From 52cc058172fe299b11d01cf5f04500de725bde07 Mon Sep 17 00:00:00 2001 From: Robert Griesemer Date: Sat, 8 May 2010 13:52:36 -0700 Subject: [PATCH] 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 --- src/pkg/big/arith.go | 54 ++++++++++---------- src/pkg/big/arith_386.s | 58 ++++++++++----------- src/pkg/big/arith_amd64.s | 58 ++++++++++----------- src/pkg/big/arith_test.go | 28 +++++----- src/pkg/big/nat.go | 105 ++++++++++++++++---------------------- 5 files changed, 142 insertions(+), 161 deletions(-) diff --git a/src/pkg/big/arith.go b/src/pkg/big/arith.go index eef93734a4..52bb3e165d 100644 --- a/src/pkg/big/arith.go +++ b/src/pkg/big/arith.go @@ -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_g(z, x, y []Word, n int) (c Word) { - for i := 0; i < n; i++ { +func addVV(z, x, y []Word) (c Word) +func addVV_g(z, x, y []Word) (c Word) { + for i := range z { c, z[i] = addWW_g(x[i], y[i], c) } return } -func subVV(z, x, y []Word, n int) (c Word) -func subVV_g(z, x, y []Word, n int) (c Word) { - for i := 0; i < n; i++ { +func subVV(z, x, y []Word) (c Word) +func subVV_g(z, x, y []Word) (c Word) { + for i := range z { c, z[i] = subWW_g(x[i], y[i], c) } return } -func addVW(z, x []Word, y Word, n int) (c Word) -func addVW_g(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) (c Word) { c = y - for i := 0; i < n; i++ { + for i := range z { c, z[i] = addWW_g(x[i], c, 0) } return } -func subVW(z, x []Word, y Word, n int) (c Word) -func subVW_g(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) (c Word) { c = y - for i := 0; i < n; i++ { + for i := range z { c, z[i] = subWW_g(x[i], c, 0) } return } -func shlVW(z, x []Word, s Word, n int) (c Word) -func shlVW_g(z, x []Word, s Word, n int) (c Word) { - if n > 0 { +func shlVW(z, x []Word, s Word) (c Word) +func shlVW_g(z, x []Word, s Word) (c Word) { + if n := len(z); n > 0 { ŝ := _W - s w1 := x[n-1] c = w1 >> ŝ @@ -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_g(z, x []Word, s Word, n int) (c Word) { - if n > 0 { +func shrVW(z, x []Word, s Word) (c Word) +func shrVW_g(z, x []Word, s Word) (c Word) { + if n := len(z); n > 0 { ŝ := _W - s w1 := x[0] c = w1 << ŝ @@ -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_g(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) (c Word) { c = r - for i := 0; i < n; i++ { + for i := range z { c, z[i] = mulAddWWW_g(x[i], y, c) } return } -func addMulVVW(z, x []Word, y Word, n int) (c Word) -func addMulVVW_g(z, x []Word, y Word, n int) (c Word) { - for i := 0; i < n; i++ { +func addMulVVW(z, x []Word, y Word) (c Word) +func addMulVVW_g(z, x []Word, y Word) (c Word) { + for i := range z { z1, z0 := mulAddWWW_g(x[i], y, z[i]) c, z[i] = addWW_g(z0, c, 0) c += z1 @@ -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_g(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) (r Word) { 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) } return diff --git a/src/pkg/big/arith_386.s b/src/pkg/big/arith_386.s index b50172ba3e..08eb5d4d50 100644 --- a/src/pkg/big/arith_386.s +++ b/src/pkg/big/arith_386.s @@ -5,12 +5,12 @@ // This file provides fast assembly versions for the elementary // 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 MOVL z+0(FP), DI MOVL x+12(FP), SI MOVL y+24(FP), CX - MOVL n+36(FP), BP + MOVL n+4(FP), BP MOVL $0, BX // i = 0 MOVL $0, DX // c = 0 JMP E1 @@ -25,17 +25,17 @@ L1: MOVL (SI)(BX*4), AX E1: CMPL BX, BP // i < n JL L1 - MOVL DX, c+40(FP) + MOVL DX, c+36(FP) 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) TEXT ·subVV(SB),7,$0 MOVL z+0(FP), DI MOVL x+12(FP), SI MOVL y+24(FP), CX - MOVL n+36(FP), BP + MOVL n+4(FP), BP MOVL $0, BX // i = 0 MOVL $0, DX // c = 0 JMP E2 @@ -50,16 +50,16 @@ L2: MOVL (SI)(BX*4), AX E2: CMPL BX, BP // i < n JL L2 - MOVL DX, c+40(FP) + MOVL DX, c+36(FP) 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 MOVL z+0(FP), DI MOVL x+12(FP), SI MOVL y+24(FP), AX // c = y - MOVL n+28(FP), BP + MOVL n+4(FP), BP MOVL $0, BX // i = 0 JMP E3 @@ -72,16 +72,16 @@ L3: ADDL (SI)(BX*4), AX E3: CMPL BX, BP // i < n JL L3 - MOVL AX, c+32(FP) + MOVL AX, c+28(FP) 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 