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Commit 705c0382 authored by Russ Cox's avatar Russ Cox
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big: arm assembly, faster software mulWW, divWW 

Reduces time spent running crypto/rsa test by 65%.

Fixes #1227.

R=gri, PeterGo
CC=golang-dev
https://golang.org/cl/2743041
parent a8abb64a
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Showing with 326 additions and 189 deletions
src/pkg/big/arith.go
View file @ 705c0382
......@@ -56,161 +56,29 @@ func subWW_g(x, y, c Word) (z1, z0 Word) {
// z1<<_W + z0 = x*y
// Adapted from Warren, Hacker's Delight, p. 132.
func mulWW_g(x, y Word) (z1, z0 Word) {
// Split x and y into 2 halfWords each, multiply
// the halfWords separately while avoiding overflow,
// and return the product as 2 Words.
if x < y {
x, y = y, x
}
if x < _B2 {
// y < _B2 because y <= x
// sub-digits of x and y are (0, x) and (0, y)
// z = z[0] = x*y
z0 = x * y
return
}
if y < _B2 {
// sub-digits of x and y are (x1, x0) and (0, y)
// x = (x1*_B2 + x0)
// y = (y1*_B2 + y0)
x1, x0 := x>>_W2, x&_M2
// x*y = t2*_B2*_B2 + t1*_B2 + t0
t0 := x0 * y
t1 := x1 * y
// compute result digits but avoid overflow
// z = z[1]*_B + z[0] = x*y
z0 = t1<<_W2 + t0
z1 = (t1 + t0>>_W2) >> _W2
return
}
// general case
// sub-digits of x and y are (x1, x0) and (y1, y0)
// x = (x1*_B2 + x0)
// y = (y1*_B2 + y0)
x1, x0 := x>>_W2, x&_M2
y1, y0 := y>>_W2, y&_M2
// x*y = t2*_B2*_B2 + t1*_B2 + t0
t0 := x0 * y0
// t1 := x1*y0 + x0*y1;
var c Word
t1 := x1 * y0
t1a := t1
t1 += x0 * y1
if t1 < t1a {
c++
}
t2 := x1*y1 + c*_B2
// compute result digits but avoid overflow
// z = z[1]*_B + z[0] = x*y
// This may overflow, but that's ok because we also sum t1 and t0 above
// and we take care of the overflow there.
z0 = t1<<_W2 + t0
// z1 = t2 + (t1 + t0>>_W2)>>_W2;
var c3 Word
z1 = t1 + t0>>_W2
if z1 < t1 {
c3++
}
z1 >>= _W2
z1 += c3 * _B2
z1 += t2
x0 := x & _M2
x1 := x >> _W2
y0 := y & _M2
y1 := y >> _W2
w0 := x0 * y0
t := x1*y0 + w0>>_W2
w1 := t & _M2
w2 := t >> _W2
w1 += x0 * y1
z1 = x1*y1 + w2 + w1>>_W2
z0 = x * y
return
}
// z1<<_W + z0 = x*y + c
func mulAddWWW_g(x, y, c Word) (z1, z0 Word) {
// Split x and y into 2 halfWords each, multiply
// the halfWords separately while avoiding overflow,
// and return the product as 2 Words.
// TODO(gri) Should implement special cases for faster execution.
// general case
// sub-digits of x, y, and c are (x1, x0), (y1, y0), (c1, c0)
// x = (x1*_B2 + x0)
// y = (y1*_B2 + y0)
x1, x0 := x>>_W2, x&_M2
y1, y0 := y>>_W2, y&_M2
c1, c0 := c>>_W2, c&_M2
// x*y + c = t2*_B2*_B2 + t1*_B2 + t0
// (1<<32-1)^2 == 1<<64 - 1<<33 + 1, so there's space to add c0 in here.
t0 := x0*y0 + c0
// t1 := x1*y0 + x0*y1 + c1;
var c2 Word // extra carry
t1 := x1*y0 + c1
t1a := t1
t1 += x0 * y1
if t1 < t1a { // If the number got smaller then we overflowed.
