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Commit 52cc0581 authored by Robert Griesemer's avatar Robert Griesemer
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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
parent 61eb0e71
Hide whitespace changes
Inline Side-by-side
Showing with 142 additions and 161 deletions
src/pkg/big/arith.go
View file @ 52cc0581
...@@ -284,47 +284,47 @@ func divWW_g(x1, x0, y Word) (q, r Word) { ...@@ -284,47 +284,47 @@ func divWW_g(x1, x0, y Word) (q, r Word) {
} }
func addVV(z, x, y []Word, n int) (c Word) func addVV(z, x, y []Word) (c Word)
func addVV_g(z, x, y []Word, n int) (c Word) { func addVV_g(z, x, y []Word) (c Word) {
for i := 0; i < n; i++ { for i := range z {
c, z[i] = addWW_g(x[i], y[i], c) c, z[i] = addWW_g(x[i], y[i], c)
} }
return return
} }
func subVV(z, x, y []Word, n int) (c Word) func subVV(z, x, y []Word) (c Word)
func subVV_g(z, x, y []Word, n int) (c Word) { func subVV_g(z, x, y []Word) (c Word) {
for i := 0; i < n; i++ { for i := range z {
c, z[i] = subWW_g(x[i], y[i], c) c, z[i] = subWW_g(x[i], y[i], c)
} }
return return
} }
func addVW(z, x []Word, y Word, n int) (c Word) func addVW(z, x []Word, y Word) (c Word)
func addVW_g(z, x []Word, y Word, n int) (c Word) { func addVW_g(z, x []Word, y Word) (c Word) {
c = y c = y
for i := 0; i < n; i++ { for i := range z {
c, z[i] = addWW_g(x[i], c, 0) c, z[i] = addWW_g(x[i], c, 0)
} }
return return
} }
func subVW(z, x []Word, y Word, n int) (c Word) func subVW(z, x []Word, y Word) (c Word)
func subVW_g(z, x []Word, y Word, n int) (c Word) { func subVW_g(z, x []Word, y Word) (c Word) {
c = y c = y
for i := 0; i < n; i++ { for i := range z {
c, z[i] = subWW_g(x[i], c, 0) c, z[i] = subWW_g(x[i], c, 0)
} }
return return
} }
func shlVW(z, x []Word, s Word, n int) (c Word) func shlVW(z, x []Word, s Word) (c Word)
func shlVW_g(z, x []Word, s Word, n int) (c Word) { func shlVW_g(z, x []Word, s Word) (c Word) {
if n > 0 { if n := len(z); n > 0 {
ŝ := _W - s ŝ := _W - s
w1 := x[n-1] w1 := x[n-1]
c = w1 >> ŝ c = w1 >> ŝ
...@@ -339,9 +339,9 @@ func shlVW_g(z, x []Word, s Word, n int) (c Word) { ...@@ -339,9 +339,9 @@ func shlVW_g(z, x []Word, s Word, n int) (c Word) {
} }
func shrVW(z, x []Word, s Word, n int) (c Word) func shrVW(z, x []Word, s Word) (c Word)
func shrVW_g(z, x []Word, s Word, n int) (c Word) { func shrVW_g(z, x []Word, s Word) (c Word) {
if n > 0 { if n := len(z); n > 0 {
ŝ := _W - s ŝ := _W - s
w1 := x[0] w1 := x[0]
c = w1 << ŝ c = w1 << ŝ
...@@ -356,19 +356,19 @@ func shrVW_g(z, x []Word, s Word, n int) (c Word) { ...@@ -356,19 +356,19 @@ func shrVW_g(z, x []Word, s Word, n int) (c Word) {
} }
func mulAddVWW(z, x []Word, y, r Word, n int) (c Word) func mulAddVWW(z, x []Word, y, r Word) (c Word)
func mulAddVWW_g(z, x []Word, y, r Word, n int) (c Word) { func mulAddVWW_g(z, x []Word, y, r Word) (c Word) {
c = r c = r
for i := 0; i < n; i++ { for i := range z {
c, z[i] = mulAddWWW_g(x[i], y, c) c, z[i] = mulAddWWW_g(x[i], y, c)
} }
return return
} }
func addMulVVW(z, x []Word, y Word, n int) (c Word) func addMulVVW(z, x []Word, y Word) (c Word)
func addMulVVW_g(z, x []Word, y Word, n int) (c Word) { func addMulVVW_g(z, x []Word, y Word) (c Word) {
for i := 0; i < n; i++ { for i := range z {
z1, z0 := mulAddWWW_g(x[i], y, z[i]) z1, z0 := mulAddWWW_g(x[i], y, z[i])
c, z[i] = addWW_g(z0, c, 0) c, z[i] = addWW_g(z0, c, 0)
c += z1 c += z1
...@@ -377,10 +377,10 @@ func addMulVVW_g(z, x []Word, y Word, n int) (c Word) { ...@@ -377,10 +377,10 @@ func addMulVVW_g(z, x []Word, y Word, n int) (c Word) {
} }
func divWVW(z []Word, xn Word, x []Word, y Word, n int) (r Word) func divWVW(z []Word, xn Word, x []Word, y Word) (r Word)
func divWVW_g(z []Word, xn Word, x []Word, y Word, n int) (r Word) { func divWVW_g(z []Word, xn Word, x []Word, y Word) (r Word) {
r = xn r = xn
for i := n - 1; i >= 0; i-- { for i := len(z) - 1; i >= 0; i-- {
z[i], r = divWW_g(r, x[i], y) z[i], r = divWW_g(r, x[i], y)
} }
return return
......
