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-rw-r--r--src/pkg/math/big/arith.go240
-rw-r--r--src/pkg/math/big/arith_386.s278
-rw-r--r--src/pkg/math/big/arith_amd64.s401
-rw-r--r--src/pkg/math/big/arith_amd64p32.s41
-rw-r--r--src/pkg/math/big/arith_arm.s300
-rw-r--r--src/pkg/math/big/arith_decl.go19
-rw-r--r--src/pkg/math/big/arith_test.go456
-rw-r--r--src/pkg/math/big/calibrate_test.go88
-rw-r--r--src/pkg/math/big/example_test.go51
-rw-r--r--src/pkg/math/big/gcd_test.go47
-rw-r--r--src/pkg/math/big/hilbert_test.go160
-rw-r--r--src/pkg/math/big/int.go1011
-rw-r--r--src/pkg/math/big/int_test.go1601
-rw-r--r--src/pkg/math/big/nat.go1508
-rw-r--r--src/pkg/math/big/nat_test.go771
-rw-r--r--src/pkg/math/big/rat.go600
-rw-r--r--src/pkg/math/big/rat_test.go994
17 files changed, 0 insertions, 8566 deletions
diff --git a/src/pkg/math/big/arith.go b/src/pkg/math/big/arith.go
deleted file mode 100644
index 3d5a8682d..000000000
--- a/src/pkg/math/big/arith.go
+++ /dev/null
@@ -1,240 +0,0 @@
-// Copyright 2009 The Go Authors. All rights reserved.
-// Use of this source code is governed by a BSD-style
-// license that can be found in the LICENSE file.
-
-// This file provides Go implementations of elementary multi-precision
-// arithmetic operations on word vectors. Needed for platforms without
-// assembly implementations of these routines.
-
-package big
-
-// A Word represents a single digit of a multi-precision unsigned integer.
-type Word uintptr
-
-const (
- // Compute the size _S of a Word in bytes.
- _m = ^Word(0)
- _logS = _m>>8&1 + _m>>16&1 + _m>>32&1
- _S = 1 << _logS
-
- _W = _S << 3 // word size in bits
- _B = 1 << _W // digit base
- _M = _B - 1 // digit mask
-
- _W2 = _W / 2 // half word size in bits
- _B2 = 1 << _W2 // half digit base
- _M2 = _B2 - 1 // half digit mask
-)
-
-// ----------------------------------------------------------------------------
-// Elementary operations on words
-//
-// These operations are used by the vector operations below.
-
-// z1<<_W + z0 = x+y+c, with c == 0 or 1
-func addWW_g(x, y, c Word) (z1, z0 Word) {
- yc := y + c
- z0 = x + yc
- if z0 < x || yc < y {
- z1 = 1
- }
- return
-}
-
-// z1<<_W + z0 = x-y-c, with c == 0 or 1
-func subWW_g(x, y, c Word) (z1, z0 Word) {
- yc := y + c
- z0 = x - yc
- if z0 > x || yc < y {
- z1 = 1
- }
- return
-}
-
-// z1<<_W + z0 = x*y
-// Adapted from Warren, Hacker's Delight, p. 132.
-func mulWW_g(x, y Word) (z1, z0 Word) {
- 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) {
- z1, zz0 := mulWW(x, y)
- if z0 = zz0 + c; z0 < zz0 {
- z1++
- }
- return
-}
-
-// Length of x in bits.
-func bitLen_g(x Word) (n int) {
- for ; x >= 0x8000; x >>= 16 {
- n += 16
- }
- if x >= 0x80 {
- x >>= 8
- n += 8
- }
- if x >= 0x8 {
- x >>= 4
- n += 4
- }
- if x >= 0x2 {
- x >>= 2
- n += 2
- }
- if x >= 0x1 {
- n++
- }
- return
-}
-
-// log2 computes the integer binary logarithm of x.
-// The result is the integer n for which 2^n <= x < 2^(n+1).
-// If x == 0, the result is -1.
-func log2(x Word) int {
- return bitLen(x) - 1
-}
-
-// Number of leading zeros in x.
-func leadingZeros(x Word) uint {
- return uint(_W - bitLen(x))
-}
-
-// 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
- }
-
- 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
-
- for q1 >= _B2 || q1*vn0 > _B2*rhat+un1 {
- q1--
- rhat += vn1
- if rhat >= _B2 {
- break
- }
- }
-
- un21 := un32*_B2 + un1 - q1*v
- q0 := un21 / vn1
- rhat = un21 - q0*vn1
-
- for q0 >= _B2 || q0*vn0 > _B2*rhat+un0 {
- q0--
- rhat += vn1
- if rhat >= _B2 {
- break
- }
- }
-
- return q1*_B2 + q0, (un21*_B2 + un0 - q0*v) >> s
-}
-
-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_g(z, x, y []Word) (c Word) {
- for i := range z {
- c, z[i] = subWW_g(x[i], y[i], c)
- }
- return
-}
-
-func addVW_g(z, x []Word, y Word) (c Word) {
- c = y
- for i := range z {
- c, z[i] = addWW_g(x[i], c, 0)
- }
- return
-}
-
-func subVW_g(z, x []Word, y Word) (c Word) {
- c = y
- for i := range z {
- c, z[i] = subWW_g(x[i], c, 0)
- }
- return
-}
-
-func shlVU_g(z, x []Word, s uint) (c Word) {
- if n := len(z); n > 0 {
- ŝ := _W - s
- w1 := x[n-1]
- c = w1 >> ŝ
- for i := n - 1; i > 0; i-- {
- w := w1
- w1 = x[i-1]
- z[i] = w<<s | w1>>ŝ
- }
- z[0] = w1 << s
- }
- return
-}
-
-func shrVU_g(z, x []Word, s uint) (c Word) {
- if n := len(z); n > 0 {
- ŝ := _W - s
- w1 := x[0]
- c = w1 << ŝ
- for i := 0; i < n-1; i++ {
- w := w1
- w1 = x[i+1]
- z[i] = w>>s | w1<<ŝ
- }
- z[n-1] = w1 >> s
- }
- return
-}
-
-func mulAddVWW_g(z, x []Word, y, r Word) (c Word) {
- c = r
- for i := range z {
- c, z[i] = mulAddWWW_g(x[i], y, c)
- }
- return
-}
-
-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
- }
- return
-}
-
-func divWVW_g(z []Word, xn Word, x []Word, y Word) (r Word) {
- r = xn
- for i := len(z) - 1; i >= 0; i-- {
- z[i], r = divWW_g(r, x[i], y)
- }
- return
-}
diff --git a/src/pkg/math/big/arith_386.s b/src/pkg/math/big/arith_386.s
deleted file mode 100644
index 15b036c65..000000000
--- a/src/pkg/math/big/arith_386.s
+++ /dev/null
@@ -1,278 +0,0 @@
-// Copyright 2009 The Go Authors. All rights reserved.
-// Use of this source code is governed by a BSD-style
-// license that can be found in the LICENSE file.
-
-#include "../../../cmd/ld/textflag.h"
-
-// This file provides fast assembly versions for the elementary
-// arithmetic operations on vectors implemented in arith.go.
-
-// func mulWW(x, y Word) (z1, z0 Word)
-TEXT ·mulWW(SB),NOSPLIT,$0
- MOVL x+0(FP), AX
- MULL y+4(FP)
- MOVL DX, z1+8(FP)
- MOVL AX, z0+12(FP)
- RET
-
-
-// func divWW(x1, x0, y Word) (q, r Word)
-TEXT ·divWW(SB),NOSPLIT,$0
- MOVL x1+0(FP), DX
- MOVL x0+4(FP), AX
- DIVL y+8(FP)
- MOVL AX, q+12(FP)
- MOVL DX, r+16(FP)
- RET
-
-
-// func addVV(z, x, y []Word) (c Word)
-TEXT ·addVV(SB),NOSPLIT,$0
- MOVL z+0(FP), DI
- MOVL x+12(FP), SI
- MOVL y+24(FP), CX
- MOVL z_len+4(FP), BP
- MOVL $0, BX // i = 0
- MOVL $0, DX // c = 0
- JMP E1
-
-L1: MOVL (SI)(BX*4), AX
- RCRL $1, DX
- ADCL (CX)(BX*4), AX
- RCLL $1, DX
- MOVL AX, (DI)(BX*4)
- ADDL $1, BX // i++
-
-E1: CMPL BX, BP // i < n
- JL L1
-
- MOVL DX, c+36(FP)
- RET
-
-
-// func subVV(z, x, y []Word) (c Word)
-// (same as addVV except for SBBL instead of ADCL and label names)
-TEXT ·subVV(SB),NOSPLIT,$0
- MOVL z+0(FP), DI
- MOVL x+12(FP), SI
- MOVL y+24(FP), CX
- MOVL z_len+4(FP), BP
- MOVL $0, BX // i = 0
- MOVL $0, DX // c = 0
- JMP E2
-
-L2: MOVL (SI)(BX*4), AX
- RCRL $1, DX
- SBBL (CX)(BX*4), AX
- RCLL $1, DX
- MOVL AX, (DI)(BX*4)
- ADDL $1, BX // i++
-
-E2: CMPL BX, BP // i < n
- JL L2
-
- MOVL DX, c+36(FP)
- RET
-
-
-// func addVW(z, x []Word, y Word) (c Word)
-TEXT ·addVW(SB),NOSPLIT,$0
- MOVL z+0(FP), DI
- MOVL x+12(FP), SI
- MOVL y+24(FP), AX // c = y
- MOVL z_len+4(FP), BP
- MOVL $0, BX // i = 0
- JMP E3
-
-L3: ADDL (SI)(BX*4), AX
- MOVL AX, (DI)(BX*4)
- RCLL $1, AX
- ANDL $1, AX
- ADDL $1, BX // i++
-
-E3: CMPL BX, BP // i < n
- JL L3
-
- MOVL AX, c+28(FP)
- RET
-
-
-// func subVW(z, x []Word, y Word) (c Word)
-TEXT ·subVW(SB),NOSPLIT,$0
- MOVL z+0(FP), DI
- MOVL x+12(FP), SI
- MOVL y+24(FP), AX // c = y
- MOVL z_len+4(FP), BP
- MOVL $0, BX // i = 0
- JMP E4
-
-L4: MOVL (SI)(BX*4), DX // TODO(gri) is there a reverse SUBL?