MOVL z+0(FP), DI MOVL x+12(FP), SI MOVL y+24(FP), AX // c = y - MOVL n+28(FP), BP + MOVL n+4(FP), BP MOVL $0, BX // i = 0 JMP E4 @@ -95,13 +95,13 @@ L4: MOVL (SI)(BX*4), DX // TODO(gri) is there a reverse SUBL? E4: CMPL BX, BP // i < n JL L4 - MOVL AX, c+32(FP) + MOVL AX, c+28(FP) 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 - MOVL n+28(FP), BX // i = n + MOVL n+4(FP), BX // i = n SUBL $1, BX // i-- JL X8b // i < 0 (n <= 0) @@ -112,7 +112,7 @@ TEXT ·shlVW(SB),7,$0 MOVL (SI)(BX*4), AX // w1 = x[n-1] MOVL $0, DX SHLL CX, DX:AX // w1>>ŝ - MOVL DX, c+32(FP) + MOVL DX, c+28(FP) CMPL BX, $0 JLE X8a // i <= 0 @@ -130,13 +130,13 @@ X8a: SHLL CX, AX // w1<>s MOVL AX, (DI)(BP*4) // z[n-1] = w1>>s RET -X9b: MOVL $0, c+32(FP) +X9b: MOVL $0, c+28(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 MOVL z+0(FP), DI MOVL x+12(FP), SI MOVL y+24(FP), BP MOVL r+28(FP), CX // c = r - MOVL n+32(FP), BX + MOVL n+4(FP), BX LEAL (DI)(BX*4), DI LEAL (SI)(BX*4), SI NEGL BX // i = -n @@ -194,16 +194,16 @@ L5: MOVL (SI)(BX*4), AX E5: CMPL BX, $0 // i < 0 JL L5 - MOVL CX, c+36(FP) + MOVL CX, c+32(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 MOVL z+0(FP), DI MOVL x+12(FP), SI MOVL y+24(FP), BP - MOVL n+28(FP), BX + MOVL n+4(FP), BX LEAL (DI)(BX*4), DI LEAL (SI)(BX*4), SI NEGL BX // i = -n @@ -223,17 +223,17 @@ L6: MOVL (SI)(BX*4), AX E6: CMPL BX, $0 // i < 0 JL L6 - MOVL CX, c+32(FP) + MOVL CX, c+28(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 MOVL z+0(FP), DI MOVL xn+12(FP), DX // r = xn MOVL x+16(FP), SI MOVL y+28(FP), CX - MOVL n+32(FP), BX // i = n + MOVL n+4(FP), BX // i = n JMP E7 L7: MOVL (SI)(BX*4), AX @@ -243,5 +243,5 @@ L7: MOVL (SI)(BX*4), AX E7: SUBL $1, BX // i-- JGE L7 // i >= 0 - MOVL DX, r+36(FP) + MOVL DX, r+32(FP) RET diff --git a/src/pkg/big/arith_amd64.s b/src/pkg/big/arith_amd64.s index 9f30cee506..1dd95ec534 100644 --- a/src/pkg/big/arith_amd64.s +++ b/src/pkg/big/arith_amd64.s @@ -7,12 +7,12 @@ // 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 MOVQ z+0(FP), R10 MOVQ x+16(FP), R8 MOVQ y+32(FP), R9 - MOVL n+48(FP), R11 + MOVL n+8(FP), R11 MOVQ $0, BX // i = 0 MOVQ $0, DX // c = 0 JMP E1 @@ -27,17 +27,17 @@ L1: MOVQ (R8)(BX*8), AX E1: CMPQ BX, R11 // i < n JL L1 - MOVQ DX, c+56(FP) + MOVQ DX, c+48(FP) 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) TEXT ·subVV(SB),7,$0 MOVQ z+0(FP), R10 MOVQ x+16(FP), R8 MOVQ y+32(FP), R9 - MOVL n+48(FP), R11 + MOVL n+8(FP), R11 MOVQ $0, BX // i = 0 MOVQ $0, DX // c = 0 JMP E2 @@ -52,16 +52,16 @@ L2: MOVQ (R8)(BX*8), AX E2: CMPQ BX, R11 // i < n JL L2 - MOVQ DX, c+56(FP) + MOVQ DX, c+48(FP) 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 MOVQ z+0(FP), R10 MOVQ x+16(FP), R8 MOVQ y+32(FP), AX // c = y - MOVL n+40(FP), R11 + MOVL n+8(FP), R11 MOVQ $0, BX // i = 0 JMP E3 @@ -74,16 +74,16 @@ L3: ADDQ (R8)(BX*8), AX E3: CMPQ BX, R11 // i < n JL L3 - MOVQ AX, c+48(FP) + MOVQ AX, c+40(FP) 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 MOVQ z+0(FP), R10 MOVQ x+16(FP), R8 MOVQ y+32(FP), AX // c = y - MOVL n+40(FP), R11 + MOVL n+8(FP), R11 MOVQ $0, BX // i = 0 JMP E4 @@ -97,13 +97,13 @@ L4: MOVQ (R8)(BX*8), DX // TODO(gri) is there a reverse SUBQ? E4: CMPQ BX, R11 // i < n JL L4 - MOVQ AX, c+48(FP) + MOVQ AX, c+40(FP) 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 - MOVL n+40(FP), BX // i = n + MOVL n+8(FP), BX // i = n SUBL $1, BX // i-- JL X8b // i < 0 (n <= 0) @@ -114,7 +114,7 @@ TEXT ·shlVW(SB),7,$0 MOVQ (R8)(BX*8), AX // w1 = x[n-1] MOVQ $0, DX SHLQ CX, DX:AX // w1>>ŝ - MOVQ DX, c+48(FP) + MOVQ DX, c+40(FP) CMPL BX, $0 JLE X8a // i <= 0 @@ -132,13 +132,13 @@ X8a: SHLQ 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 diff --git a/src/pkg/big/arith_test.go b/src/pkg/big/arith_test.go index b581bc2783..efdb65123f 100644 --- a/src/pkg/big/arith_test.go +++ b/src/pkg/big/arith_test.go @@ -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]) diff --git a/src/pkg/big/nat.go b/src/pkg/big/nat.go index 46fe3492ac..f752ce6477 100755 --- a/src/pkg/big/nat.go +++ b/src/pkg/big/nat.go @@ -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)