src/pkg/big/arith_386.s
View file @ 52cc0581
...@@ -5,12 +5,12 @@ ...@@ -5,12 +5,12 @@
// This file provides fast assembly versions for the elementary // This file provides fast assembly versions for the elementary
// arithmetic operations on vectors implemented in arith.go. // arithmetic operations on vectors implemented in arith.go.
// func addVV(z, x, y []Word, n int) (c Word) // func addVV(z, x, y []Word) (c Word)
TEXT ·addVV(SB),7,$0 TEXT ·addVV(SB),7,$0
MOVL z+0(FP), DI MOVL z+0(FP), DI
MOVL x+12(FP), SI MOVL x+12(FP), SI
MOVL y+24(FP), CX MOVL y+24(FP), CX
MOVL n+36(FP), BP MOVL n+4(FP), BP
MOVL $0, BX // i = 0 MOVL $0, BX // i = 0
MOVL $0, DX // c = 0 MOVL $0, DX // c = 0
JMP E1 JMP E1
...@@ -25,17 +25,17 @@ L1: MOVL (SI)(BX*4), AX ...@@ -25,17 +25,17 @@ L1: MOVL (SI)(BX*4), AX
E1: CMPL BX, BP // i < n E1: CMPL BX, BP // i < n
JL L1 JL L1
MOVL DX, c+40(FP) MOVL DX, c+36(FP)
RET RET
// func subVV(z, x, y []Word, n int) (c Word) // func subVV(z, x, y []Word) (c Word)
// (same as addVV except for SBBL instead of ADCL and label names) // (same as addVV except for SBBL instead of ADCL and label names)
TEXT ·subVV(SB),7,$0 TEXT ·subVV(SB),7,$0
MOVL z+0(FP), DI MOVL z+0(FP), DI
MOVL x+12(FP), SI MOVL x+12(FP), SI
MOVL y+24(FP), CX MOVL y+24(FP), CX
MOVL n+36(FP), BP MOVL n+4(FP), BP
MOVL $0, BX // i = 0 MOVL $0, BX // i = 0
MOVL $0, DX // c = 0 MOVL $0, DX // c = 0
JMP E2 JMP E2
...@@ -50,16 +50,16 @@ L2: MOVL (SI)(BX*4), AX ...@@ -50,16 +50,16 @@ L2: MOVL (SI)(BX*4), AX
E2: CMPL BX, BP // i < n E2: CMPL BX, BP // i < n
JL L2 JL L2
MOVL DX, c+40(FP) MOVL DX, c+36(FP)
RET RET
// func addVW(z, x []Word, y Word, n int) (c Word) // func addVW(z, x []Word, y Word) (c Word)
TEXT ·addVW(SB),7,$0 TEXT ·addVW(SB),7,$0
MOVL z+0(FP), DI MOVL z+0(FP), DI
MOVL x+12(FP), SI MOVL x+12(FP), SI
MOVL y+24(FP), AX // c = y MOVL y+24(FP), AX // c = y
MOVL n+28(FP), BP MOVL n+4(FP), BP
MOVL $0, BX // i = 0 MOVL $0, BX // i = 0
JMP E3 JMP E3
...@@ -72,16 +72,16 @@ L3: ADDL (SI)(BX*4), AX ...@@ -72,16 +72,16 @@ L3: ADDL (SI)(BX*4), AX
E3: CMPL BX, BP // i < n E3: CMPL BX, BP // i < n
JL L3 JL L3
MOVL AX, c+32(FP) MOVL AX, c+28(FP)
RET RET
// func subVW(z, x []Word, y Word, n int) (c Word) // func subVW(z, x []Word, y Word) (c Word)
TEXT ·subVW(SB),7,$0 TEXT ·subVW(SB),7,$0
MOVL z+0(FP), DI MOVL z+0(FP), DI
MOVL x+12(FP), SI MOVL x+12(FP), SI
MOVL y+24(FP), AX // c = y MOVL y+24(FP), AX // c = y
MOVL n+28(FP), BP MOVL n+4(FP), BP
MOVL $0, BX // i = 0 MOVL $0, BX // i = 0
JMP E4 JMP E4
...@@ -95,13 +95,13 @@ L4: MOVL (SI)(BX*4), DX // TODO(gri) is there a reverse SUBL? ...@@ -95,13 +95,13 @@ L4: MOVL (SI)(BX*4), DX // TODO(gri) is there a reverse SUBL?