- SUBL AX, DX
- MOVL DX, (DI)(BX*4)
- RCLL $1, AX
- ANDL $1, AX
- ADDL $1, BX // i++
-
-E4: CMPL BX, BP // i < n
- JL L4
-
- MOVL AX, c+28(FP)
- RET
-
-
-// func shlVU(z, x []Word, s uint) (c Word)
-TEXT ·shlVU(SB),NOSPLIT,$0
- MOVL z_len+4(FP), BX // i = z
- SUBL $1, BX // i--
- JL X8b // i < 0 (n <= 0)
-
- // n > 0
- MOVL z+0(FP), DI
- MOVL x+12(FP), SI
- MOVL s+24(FP), CX
- MOVL (SI)(BX*4), AX // w1 = x[n-1]
- MOVL $0, DX
- SHLL CX, DX:AX // w1>>ŝ
- MOVL DX, c+28(FP)
-
- CMPL BX, $0
- JLE X8a // i <= 0
-
- // i > 0
-L8: MOVL AX, DX // w = w1
- MOVL -4(SI)(BX*4), AX // w1 = x[i-1]
- SHLL CX, DX:AX // w<<s | w1>>ŝ
- MOVL DX, (DI)(BX*4) // z[i] = w<<s | w1>>ŝ
- SUBL $1, BX // i--
- JG L8 // i > 0
-
- // i <= 0
-X8a: SHLL CX, AX // w1<<s
- MOVL AX, (DI) // z[0] = w1<<s
- RET
-
-X8b: MOVL $0, c+28(FP)
- RET
-
-
-// func shrVU(z, x []Word, s uint) (c Word)
-TEXT ·shrVU(SB),NOSPLIT,$0
- MOVL z_len+4(FP), BP
- SUBL $1, BP // n--
- JL X9b // n < 0 (n <= 0)
-
- // n > 0
- MOVL z+0(FP), DI
- MOVL x+12(FP), SI
- MOVL s+24(FP), CX
- MOVL (SI), AX // w1 = x[0]
- MOVL $0, DX
- SHRL CX, DX:AX // w1<<ŝ
- MOVL DX, c+28(FP)
-
- MOVL $0, BX // i = 0
- JMP E9
-
- // i < n-1
-L9: MOVL AX, DX // w = w1
- MOVL 4(SI)(BX*4), AX // w1 = x[i+1]
- SHRL CX, DX:AX // w>>s | w1<<ŝ
- MOVL DX, (DI)(BX*4) // z[i] = w>>s | w1<<ŝ
- ADDL $1, BX // i++
-
-E9: CMPL BX, BP
- JL L9 // i < n-1
-
- // i >= n-1
-X9a: SHRL CX, AX // w1>>s
- MOVL AX, (DI)(BP*4) // z[n-1] = w1>>s
- RET
-
-X9b: MOVL $0, c+28(FP)
- RET
-
-
-// func mulAddVWW(z, x []Word, y, r Word) (c Word)
-TEXT ·mulAddVWW(SB),NOSPLIT,$0
- MOVL z+0(FP), DI
- MOVL x+12(FP), SI
- MOVL y+24(FP), BP
- MOVL r+28(FP), CX // c = r
- MOVL z_len+4(FP), BX
- LEAL (DI)(BX*4), DI
- LEAL (SI)(BX*4), SI
- NEGL BX // i = -n
- JMP E5
-
-L5: MOVL (SI)(BX*4), AX
- MULL BP
- ADDL CX, AX
- ADCL $0, DX
- MOVL AX, (DI)(BX*4)
- MOVL DX, CX
- ADDL $1, BX // i++
-
-E5: CMPL BX, $0 // i < 0
- JL L5
-
- MOVL CX, c+32(FP)
- RET
-
-
-// func addMulVVW(z, x []Word, y Word) (c Word)
-TEXT ·addMulVVW(SB),NOSPLIT,$0
- MOVL z+0(FP), DI
- MOVL x+12(FP), SI
- MOVL y+24(FP), BP
- MOVL z_len+4(FP), BX
- LEAL (DI)(BX*4), DI
- LEAL (SI)(BX*4), SI
- NEGL BX // i = -n
- MOVL $0, CX // c = 0
- JMP E6
-
-L6: MOVL (SI)(BX*4), AX
- MULL BP
- ADDL CX, AX
- ADCL $0, DX
- ADDL AX, (DI)(BX*4)
- ADCL $0, DX
- MOVL DX, CX
- ADDL $1, BX // i++
-
-E6: CMPL BX, $0 // i < 0
- JL L6
-
- MOVL CX, c+28(FP)
- RET
-
-
-// func divWVW(z* Word, xn Word, x []Word, y Word) (r Word)
-TEXT ·divWVW(SB),NOSPLIT,$0
- MOVL z+0(FP), DI
- MOVL xn+12(FP), DX // r = xn
- MOVL x+16(FP), SI
- MOVL y+28(FP), CX
- MOVL z_len+4(FP), BX // i = z
- JMP E7
-
-L7: MOVL (SI)(BX*4), AX
- DIVL CX
- MOVL AX, (DI)(BX*4)
-
-E7: SUBL $1, BX // i--
- JGE L7 // i >= 0
-
- MOVL DX, r+32(FP)
- RET
-
-// func bitLen(x Word) (n int)
-TEXT ·bitLen(SB),NOSPLIT,$0
- BSRL x+0(FP), AX
- JZ Z1
- INCL AX
- MOVL AX, n+4(FP)
- RET
-
-Z1: MOVL $0, n+4(FP)
- RET
diff --git a/src/pkg/math/big/arith_amd64.s b/src/pkg/math/big/arith_amd64.s
deleted file mode 100644
index e2113a7e3..000000000
--- a/src/pkg/math/big/arith_amd64.s
+++ /dev/null
@@ -1,401 +0,0 @@
-// Copyright 2009 The Go Authors. All rights reserved.
-// Use of this source code is governed by a BSD-style
-// license that can be found in the LICENSE file.
-
-#include "../../../cmd/ld/textflag.h"
-
-// This file provides fast assembly versions for the elementary
-// arithmetic operations on vectors implemented in arith.go.
-
-// Literal instruction for MOVQ $0, CX.
-// (MOVQ $0, reg is translated to XORQ reg, reg and clears CF.)
-#define ZERO_CX BYTE $0x48; \
- BYTE $0xc7; \
- BYTE $0xc1; \
- BYTE $0x00; \
- BYTE $0x00; \
- BYTE $0x00; \
- BYTE $0x00
-
-// func mulWW(x, y Word) (z1, z0 Word)
-TEXT ·mulWW(SB),NOSPLIT,$0
- MOVQ x+0(FP), AX
- MULQ y+8(FP)
- MOVQ DX, z1+16(FP)
- MOVQ AX, z0+24(FP)
- RET
-
-
-// func divWW(x1, x0, y Word) (q, r Word)
-TEXT ·divWW(SB),NOSPLIT,$0
- MOVQ x1+0(FP), DX
- MOVQ x0+8(FP), AX
- DIVQ y+16(FP)
- MOVQ AX, q+24(FP)
- MOVQ DX, r+32(FP)
- RET
-
-
-// func addVV(z, x, y []Word) (c Word)
-TEXT ·addVV(SB),NOSPLIT,$0
- MOVQ z_len+8(FP), DI
- MOVQ x+24(FP), R8
- MOVQ y+48(FP), R9
- MOVQ z+0(FP), R10
-
- MOVQ $0, CX // c = 0
- MOVQ $0, SI // i = 0
-
- // s/JL/JMP/ below to disable the unrolled loop
- SUBQ $4, DI // n -= 4
- JL V1 // if n < 0 goto V1
-
-U1: // n >= 0
- // regular loop body unrolled 4x
- RCRQ $1, CX // CF = c
- MOVQ 0(R8)(SI*8), R11
- MOVQ 8(R8)(SI*8), R12
- MOVQ 16(R8)(SI*8), R13
- MOVQ 24(R8)(SI*8), R14
- ADCQ 0(R9)(SI*8), R11
- ADCQ 8(R9)(SI*8), R12
- ADCQ 16(R9)(SI*8), R13
- ADCQ 24(R9)(SI*8), R14
- MOVQ R11, 0(R10)(SI*8)
- MOVQ R12, 8(R10)(SI*8)
- MOVQ R13, 16(R10)(SI*8)
- MOVQ R14, 24(R10)(SI*8)
- RCLQ $1, CX // c = CF
-
- ADDQ $4, SI // i += 4
- SUBQ $4, DI // n -= 4
- JGE U1 // if n >= 0 goto U1
-
-V1: ADDQ $4, DI // n += 4
- JLE E1 // if n <= 0 goto E1
-
-L1: // n > 0
- RCRQ $1, CX // CF = c
- MOVQ 0(R8)(SI*8), R11
- ADCQ 0(R9)(SI*8), R11
- MOVQ R11, 0(R10)(SI*8)
- RCLQ $1, CX // c = CF
-
- ADDQ $1, SI // i++
- SUBQ $1, DI // n--
- JG L1 // if n > 0 goto L1
-
-E1: MOVQ CX, c+72(FP) // return c
- RET
-
-
-// func subVV(z, x, y []Word) (c Word)
-// (same as addVV except for SBBQ instead of ADCQ and label names)
-TEXT ·subVV(SB),NOSPLIT,$0
- MOVQ z_len+8(FP), DI
- MOVQ x+24(FP), R8
- MOVQ y+48(FP), R9
- MOVQ z+0(FP), R10
-
- MOVQ $0, CX // c = 0
- MOVQ $0, SI // i = 0
-
- // s/JL/JMP/ below to disable the unrolled loop
- SUBQ $4, DI // n -= 4
- JL V2 // if n < 0 goto V2
-
-U2: // n >= 0
- // regular loop body unrolled 4x
- RCRQ $1, CX // CF = c
- MOVQ 0(R8)(SI*8), R11
- MOVQ 8(R8)(SI*8), R12
- MOVQ 16(R8)(SI*8), R13
- MOVQ 24(R8)(SI*8), R14
- SBBQ 0(R9)(SI*8), R11
- SBBQ 8(R9)(SI*8), R12
- SBBQ 16(R9)(SI*8), R13
- SBBQ 24(R9)(SI*8), R14
- MOVQ R11, 0(R10)(SI*8)
- MOVQ R12, 8(R10)(SI*8)
- MOVQ R13, 16(R10)(SI*8)
- MOVQ R14, 24(R10)(SI*8)
- RCLQ $1, CX // c = CF
-
- ADDQ $4, SI // i += 4
- SUBQ $4, DI // n -= 4
- JGE U2 // if n >= 0 goto U2
-
-V2: ADDQ $4, DI // n += 4
- JLE E2 // if n <= 0 goto E2
-
-L2: // n > 0
- RCRQ $1, CX // CF = c
- MOVQ 0(R8)(SI*8), R11
- SBBQ 0(R9)(SI*8), R11
- MOVQ R11, 0(R10)(SI*8)
- RCLQ $1, CX // c = CF
-