c2++
z1, zz0 := mulWW(x, y)
if z0 = zz0 + c; z0 < zz0 {
z1++
}
t2 := x1*y1 + c2*_B2
// compute result digits but avoid overflow
// z = z[1]*_B + z[0] = x*y
// z0 = t1<<_W2 + t0;
// This may overflow, but that's ok because we also sum t1 and t0 below
// and we take care of the overflow there.
z0 = t1<<_W2 + t0
var c3 Word
z1 = t1 + t0>>_W2
if z1 < t1 {
c3++
}
z1 >>= _W2
z1 += t2 + c3*_B2
return
}
// q = (x1<<_W + x0 - r)/y
// The most significant bit of y must be 1.
func divStep(x1, x0, y Word) (q, r Word) {
d1, d0 := y>>_W2, y&_M2
q1, r1 := x1/d1, x1%d1
m := q1 * d0
r1 = r1*_B2 | x0>>_W2
if r1 < m {
q1--
r1 += y
if r1 >= y && r1 < m {
q1--
r1 += y
}
}
r1 -= m
r0 := r1 % d1
q0 := r1 / d1
m = q0 * d0
r0 = r0*_B2 | x0&_M2
if r0 < m {
q0--
r0 += y
if r0 >= y && r0 < m {
q0--
r0 += y
}
}
r0 -= m
q = q1*_B2 | q0
r = r0
return
}
......@@ -241,46 +109,48 @@ func leadingZeros(x Word) uint {
}
// q = (x1<<_W + x0 - r)/y
func divWW_g(x1, x0, y Word) (q, r Word) {
if x1 == 0 {
q, r = x0/y, x0%y
return
// q = (u1<<_W + u0 - r)/y
// Adapted from Warren, Hacker's Delight, p. 152.
func divWW_g(u1, u0, v Word) (q, r Word) {
if u1 >= v {
return 1<<_W - 1, 1<<_W - 1
}
var q0, q1 Word
z := leadingZeros(y)
if y > x1 {
if z != 0 {
y <<= z
x1 = (x1 << z) | (x0 >> (_W - z))
x0 <<= z
}
q0, x0 = divStep(x1, x0, y)
q1 = 0
} else {
if z == 0 {
x1 -= y
q1 = 1
} else {
z1 := _W - z
y <<= z
x2 := x1 >> z1
x1 = (x1 << z) | (x0 >> z1)
x0 <<= z
q1, x1 = divStep(x2, x1, y)
}
s := leadingZeros(v)
v <<= s
vn1 := v >> _W2
vn0 := v & _M2
un32 := u1<<s | u0>>(_W-s)
un10 := u0 << s
un1 := un10 >> _W2
un0 := un10 & _M2
q1 := un32 / vn1
rhat := un32 - q1*vn1
q0, x0 = divStep(x1, x0, y)
again1:
if q1 >= _B2 || q1*vn0 > _B2*rhat+un1 {
q1--
rhat += vn1
if rhat < _B2 {
goto again1
}
}
r = x0 >> z
un21 := un32*_B2 + un1 - q1*v
q0 := un21 / vn1
rhat = un21 - q0*vn1
if q1 != 0 {
panic("div out of range")
again2:
if q0 >= _B2 || q0*vn0 > _B2*rhat+un0 {
q0--
rhat += vn1
if rhat < _B2 {
goto again2
}
}
return q0, r
return q1*_B2 + q0, (un21*_B2 + un0 - q0*v) >> s
}
......
src/pkg/big/arith_arm.s
View file @ 705c0382
......@@ -5,36 +5,302 @@
// This file provides fast assembly versions for the elementary
// arithmetic operations on vectors implemented in arith.go.
// TODO(gri) Implement these routines.
