mirror of
https://github.com/golang/go
synced 2024-11-20 04:14:49 -07:00
big: cleanups and performance tuning
- removed last argument (n) from all core arithmetic routines; instead, use the length of the result - simplified nat.make implementation and chose a better capacity for new values, removed a TODO in the process Changing the constant e from 1 (old) to 4 (new) improved pidigits -s -n 10000 by ~9% (on a 3.06GHz Intel Core 2 Duo): user 0m3.882s (old) user 0m3.549s (new) R=rsc CC=golang-dev https://golang.org/cl/1133043
This commit is contained in:
Robert Griesemer
parent
61eb0e71f2
commit
52cc058172
@ -284,47 +284,47 @@ func divWW_g(x1, x0, y Word) (q, r Word) {
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}
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func addVV(z, x, y []Word, n int) (c Word)
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func addVV_g(z, x, y []Word, n int) (c Word) {
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for i := 0; i < n; i++ {
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func addVV(z, x, y []Word) (c Word)
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func addVV_g(z, x, y []Word) (c Word) {
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for i := range z {
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c, z[i] = addWW_g(x[i], y[i], c)
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}
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return
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}
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func subVV(z, x, y []Word, n int) (c Word)
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func subVV_g(z, x, y []Word, n int) (c Word) {
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for i := 0; i < n; i++ {
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func subVV(z, x, y []Word) (c Word)
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func subVV_g(z, x, y []Word) (c Word) {
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for i := range z {
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c, z[i] = subWW_g(x[i], y[i], c)
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}
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return
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}
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func addVW(z, x []Word, y Word, n int) (c Word)
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func addVW_g(z, x []Word, y Word, n int) (c Word) {
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func addVW(z, x []Word, y Word) (c Word)
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func addVW_g(z, x []Word, y Word) (c Word) {
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c = y
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for i := 0; i < n; i++ {
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for i := range z {
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c, z[i] = addWW_g(x[i], c, 0)
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}
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return
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}
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func subVW(z, x []Word, y Word, n int) (c Word)
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func subVW_g(z, x []Word, y Word, n int) (c Word) {
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func subVW(z, x []Word, y Word) (c Word)
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func subVW_g(z, x []Word, y Word) (c Word) {
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c = y
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for i := 0; i < n; i++ {
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for i := range z {
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c, z[i] = subWW_g(x[i], c, 0)
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}
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return
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}
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func shlVW(z, x []Word, s Word, n int) (c Word)
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func shlVW_g(z, x []Word, s Word, n int) (c Word) {
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if n > 0 {
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func shlVW(z, x []Word, s Word) (c Word)
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func shlVW_g(z, x []Word, s Word) (c Word) {
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if n := len(z); n > 0 {
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ŝ := _W - s
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w1 := x[n-1]
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c = w1 >> ŝ
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@ -339,9 +339,9 @@ func shlVW_g(z, x []Word, s Word, n int) (c Word) {
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}
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func shrVW(z, x []Word, s Word, n int) (c Word)
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func shrVW_g(z, x []Word, s Word, n int) (c Word) {
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if n > 0 {
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func shrVW(z, x []Word, s Word) (c Word)
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func shrVW_g(z, x []Word, s Word) (c Word) {
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if n := len(z); n > 0 {
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ŝ := _W - s
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w1 := x[0]
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c = w1 << ŝ
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@ -356,19 +356,19 @@ func shrVW_g(z, x []Word, s Word, n int) (c Word) {
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}
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func mulAddVWW(z, x []Word, y, r Word, n int) (c Word)
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func mulAddVWW_g(z, x []Word, y, r Word, n int) (c Word) {
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func mulAddVWW(z, x []Word, y, r Word) (c Word)
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func mulAddVWW_g(z, x []Word, y, r Word) (c Word) {
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c = r
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for i := 0; i < n; i++ {
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for i := range z {
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c, z[i] = mulAddWWW_g(x[i], y, c)
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}
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return
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}
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func addMulVVW(z, x []Word, y Word, n int) (c Word)
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func addMulVVW_g(z, x []Word, y Word, n int) (c Word) {
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for i := 0; i < n; i++ {
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func addMulVVW(z, x []Word, y Word) (c Word)
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func addMulVVW_g(z, x []Word, y Word) (c Word) {
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for i := range z {
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z1, z0 := mulAddWWW_g(x[i], y, z[i])
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c, z[i] = addWW_g(z0, c, 0)
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c += z1
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@ -377,10 +377,10 @@ func addMulVVW_g(z, x []Word, y Word, n int) (c Word) {
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}
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func divWVW(z []Word, xn Word, x []Word, y Word, n int) (r Word)
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func divWVW_g(z []Word, xn Word, x []Word, y Word, n int) (r Word) {
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func divWVW(z []Word, xn Word, x []Word, y Word) (r Word)
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func divWVW_g(z []Word, xn Word, x []Word, y Word) (r Word) {
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r = xn
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for i := n - 1; i >= 0; i-- {
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for i := len(z) - 1; i >= 0; i-- {
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z[i], r = divWW_g(r, x[i], y)
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}
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return
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@ -5,12 +5,12 @@
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// This file provides fast assembly versions for the elementary
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// arithmetic operations on vectors implemented in arith.go.