- ADDQ $1, SI // i++
- SUBQ $1, DI // n--
- JG L2 // if n > 0 goto L2
-
-E2: MOVQ CX, c+72(FP) // return c
- RET
-
-
-// func addVW(z, x []Word, y Word) (c Word)
-TEXT ·addVW(SB),NOSPLIT,$0
- MOVQ z_len+8(FP), DI
- MOVQ x+24(FP), R8
- MOVQ y+48(FP), CX // c = y
- MOVQ z+0(FP), R10
-
- MOVQ $0, SI // i = 0
-
- // s/JL/JMP/ below to disable the unrolled loop
- SUBQ $4, DI // n -= 4
- JL V3 // if n < 4 goto V3
-
-U3: // n >= 0
- // regular loop body unrolled 4x
- MOVQ 0(R8)(SI*8), R11
- MOVQ 8(R8)(SI*8), R12
- MOVQ 16(R8)(SI*8), R13
- MOVQ 24(R8)(SI*8), R14
- ADDQ CX, R11
- ZERO_CX
- ADCQ $0, R12
- ADCQ $0, R13
- ADCQ $0, R14
- SETCS CX // c = CF
- MOVQ R11, 0(R10)(SI*8)
- MOVQ R12, 8(R10)(SI*8)
- MOVQ R13, 16(R10)(SI*8)
- MOVQ R14, 24(R10)(SI*8)
-
- ADDQ $4, SI // i += 4
- SUBQ $4, DI // n -= 4
- JGE U3 // if n >= 0 goto U3
-
-V3: ADDQ $4, DI // n += 4
- JLE E3 // if n <= 0 goto E3
-
-L3: // n > 0
- ADDQ 0(R8)(SI*8), CX
- MOVQ CX, 0(R10)(SI*8)
- ZERO_CX
- RCLQ $1, CX // c = CF
-
- ADDQ $1, SI // i++
- SUBQ $1, DI // n--
- JG L3 // if n > 0 goto L3
-
-E3: MOVQ CX, c+56(FP) // return c
- RET
-
-
-// func subVW(z, x []Word, y Word) (c Word)
-// (same as addVW except for SUBQ/SBBQ instead of ADDQ/ADCQ and label names)
-TEXT ·subVW(SB),NOSPLIT,$0
- MOVQ z_len+8(FP), DI
- MOVQ x+24(FP), R8
- MOVQ y+48(FP), CX // c = y
- MOVQ z+0(FP), R10
-
- MOVQ $0, SI // i = 0
-
- // s/JL/JMP/ below to disable the unrolled loop
- SUBQ $4, DI // n -= 4
- JL V4 // if n < 4 goto V4
-
-U4: // n >= 0
- // regular loop body unrolled 4x
- MOVQ 0(R8)(SI*8), R11
- MOVQ 8(R8)(SI*8), R12
- MOVQ 16(R8)(SI*8), R13
- MOVQ 24(R8)(SI*8), R14
- SUBQ CX, R11
- ZERO_CX
- SBBQ $0, R12
- SBBQ $0, R13
- SBBQ $0, R14
- SETCS CX // c = CF
- MOVQ R11, 0(R10)(SI*8)
- MOVQ R12, 8(R10)(SI*8)
- MOVQ R13, 16(R10)(SI*8)
- MOVQ R14, 24(R10)(SI*8)
-
- ADDQ $4, SI // i += 4
- SUBQ $4, DI // n -= 4
- JGE U4 // if n >= 0 goto U4
-
-V4: ADDQ $4, DI // n += 4
- JLE E4 // if n <= 0 goto E4
-
-L4: // n > 0
- MOVQ 0(R8)(SI*8), R11
- SUBQ CX, R11
- MOVQ R11, 0(R10)(SI*8)
- ZERO_CX
- RCLQ $1, CX // c = CF
-
- ADDQ $1, SI // i++
- SUBQ $1, DI // n--
- JG L4 // if n > 0 goto L4
-
-E4: MOVQ CX, c+56(FP) // return c
- RET
-
-
-// func shlVU(z, x []Word, s uint) (c Word)
-TEXT ·shlVU(SB),NOSPLIT,$0
- MOVQ z_len+8(FP), BX // i = z
- SUBQ $1, BX // i--
- JL X8b // i < 0 (n <= 0)
-
- // n > 0
- MOVQ z+0(FP), R10
- MOVQ x+24(FP), R8
- MOVQ s+48(FP), CX
- MOVQ (R8)(BX*8), AX // w1 = x[n-1]
- MOVQ $0, DX
- SHLQ CX, DX:AX // w1>>ŝ
- MOVQ DX, c+56(FP)
-
- CMPQ BX, $0
- JLE X8a // i <= 0
-
- // i > 0
-L8: MOVQ AX, DX // w = w1
- MOVQ -8(R8)(BX*8), AX // w1 = x[i-1]
- SHLQ CX, DX:AX // w<<s | w1>>ŝ
- MOVQ DX, (R10)(BX*8) // z[i] = w<<s | w1>>ŝ
- SUBQ $1, BX // i--
- JG L8 // i > 0
-
- // i <= 0
-X8a: SHLQ CX, AX // w1<<s
- MOVQ AX, (R10) // z[0] = w1<<s
- RET
-
-X8b: MOVQ $0, c+56(FP)
- RET
-
-
-// func shrVU(z, x []Word, s uint) (c Word)
-TEXT ·shrVU(SB),NOSPLIT,$0
- MOVQ z_len+8(FP), R11
- SUBQ $1, R11 // n--
- JL X9b // n < 0 (n <= 0)
-
- // n > 0
- MOVQ z+0(FP), R10
- MOVQ x+24(FP), R8
- MOVQ s+48(FP), CX
- MOVQ (R8), AX // w1 = x[0]
- MOVQ $0, DX
- SHRQ CX, DX:AX // w1<<ŝ
- MOVQ DX, c+56(FP)
-
- MOVQ $0, BX // i = 0
- JMP E9
-
- // i < n-1
-L9: MOVQ AX, DX // w = w1
- MOVQ 8(R8)(BX*8), AX // w1 = x[i+1]
- SHRQ CX, DX:AX // w>>s | w1<<ŝ
- MOVQ DX, (R10)(BX*8) // z[i] = w>>s | w1<<ŝ
- ADDQ $1, BX // i++
-
-E9: CMPQ BX, R11
- JL L9 // i < n-1
-
- // i >= n-1
-X9a: SHRQ CX, AX // w1>>s
- MOVQ AX, (R10)(R11*8) // z[n-1] = w1>>s
- RET
-
-X9b: MOVQ $0, c+56(FP)
- RET
-
-
-// func mulAddVWW(z, x []Word, y, r Word) (c Word)
-TEXT ·mulAddVWW(SB),NOSPLIT,$0
- MOVQ z+0(FP), R10
- MOVQ x+24(FP), R8
- MOVQ y+48(FP), R9
- MOVQ r+56(FP), CX // c = r
- MOVQ z_len+8(FP), R11
- MOVQ $0, BX // i = 0
- JMP E5
-
-L5: MOVQ (R8)(BX*8), AX
- MULQ R9
- ADDQ CX, AX
- ADCQ $0, DX
- MOVQ AX, (R10)(BX*8)
- MOVQ DX, CX
- ADDQ $1, BX // i++
-
-E5: CMPQ BX, R11 // i < n
- JL L5
-
- MOVQ CX, c+64(FP)
- RET
-
-
-// func addMulVVW(z, x []Word, y Word) (c Word)
-TEXT ·addMulVVW(SB),NOSPLIT,$0
- MOVQ z+0(FP), R10
- MOVQ x+24(FP), R8
- MOVQ y+48(FP), R9
- MOVQ z_len+8(FP), R11
- MOVQ $0, BX // i = 0
- MOVQ $0, CX // c = 0
- JMP E6
-
-L6: MOVQ (R8)(BX*8), AX
- MULQ R9
- ADDQ CX, AX
- ADCQ $0, DX
- ADDQ AX, (R10)(BX*8)
- ADCQ $0, DX
- MOVQ DX, CX
- ADDQ $1, BX // i++
-
-E6: CMPQ BX, R11 // i < n
- JL L6
-
- MOVQ CX, c+56(FP)
- RET
-
-
-// func divWVW(z []Word, xn Word, x []Word, y Word) (r Word)
-TEXT ·divWVW(SB),NOSPLIT,$0
- MOVQ z+0(FP), R10
- MOVQ xn+24(FP), DX // r = xn
- MOVQ x+32(FP), R8
- MOVQ y+56(FP), R9
- MOVQ z_len+8(FP), BX // i = z
- JMP E7
-
-L7: MOVQ (R8)(BX*8), AX
- DIVQ R9
- MOVQ AX, (R10)(BX*8)
-
-E7: SUBQ $1, BX // i--
- JGE L7 // i >= 0
-
- MOVQ DX, r+64(FP)
- RET
-
-// func bitLen(x Word) (n int)
-TEXT ·bitLen(SB),NOSPLIT,$0
- BSRQ x+0(FP), AX
- JZ Z1
- ADDQ $1, AX
- MOVQ AX, n+8(FP)
- RET
-
-Z1: MOVQ $0, n+8(FP)
- RET
diff --git a/src/pkg/math/big/arith_amd64p32.s b/src/pkg/math/big/arith_amd64p32.s
deleted file mode 100644
index 227870a00..000000000
--- a/src/pkg/math/big/arith_amd64p32.s
+++ /dev/null
@@ -1,41 +0,0 @@
-// Copyright 2013 The Go Authors. All rights reserved.
-// Use of this source code is governed by a BSD-style
-// license that can be found in the LICENSE file.
-
-#include "../../../cmd/ld/textflag.h"
-
-TEXT ·mulWW(SB),NOSPLIT,$0
- JMP ·mulWW_g(SB)
-
-TEXT ·divWW(SB),NOSPLIT,$0
- JMP ·divWW_g(SB)
-
-TEXT ·addVV(SB),NOSPLIT,$0
- JMP ·addVV_g(SB)
-
-TEXT ·subVV(SB),NOSPLIT,$0
- JMP ·subVV_g(SB)
-
-TEXT ·addVW(SB),NOSPLIT,$0
- JMP ·addVW_g(SB)
-
-TEXT ·subVW(SB),NOSPLIT,$0
- JMP ·subVW_g(SB)
-
-TEXT ·shlVU(SB),NOSPLIT,$0
- JMP ·shlVU_g(SB)
-
-TEXT ·shrVU(SB),NOSPLIT,$0
- JMP ·shrVU_g(SB)
-
-TEXT ·mulAddVWW(SB),NOSPLIT,$0
- JMP ·mulAddVWW_g(SB)
-
-TEXT ·addMulVVW(SB),NOSPLIT,$0
- JMP ·addMulVVW_g(SB)
-
-TEXT ·divWVW(SB),NOSPLIT,$0
- JMP ·divWVW_g(SB)
-
-TEXT ·bitLen(SB),NOSPLIT,$0
- JMP ·bitLen_g(SB)
diff --git a/src/pkg/math/big/arith_arm.s b/src/pkg/math/big/arith_arm.s
deleted file mode 100644
index 8d36761c4..000000000
--- a/src/pkg/math/big/arith_arm.s
+++ /dev/null
@@ -1,300 +0,0 @@
-// Copyright 2009 The Go Authors. All rights reserved.