E4: CMPL BX, BP // i < n E4: CMPL BX, BP // i < n
JL L4 JL L4
MOVL AX, c+32(FP) MOVL AX, c+28(FP)
RET RET
// func shlVW(z, x []Word, s Word, n int) (c Word) // func shlVW(z, x []Word, s Word) (c Word)
TEXT ·shlVW(SB),7,$0 TEXT ·shlVW(SB),7,$0
MOVL n+28(FP), BX // i = n MOVL n+4(FP), BX // i = n
SUBL $1, BX // i-- SUBL $1, BX // i--
JL X8b // i < 0 (n <= 0) JL X8b // i < 0 (n <= 0)
...@@ -112,7 +112,7 @@ TEXT ·shlVW(SB),7,$0 ...@@ -112,7 +112,7 @@ TEXT ·shlVW(SB),7,$0
MOVL (SI)(BX*4), AX // w1 = x[n-1] MOVL (SI)(BX*4), AX // w1 = x[n-1]
MOVL $0, DX MOVL $0, DX
SHLL CX, DX:AX // w1>>ŝ SHLL CX, DX:AX // w1>>ŝ
MOVL DX, c+32(FP) MOVL DX, c+28(FP)
CMPL BX, $0 CMPL BX, $0
JLE X8a // i <= 0 JLE X8a // i <= 0
...@@ -130,13 +130,13 @@ X8a: SHLL CX, AX // w1<<s ...@@ -130,13 +130,13 @@ X8a: SHLL CX, AX // w1<<s
MOVL AX, (DI) // z[0] = w1<<s MOVL AX, (DI) // z[0] = w1<<s
RET RET
X8b: MOVL $0, c+32(FP) X8b: MOVL $0, c+28(FP)
RET 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 TEXT ·shrVW(SB),7,$0
MOVL n+28(FP), BP MOVL n+4(FP), BP
SUBL $1, BP // n-- SUBL $1, BP // n--
JL X9b // n < 0 (n <= 0) JL X9b // n < 0 (n <= 0)
...@@ -147,7 +147,7 @@ TEXT ·shrVW(SB),7,$0 ...@@ -147,7 +147,7 @@ TEXT ·shrVW(SB),7,$0
MOVL (SI), AX // w1 = x[0] MOVL (SI), AX // w1 = x[0]
MOVL $0, DX MOVL $0, DX
SHRL CX, DX:AX // w1<<ŝ SHRL CX, DX:AX // w1<<ŝ
MOVL DX, c+32(FP) MOVL DX, c+28(FP)
MOVL $0, BX // i = 0 MOVL $0, BX // i = 0
JMP E9 JMP E9
...@@ -167,17 +167,17 @@ X9a: SHRL CX, AX // w1>>s ...@@ -167,17 +167,17 @@ X9a: SHRL CX, AX // w1>>s
MOVL AX, (DI)(BP*4) // z[n-1] = w1>>s MOVL AX, (DI)(BP*4) // z[n-1] = w1>>s
RET RET
X9b: MOVL $0, c+32(FP) X9b: MOVL $0, c+28(FP)
RET 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 TEXT ·mulAddVWW(SB),7,$0
MOVL z+0(FP), DI MOVL z+0(FP), DI
MOVL x+12(FP), SI MOVL x+12(FP), SI
MOVL y+24(FP), BP MOVL y+24(FP), BP
MOVL r+28(FP), CX // c = r MOVL r+28(FP), CX // c = r
MOVL n+32(FP), BX MOVL n+4(FP), BX
LEAL (DI)(BX*4), DI LEAL (DI)(BX*4), DI
LEAL (SI)(BX*4), SI LEAL (SI)(BX*4), SI
NEGL BX // i = -n NEGL BX // i = -n
...@@ -194,16 +194,16 @@ L5: MOVL (SI)(BX*4), AX ...@@ -194,16 +194,16 @@ L5: MOVL (SI)(BX*4), AX
E5: CMPL BX, $0 // i < 0 E5: CMPL BX, $0 // i < 0
JL L5 JL L5
MOVL CX, c+36(FP) MOVL CX, c+32(FP)
RET 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 TEXT ·addMulVVW(SB),7,$0
MOVL z+0(FP), DI MOVL z+0(FP), DI
MOVL x+12(FP), SI MOVL x+12(FP), SI
MOVL y+24(FP), BP MOVL y+24(FP), BP
MOVL n+28(FP), BX MOVL n+4(FP), BX
LEAL (DI)(BX*4), DI LEAL (DI)(BX*4), DI
LEAL (SI)(BX*4), SI LEAL (SI)(BX*4), SI
NEGL BX // i = -n NEGL BX // i = -n
...@@ -223,17 +223,17 @@ L6: MOVL (SI)(BX*4), AX ...@@ -223,17 +223,17 @@ L6: MOVL (SI)(BX*4), AX
E6: CMPL BX, $0 // i < 0 E6: CMPL BX, $0 // i < 0
JL L6 JL L6
MOVL CX, c+32(FP) MOVL CX, c+28(FP)
RET 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 TEXT ·divWVW(SB),7,$0
MOVL z+0(FP), DI MOVL z+0(FP), DI
MOVL xn+12(FP), DX // r = xn MOVL xn+12(FP), DX // r = xn