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// func addVV(z, x, y []Word, n int) (c Word)
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// func addVV(z, x, y []Word) (c Word)
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TEXT ·addVV(SB),7,$0
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MOVL z+0(FP), DI
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MOVL x+12(FP), SI
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MOVL y+24(FP), CX
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MOVL n+36(FP), BP
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MOVL n+4(FP), BP
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MOVL $0, BX // i = 0
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MOVL $0, DX // c = 0
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JMP E1
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@ -25,17 +25,17 @@ L1: MOVL (SI)(BX*4), AX
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E1: CMPL BX, BP // i < n
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JL L1
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MOVL DX, c+40(FP)
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MOVL DX, c+36(FP)
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RET
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// func subVV(z, x, y []Word, n int) (c Word)
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// func subVV(z, x, y []Word) (c Word)
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// (same as addVV except for SBBL instead of ADCL and label names)
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TEXT ·subVV(SB),7,$0
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MOVL z+0(FP), DI
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MOVL x+12(FP), SI
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MOVL y+24(FP), CX
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MOVL n+36(FP), BP
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MOVL n+4(FP), BP
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MOVL $0, BX // i = 0
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MOVL $0, DX // c = 0
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JMP E2
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@ -50,16 +50,16 @@ L2: MOVL (SI)(BX*4), AX
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E2: CMPL BX, BP // i < n
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JL L2
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MOVL DX, c+40(FP)
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MOVL DX, c+36(FP)
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RET
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// func addVW(z, x []Word, y Word, n int) (c Word)
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// func addVW(z, x []Word, y Word) (c Word)
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TEXT ·addVW(SB),7,$0
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MOVL z+0(FP), DI
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MOVL x+12(FP), SI
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MOVL y+24(FP), AX // c = y
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MOVL n+28(FP), BP
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MOVL n+4(FP), BP
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MOVL $0, BX // i = 0
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JMP E3
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@ -72,16 +72,16 @@ L3: ADDL (SI)(BX*4), AX
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E3: CMPL BX, BP // i < n
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JL L3
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MOVL AX, c+32(FP)
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MOVL AX, c+28(FP)
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RET
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// func subVW(z, x []Word, y Word, n int) (c Word)
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// func subVW(z, x []Word, y Word) (c Word)
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TEXT ·subVW(SB),7,$0
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MOVL z+0(FP), DI
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MOVL x+12(FP), SI
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MOVL y+24(FP), AX // c = y
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MOVL n+28(FP), BP
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MOVL n+4(FP), BP
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MOVL $0, BX // i = 0
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JMP E4
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@ -95,13 +95,13 @@ L4: MOVL (SI)(BX*4), DX // TODO(gri) is there a reverse SUBL?