#define CFLAG 29 // bit position of carry flag
// func addVV(z, x, y []Word) (c Word)
TEXT ·addVV(SB),7,$0
B ·addVV_g(SB)
MOVW $0, R0
MOVW z+0(FP), R1
MOVW x+12(FP), R2
MOVW y+24(FP), R3
MOVW n+4(FP), R4
MOVW R4<<2, R4
ADD R1, R4
B E1
L1:
MOVW.P 4(R2), R5
MOVW.P 4(R3), R6
MOVW R0, CPSR
ADC.S R6, R5
MOVW.P R5, 4(R1)
MOVW CPSR, R0
E1:
CMP R1, R4
BNE L1
MOVW R0>>CFLAG, R0
AND $1, R0
MOVW R0, c+36(FP)
RET
// func subVV(z, x, y []Word) (c Word)
// (same as addVV except for SBC instead of ADC and label names)
TEXT ·subVV(SB),7,$0
B ·subVV_g(SB)
MOVW $(1<<CFLAG), R0
MOVW z+0(FP), R1
MOVW x+12(FP), R2
MOVW y+24(FP), R3
MOVW n+4(FP), R4
MOVW R4<<2, R4
ADD R1, R4
B E2
L2:
MOVW.P 4(R2), R5
MOVW.P 4(R3), R6
MOVW R0, CPSR
SBC.S R6, R5
MOVW.P R5, 4(R1)
MOVW CPSR, R0
E2:
CMP R1, R4
BNE L2
MOVW R0>>CFLAG, R0
AND $1, R0
EOR $1, R0
MOVW R0, c+36(FP)
RET
// func addVW(z, x []Word, y Word) (c Word)
TEXT ·addVW(SB),7,$0
B ·addVW_g(SB)
MOVW z+0(FP), R1
MOVW x+12(FP), R2
MOVW y+24(FP), R3
MOVW n+4(FP), R4
MOVW R4<<2, R4
ADD R1, R4
CMP R1, R4
BNE L3a
MOVW R3, c+28(FP)
RET
L3a:
MOVW.P 4(R2), R5
ADD.S R3, R5
MOVW.P R5, 4(R1)
MOVW CPSR, R0
B E3
L3:
MOVW.P 4(R2), R5
MOVW R0, CPSR
ADC.S $0, R5
MOVW.P R5, 4(R1)
MOVW CPSR, R0
E3:
CMP R1, R4
BNE L3
MOVW R0>>CFLAG, R0
AND $1, R0
MOVW R0, c+28(FP)
RET
TEXT ·subVW(SB),7,$0
B ·subVW_g(SB)
MOVW z+0(FP), R1
MOVW x+12(FP), R2
MOVW y+24(FP), R3
MOVW n+4(FP), R4
MOVW R4<<2, R4
ADD R1, R4
CMP R1, R4
BNE L4a
MOVW R3, c+28(FP)
RET
L4a:
MOVW.P 4(R2), R5
SUB.S R3, R5
MOVW.P R5, 4(R1)
MOVW CPSR, R0
B E4
L4:
MOVW.P 4(R2), R5
MOVW R0, CPSR
SBC.S $0, R5
MOVW.P R5, 4(R1)
MOVW CPSR, R0
E4:
CMP R1, R4
BNE L4
MOVW R0>>CFLAG, R0
AND $1, R0
EOR $1, R0
MOVW R0, c+28(FP)
RET
// func shlVW(z, x []Word, s Word) (c Word)
TEXT ·shlVW(SB),7,$0
B ·shlVW_g(SB)
MOVW n+4(FP), R5
CMP $0, R5
BEQ X7
MOVW z+0(FP), R1
MOVW x+12(FP), R2
MOVW R5<<2, R5
ADD R5, R2
ADD R1, R5
MOVW s+24(FP), R3
CMP $0, R3 // shift 0 is special
BEQ Y7
ADD $4, R1 // stop one word early
MOVW $32, R4
SUB R3, R4
MOVW $0, R7
MOVW.W -4(R2), R6
MOVW R6<<R3, R7
MOVW R6>>R4, R6
MOVW R6, c+28(FP)
B E7
L7:
MOVW.W -4(R2), R6
ORR R6>>R4, R7