MOVL x+16(FP), SI MOVL x+16(FP), SI
MOVL y+28(FP), CX MOVL y+28(FP), CX
MOVL n+32(FP), BX // i = n MOVL n+4(FP), BX // i = n
JMP E7 JMP E7
L7: MOVL (SI)(BX*4), AX L7: MOVL (SI)(BX*4), AX
...@@ -243,5 +243,5 @@ L7: MOVL (SI)(BX*4), AX ...@@ -243,5 +243,5 @@ L7: MOVL (SI)(BX*4), AX
E7: SUBL $1, BX // i-- E7: SUBL $1, BX // i--
JGE L7 // i >= 0 JGE L7 // i >= 0
MOVL DX, r+36(FP) MOVL DX, r+32(FP)
RET RET
src/pkg/big/arith_amd64.s
View file @ 52cc0581
...@@ -7,12 +7,12 @@ ...@@ -7,12 +7,12 @@
// TODO(gri) - experiment with unrolled loops for faster execution // TODO(gri) - experiment with unrolled loops for faster execution
// func addVV(z, x, y []Word, n int) (c Word) // func addVV(z, x, y []Word) (c Word)
TEXT ·addVV(SB),7,$0 TEXT ·addVV(SB),7,$0
MOVQ z+0(FP), R10 MOVQ z+0(FP), R10
MOVQ x+16(FP), R8 MOVQ x+16(FP), R8
MOVQ y+32(FP), R9 MOVQ y+32(FP), R9
MOVL n+48(FP), R11 MOVL n+8(FP), R11
MOVQ $0, BX // i = 0 MOVQ $0, BX // i = 0
MOVQ $0, DX // c = 0 MOVQ $0, DX // c = 0
JMP E1 JMP E1
...@@ -27,17 +27,17 @@ L1: MOVQ (R8)(BX*8), AX ...@@ -27,17 +27,17 @@ L1: MOVQ (R8)(BX*8), AX
E1: CMPQ BX, R11 // i < n E1: CMPQ BX, R11 // i < n
JL L1 JL L1
MOVQ DX, c+56(FP) MOVQ DX, c+48(FP)
RET RET
// func subVV(z, x, y []Word, n int) (c Word) // func subVV(z, x, y []Word) (c Word)
// (same as addVV_s except for SBBQ instead of ADCQ and label names) // (same as addVV_s except for SBBQ instead of ADCQ and label names)
TEXT ·subVV(SB),7,$0 TEXT ·subVV(SB),7,$0
MOVQ z+0(FP), R10 MOVQ z+0(FP), R10
MOVQ x+16(FP), R8 MOVQ x+16(FP), R8
MOVQ y+32(FP), R9 MOVQ y+32(FP), R9
MOVL n+48(FP), R11 MOVL n+8(FP), R11
MOVQ $0, BX // i = 0 MOVQ $0, BX // i = 0
MOVQ $0, DX // c = 0 MOVQ $0, DX // c = 0
JMP E2 JMP E2
...@@ -52,16 +52,16 @@ L2: MOVQ (R8)(BX*8), AX ...@@ -52,16 +52,16 @@ L2: MOVQ (R8)(BX*8), AX
E2: CMPQ BX, R11 // i < n E2: CMPQ BX, R11 // i < n
JL L2 JL L2
MOVQ DX, c+56(FP) MOVQ DX, c+48(FP)
RET RET
// func addVW(z, x []Word, y Word, n int) (c Word) // func addVW(z, x []Word, y Word) (c Word)
TEXT ·addVW(SB),7,$0 TEXT ·addVW(SB),7,$0
MOVQ z+0(FP), R10 MOVQ z+0(FP), R10
MOVQ x+16(FP), R8 MOVQ x+16(FP), R8
MOVQ y+32(FP), AX // c = y MOVQ y+32(FP), AX // c = y
MOVL n+40(FP), R11 MOVL n+8(FP), R11
MOVQ $0, BX // i = 0 MOVQ $0, BX // i = 0
JMP E3 JMP E3
...@@ -74,16 +74,16 @@ L3: ADDQ (R8)(BX*8), AX ...@@ -74,16 +74,16 @@ L3: ADDQ (R8)(BX*8), AX
E3: CMPQ BX, R11 // i < n E3: CMPQ BX, R11 // i < n
JL L3 JL L3
MOVQ AX, c+48(FP) MOVQ AX, c+40(FP)
RET RET
// func subVW(z, x []Word, y Word, n int) (c Word) // func subVW(z, x []Word, y Word) (c Word)
TEXT ·subVW(SB),7,$0 TEXT ·subVW(SB),7,$0
MOVQ z+0(FP), R10 MOVQ z+0(FP), R10
MOVQ x+16(FP), R8 MOVQ x+16(FP), R8
MOVQ y+32(FP), AX // c = y MOVQ y+32(FP), AX // c = y
MOVL n+40(FP), R11 MOVL n+8(FP), R11
MOVQ $0, BX // i = 0 MOVQ $0, BX // i = 0
JMP E4 JMP E4
...@@ -97,13 +97,13 @@ L4: MOVQ (R8)(BX*8), DX // TODO(gri) is there a reverse SUBQ? ...@@ -97,13 +97,13 @@ L4: MOVQ (R8)(BX*8), DX // TODO(gri) is there a reverse SUBQ?