-// Use of this source code is governed by a BSD-style
-// license that can be found in the LICENSE file.
-
-#include "../../../cmd/ld/textflag.h"
-
-// This file provides fast assembly versions for the elementary
-// arithmetic operations on vectors implemented in arith.go.
-
-// func addVV(z, x, y []Word) (c Word)
-TEXT ·addVV(SB),NOSPLIT,$0
- ADD.S $0, R0 // clear carry flag
- MOVW z+0(FP), R1
- MOVW z_len+4(FP), R4
- MOVW x+12(FP), R2
- MOVW y+24(FP), R3
- ADD R4<<2, R1, R4
- B E1
-L1:
- MOVW.P 4(R2), R5
- MOVW.P 4(R3), R6
- ADC.S R6, R5
- MOVW.P R5, 4(R1)
-E1:
- TEQ R1, R4
- BNE L1
-
- MOVW $0, R0
- MOVW.CS $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),NOSPLIT,$0
- SUB.S $0, R0 // clear borrow flag
- MOVW z+0(FP), R1
- MOVW z_len+4(FP), R4
- MOVW x+12(FP), R2
- MOVW y+24(FP), R3
- ADD R4<<2, R1, R4
- B E2
-L2:
- MOVW.P 4(R2), R5
- MOVW.P 4(R3), R6
- SBC.S R6, R5
- MOVW.P R5, 4(R1)
-E2:
- TEQ R1, R4
- BNE L2
-
- MOVW $0, R0
- MOVW.CC $1, R0
- MOVW R0, c+36(FP)
- RET
-
-
-// func addVW(z, x []Word, y Word) (c Word)
-TEXT ·addVW(SB),NOSPLIT,$0
- MOVW z+0(FP), R1
- MOVW z_len+4(FP), R4
- MOVW x+12(FP), R2
- MOVW y+24(FP), R3
- ADD R4<<2, R1, R4
- TEQ 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)
- B E3
-L3:
- MOVW.P 4(R2), R5
- ADC.S $0, R5
- MOVW.P R5, 4(R1)
-E3:
- TEQ R1, R4
- BNE L3
-
- MOVW $0, R0
- MOVW.CS $1, R0
- MOVW R0, c+28(FP)
- RET
-
-
-// func subVW(z, x []Word, y Word) (c Word)
-TEXT ·subVW(SB),NOSPLIT,$0
- MOVW z+0(FP), R1
- MOVW z_len+4(FP), R4
- MOVW x+12(FP), R2
- MOVW y+24(FP), R3
- ADD R4<<2, R1, R4
- TEQ 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)
- B E4
-L4:
- MOVW.P 4(R2), R5
- SBC.S $0, R5
- MOVW.P R5, 4(R1)
-E4:
- TEQ R1, R4
- BNE L4
-
- MOVW $0, R0
- MOVW.CC $1, R0
- MOVW R0, c+28(FP)
- RET
-
-
-// func shlVU(z, x []Word, s uint) (c Word)
-TEXT ·shlVU(SB),NOSPLIT,$0
- MOVW z_len+4(FP), R5
- TEQ $0, R5
- BEQ X7
-
- MOVW z+0(FP), R1
- MOVW x+12(FP), R2
- ADD R5<<2, R2, R2
- ADD R5<<2, R1, R5
- MOVW s+24(FP), R3
- TEQ $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:
- TEQ 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)
- TEQ R1, R5
- BNE Y7
-
-X7:
- MOVW $0, R1
- MOVW R1, c+28(FP)
- RET
-
-
-// func shrVU(z, x []Word, s uint) (c Word)
-TEXT ·shrVU(SB),NOSPLIT,$0
- MOVW z_len+4(FP), R5
- TEQ $0, R5
- BEQ X6
-
- MOVW z+0(FP), R1
- MOVW x+12(FP), R2
- ADD R5<<2, R1, R5
- MOVW s+24(FP), R3
- TEQ $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:
- TEQ 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)
- TEQ R1, R5
- BNE Y6
-
-X6:
- MOVW $0, R1
- MOVW R1, c+28(FP)
- RET
-
-
-// func mulAddVWW(z, x []Word, y, r Word) (c Word)
-TEXT ·mulAddVWW(SB),NOSPLIT,$0
- MOVW $0, R0
- MOVW z+0(FP), R1
- MOVW z_len+4(FP), R5
- MOVW x+12(FP), R2
- MOVW y+24(FP), R3
- MOVW r+28(FP), R4
- ADD R5<<2, 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:
- TEQ R1, R5
- BNE L8
-
- MOVW R4, c+32(FP)
- RET
-
-
-// func addMulVVW(z, x []Word, y Word) (c Word)
-TEXT ·addMulVVW(SB),NOSPLIT,$0
- MOVW $0, R0
- MOVW z+0(FP), R1
- MOVW z_len+4(FP), R5
- MOVW x+12(FP), R2
- MOVW y+24(FP), R3
- ADD R5<<2, 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:
- TEQ R1, R5
- BNE L9
-
- MOVW R4, c+28(FP)
- RET
-
-
-// func divWVW(z* Word, xn Word, x []Word, y Word) (r Word)
-TEXT ·divWVW(SB),NOSPLIT,$0
- // ARM has no multiword division, so use portable code.
- B ·divWVW_g(SB)
-
-
-// func divWW(x1, x0, y Word) (q, r Word)
-TEXT ·divWW(SB),NOSPLIT,$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),NOSPLIT,$0
- 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
-
-// func bitLen(x Word) (n int)
-TEXT ·bitLen(SB),NOSPLIT,$0
- MOVW x+0(FP), R0
- CLZ R0, R0
- RSB $32, R0
- MOVW R0, n+4(FP)
- RET
diff --git a/src/pkg/math/big/arith_decl.go b/src/pkg/math/big/arith_decl.go
deleted file mode 100644
index 068cc8d93..000000000
--- a/src/pkg/math/big/arith_decl.go
+++ /dev/null
@@ -1,19 +0,0 @@
-// Copyright 2010 The Go Authors. All rights reserved.
-// Use of this source code is governed by a BSD-style
-// license that can be found in the LICENSE file.
-
-package big
-
-// implemented in arith_$GOARCH.s
-func mulWW(x, y Word) (z1, z0 Word)
-func divWW(x1, x0, y Word) (q, r Word)
-func addVV(z, x, y []Word) (c Word)
-func subVV(z, x, y []Word) (c Word)
-func addVW(z, x []Word, y Word) (c Word)
-func subVW(z, x []Word, y Word) (c Word)
-func shlVU(z, x []Word, s uint) (c Word)
-func shrVU(z, x []Word, s uint) (c Word)
-func mulAddVWW(z, x []Word, y, r Word) (c Word)
-func addMulVVW(z, x []Word, y Word) (c Word)
-func divWVW(z []Word, xn Word, x []Word, y Word) (r Word)
-func bitLen(x Word) (n int)
diff --git a/src/pkg/math/big/arith_test.go b/src/pkg/math/big/arith_test.go
deleted file mode 100644
index 3615a659c..000000000
--- a/src/pkg/math/big/arith_test.go
+++ /dev/null
@@ -1,456 +0,0 @@
-// Copyright 2009 The Go Authors. All rights reserved.
-// Use of this source code is governed by a BSD-style
-// license that can be found in the LICENSE file.
-
-package big
-
-import (
- "math/rand"
- "testing"
-)
-
-type funWW func(x, y, c Word) (z1, z0 Word)
-type argWW struct {
- x, y, c, z1, z0 Word
-}
-
-var sumWW = []argWW{
- {0, 0, 0, 0, 0},
- {0, 1, 0, 0, 1},
- {0, 0, 1, 0, 1},
- {0, 1, 1, 0, 2},
- {12345, 67890, 0, 0, 80235},
- {12345, 67890, 1, 0, 80236},
- {_M, 1, 0, 1, 0},
- {_M, 0, 1, 1, 0},
- {_M, 1, 1, 1, 1},
- {_M, _M, 0, 1, _M - 1},
- {_M, _M, 1, 1, _M},
-}
-
-func testFunWW(t *testing.T, msg string, f funWW, a argWW) {
- z1, z0 := f(a.x, a.y, a.c)
- if z1 != a.z1 || z0 != a.z0 {
- t.Errorf("%s%+v\n\tgot z1:z0 = %#x:%#x; want %#x:%#x", msg, a, z1, z0, a.z1, a.z0)
- }
-}
-
-func TestFunWW(t *testing.T) {
- for _, a := range sumWW {
- arg := a
- testFunWW(t, "addWW_g", addWW_g, arg)
-
- arg = argWW{a.y, a.x, a.c, a.z1, a.z0}
- testFunWW(t, "addWW_g symmetric", addWW_g, arg)
-
- arg = argWW{a.z0, a.x, a.c, a.z1, a.y}
- testFunWW(t, "subWW_g", subWW_g, arg)
-
- arg = argWW{a.z0, a.y, a.c, a.z1, a.x}
- testFunWW(t, "subWW_g symmetric", subWW_g, arg)
- }
-}
-
-type funVV func(z, x, y []Word) (c Word)
-type argVV struct {
- z, x, y nat
- c Word
-}
-
-var sumVV = []argVV{
- {},
- {nat{0}, nat{0}, nat{0}, 0},
- {nat{1}, nat{1}, nat{0}, 0},
- {nat{0}, nat{_M}, nat{1}, 1},
- {nat{80235}, nat{12345}, nat{67890}, 0},
- {nat{_M - 1}, nat{_M}, nat{_M}, 1},
- {nat{0, 0, 0, 0}, nat{_M, _M, _M, _M}, nat{1, 0, 0, 0}, 1},
- {nat{0, 0, 0, _M}, nat{_M, _M, _M, _M - 1}, nat{1, 0, 0, 0}, 0},
- {nat{0, 0, 0, 0}, nat{_M, 0, _M, 0}, nat{1, _M, 0, _M}, 1},
-}
-
-func testFunVV(t *testing.T, msg string, f funVV, a argVV) {
- 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])
- break
- }
- }
- if c != a.c {
- t.Errorf("%s%+v\n\tgot c = %#x; want %#x", msg, a, c, a.c)
- }
-}
-
-func TestFunVV(t *testing.T) {
- for _, a := range sumVV {
- arg := a
- testFunVV(t, "addVV_g", addVV_g, arg)
- testFunVV(t, "addVV", addVV, arg)
-
- arg = argVV{a.z, a.y, a.x, a.c}
- testFunVV(t, "addVV_g symmetric", addVV_g, arg)
- testFunVV(t, "addVV symmetric", addVV, arg)
-
- arg = argVV{a.x, a.z, a.y, a.c}
- testFunVV(t, "subVV_g", subVV_g, arg)
- testFunVV(t, "subVV", subVV, arg)
-
- arg = argVV{a.y, a.z, a.x, a.c}
- testFunVV(t, "subVV_g symmetric", subVV_g, arg)
- testFunVV(t, "subVV symmetric", subVV, arg)
- }
-}
-
-// Always the same seed for reproducible results.