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E4: CMPL BX, BP // i < n
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JL L4
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MOVL AX, c+32(FP)
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MOVL AX, c+28(FP)
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RET
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// func shlVW(z, x []Word, s Word, n int) (c Word)
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// func shlVW(z, x []Word, s Word) (c Word)
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TEXT ·shlVW(SB),7,$0
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MOVL n+28(FP), BX // i = n
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MOVL n+4(FP), BX // i = n
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SUBL $1, BX // i--
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JL X8b // i < 0 (n <= 0)
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@ -112,7 +112,7 @@ TEXT ·shlVW(SB),7,$0
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MOVL (SI)(BX*4), AX // w1 = x[n-1]
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MOVL $0, DX
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SHLL CX, DX:AX // w1>>ŝ
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MOVL DX, c+32(FP)
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MOVL DX, c+28(FP)
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CMPL BX, $0
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JLE X8a // i <= 0
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@ -130,13 +130,13 @@ X8a: SHLL CX, AX // w1<<s
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MOVL AX, (DI) // z[0] = w1<<s
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RET
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X8b: MOVL $0, c+32(FP)
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X8b: MOVL $0, c+28(FP)
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RET
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// func shrVW(z, x []Word, s Word, n int) (c Word)
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// func shrVW(z, x []Word, s Word) (c Word)
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TEXT ·shrVW(SB),7,$0
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MOVL n+28(FP), BP
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MOVL n+4(FP), BP
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SUBL $1, BP // n--
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JL X9b // n < 0 (n <= 0)
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@ -147,7 +147,7 @@ TEXT ·shrVW(SB),7,$0
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MOVL (SI), AX // w1 = x[0]
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MOVL $0, DX
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SHRL CX, DX:AX // w1<<ŝ
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MOVL DX, c+32(FP)
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MOVL DX, c+28(FP)
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MOVL $0, BX // i = 0
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JMP E9
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@ -167,17 +167,17 @@ X9a: SHRL CX, AX // w1>>s
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MOVL AX, (DI)(BP*4) // z[n-1] = w1>>s
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RET
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X9b: MOVL $0, c+32(FP)
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X9b: MOVL $0, c+28(FP)
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RET
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// func mulAddVWW(z, x []Word, y, r Word, n int) (c Word)
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// func mulAddVWW(z, x []Word, y, r Word) (c Word)
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TEXT ·mulAddVWW(SB),7,$0
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MOVL z+0(FP), DI
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MOVL x+12(FP), SI
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MOVL y+24(FP), BP
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MOVL r+28(FP), CX // c = r
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MOVL n+32(FP), BX
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MOVL n+4(FP), BX
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LEAL (DI)(BX*4), DI
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LEAL (SI)(BX*4), SI
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NEGL BX // i = -n
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@ -194,16 +194,16 @@ L5: MOVL (SI)(BX*4), AX
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E5: CMPL BX, $0 // i < 0
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JL L5
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MOVL CX, c+36(FP)
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MOVL CX, c+32(FP)
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RET
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// func addMulVVW(z, x []Word, y Word, n int) (c Word)
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// func addMulVVW(z, x []Word, y Word) (c Word)
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TEXT ·addMulVVW(SB),7,$0
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MOVL z+0(FP), DI
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MOVL x+12(FP), SI
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MOVL y+24(FP), BP
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MOVL n+28(FP), BX
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MOVL n+4(FP), BX
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LEAL (DI)(BX*4), DI
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LEAL (SI)(BX*4), SI
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NEGL BX // i = -n
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@ -223,17 +223,17 @@ L6: MOVL (SI)(BX*4), AX
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E6: CMPL BX, $0 // i < 0
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JL L6
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MOVL CX, c+32(FP)
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MOVL CX, c+28(FP)
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RET