E4: CMPQ BX, R11 // i < n E4: CMPQ BX, R11 // i < n
JL L4 JL L4
MOVQ AX, c+48(FP) MOVQ AX, c+40(FP)
RET RET
// func shlVW(z, x []Word, s Word, n int) (c Word) // func shlVW(z, x []Word, s Word) (c Word)
TEXT ·shlVW(SB),7,$0 TEXT ·shlVW(SB),7,$0
MOVL n+40(FP), BX // i = n MOVL n+8(FP), BX // i = n
SUBL $1, BX // i-- SUBL $1, BX // i--
JL X8b // i < 0 (n <= 0) JL X8b // i < 0 (n <= 0)
...@@ -114,7 +114,7 @@ TEXT ·shlVW(SB),7,$0 ...@@ -114,7 +114,7 @@ TEXT ·shlVW(SB),7,$0
MOVQ (R8)(BX*8), AX // w1 = x[n-1] MOVQ (R8)(BX*8), AX // w1 = x[n-1]
MOVQ $0, DX MOVQ $0, DX
SHLQ CX, DX:AX // w1>>ŝ SHLQ CX, DX:AX // w1>>ŝ
MOVQ DX, c+48(FP) MOVQ DX, c+40(FP)
CMPL BX, $0 CMPL BX, $0
JLE X8a // i <= 0 JLE X8a // i <= 0
...@@ -132,13 +132,13 @@ X8a: SHLQ CX, AX // w1<<s ...@@ -132,13 +132,13 @@ X8a: SHLQ CX, AX // w1<<s
MOVQ AX, (R10) // z[0] = w1<<s MOVQ AX, (R10) // z[0] = w1<<s
RET RET
X8b: MOVQ $0, c+48(FP) X8b: MOVQ $0, c+40(FP)
RET 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 TEXT ·shrVW(SB),7,$0
MOVL n+40(FP), R11 MOVL n+8(FP), R11
SUBL $1, R11 // n-- SUBL $1, R11 // n--
JL X9b // n < 0 (n <= 0) JL X9b // n < 0 (n <= 0)
...@@ -149,7 +149,7 @@ TEXT ·shrVW(SB),7,$0 ...@@ -149,7 +149,7 @@ TEXT ·shrVW(SB),7,$0
MOVQ (R8), AX // w1 = x[0] MOVQ (R8), AX // w1 = x[0]
MOVQ $0, DX MOVQ $0, DX
SHRQ CX, DX:AX // w1<<ŝ SHRQ CX, DX:AX // w1<<ŝ
MOVQ DX, c+48(FP) MOVQ DX, c+40(FP)
MOVQ $0, BX // i = 0 MOVQ $0, BX // i = 0
JMP E9 JMP E9
...@@ -169,17 +169,17 @@ X9a: SHRQ CX, AX // w1>>s ...@@ -169,17 +169,17 @@ X9a: SHRQ CX, AX // w1>>s
MOVQ AX, (R10)(R11*8) // z[n-1] = w1>>s MOVQ AX, (R10)(R11*8) // z[n-1] = w1>>s
RET RET
X9b: MOVQ $0, c+48(FP) X9b: MOVQ $0, c+40(FP)
RET 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 TEXT ·mulAddVWW(SB),7,$0
MOVQ z+0(FP), R10 MOVQ z+0(FP), R10
MOVQ x+16(FP), R8 MOVQ x+16(FP), R8
MOVQ y+32(FP), R9 MOVQ y+32(FP), R9
MOVQ r+40(FP), CX // c = r MOVQ r+40(FP), CX // c = r
MOVL n+48(FP), R11 MOVL n+8(FP), R11
MOVQ $0, BX // i = 0 MOVQ $0, BX // i = 0
JMP E5 JMP E5
...@@ -194,16 +194,16 @@ L5: MOVQ (R8)(BX*8), AX ...@@ -194,16 +194,16 @@ L5: MOVQ (R8)(BX*8), AX
E5: CMPQ BX, R11 // i < n E5: CMPQ BX, R11 // i < n
JL L5 JL L5
MOVQ CX, c+56(FP) MOVQ CX, c+48(FP)
RET 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 TEXT ·addMulVVW(SB),7,$0
MOVQ z+0(FP), R10 MOVQ z+0(FP), R10
MOVQ x+16(FP), R8 MOVQ x+16(FP), R8
MOVQ y+32(FP), R9 MOVQ y+32(FP), R9
MOVL n+40(FP), R11 MOVL n+8(FP), R11
MOVQ $0, BX // i = 0 MOVQ $0, BX // i = 0
MOVQ $0, CX // c = 0 MOVQ $0, CX // c = 0
JMP E6 JMP E6
...@@ -221,17 +221,17 @@ L6: MOVQ (R8)(BX*8), AX ...@@ -221,17 +221,17 @@ L6: MOVQ (R8)(BX*8), AX
E6: CMPQ BX, R11 // i < n E6: CMPQ BX, R11 // i < n
JL L6 JL L6
MOVQ CX, c+48(FP) MOVQ CX, c+40(FP)
RET 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 TEXT ·divWVW(SB),7,$0
MOVQ z+0(FP), R10 MOVQ z+0(FP), R10
MOVQ xn+16(FP), DX // r = xn MOVQ xn+16(FP), DX // r = xn
MOVQ x+24(FP), R8 MOVQ x+24(FP), R8
MOVQ y+40(FP), R9 MOVQ y+40(FP), R9
MOVL n+48(FP), BX // i = n MOVL n+8(FP), BX // i = n
JMP E7 JMP E7
L7: MOVQ (R8)(BX*8), AX L7: MOVQ (R8)(BX*8), AX