-var rnd = rand.New(rand.NewSource(0))
-
-func rndW() Word {
- return Word(rnd.Int63()<<1 | rnd.Int63n(2))
-}
-
-func rndV(n int) []Word {
- v := make([]Word, n)
- for i := range v {
- v[i] = rndW()
- }
- return v
-}
-
-func benchmarkFunVV(b *testing.B, f funVV, n int) {
- x := rndV(n)
- y := rndV(n)
- z := make([]Word, n)
- b.SetBytes(int64(n * _W))
- b.ResetTimer()
- for i := 0; i < b.N; i++ {
- f(z, x, y)
- }
-}
-
-func BenchmarkAddVV_1(b *testing.B) { benchmarkFunVV(b, addVV, 1) }
-func BenchmarkAddVV_2(b *testing.B) { benchmarkFunVV(b, addVV, 2) }
-func BenchmarkAddVV_3(b *testing.B) { benchmarkFunVV(b, addVV, 3) }
-func BenchmarkAddVV_4(b *testing.B) { benchmarkFunVV(b, addVV, 4) }
-func BenchmarkAddVV_5(b *testing.B) { benchmarkFunVV(b, addVV, 5) }
-func BenchmarkAddVV_1e1(b *testing.B) { benchmarkFunVV(b, addVV, 1e1) }
-func BenchmarkAddVV_1e2(b *testing.B) { benchmarkFunVV(b, addVV, 1e2) }
-func BenchmarkAddVV_1e3(b *testing.B) { benchmarkFunVV(b, addVV, 1e3) }
-func BenchmarkAddVV_1e4(b *testing.B) { benchmarkFunVV(b, addVV, 1e4) }
-func BenchmarkAddVV_1e5(b *testing.B) { benchmarkFunVV(b, addVV, 1e5) }
-
-type funVW func(z, x []Word, y Word) (c Word)
-type argVW struct {
- z, x nat
- y Word
- c Word
-}
-
-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},
- {nat{0}, nat{_M}, 1, 1},
- {nat{0, 0, 0, 0}, nat{_M, _M, _M, _M}, 1, 1},
-}
-
-var prodVW = []argVW{
- {},
- {nat{0}, nat{0}, 0, 0},
- {nat{0}, nat{_M}, 0, 0},
- {nat{0}, nat{0}, _M, 0},
- {nat{1}, nat{1}, 1, 0},
- {nat{22793}, nat{991}, 23, 0},
- {nat{0, 0, 0, 22793}, nat{0, 0, 0, 991}, 23, 0},
- {nat{0, 0, 0, 0}, nat{7893475, 7395495, 798547395, 68943}, 0, 0},
- {nat{0, 0, 0, 0}, nat{0, 0, 0, 0}, 894375984, 0},
- {nat{_M << 1 & _M}, nat{_M}, 1 << 1, _M >> (_W - 1)},
- {nat{_M << 7 & _M}, nat{_M}, 1 << 7, _M >> (_W - 7)},
- {nat{_M << 7 & _M, _M, _M, _M}, nat{_M, _M, _M, _M}, 1 << 7, _M >> (_W - 7)},
-}
-
-var lshVW = []argVW{
- {},
- {nat{0}, nat{0}, 0, 0},
- {nat{0}, nat{0}, 1, 0},
- {nat{0}, nat{0}, 20, 0},
-
- {nat{_M}, nat{_M}, 0, 0},
- {nat{_M << 1 & _M}, nat{_M}, 1, 1},
- {nat{_M << 20 & _M}, nat{_M}, 20, _M >> (_W - 20)},
-
- {nat{_M, _M, _M}, nat{_M, _M, _M}, 0, 0},
- {nat{_M << 1 & _M, _M, _M}, nat{_M, _M, _M}, 1, 1},
- {nat{_M << 20 & _M, _M, _M}, nat{_M, _M, _M}, 20, _M >> (_W - 20)},
-}
-
-var rshVW = []argVW{
- {},
- {nat{0}, nat{0}, 0, 0},
- {nat{0}, nat{0}, 1, 0},
- {nat{0}, nat{0}, 20, 0},
-
- {nat{_M}, nat{_M}, 0, 0},
- {nat{_M >> 1}, nat{_M}, 1, _M << (_W - 1) & _M},
- {nat{_M >> 20}, nat{_M}, 20, _M << (_W - 20) & _M},
-
- {nat{_M, _M, _M}, nat{_M, _M, _M}, 0, 0},
- {nat{_M, _M, _M >> 1}, nat{_M, _M, _M}, 1, _M << (_W - 1) & _M},
- {nat{_M, _M, _M >> 20}, nat{_M, _M, _M}, 20, _M << (_W - 20) & _M},
-}
-
-func testFunVW(t *testing.T, msg string, f funVW, a argVW) {
- 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])
- break
- }
- }
- if c != a.c {
- t.Errorf("%s%+v\n\tgot c = %#x; want %#x", msg, a, c, a.c)
- }
-}
-
-func makeFunVW(f func(z, x []Word, s uint) (c Word)) funVW {
- return func(z, x []Word, s Word) (c Word) {
- return f(z, x, uint(s))
- }
-}
-
-func TestFunVW(t *testing.T) {
- for _, a := range sumVW {
- arg := a
- testFunVW(t, "addVW_g", addVW_g, arg)
- testFunVW(t, "addVW", addVW, arg)
-
- arg = argVW{a.x, a.z, a.y, a.c}
- testFunVW(t, "subVW_g", subVW_g, arg)
- testFunVW(t, "subVW", subVW, arg)
- }
-
- shlVW_g := makeFunVW(shlVU_g)
- shlVW := makeFunVW(shlVU)
- for _, a := range lshVW {
- arg := a
- testFunVW(t, "shlVU_g", shlVW_g, arg)
- testFunVW(t, "shlVU", shlVW, arg)
- }
-
- shrVW_g := makeFunVW(shrVU_g)
- shrVW := makeFunVW(shrVU)
- for _, a := range rshVW {
- arg := a
- testFunVW(t, "shrVU_g", shrVW_g, arg)
- testFunVW(t, "shrVU", shrVW, arg)
- }
-}
-
-func benchmarkFunVW(b *testing.B, f funVW, n int) {
- x := rndV(n)
- y := rndW()
- z := make([]Word, n)
- b.SetBytes(int64(n * _W))
- b.ResetTimer()
- for i := 0; i < b.N; i++ {
- f(z, x, y)
- }
-}
-
-func BenchmarkAddVW_1(b *testing.B) { benchmarkFunVW(b, addVW, 1) }
-func BenchmarkAddVW_2(b *testing.B) { benchmarkFunVW(b, addVW, 2) }
-func BenchmarkAddVW_3(b *testing.B) { benchmarkFunVW(b, addVW, 3) }
-func BenchmarkAddVW_4(b *testing.B) { benchmarkFunVW(b, addVW, 4) }
-func BenchmarkAddVW_5(b *testing.B) { benchmarkFunVW(b, addVW, 5) }
-func BenchmarkAddVW_1e1(b *testing.B) { benchmarkFunVW(b, addVW, 1e1) }
-func BenchmarkAddVW_1e2(b *testing.B) { benchmarkFunVW(b, addVW, 1e2) }
-func BenchmarkAddVW_1e3(b *testing.B) { benchmarkFunVW(b, addVW, 1e3) }
-func BenchmarkAddVW_1e4(b *testing.B) { benchmarkFunVW(b, addVW, 1e4) }
-func BenchmarkAddVW_1e5(b *testing.B) { benchmarkFunVW(b, addVW, 1e5) }
-
-type funVWW func(z, x []Word, y, r Word) (c Word)
-type argVWW struct {
- z, x nat
- y, r Word
- c Word
-}
-
-var prodVWW = []argVWW{
- {},
- {nat{0}, nat{0}, 0, 0, 0},
- {nat{991}, nat{0}, 0, 991, 0},
- {nat{0}, nat{_M}, 0, 0, 0},
- {nat{991}, nat{_M}, 0, 991, 0},
- {nat{0}, nat{0}, _M, 0, 0},
- {nat{991}, nat{0}, _M, 991, 0},
- {nat{1}, nat{1}, 1, 0, 0},
- {nat{992}, nat{1}, 1, 991, 0},
- {nat{22793}, nat{991}, 23, 0, 0},
- {nat{22800}, nat{991}, 23, 7, 0},
- {nat{0, 0, 0, 22793}, nat{0, 0, 0, 991}, 23, 0, 0},
- {nat{7, 0, 0, 22793}, nat{0, 0, 0, 991}, 23, 7, 0},
- {nat{0, 0, 0, 0}, nat{7893475, 7395495, 798547395, 68943}, 0, 0, 0},
- {nat{991, 0, 0, 0}, nat{7893475, 7395495, 798547395, 68943}, 0, 991, 0},
- {nat{0, 0, 0, 0}, nat{0, 0, 0, 0}, 894375984, 0, 0},
- {nat{991, 0, 0, 0}, nat{0, 0, 0, 0}, 894375984, 991, 0},
- {nat{_M << 1 & _M}, nat{_M}, 1 << 1, 0, _M >> (_W - 1)},
- {nat{_M<<1&_M + 1}, nat{_M}, 1 << 1, 1, _M >> (_W - 1)},
- {nat{_M << 7 & _M}, nat{_M}, 1 << 7, 0, _M >> (_W - 7)},
- {nat{_M<<7&_M + 1<<6}, nat{_M}, 1 << 7, 1 << 6, _M >> (_W - 7)},
- {nat{_M << 7 & _M, _M, _M, _M}, nat{_M, _M, _M, _M}, 1 << 7, 0, _M >> (_W - 7)},
- {nat{_M<<7&_M + 1<<6, _M, _M, _M}, nat{_M, _M, _M, _M}, 1 << 7, 1 << 6, _M >> (_W - 7)},
-}
-
-func testFunVWW(t *testing.T, msg string, f funVWW, a argVWW) {
- 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])
- break
- }
- }
- if c != a.c {
- t.Errorf("%s%+v\n\tgot c = %#x; want %#x", msg, a, c, a.c)
- }
-}
-
-// 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) (r Word)
-type argWVW struct {
- z nat
- xn Word
- x nat
- y Word
- r Word
-}
-
-func testFunWVW(t *testing.T, msg string, f funWVW, a argWVW) {
- 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])
- break
- }
- }
- if r != a.r {
- t.Errorf("%s%+v\n\tgot r = %#x; want %#x", msg, a, r, a.r)
- }
-}
-
-func TestFunVWW(t *testing.T) {
- for _, a := range prodVWW {
- arg := a
- testFunVWW(t, "mulAddVWW_g", mulAddVWW_g, arg)
- testFunVWW(t, "mulAddVWW", mulAddVWW, arg)
-
- if a.y != 0 && a.r < a.y {
- arg := argWVW{a.x, a.c, a.z, a.y, a.r}
- testFunWVW(t, "divWVW_g", divWVW_g, arg)
- testFunWVW(t, "divWVW", divWVW, arg)
- }
- }
-}
-
-var mulWWTests = []struct {
- x, y Word
- q, r Word
-}{
- {_M, _M, _M - 1, 1},
- // 32 bit only: {0xc47dfa8c, 50911, 0x98a4, 0x998587f4},
-}
-
-func TestMulWW(t *testing.T) {
- for i, test := range mulWWTests {
- q, r := mulWW_g(test.x, test.y)
- if q != test.q || r != test.r {
- t.Errorf("#%d got (%x, %x) want (%x, %x)", i, q, r, test.q, test.r)
- }
- }
-}
-
-var mulAddWWWTests = []struct {
- x, y, c Word
- q, r Word
-}{
- // TODO(agl): These will only work on 64-bit platforms.