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// divWVW(z* Word, xn Word, x []Word, y Word, n int) (r Word)
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// divWVW(z* Word, xn Word, x []Word, y Word) (r Word)
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TEXT ·divWVW(SB),7,$0
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MOVL z+0(FP), DI
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MOVL xn+12(FP), DX // r = xn
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MOVL x+16(FP), SI
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MOVL y+28(FP), CX
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MOVL n+32(FP), BX // i = n
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MOVL n+4(FP), BX // i = n
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JMP E7
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L7: MOVL (SI)(BX*4), AX
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@ -243,5 +243,5 @@ L7: MOVL (SI)(BX*4), AX
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E7: SUBL $1, BX // i--
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JGE L7 // i >= 0
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MOVL DX, r+36(FP)
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MOVL DX, r+32(FP)
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RET
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@ -7,12 +7,12 @@
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// TODO(gri) - experiment with unrolled loops for faster execution
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// func addVV(z, x, y []Word, n int) (c Word)
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// func addVV(z, x, y []Word) (c Word)
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TEXT ·addVV(SB),7,$0
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MOVQ z+0(FP), R10
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MOVQ x+16(FP), R8
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MOVQ y+32(FP), R9
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MOVL n+48(FP), R11
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MOVL n+8(FP), R11
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MOVQ $0, BX // i = 0
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MOVQ $0, DX // c = 0
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JMP E1
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@ -27,17 +27,17 @@ L1: MOVQ (R8)(BX*8), AX
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E1: CMPQ BX, R11 // i < n
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JL L1
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MOVQ DX, c+56(FP)
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MOVQ DX, c+48(FP)
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RET
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// func subVV(z, x, y []Word, n int) (c Word)
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// func subVV(z, x, y []Word) (c Word)
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// (same as addVV_s except for SBBQ instead of ADCQ and label names)
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TEXT ·subVV(SB),7,$0
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MOVQ z+0(FP), R10
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MOVQ x+16(FP), R8
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MOVQ y+32(FP), R9
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MOVL n+48(FP), R11
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MOVL n+8(FP), R11
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MOVQ $0, BX // i = 0
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MOVQ $0, DX // c = 0
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JMP E2
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@ -52,16 +52,16 @@ L2: MOVQ (R8)(BX*8), AX
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E2: CMPQ BX, R11 // i < n
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JL L2
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MOVQ DX, c+56(FP)
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MOVQ DX, c+48(FP)
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RET
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// func addVW(z, x []Word, y Word, n int) (c Word)
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// func addVW(z, x []Word, y Word) (c Word)
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TEXT ·addVW(SB),7,$0
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MOVQ z+0(FP), R10
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MOVQ x+16(FP), R8
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MOVQ y+32(FP), AX // c = y
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MOVL n+40(FP), R11
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MOVL n+8(FP), R11
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MOVQ $0, BX // i = 0
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JMP E3
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@ -74,16 +74,16 @@ L3: ADDQ (R8)(BX*8), AX
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E3: CMPQ BX, R11 // i < n
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JL L3
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MOVQ AX, c+48(FP)
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MOVQ AX, c+40(FP)
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RET
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// func subVW(z, x []Word, y Word, n int) (c Word)
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// func subVW(z, x []Word, y Word) (c Word)
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TEXT ·subVW(SB),7,$0
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MOVQ z+0(FP), R10
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MOVQ x+16(FP), R8
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MOVQ y+32(FP), AX // c = y
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MOVL n+40(FP), R11
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MOVL n+8(FP), R11
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MOVQ $0, BX // i = 0
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JMP E4
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@ -97,13 +97,13 @@ L4: MOVQ (R8)(BX*8), DX // TODO(gri) is there a reverse SUBQ?
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E4: CMPQ BX, R11 // i < n