...@@ -241,5 +241,5 @@ L7: MOVQ (R8)(BX*8), AX ...@@ -241,5 +241,5 @@ L7: MOVQ (R8)(BX*8), AX
E7: SUBL $1, BX // i-- E7: SUBL $1, BX // i--
JGE L7 // i >= 0 JGE L7 // i >= 0
MOVQ DX, r+56(FP) MOVQ DX, r+48(FP)
RET RET
src/pkg/big/arith_test.go
View file @ 52cc0581
...@@ -52,7 +52,7 @@ func TestFunWW(t *testing.T) { ...@@ -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 { type argVV struct {
z, x, y nat z, x, y nat
c Word c Word
...@@ -72,9 +72,8 @@ var sumVV = []argVV{ ...@@ -72,9 +72,8 @@ var sumVV = []argVV{
func testFunVV(t *testing.T, msg string, f funVV, a argVV) { func testFunVV(t *testing.T, msg string, f funVV, a argVV) {
n := len(a.z) z := make(nat, len(a.z))
z := make(nat, n) c := f(z, a.x, a.y)
c := f(z, a.x, a.y, n)
for i, zi := range z { for i, zi := range z {
if zi != a.z[i] { if zi != a.z[i] {
t.Errorf("%s%+v\n\tgot z[%d] = %#x; want %#x", msg, a, i, 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) { ...@@ -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 { type argVW struct {
z, x nat z, x nat
y Word y Word
...@@ -171,9 +170,8 @@ var rshVW = []argVW{ ...@@ -171,9 +170,8 @@ var rshVW = []argVW{
func testFunVW(t *testing.T, msg string, f funVW, a argVW) { func testFunVW(t *testing.T, msg string, f funVW, a argVW) {
n := len(a.z) z := make(nat, len(a.z))
z := make(nat, n) c := f(z, a.x, a.y)
c := f(z, a.x, a.y, n)
for i, zi := range z { for i, zi := range z {
if zi != a.z[i] { if zi != a.z[i] {
t.Errorf("%s%+v\n\tgot z[%d] = %#x; want %#x", msg, a, i, 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) { ...@@ -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 { type argVWW struct {
z, x nat z, x nat
y, r Word y, r Word
...@@ -246,9 +244,8 @@ var prodVWW = []argVWW{ ...@@ -246,9 +244,8 @@ var prodVWW = []argVWW{
func testFunVWW(t *testing.T, msg string, f funVWW, a argVWW) { func testFunVWW(t *testing.T, msg string, f funVWW, a argVWW) {
n := len(a.z) z := make(nat, len(a.z))
z := make(nat, n) c := f(z, a.x, a.y, a.r)
c := f(z, a.x, a.y, a.r, n)
for i, zi := range z { for i, zi := range z {
if zi != a.z[i] { if zi != a.z[i] {
t.Errorf("%s%+v\n\tgot z[%d] = %#x; want %#x", msg, a, i, 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) { ...@@ -264,7 +261,7 @@ func testFunVWW(t *testing.T, msg string, f funVWW, a argVWW) {
// TODO(gri) mulAddVWW and divWVW are symmetric operations but // TODO(gri) mulAddVWW and divWVW are symmetric operations but
// their signature is not symmetric. Try to unify. // 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 { type argWVW struct {
z nat z nat
xn Word xn Word
...@@ -274,9 +271,8 @@ type argWVW struct { ...@@ -274,9 +271,8 @@ type argWVW struct {
} }
func testFunWVW(t *testing.T, msg string, f funWVW, a argWVW) { func testFunWVW(t *testing.T, msg string, f funWVW, a argWVW) {
n := len(a.z) z := make(nat, len(a.z))
z := make(nat, n) r := f(z, a.xn, a.x, a.y)
r := f(z, a.xn, a.x, a.y, n)
for i, zi := range z { for i, zi := range z {
if zi != a.z[i] { if zi != a.z[i] {
t.Errorf("%s%+v\n\tgot z[%d] = %#x; want %#x", msg, a, i, zi, a.z[i]) t.Errorf("%s%+v\n\tgot z[%d] = %#x; want %#x", msg, a, i, zi, a.z[i])
......