- // {15064310297182388543, 0xe7df04d2d35d5d80, 13537600649892366549, 13644450054494335067, 10832252001440893781},
- // {15064310297182388543, 0xdab2f18048baa68d, 13644450054494335067, 12869334219691522700, 14233854684711418382},
- {_M, _M, 0, _M - 1, 1},
- {_M, _M, _M, _M, 0},
-}
-
-func TestMulAddWWW(t *testing.T) {
- for i, test := range mulAddWWWTests {
- q, r := mulAddWWW_g(test.x, test.y, test.c)
- if q != test.q || r != test.r {
- t.Errorf("#%d got (%x, %x) want (%x, %x)", i, q, r, test.q, test.r)
- }
- }
-}
-
-func benchmarkAddMulVVW(b *testing.B, n int) {
- x := rndV(n)
- y := rndW()
- z := make([]Word, n)
- b.SetBytes(int64(n * _W))
- b.ResetTimer()
- for i := 0; i < b.N; i++ {
- addMulVVW(z, x, y)
- }
-}
-
-func BenchmarkAddMulVVW_1(b *testing.B) { benchmarkAddMulVVW(b, 1) }
-func BenchmarkAddMulVVW_2(b *testing.B) { benchmarkAddMulVVW(b, 2) }
-func BenchmarkAddMulVVW_3(b *testing.B) { benchmarkAddMulVVW(b, 3) }
-func BenchmarkAddMulVVW_4(b *testing.B) { benchmarkAddMulVVW(b, 4) }
-func BenchmarkAddMulVVW_5(b *testing.B) { benchmarkAddMulVVW(b, 5) }
-func BenchmarkAddMulVVW_1e1(b *testing.B) { benchmarkAddMulVVW(b, 1e1) }
-func BenchmarkAddMulVVW_1e2(b *testing.B) { benchmarkAddMulVVW(b, 1e2) }
-func BenchmarkAddMulVVW_1e3(b *testing.B) { benchmarkAddMulVVW(b, 1e3) }
-func BenchmarkAddMulVVW_1e4(b *testing.B) { benchmarkAddMulVVW(b, 1e4) }
-func BenchmarkAddMulVVW_1e5(b *testing.B) { benchmarkAddMulVVW(b, 1e5) }
-
-func testWordBitLen(t *testing.T, fname string, f func(Word) int) {
- for i := 0; i <= _W; i++ {
- x := Word(1) << uint(i-1) // i == 0 => x == 0
- n := f(x)
- if n != i {
- t.Errorf("got %d; want %d for %s(%#x)", n, i, fname, x)
- }
- }
-}
-
-func TestWordBitLen(t *testing.T) {
- testWordBitLen(t, "bitLen", bitLen)
- testWordBitLen(t, "bitLen_g", bitLen_g)
-}
-
-// runs b.N iterations of bitLen called on a Word containing (1 << nbits)-1.
-func benchmarkBitLenN(b *testing.B, nbits uint) {
- testword := Word((uint64(1) << nbits) - 1)
- for i := 0; i < b.N; i++ {
- bitLen(testword)
- }
-}
-
-// Individual bitLen tests. Numbers chosen to examine both sides
-// of powers-of-two boundaries.
-func BenchmarkBitLen0(b *testing.B) { benchmarkBitLenN(b, 0) }
-func BenchmarkBitLen1(b *testing.B) { benchmarkBitLenN(b, 1) }
-func BenchmarkBitLen2(b *testing.B) { benchmarkBitLenN(b, 2) }
-func BenchmarkBitLen3(b *testing.B) { benchmarkBitLenN(b, 3) }
-func BenchmarkBitLen4(b *testing.B) { benchmarkBitLenN(b, 4) }
-func BenchmarkBitLen5(b *testing.B) { benchmarkBitLenN(b, 5) }
-func BenchmarkBitLen8(b *testing.B) { benchmarkBitLenN(b, 8) }
-func BenchmarkBitLen9(b *testing.B) { benchmarkBitLenN(b, 9) }
-func BenchmarkBitLen16(b *testing.B) { benchmarkBitLenN(b, 16) }
-func BenchmarkBitLen17(b *testing.B) { benchmarkBitLenN(b, 17) }
-func BenchmarkBitLen31(b *testing.B) { benchmarkBitLenN(b, 31) }
diff --git a/src/pkg/math/big/calibrate_test.go b/src/pkg/math/big/calibrate_test.go
deleted file mode 100644
index f69ffbf5c..000000000
--- a/src/pkg/math/big/calibrate_test.go
+++ /dev/null
@@ -1,88 +0,0 @@
-// Copyright 2009 The Go Authors. All rights reserved.
-// Use of this source code is governed by a BSD-style
-// license that can be found in the LICENSE file.
-
-// This file prints execution times for the Mul benchmark
-// given different Karatsuba thresholds. The result may be
-// used to manually fine-tune the threshold constant. The
-// results are somewhat fragile; use repeated runs to get
-// a clear picture.
-
-// Usage: go test -run=TestCalibrate -calibrate
-
-package big
-
-import (
- "flag"
- "fmt"
- "testing"
- "time"
-)
-
-var calibrate = flag.Bool("calibrate", false, "run calibration test")
-
-func karatsubaLoad(b *testing.B) {
- BenchmarkMul(b)
-}
-
-// measureKaratsuba returns the time to run a Karatsuba-relevant benchmark
-// given Karatsuba threshold th.
-func measureKaratsuba(th int) time.Duration {
- th, karatsubaThreshold = karatsubaThreshold, th
- res := testing.Benchmark(karatsubaLoad)
- karatsubaThreshold = th
- return time.Duration(res.NsPerOp())
-}
-
-func computeThresholds() {
- fmt.Printf("Multiplication times for varying Karatsuba thresholds\n")
- fmt.Printf("(run repeatedly for good results)\n")
-
- // determine Tk, the work load execution time using basic multiplication
- Tb := measureKaratsuba(1e9) // th == 1e9 => Karatsuba multiplication disabled
- fmt.Printf("Tb = %10s\n", Tb)
-
- // thresholds
- th := 4
- th1 := -1
- th2 := -1
-
- var deltaOld time.Duration
- for count := -1; count != 0 && th < 128; count-- {
- // determine Tk, the work load execution time using Karatsuba multiplication
- Tk := measureKaratsuba(th)
-
- // improvement over Tb
- delta := (Tb - Tk) * 100 / Tb
-
- fmt.Printf("th = %3d Tk = %10s %4d%%", th, Tk, delta)
-
- // determine break-even point
- if Tk < Tb && th1 < 0 {
- th1 = th
- fmt.Print(" break-even point")
- }
-
- // determine diminishing return
- if 0 < delta && delta < deltaOld && th2 < 0 {
- th2 = th
- fmt.Print(" diminishing return")
- }
- deltaOld = delta
-
- fmt.Println()
-
- // trigger counter
- if th1 >= 0 && th2 >= 0 && count < 0 {
- count = 10 // this many extra measurements after we got both thresholds
- }
-
- th++
- }
-}
-
-func TestCalibrate(t *testing.T) {
- if *calibrate {
- computeThresholds()
- }
-}
diff --git a/src/pkg/math/big/example_test.go b/src/pkg/math/big/example_test.go
deleted file mode 100644
index 078be47f9..000000000
--- a/src/pkg/math/big/example_test.go
+++ /dev/null
@@ -1,51 +0,0 @@
-// Copyright 2012 The Go Authors. All rights reserved.
-// Use of this source code is governed by a BSD-style
-// license that can be found in the LICENSE file.
-
-package big_test
-
-import (
- "fmt"
- "log"
- "math/big"
-)
-
-func ExampleRat_SetString() {
- r := new(big.Rat)
- r.SetString("355/113")
- fmt.Println(r.FloatString(3))
- // Output: 3.142
-}
-
-func ExampleInt_SetString() {
- i := new(big.Int)
- i.SetString("644", 8) // octal
- fmt.Println(i)
- // Output: 420
-}
-
-func ExampleRat_Scan() {
- // The Scan function is rarely used directly;
- // the fmt package recognizes it as an implementation of fmt.Scanner.
- r := new(big.Rat)
- _, err := fmt.Sscan("1.5000", r)
- if err != nil {
- log.Println("error scanning value:", err)
- } else {
- fmt.Println(r)
- }
- // Output: 3/2
-}
-
-func ExampleInt_Scan() {
- // The Scan function is rarely used directly;
- // the fmt package recognizes it as an implementation of fmt.Scanner.