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JL L4
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MOVQ AX, c+48(FP)
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MOVQ AX, c+40(FP)
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RET
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// func shlVW(z, x []Word, s Word, n int) (c Word)
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// func shlVW(z, x []Word, s Word) (c Word)
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TEXT ·shlVW(SB),7,$0
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MOVL n+40(FP), BX // i = n
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MOVL n+8(FP), BX // i = n
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SUBL $1, BX // i--
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JL X8b // i < 0 (n <= 0)
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@ -114,7 +114,7 @@ TEXT ·shlVW(SB),7,$0
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MOVQ (R8)(BX*8), AX // w1 = x[n-1]
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MOVQ $0, DX
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SHLQ CX, DX:AX // w1>>ŝ
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MOVQ DX, c+48(FP)
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MOVQ DX, c+40(FP)
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CMPL BX, $0
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JLE X8a // i <= 0
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@ -132,13 +132,13 @@ X8a: SHLQ CX, AX // w1<<s
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MOVQ AX, (R10) // z[0] = w1<<s
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RET
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X8b: MOVQ $0, c+48(FP)
|
||||
X8b: MOVQ $0, c+40(FP)
|
||||
RET
|
||||
|
||||
|
||||
// func shrVW(z, x []Word, s Word, n int) (c Word)
|
||||
// func shrVW(z, x []Word, s Word) (c Word)
|
||||
TEXT ·shrVW(SB),7,$0
|
||||
MOVL n+40(FP), R11
|
||||
MOVL n+8(FP), R11
|
||||
SUBL $1, R11 // n--
|
||||
JL X9b // n < 0 (n <= 0)
|
||||
|
||||
@ -149,7 +149,7 @@ TEXT ·shrVW(SB),7,$0
|
||||
MOVQ (R8), AX // w1 = x[0]
|
||||
MOVQ $0, DX
|
||||
SHRQ CX, DX:AX // w1<<ŝ
|
||||
MOVQ DX, c+48(FP)
|
||||
MOVQ DX, c+40(FP)
|
||||
|
||||
MOVQ $0, BX // i = 0
|
||||
JMP E9
|
||||
@ -169,17 +169,17 @@ X9a: SHRQ CX, AX // w1>>s
|
||||
MOVQ AX, (R10)(R11*8) // z[n-1] = w1>>s
|
||||
RET
|
||||
|
||||
X9b: MOVQ $0, c+48(FP)
|
||||
X9b: MOVQ $0, c+40(FP)
|
||||
RET
|
||||
|
||||
|
||||
// func mulAddVWW(z, x []Word, y, r Word, n int) (c Word)
|
||||
// func mulAddVWW(z, x []Word, y, r Word) (c Word)
|
||||
TEXT ·mulAddVWW(SB),7,$0
|
||||
MOVQ z+0(FP), R10
|
||||
MOVQ x+16(FP), R8
|
||||
MOVQ y+32(FP), R9
|
||||
MOVQ r+40(FP), CX // c = r
|
||||
MOVL n+48(FP), R11
|
||||
MOVL n+8(FP), R11
|
||||
MOVQ $0, BX // i = 0
|
||||
JMP E5
|
||||
|
||||
@ -194,16 +194,16 @@ L5: MOVQ (R8)(BX*8), AX
|
||||
E5: CMPQ BX, R11 // i < n
|
||||
JL L5
|
||||
|
||||
MOVQ CX, c+56(FP)
|
||||
MOVQ CX, c+48(FP)
|
||||
RET
|
||||
|
||||
|
||||
// func addMulVVW(z, x []Word, y Word, n int) (c Word)
|
||||
// func addMulVVW(z, x []Word, y Word) (c Word)
|
||||
TEXT ·addMulVVW(SB),7,$0
|
||||
MOVQ z+0(FP), R10
|
||||
MOVQ x+16(FP), R8
|
||||
MOVQ y+32(FP), R9
|
||||
MOVL n+40(FP), R11
|
||||
MOVL n+8(FP), R11
|
||||
MOVQ $0, BX // i = 0
|
||||
MOVQ $0, CX // c = 0
|
||||
JMP E6
|
||||
@ -221,17 +221,17 @@ L6: MOVQ (R8)(BX*8), AX
|
||||
E6: CMPQ BX, R11 // i < n
|
||||
JL L6
|
||||
|
||||
MOVQ CX, c+48(FP)
|
||||
MOVQ CX, c+40(FP)
|
||||
RET
|
||||
|
||||
|
||||
// divWVW(z []Word, xn Word, x []Word, y Word, n int) (r Word)
|
||||
// divWVW(z []Word, xn Word, x []Word, y Word) (r Word)
|
||||
TEXT ·divWVW(SB),7,$0
|
||||
MOVQ z+0(FP), R10
|
||||
MOVQ xn+16(FP), DX // r = xn
|
||||
MOVQ x+24(FP), R8
|
||||
MOVQ y+40(FP), R9
|
||||
MOVL n+48(FP), BX // i = n
|
||||
MOVL n+8(FP), BX // i = n
|
||||
JMP E7
|
||||
|
||||
L7: MOVQ (R8)(BX*8), AX
|
||||
@ -241,5 +241,5 @@ L7: MOVQ (R8)(BX*8), AX
|
||||
E7: SUBL $1, BX // i--
|
||||
JGE L7 // i >= 0
|
||||
|
||||
MOVQ DX, r+56(FP)
|
||||
MOVQ DX, r+48(FP)
|
||||
RET
|
||||
|
||||
@ -52,7 +52,7 @@ func TestFunWW(t *testing.T) {
|
||||
}
|
||||
|
||||
|
||||
type funVV func(z, x, y []Word, n int) (c Word)
|
||||
type funVV func(z, x, y []Word) (c Word)
|
||||
type argVV struct {
|
||||
z, x, y nat
|
||||
c Word
|
||||
@ -72,9 +72,8 @@ var sumVV = []argVV{
|
||||
|
||||
|
||||
func testFunVV(t *testing.T, msg string, f funVV, a argVV) {
|
||||
n := len(a.z)
|
||||
z := make(nat, n)
|
||||
c := f(z, a.x, a.y, n)
|
||||
z := make(nat, len(a.z))
|
||||
c := f(z, a.x, a.y)
|
||||
for i, zi := range z {
|
||||
if zi != a.z[i] {
|
||||
t.Errorf("%s%+v\n\tgot z[%d] = %#x; want %#x", msg, a, i, zi, a.z[i])
|
||||
@ -108,7 +107,7 @@ func TestFunVV(t *testing.T) {
|
||||
}
|
||||
|
||||
|
||||
type funVW func(z, x []Word, y Word, n int) (c Word)
|
||||
type funVW func(z, x []Word, y Word) (c Word)
|
||||
type argVW struct {
|
||||
z, x nat
|
||||
y Word
|
||||
@ -171,9 +170,8 @@ var rshVW = []argVW{
|
||||
|
||||
|
||||
func testFunVW(t *testing.T, msg string, f funVW, a argVW) {
|
||||
n := len(a.z)
|
||||
z := make(nat, n)
|
||||
c := f(z, a.x, a.y, n)
|
||||
z := make(nat, len(a.z))
|
||||
c := f(z, a.x, a.y)
|
||||
for i, zi := range z {
|
||||
if zi != a.z[i] {
|
||||
t.Errorf("%s%+v\n\tgot z[%d] = %#x; want %#x", msg, a, i, zi, a.z[i])
|
||||
@ -211,7 +209,7 @@ func TestFunVW(t *testing.T) {
|
||||
}
|
||||
|
||||
|
||||
type funVWW func(z, x []Word, y, r Word, n int) (c Word)
|
||||
type funVWW func(z, x []Word, y, r Word) (c Word)
|
||||
type argVWW struct {
|
||||
z, x nat
|
||||
y, r Word
|
||||
@ -246,9 +244,8 @@ var prodVWW = []argVWW{
|
||||
|
||||
|
||||
func testFunVWW(t *testing.T, msg string, f funVWW, a argVWW) {
|
||||
n := len(a.z)
|
||||
z := make(nat, n)
|
||||
c := f(z, a.x, a.y, a.r, n)
|
||||
z := make(nat, len(a.z))
|
||||
c := f(z, a.x, a.y, a.r)
|
||||
for i, zi := range z {
|
||||
if zi != a.z[i] {
|
||||
t.Errorf("%s%+v\n\tgot z[%d] = %#x; want %#x", msg, a, i, zi, a.z[i])
|
||||
@ -264,7 +261,7 @@ func testFunVWW(t *testing.T, msg string, f funVWW, a argVWW) {
|
||||
// TODO(gri) mulAddVWW and divWVW are symmetric operations but
|
||||
// their signature is not symmetric. Try to unify.