src/pkg/big/nat.go
View file @ 52cc0581
...@@ -42,11 +42,10 @@ var ( ...@@ -42,11 +42,10 @@ var (
) )
func (z nat) clear() nat { func (z nat) clear() {
for i := range z { for i := range z {
z[i] = 0 z[i] = 0
} }
return z
} }
...@@ -55,26 +54,18 @@ func (z nat) norm() nat { ...@@ -55,26 +54,18 @@ func (z nat) norm() nat {
for i > 0 && z[i-1] == 0 { for i > 0 && z[i-1] == 0 {
i-- i--
} }
z = z[0:i] return z[0:i]
return z
} }
// TODO(gri) Consider changing "make" such that is does not reserve space func (z nat) make(n int) nat {
// for a potential carry; instead callers must provide the correct if n <= cap(z) {
// m (+1). Should lead to clearer code and shorter allocations on return z[0:n] // reuse z
// 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
}
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 { ...@@ -98,7 +89,7 @@ func (z nat) new(x uint64) nat {
// split x into n words // split x into n words
z = z.make(n) z = z.make(n)
for i := 0; i < n; i++ { for i := range z {
z[i] = Word(x & _M) z[i] = Word(x & _M)
x >>= _W x >>= _W
} }
...@@ -132,17 +123,14 @@ func (z nat) add(x, y nat) nat { ...@@ -132,17 +123,14 @@ func (z nat) add(x, y nat) nat {
} }
// m > 0 // m > 0
z = z.make(m) z = z.make(m + 1)
c := addVV(z, x, y, n) c := addVV(z[0:n], x, y)
if m > n { if m > n {
c = addVW(z[n:], x[n:], c, m-n) c = addVW(z[n:m], x[n:], c)
}
if c > 0 {
z = z[0 : m+1]
z[m] = c
} }
z[m] = c
return z return z.norm()
} }
...@@ -163,9 +151,9 @@ func (z nat) sub(x, y nat) nat { ...@@ -163,9 +151,9 @@ func (z nat) sub(x, y nat) nat {
// m > 0 // m > 0
z = z.make(m) z = z.make(m)
c := subVV(z, x, y, n) c := subVV(z[0:n], x, y)
if m > n { if m > n {
c = subVW(z[n:], x[n:], c, m-n) c = subVW(z[n:], x[n:], c)
} }
if c != 0 { if c != 0 {
panic("underflow") panic("underflow")
...@@ -210,14 +198,10 @@ func (z nat) mulAddWW(x nat, y, r Word) nat { ...@@ -210,14 +198,10 @@ func (z nat) mulAddWW(x nat, y, r Word) nat {
} }
// m > 0 // m > 0
z = z.make(m) z = z.make(m + 1)
c := mulAddVWW(z, x, y, r, m) z[m] = mulAddVWW(z[0:m], x, y, r)
if c > 0 {
z = z[0 : m+1]
z[m] = c
}
return z return z.norm()
} }
...@@ -227,7 +211,7 @@ func basicMul(z, x, y nat) { ...@@ -227,7 +211,7 @@ func basicMul(z, x, y nat) {
z[0 : len(x)+len(y)].clear() // initialize z z[0 : len(x)+len(y)].clear() // initialize z
for i, d := range y { for i, d := range y {
if d != 0 { 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) { ...@@ -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. // 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. // Factored out for readability - do not use outside karatsuba.
func karatsubaAdd(z, x nat, n int) { func karatsubaAdd(z, x nat, n int) {
if c := addVV(z, z, x, n); c != 0 { if c := addVV(z[0:n], z, x); c != 0 {
addVW(z[n:], z[n:], c, n>>1) addVW(z[n:n+n>>1], z[n:], c)
} }
} }
// Like karatsubaAdd, but does subtract. // Like karatsubaAdd, but does subtract.