- i := new(big.Int)
- _, err := fmt.Sscan("18446744073709551617", i)
- if err != nil {
- log.Println("error scanning value:", err)
- } else {
- fmt.Println(i)
- }
- // Output: 18446744073709551617
-}
diff --git a/src/pkg/math/big/gcd_test.go b/src/pkg/math/big/gcd_test.go
deleted file mode 100644
index c0b9f5830..000000000
--- a/src/pkg/math/big/gcd_test.go
+++ /dev/null
@@ -1,47 +0,0 @@
-// Copyright 2012 The Go Authors. All rights reserved.
-// Use of this source code is governed by a BSD-style
-// license that can be found in the LICENSE file.
-
-// This file implements a GCD benchmark.
-// Usage: go test math/big -test.bench GCD
-
-package big
-
-import (
- "math/rand"
- "testing"
-)
-
-// randInt returns a pseudo-random Int in the range [1<<(size-1), (1<<size) - 1]
-func randInt(r *rand.Rand, size uint) *Int {
- n := new(Int).Lsh(intOne, size-1)
- x := new(Int).Rand(r, n)
- return x.Add(x, n) // make sure result > 1<<(size-1)
-}
-
-func runGCD(b *testing.B, aSize, bSize uint) {
- b.StopTimer()
- var r = rand.New(rand.NewSource(1234))
- aa := randInt(r, aSize)
- bb := randInt(r, bSize)
- b.StartTimer()
- for i := 0; i < b.N; i++ {
- new(Int).GCD(nil, nil, aa, bb)
- }
-}
-
-func BenchmarkGCD10x10(b *testing.B) { runGCD(b, 10, 10) }
-func BenchmarkGCD10x100(b *testing.B) { runGCD(b, 10, 100) }
-func BenchmarkGCD10x1000(b *testing.B) { runGCD(b, 10, 1000) }
-func BenchmarkGCD10x10000(b *testing.B) { runGCD(b, 10, 10000) }
-func BenchmarkGCD10x100000(b *testing.B) { runGCD(b, 10, 100000) }
-func BenchmarkGCD100x100(b *testing.B) { runGCD(b, 100, 100) }
-func BenchmarkGCD100x1000(b *testing.B) { runGCD(b, 100, 1000) }
-func BenchmarkGCD100x10000(b *testing.B) { runGCD(b, 100, 10000) }
-func BenchmarkGCD100x100000(b *testing.B) { runGCD(b, 100, 100000) }
-func BenchmarkGCD1000x1000(b *testing.B) { runGCD(b, 1000, 1000) }
-func BenchmarkGCD1000x10000(b *testing.B) { runGCD(b, 1000, 10000) }
-func BenchmarkGCD1000x100000(b *testing.B) { runGCD(b, 1000, 100000) }
-func BenchmarkGCD10000x10000(b *testing.B) { runGCD(b, 10000, 10000) }
-func BenchmarkGCD10000x100000(b *testing.B) { runGCD(b, 10000, 100000) }
-func BenchmarkGCD100000x100000(b *testing.B) { runGCD(b, 100000, 100000) }
diff --git a/src/pkg/math/big/hilbert_test.go b/src/pkg/math/big/hilbert_test.go
deleted file mode 100644
index 1a84341b3..000000000
--- a/src/pkg/math/big/hilbert_test.go
+++ /dev/null
@@ -1,160 +0,0 @@
-// Copyright 2009 The Go Authors. All rights reserved.
-// Use of this source code is governed by a BSD-style
-// license that can be found in the LICENSE file.
-
-// A little test program and benchmark for rational arithmetics.
-// Computes a Hilbert matrix, its inverse, multiplies them
-// and verifies that the product is the identity matrix.
-
-package big
-
-import (
- "fmt"
- "testing"
-)
-
-type matrix struct {
- n, m int
- a []*Rat
-}
-
-func (a *matrix) at(i, j int) *Rat {
- if !(0 <= i && i < a.n && 0 <= j && j < a.m) {
- panic("index out of range")
- }
- return a.a[i*a.m+j]
-}
-
-func (a *matrix) set(i, j int, x *Rat) {
- if !(0 <= i && i < a.n && 0 <= j && j < a.m) {
- panic("index out of range")
- }
- a.a[i*a.m+j] = x
-}
-
-func newMatrix(n, m int) *matrix {
- if !(0 <= n && 0 <= m) {
- panic("illegal matrix")
- }
- a := new(matrix)
- a.n = n
- a.m = m
- a.a = make([]*Rat, n*m)
- return a
-}
-
-func newUnit(n int) *matrix {
- a := newMatrix(n, n)
- for i := 0; i < n; i++ {
- for j := 0; j < n; j++ {
- x := NewRat(0, 1)
- if i == j {
- x.SetInt64(1)
- }
- a.set(i, j, x)
- }
- }
- return a
-}
-
-func newHilbert(n int) *matrix {
- a := newMatrix(n, n)
- for i := 0; i < n; i++ {
- for j := 0; j < n; j++ {
- a.set(i, j, NewRat(1, int64(i+j+1)))
- }
- }
- return a
-}
-
-func newInverseHilbert(n int) *matrix {
- a := newMatrix(n, n)
- for i := 0; i < n; i++ {
- for j := 0; j < n; j++ {
- x1 := new(Rat).SetInt64(int64(i + j + 1))
- x2 := new(Rat).SetInt(new(Int).Binomial(int64(n+i), int64(n-j-1)))
- x3 := new(Rat).SetInt(new(Int).Binomial(int64(n+j), int64(n-i-1)))
- x4 := new(Rat).SetInt(new(Int).Binomial(int64(i+j), int64(i)))
-
- x1.Mul(x1, x2)
- x1.Mul(x1, x3)
- x1.Mul(x1, x4)
- x1.Mul(x1, x4)
-
- if (i+j)&1 != 0 {
- x1.Neg(x1)
- }
-
- a.set(i, j, x1)
- }
- }
- return a
-}
-
-func (a *matrix) mul(b *matrix) *matrix {
- if a.m != b.n {
- panic("illegal matrix multiply")
- }
- c := newMatrix(a.n, b.m)
- for i := 0; i < c.n; i++ {
- for j := 0; j < c.m; j++ {
- x := NewRat(0, 1)
- for k := 0; k < a.m; k++ {
- x.Add(x, new(Rat).Mul(a.at(i, k), b.at(k, j)))
- }
- c.set(i, j, x)
- }
- }
- return c
-}
-
-func (a *matrix) eql(b *matrix) bool {
- if a.n != b.n || a.m != b.m {
- return false
- }
- for i := 0; i < a.n; i++ {
- for j := 0; j < a.m; j++ {
- if a.at(i, j).Cmp(b.at(i, j)) != 0 {
- return false
- }
- }
- }
- return true
-}
-
-func (a *matrix) String() string {
- s := ""
- for i := 0; i < a.n; i++ {
- for j := 0; j < a.m; j++ {
- s += fmt.Sprintf("\t%s", a.at(i, j))
- }
- s += "\n"
- }
- return s
-}
-
-func doHilbert(t *testing.T, n int) {
- a := newHilbert(n)
- b := newInverseHilbert(n)
- I := newUnit(n)
- ab := a.mul(b)
- if !ab.eql(I) {
- if t == nil {
- panic("Hilbert failed")
- }
- t.Errorf("a = %s\n", a)
- t.Errorf("b = %s\n", b)
- t.Errorf("a*b = %s\n", ab)
- t.Errorf("I = %s\n", I)
- }
-}
-
-func TestHilbert(t *testing.T) {
- doHilbert(t, 10)
-}
-
-func BenchmarkHilbert(b *testing.B) {
- for i := 0; i < b.N; i++ {
- doHilbert(nil, 10)
- }
-}
diff --git a/src/pkg/math/big/int.go b/src/pkg/math/big/int.go
deleted file mode 100644
index 269949d61..000000000
--- a/src/pkg/math/big/int.go
+++ /dev/null
@@ -1,1011 +0,0 @@
-// Copyright 2009 The Go Authors. All rights reserved.
-// Use of this source code is governed by a BSD-style
-// license that can be found in the LICENSE file.
-
-// This file implements signed multi-precision integers.
-
-package big
-
-import (
- "errors"
- "fmt"
- "io"
- "math/rand"
- "strings"
-)
-
-// An Int represents a signed multi-precision integer.
-// The zero value for an Int represents the value 0.
-type Int struct {
- neg bool // sign
- abs nat // absolute value of the integer
-}
-
-var intOne = &Int{false, natOne}
-
-// Sign returns:
-//
-// -1 if x < 0
-// 0 if x == 0
-// +1 if x > 0
-//
-func (x *Int) Sign() int {
- if len(x.abs) == 0 {
- return 0
- }
- if x.neg {
- return -1
- }
- return 1
-}
-
-// SetInt64 sets z to x and returns z.
-func (z *Int) SetInt64(x int64) *Int {
- neg := false
- if x < 0 {
- neg = true
- x = -x
- }
- z.abs = z.abs.setUint64(uint64(x))
- z.neg = neg
- return z
-}
-
-// SetUint64 sets z to x and returns z.
-func (z *Int) SetUint64(x uint64) *Int {
- z.abs = z.abs.setUint64(x)
- z.neg = false
- return z
-}
-
-// NewInt allocates and returns a new Int set to x.
-func NewInt(x int64) *Int {
- return new(Int).SetInt64(x)
-}
-
-// Set sets z to x and returns z.
-func (z *Int) Set(x *Int) *Int {
- if z != x {
- z.abs = z.abs.set(x.abs)
- z.neg = x.neg
- }
- return z
-}
-
-// Bits provides raw (unchecked but fast) access to x by returning its
-// absolute value as a little-endian Word slice. The result and x share
-// the same underlying array.
-// Bits is intended to support implementation of missing low-level Int
-// functionality outside this package; it should be avoided otherwise.
-func (x *Int) Bits() []Word {
- return x.abs
-}
-
-// SetBits provides raw (unchecked but fast) access to z by setting its
-// value to abs, interpreted as a little-endian Word slice, and returning
-// z. The result and abs share the same underlying array.
-// SetBits is intended to support implementation of missing low-level Int
-// functionality outside this package; it should be avoided otherwise.
-func (z *Int) SetBits(abs []Word) *Int {
- z.abs = nat(abs).norm()
- z.neg = false
- return z
-}
-
-// Abs sets z to |x| (the absolute value of x) and returns z.
-func (z *Int) Abs(x *Int) *Int {
- z.Set(x)
- z.neg = false
- return z
-}
-
-// Neg sets z to -x and returns z.
-func (z *Int) Neg(x *Int) *Int {
- z.Set(x)
- z.neg = len(z.abs) > 0 && !z.neg // 0 has no sign
- return z
-}
-
-// Add sets z to the sum x+y and returns z.