|
||||
|
||||
type funWVW func(z []Word, xn Word, x []Word, y Word, n int) (r Word)
|
||||
type funWVW func(z []Word, xn Word, x []Word, y Word) (r Word)
|
||||
type argWVW struct {
|
||||
z nat
|
||||
xn Word
|
||||
@ -274,9 +271,8 @@ type argWVW struct {
|
||||
}
|
||||
|
||||
func testFunWVW(t *testing.T, msg string, f funWVW, a argWVW) {
|
||||
n := len(a.z)
|
||||
z := make(nat, n)
|
||||
r := f(z, a.xn, a.x, a.y, n)
|
||||
z := make(nat, len(a.z))
|
||||
r := f(z, a.xn, a.x, a.y)
|
||||
for i, zi := range z {
|
||||
if zi != a.z[i] {
|
||||
t.Errorf("%s%+v\n\tgot z[%d] = %#x; want %#x", msg, a, i, zi, a.z[i])
|
||||
|
||||
@ -42,11 +42,10 @@ var (
|
||||
)
|
||||
|
||||
|
||||
func (z nat) clear() nat {
|
||||
func (z nat) clear() {
|
||||
for i := range z {
|
||||
z[i] = 0
|
||||
}
|
||||
return z
|
||||
}
|
||||
|
||||
|
||||
@ -55,26 +54,18 @@ func (z nat) norm() nat {
|
||||
for i > 0 && z[i-1] == 0 {
|
||||
i--
|
||||
}
|
||||
z = z[0:i]
|
||||
return z
|
||||
return z[0:i]
|
||||
}
|
||||
|
||||
|
||||
// TODO(gri) Consider changing "make" such that is does not reserve space
|
||||
// for a potential carry; instead callers must provide the correct
|
||||
// m (+1). Should lead to clearer code and shorter allocations on
|
||||
// average.
|
||||
|
||||
func (z nat) make(m int) nat {
|
||||
if cap(z) > m {
|
||||
return z[0:m] // reuse z - has at least one extra word for a carry, if any
|
||||
func (z nat) make(n int) nat {
|
||||
if n <= cap(z) {
|
||||
return z[0:n] // reuse z
|
||||
}
|
||||
|
||||
c := 4 // minimum capacity
|
||||
if m > c {
|
||||
c = m
|
||||
}
|
||||
return make(nat, m, c+1) // +1: extra word for a carry, if any
|
||||
// Choosing a good value for e has significant performance impact
|
||||
// because it increases the chance that a value can be reused.
