] + [R12:R11:R10:R9]
// where R4 is carried from the previous iteration, R8:R7:R6:R5 hold the next
// 4 words of x, R3 is y and R12:R11:R10:R9 are part of the result z.
loop:
CBZ R0, done
LDP.P 16(R2), (R5, R6)
LDP.P 16(R2), (R7, R8)
LDP (R1), (R9, R10)
ADDS R4, R9
MUL R6, R3, R14
ADCS R14, R10
MUL R7, R3, R15
LDP 16(R1), (R11, R12)
ADCS R15, R11
MUL R8, R3, R16
ADCS R16, R12
UMULH R8, R3, R20
ADC $0, R20
MUL R5, R3, R13
ADDS R13, R9
UMULH R5, R3, R17
ADCS R17, R10
UMULH R6, R3, R21
STP.P (R9, R10), 16(R1)
ADCS R21, R11
UMULH R7, R3, R19
ADCS R19, R12
STP.P (R11, R12), 16(R1)
ADC $0, R20, R4
SUB $4, R0
B loop
done:
MOVD R4, c+56(FP)
RET
// func divWVW(z []Word, xn Word, x []Word, y Word) (r Word)
TEXT ·divWVW(SB),NOSPLIT,$0
B ·divWVW_g(SB)