func karatsubaSub(z, x nat, n int) { func karatsubaSub(z, x nat, n int) {
if c := subVV(z, z, x, n); c != 0 { if c := subVV(z[0:n], z, x); c != 0 {
subVW(z[n:], z[n:], c, n>>1) subVW(z[n:n+n>>1], z[n:], c)
} }
} }
...@@ -315,16 +299,16 @@ func karatsuba(z, x, y nat) { ...@@ -315,16 +299,16 @@ func karatsuba(z, x, y nat) {
// compute xd (or the negative value if underflow occurs) // compute xd (or the negative value if underflow occurs)
s := 1 // sign of product xd*yd s := 1 // sign of product xd*yd
xd := z[2*n : 2*n+n2] 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 s = -s
subVV(xd, x0, x1, n2) // x0-x1 subVV(xd, x0, x1) // x0-x1
} }
// compute yd (or the negative value if underflow occurs) // compute yd (or the negative value if underflow occurs)
yd := z[2*n+n2 : 3*n] 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 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 // 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 { ...@@ -366,10 +350,10 @@ func alias(x, y nat) bool {
// slice, and we don't need to normalize z after each addition) // slice, and we don't need to normalize z after each addition)
func addAt(z, x nat, i int) { func addAt(z, x nat, i int) {
if n := len(x); n > 0 { 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 j := i + n
if j < len(z) { 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) { ...@@ -500,7 +484,7 @@ func (z nat) divW(x nat, y Word) (q nat, r Word) {
} }
// m > 0 // m > 0
z = z.make(m) z = z.make(m)
r = divWVW(z, 0, x, y, m) r = divWVW(z, 0, x, y)
q = z.norm() q = z.norm()
return return
} }
...@@ -549,12 +533,13 @@ func (z nat) divLarge(u, uIn, v nat) (q, r nat) { ...@@ -549,12 +533,13 @@ func (z nat) divLarge(u, uIn, v nat) (q, r nat) {
if alias(u, uIn) { if alias(u, uIn) {
u = nil // u is an alias for uIn - cannot reuse 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. // D1.
shift := Word(leadingZeros(v[n-1])) shift := Word(leadingZeros(v[n-1]))
shlVW(v, v, shift, n) shlVW(v, v, shift)
u[len(uIn)] = shlVW(u, uIn, shift, len(uIn)) u[len(uIn)] = shlVW(u[0:len(uIn)], uIn, shift)
// D2. // D2.
for j := m; j >= 0; j-- { for j := m; j >= 0; j-- {
...@@ -582,11 +567,11 @@ func (z nat) divLarge(u, uIn, v nat) (q, r nat) { ...@@ -582,11 +567,11 @@ func (z nat) divLarge(u, uIn, v nat) (q, r nat) {
} }
// D4. // 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 { if c != 0 {
c := addVV(u[j:], u[j:], v, n) c := addVV(u[j:j+n], u[j:], v)
u[j+n] += c u[j+n] += c
qhat-- qhat--
} }
...@@ -595,8 +580,8 @@ func (z nat) divLarge(u, uIn, v nat) (q, r nat) { ...@@ -595,8 +580,8 @@ func (z nat) divLarge(u, uIn, v nat) (q, r nat) {
} }
q = q.norm() q = q.norm()
shrVW(u, u, shift, len(u)) shrVW(u, u, shift)
shrVW(v, v, shift, n) shrVW(v, v, shift)
r = u.norm() r = u.norm()
return q, r return q, r
...@@ -756,7 +741,7 @@ func (z nat) shl(x nat, s uint) nat { ...@@ -756,7 +741,7 @@ func (z nat) shl(x nat, s uint) nat {
n := m + int(s/_W) n := m + int(s/_W)
z = z.make(n + 1) 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() z[0 : n-m].clear()
return z.norm() return z.norm()
...@@ -773,7 +758,7 @@ func (z nat) shr(x nat, s uint) nat { ...@@ -773,7 +758,7 @@ func (z nat) shr(x nat, s uint) nat {
// n > 0 // n > 0
z = z.make(n) z = z.make(n)
shrVW(z, x[m-n:], Word(s%_W), n) shrVW(z, x[m-n:], Word(s%_W))
return z.norm() return z.norm()
} }
...@@ -863,7 +848,7 @@ func (x nat) modW(d Word) (r Word) { ...@@ -863,7 +848,7 @@ func (x nat) modW(d Word) (r Word) {
// TODO(agl): we don't actually need to store the q value. // TODO(agl): we don't actually need to store the q value.
var q nat var q nat
q = q.make(len(x)) 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) { ...@@ -882,7 +867,7 @@ func (n nat) powersOfTwoDecompose() (q nat, k Word) {
x := trailingZeroBits(n[zeroWords]) x := trailingZeroBits(n[zeroWords])
q = q.make(len(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() q = q.norm()
k = Word(_W*zeroWords + x) k = Word(_W*zeroWords + x)
......
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