|
||||
const e = 4 // extra capacity
|
||||
return make(nat, n, n+e)
|
||||
}
|
||||
|
||||
|
||||
@ -98,7 +89,7 @@ func (z nat) new(x uint64) nat {
|
||||
|
||||
// split x into n words
|
||||
z = z.make(n)
|
||||
for i := 0; i < n; i++ {
|
||||
for i := range z {
|
||||
z[i] = Word(x & _M)
|
||||
x >>= _W
|
||||
}
|
||||
@ -132,17 +123,14 @@ func (z nat) add(x, y nat) nat {
|
||||
}
|
||||
// m > 0
|
||||
|
||||
z = z.make(m)
|
||||
c := addVV(z, x, y, n)
|
||||
z = z.make(m + 1)
|
||||
c := addVV(z[0:n], x, y)
|
||||
if m > n {
|
||||
c = addVW(z[n:], x[n:], c, m-n)
|
||||
}
|
||||
if c > 0 {
|
||||
z = z[0 : m+1]
|
||||
z[m] = c
|
||||
c = addVW(z[n:m], x[n:], c)
|
||||
}
|
||||
z[m] = c
|
||||
|
||||
return z
|
||||
return z.norm()
|
||||
}
|
||||
|
||||
|
||||
@ -163,9 +151,9 @@ func (z nat) sub(x, y nat) nat {
|
||||
// m > 0
|
||||
|
||||
z = z.make(m)
|
||||
c := subVV(z, x, y, n)
|
||||
c := subVV(z[0:n], x, y)
|
||||
if m > n {
|
||||
c = subVW(z[n:], x[n:], c, m-n)
|
||||
c = subVW(z[n:], x[n:], c)
|
||||
}
|
||||
if c != 0 {
|
||||
panic("underflow")
|
||||
@ -210,14 +198,10 @@ func (z nat) mulAddWW(x nat, y, r Word) nat {
|
||||
}
|
||||
// m > 0
|
||||
|
||||
z = z.make(m)
|
||||
c := mulAddVWW(z, x, y, r, m)
|
||||
if c > 0 {
|
||||
z = z[0 : m+1]
|
||||
z[m] = c
|
||||
}
|
||||
z = z.make(m + 1)
|
||||
z[m] = mulAddVWW(z[0:m], x, y, r)
|
||||
|
||||
return z
|
||||
return z.norm()
|
||||
}
|
||||
|
||||
|
||||
@ -227,7 +211,7 @@ func basicMul(z, x, y nat) {
|
||||
z[0 : len(x)+len(y)].clear() // initialize z
|
||||
for i, d := range y {
|
||||
if d != 0 {
|
||||
z[len(x)+i] = addMulVVW(z[i:], x, d, len(x))
|
||||
z[len(x)+i] = addMulVVW(z[i:i+len(x)], x, d)
|
||||
}
|
||||
}
|
||||
}
|
||||
@ -236,16 +220,16 @@ func basicMul(z, x, y nat) {
|
||||
// Fast version of z[0:n+n>>1].add(z[0:n+n>>1], x[0:n]) w/o bounds checks.
|
||||
// Factored out for readability - do not use outside karatsuba.
|
||||
func karatsubaAdd(z, x nat, n int) {
|
||||
if c := addVV(z, z, x, n); c != 0 {
|
||||
addVW(z[n:], z[n:], c, n>>1)
|
||||
if c := addVV(z[0:n], z, x); c != 0 {
|
||||
addVW(z[n:n+n>>1], z[n:], c)
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
// Like karatsubaAdd, but does subtract.
|
||||
func karatsubaSub(z, x nat, n int) {
|
||||
if c := subVV(z, z, x, n); c != 0 {
|
||||
subVW(z[n:], z[n:], c, n>>1)
|
||||
if c := subVV(z[0:n], z, x); c != 0 {
|
||||
subVW(z[n:n+n>>1], z[n:], c)
|
||||
}
|
||||
}
|
||||
|
||||
@ -315,16 +299,16 @@ func karatsuba(z, x, y nat) {
|
||||
// compute xd (or the negative value if underflow occurs)
|
||||
s := 1 // sign of product xd*yd
|
||||
xd := z[2*n : 2*n+n2]
|
||||
if subVV(xd, x1, x0, n2) != 0 { // x1-x0
|
||||
if subVV(xd, x1, x0) != 0 { // x1-x0
|
||||
s = -s
|
||||
subVV(xd, x0, x1, n2) // x0-x1
|
||||
subVV(xd, x0, x1) // x0-x1
|
||||
}
|
||||
|
||||
// compute yd (or the negative value if underflow occurs)
|
||||
yd := z[2*n+n2 : 3*n]
|
||||
if subVV(yd, y0, y1, n2) != 0 { // y0-y1
|
||||
if subVV(yd, y0, y1) != 0 { // y0-y1
|
||||
s = -s
|
||||
subVV(yd, y1, y0, n2) // y1-y0
|
||||
subVV(yd, y1, y0) // y1-y0
|
||||
}
|
||||
|
||||
// p = (x1-x0)*(y0-y1) == x1*y0 - x1*y1 - x0*y0 + x0*y1 for s > 0
|
||||
@ -366,10 +350,10 @@ func alias(x, y nat) bool {
|
||||
// slice, and we don't need to normalize z after each addition)
|
||||
func addAt(z, x nat, i int) {
|
||||
if n := len(x); n > 0 {
|
||||
if c := addVV(z[i:], z[i:], x, n); c != 0 {
|
||||
if c := addVV(z[i:i+n], z[i:], x); c != 0 {
|
||||
j := i + n
|
||||
if j < len(z) {
|
||||
addVW(z[j:], z[j:], c, len(z)-j)
|
||||
addVW(z[j:], z[j:], c)
|
||||
}
|
||||
}
|
||||
}
|
||||
@ -500,7 +484,7 @@ func (z nat) divW(x nat, y Word) (q nat, r Word) {
|
||||
}
|
||||
// m > 0
|
||||
z = z.make(m)
|
||||
r = divWVW(z, 0, x, y, m)
|
||||
r = divWVW(z, 0, x, y)
|
||||
q = z.norm()
|
||||
return
|
||||
}
|
||||
@ -549,12 +533,13 @@ func (z nat) divLarge(u, uIn, v nat) (q, r nat) {
|
||||
if alias(u, uIn) {
|
||||
u = nil // u is an alias for uIn - cannot reuse
|
||||
}
|
||||
u = u.make(len(uIn) + 1).clear()
|
||||
u = u.make(len(uIn) + 1)
|
||||
u.clear()
|
||||
|
||||
// D1.