MOVW.W R7, -4(R5)
MOVW R6<<R3, R7
E7:
CMP R1, R5
BNE L7
MOVW R7, -4(R5)
RET
Y7: // copy loop, because shift 0 == shift 32
MOVW.W -4(R2), R6
MOVW.W R6, -4(R5)
CMP R1, R5
BNE Y7
X7:
MOVW $0, R1
MOVW R1, c+28(FP)
RET
TEXT ·shrVW(SB),7,$0
B ·shrVW_g(SB)
MOVW n+4(FP), R5
CMP $0, R5
BEQ X6
MOVW z+0(FP), R1
MOVW x+12(FP), R2
MOVW R5<<2, R5
ADD R1, R5
MOVW s+24(FP), R3
CMP $0, R3 // shift 0 is special
BEQ Y6
SUB $4, R5 // stop one word early
MOVW $32, R4
SUB R3, R4
MOVW $0, R7
// first word
MOVW.P 4(R2), R6
MOVW R6>>R3, R7
MOVW R6<<R4, R6
MOVW R6, c+28(FP)
B E6
// word loop
L6:
MOVW.P 4(R2), R6
ORR R6<<R4, R7
MOVW.P R7, 4(R1)
MOVW R6>>R3, R7
E6:
CMP R1, R5
BNE L6
MOVW R7, 0(R1)
RET
Y6: // copy loop, because shift 0 == shift 32
MOVW.P 4(R2), R6
MOVW.P R6, 4(R1)
CMP R1, R5
BNE Y6
X6:
MOVW $0, R1
MOVW R1, c+28(FP)
RET
TEXT ·mulAddVWW(SB),7,$0
B ·mulAddVWW_g(SB)
MOVW $0, R0
MOVW z+0(FP), R1
MOVW x+12(FP), R2
MOVW y+24(FP), R3
MOVW r+28(FP), R4
MOVW n+4(FP), R5
MOVW R5<<2, R5
ADD R1, R5
B E8
// word loop
L8:
MOVW.P 4(R2), R6
MULLU R6, R3, (R7, R6)
ADD.S R4, R6
ADC R0, R7
MOVW.P R6, 4(R1)
MOVW R7, R4
E8:
CMP R1, R5
BNE L8
MOVW R4, c+32(FP)
RET
TEXT ·addMulVVW(SB),7,$0
B ·addMulVVW_g(SB)
MOVW $0, R0
MOVW z+0(FP), R1
MOVW x+12(FP), R2
MOVW y+24(FP), R3
MOVW n+4(FP), R5
MOVW R5<<2, R5
ADD R1, R5
MOVW $0, R4
B E9
// word loop
L9:
MOVW.P 4(R2), R6
MULLU R6, R3, (R7, R6)
ADD.S R4, R6
ADC R0, R7
MOVW 0(R1), R4
ADD.S R4, R6
ADC R0, R7
MOVW.P R6, 4(R1)
MOVW R7, R4
E9:
CMP R1, R5
BNE L9
MOVW R4, c+28(FP)
RET
TEXT ·divWVW(SB),7,$0
// ARM has no multiword division, so use portable code.
B ·divWVW_g(SB)
TEXT ·divWW(SB),7,$0
// ARM has no multiword division, so use portable code.
B ·divWW_g(SB)
// func mulWW(x, y Word) (z1, z0 Word)
TEXT ·mulWW(SB),7,$0
B ·mulWW_g(SB)
MOVW x+0(FP), R1
MOVW y+4(FP), R2
MULLU R1, R2, (R4, R3)
MOVW R4, z1+8(FP)
MOVW R3, z0+12(FP)
RET
src/pkg/big/arith_test.go
View file @ 705c0382
......@@ -116,6 +116,7 @@ type argVW struct {
var sumVW = []argVW{
{},
{nil, nil, 2, 2},
{nat{0}, nat{0}, 0, 0},
{nat{1}, nat{0}, 1, 0},
{nat{1}, nat{1}, 0, 0},
......
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