|
||||
shift := Word(leadingZeros(v[n-1]))
|
||||
shlVW(v, v, shift, n)
|
||||
u[len(uIn)] = shlVW(u, uIn, shift, len(uIn))
|
||||
shlVW(v, v, shift)
|
||||
u[len(uIn)] = shlVW(u[0:len(uIn)], uIn, shift)
|
||||
|
||||
// D2.
|
||||
for j := m; j >= 0; j-- {
|
||||
@ -582,11 +567,11 @@ func (z nat) divLarge(u, uIn, v nat) (q, r nat) {
|
||||
}
|
||||
|
||||
// D4.
|
||||
qhatv[n] = mulAddVWW(qhatv, v, qhat, 0, n)
|
||||
qhatv[n] = mulAddVWW(qhatv[0:n], v, qhat, 0)
|
||||
|
||||
c := subVV(u[j:], u[j:], qhatv, len(qhatv))
|
||||
c := subVV(u[j:j+len(qhatv)], u[j:], qhatv)
|
||||
if c != 0 {
|
||||
c := addVV(u[j:], u[j:], v, n)
|
||||
c := addVV(u[j:j+n], u[j:], v)
|
||||
u[j+n] += c
|
||||
qhat--
|
||||
}
|
||||
@ -595,8 +580,8 @@ func (z nat) divLarge(u, uIn, v nat) (q, r nat) {
|
||||
}
|
||||
|
||||
q = q.norm()
|
||||
shrVW(u, u, shift, len(u))
|
||||
shrVW(v, v, shift, n)
|
||||
shrVW(u, u, shift)
|
||||
shrVW(v, v, shift)
|
||||
r = u.norm()
|
||||
|
||||
return q, r
|
||||
@ -756,7 +741,7 @@ func (z nat) shl(x nat, s uint) nat {
|
||||
|
||||
n := m + int(s/_W)
|
||||
z = z.make(n + 1)
|
||||
z[n] = shlVW(z[n-m:], x, Word(s%_W), m)
|
||||
z[n] = shlVW(z[n-m:n], x, Word(s%_W))
|
||||
z[0 : n-m].clear()
|
||||
|
||||
return z.norm()
|
||||
@ -773,7 +758,7 @@ func (z nat) shr(x nat, s uint) nat {
|
||||
// n > 0
|
||||
|
||||
z = z.make(n)
|
||||
shrVW(z, x[m-n:], Word(s%_W), n)
|
||||
shrVW(z, x[m-n:], Word(s%_W))
|
||||
|
||||
return z.norm()
|
||||
}
|
||||
@ -863,7 +848,7 @@ func (x nat) modW(d Word) (r Word) {
|
||||
// TODO(agl): we don't actually need to store the q value.
|
||||
var q nat
|
||||
q = q.make(len(x))
|
||||
return divWVW(q, 0, x, d, len(x))
|
||||
return divWVW(q, 0, x, d)
|
||||
}
|
||||
|
||||
|
||||
@ -882,7 +867,7 @@ func (n nat) powersOfTwoDecompose() (q nat, k Word) {
|
||||
x := trailingZeroBits(n[zeroWords])
|
||||
|
||||
q = q.make(len(n) - zeroWords)
|
||||
shrVW(q, n[zeroWords:], Word(x), len(q))
|
||||
shrVW(q, n[zeroWords:], Word(x))
|
||||
q = q.norm()
|
||||
|
||||
k = Word(_W*zeroWords + x)
|
||||
|
||||
Loading…
Reference in New Issue
Block a user