-func (z *Int) Add(x, y *Int) *Int {
- neg := x.neg
- if x.neg == y.neg {
- // x + y == x + y
- // (-x) + (-y) == -(x + y)
- z.abs = z.abs.add(x.abs, y.abs)
- } else {
- // x + (-y) == x - y == -(y - x)
- // (-x) + y == y - x == -(x - y)
- if x.abs.cmp(y.abs) >= 0 {
- z.abs = z.abs.sub(x.abs, y.abs)
- } else {
- neg = !neg
- z.abs = z.abs.sub(y.abs, x.abs)
- }
- }
- z.neg = len(z.abs) > 0 && neg // 0 has no sign
- return z
-}
-
-// Sub sets z to the difference x-y and returns z.
-func (z *Int) Sub(x, y *Int) *Int {
- neg := x.neg
- if x.neg != y.neg {
- // x - (-y) == x + y
- // (-x) - y == -(x + y)
- z.abs = z.abs.add(x.abs, y.abs)
- } else {
- // x - y == x - y == -(y - x)
- // (-x) - (-y) == y - x == -(x - y)
- if x.abs.cmp(y.abs) >= 0 {
- z.abs = z.abs.sub(x.abs, y.abs)
- } else {
- neg = !neg
- z.abs = z.abs.sub(y.abs, x.abs)
- }
- }
- z.neg = len(z.abs) > 0 && neg // 0 has no sign
- return z
-}
-
-// Mul sets z to the product x*y and returns z.
-func (z *Int) Mul(x, y *Int) *Int {
- // x * y == x * y
- // x * (-y) == -(x * y)
- // (-x) * y == -(x * y)
- // (-x) * (-y) == x * y
- z.abs = z.abs.mul(x.abs, y.abs)
- z.neg = len(z.abs) > 0 && x.neg != y.neg // 0 has no sign
- return z
-}
-
-// MulRange sets z to the product of all integers
-// in the range [a, b] inclusively and returns z.
-// If a > b (empty range), the result is 1.
-func (z *Int) MulRange(a, b int64) *Int {
- switch {
- case a > b:
- return z.SetInt64(1) // empty range
- case a <= 0 && b >= 0:
- return z.SetInt64(0) // range includes 0
- }
- // a <= b && (b < 0 || a > 0)
-
- neg := false
- if a < 0 {
- neg = (b-a)&1 == 0
- a, b = -b, -a
- }
-
- z.abs = z.abs.mulRange(uint64(a), uint64(b))
- z.neg = neg
- return z
-}
-
-// Binomial sets z to the binomial coefficient of (n, k) and returns z.
-func (z *Int) Binomial(n, k int64) *Int {
- var a, b Int
- a.MulRange(n-k+1, n)
- b.MulRange(1, k)
- return z.Quo(&a, &b)
-}
-
-// Quo sets z to the quotient x/y for y != 0 and returns z.
-// If y == 0, a division-by-zero run-time panic occurs.
-// Quo implements truncated division (like Go); see QuoRem for more details.
-func (z *Int) Quo(x, y *Int) *Int {
- z.abs, _ = z.abs.div(nil, x.abs, y.abs)
- z.neg = len(z.abs) > 0 && x.neg != y.neg // 0 has no sign
- return z
-}
-
-// Rem sets z to the remainder x%y for y != 0 and returns z.
-// If y == 0, a division-by-zero run-time panic occurs.
-// Rem implements truncated modulus (like Go); see QuoRem for more details.
-func (z *Int) Rem(x, y *Int) *Int {
- _, z.abs = nat(nil).div(z.abs, x.abs, y.abs)
- z.neg = len(z.abs) > 0 && x.neg // 0 has no sign
- return z
-}
-
-// QuoRem sets z to the quotient x/y and r to the remainder x%y
-// and returns the pair (z, r) for y != 0.
-// If y == 0, a division-by-zero run-time panic occurs.
-//
-// QuoRem implements T-division and modulus (like Go):
-//
-// q = x/y with the result truncated to zero
-// r = x - y*q
-//
-// (See Daan Leijen, ``Division and Modulus for Computer Scientists''.)
-// See DivMod for Euclidean division and modulus (unlike Go).
-//
-func (z *Int) QuoRem(x, y, r *Int) (*Int, *Int) {
- z.abs, r.abs = z.abs.div(r.abs, x.abs, y.abs)
- z.neg, r.neg = len(z.abs) > 0 && x.neg != y.neg, len(r.abs) > 0 && x.neg // 0 has no sign
- return z, r
-}
-
-// Div sets z to the quotient x/y for y != 0 and returns z.
-// If y == 0, a division-by-zero run-time panic occurs.
-// Div implements Euclidean division (unlike Go); see DivMod for more details.
-func (z *Int) Div(x, y *Int) *Int {
- y_neg := y.neg // z may be an alias for y
- var r Int
- z.QuoRem(x, y, &r)
- if r.neg {
- if y_neg {
- z.Add(z, intOne)
- } else {
- z.Sub(z, intOne)
- }
- }
- return z
-}
-
-// Mod sets z to the modulus x%y for y != 0 and returns z.
-// If y == 0, a division-by-zero run-time panic occurs.
-// Mod implements Euclidean modulus (unlike Go); see DivMod for more details.
-func (z *Int) Mod(x, y *Int) *Int {
- y0 := y // save y
- if z == y || alias(z.abs, y.abs) {
- y0 = new(Int).Set(y)
- }
- var q Int
- q.QuoRem(x, y, z)
- if z.neg {
- if y0.neg {
- z.Sub(z, y0)
- } else {
- z.Add(z, y0)
- }
- }
- return z
-}
-
-// DivMod sets z to the quotient x div y and m to the modulus x mod y
-// and returns the pair (z, m) for y != 0.
-// If y == 0, a division-by-zero run-time panic occurs.
-//
-// DivMod implements Euclidean division and modulus (unlike Go):
-//
-// q = x div y such that
-// m = x - y*q with 0 <= m < |q|
-//
-// (See Raymond T. Boute, ``The Euclidean definition of the functions
-// div and mod''. ACM Transactions on Programming Languages and
-// Systems (TOPLAS), 14(2):127-144, New York, NY, USA, 4/1992.
-// ACM press.)
-// See QuoRem for T-division and modulus (like Go).
-//
-func (z *Int) DivMod(x, y, m *Int) (*Int, *Int) {
- y0 := y // save y
- if z == y || alias(z.abs, y.abs) {
- y0 = new(Int).Set(y)
- }
- z.QuoRem(x, y, m)
- if m.neg {
- if y0.neg {
- z.Add(z, intOne)
- m.Sub(m, y0)
- } else {
- z.Sub(z, intOne)
- m.Add(m, y0)
- }
- }
- return z, m
-}
-
-// Cmp compares x and y and returns:
-//
-// -1 if x < y
-// 0 if x == y
-// +1 if x > y
-//
-func (x *Int) Cmp(y *Int) (r int) {
- // x cmp y == x cmp y
- // x cmp (-y) == x
- // (-x) cmp y == y
- // (-x) cmp (-y) == -(x cmp y)
- switch {
- case x.neg == y.neg:
- r = x.abs.cmp(y.abs)
- if x.neg {
- r = -r
- }
- case x.neg:
- r = -1
- default:
- r = 1
- }
- return
-}
-
-func (x *Int) String() string {
- switch {
- case x == nil:
- return "<nil>"
- case x.neg:
- return "-" + x.abs.decimalString()
- }
- return x.abs.decimalString()
-}
-
-func charset(ch rune) string {
- switch ch {
- case 'b':
- return lowercaseDigits[0:2]
- case 'o':
- return lowercaseDigits[0:8]
- case 'd', 's', 'v':
- return lowercaseDigits[0:10]
- case 'x':
- return lowercaseDigits[0:16]
- case 'X':
- return uppercaseDigits[0:16]
- }
- return "" // unknown format
-}
-
-// write count copies of text to s
-func writeMultiple(s fmt.State, text string, count int) {
- if len(text) > 0 {
- b := []byte(text)
- for ; count > 0; count-- {
- s.Write(b)
- }
- }
-}
-
-// Format is a support routine for fmt.Formatter. It accepts
-// the formats 'b' (binary), 'o' (octal), 'd' (decimal), 'x'
-// (lowercase hexadecimal), and 'X' (uppercase hexadecimal).
-// Also supported are the full suite of package fmt's format
-// verbs for integral types, including '+', '-', and ' '
-// for sign control, '#' for leading zero in octal and for
-// hexadecimal, a leading "0x" or "0X" for "%#x" and "%#X"
-// respectively, specification of minimum digits precision,
-// output field width, space or zero padding, and left or
-// right justification.
-//
-func (x *Int) Format(s fmt.State, ch rune) {
- cs := charset(ch)
-
- // special cases
- switch {
- case cs == "":
- // unknown format
- fmt.Fprintf(s, "%%!%c(big.Int=%s)", ch, x.String())
- return
- case x == nil:
- fmt.Fprint(s, "<nil>")
- return
- }
-
- // determine sign character
- sign := ""
- switch {
- case x.neg:
- sign = "-"
- case s.Flag('+'): // supersedes ' ' when both specified
- sign = "+"
- case s.Flag(' '):
- sign = " "
- }
-
- // determine prefix characters for indicating output base
- prefix := ""
- if s.Flag('#') {
- switch ch {
- case 'o': // octal
- prefix = "0"
- case 'x': // hexadecimal
- prefix = "0x"
- case 'X':
- prefix = "0X"
- }
- }
-
- // determine digits with base set by len(cs) and digit characters from cs
- digits := x.abs.string(cs)
-
- // number of characters for the three classes of number padding
- var left int // space characters to left of digits for right justification ("%8d")
- var zeroes int // zero characters (actually cs[0]) as left-most digits ("%.8d")
- var right int // space characters to right of digits for left justification ("%-8d")
-
- // determine number padding from precision: the least number of digits to output
- precision, precisionSet := s.Precision()
- if precisionSet {
- switch {
- case len(digits) < precision:
- zeroes = precision - len(digits) // count of zero padding
- case digits == "0" && precision == 0:
- return // print nothing if zero value (x == 0) and zero precision ("." or ".0")
- }
- }
-
- // determine field pad from width: the least number of characters to output
- length := len(sign) + len(prefix) + zeroes + len(digits)
- if width, widthSet := s.Width(); widthSet && length < width { // pad as specified
- switch d := width - length; {
- case s.Flag('-'):
- // pad on the right with spaces; supersedes '0' when both specified
- right = d
- case s.Flag('0') && !precisionSet:
- // pad with zeroes unless precision also specified
- zeroes = d
- default:
- // pad on the left with spaces
- left = d
- }
- }
-
- // print number as [left pad][sign][prefix][zero pad][digits][right pad]
- writeMultiple(s, " ", left)
- writeMultiple(s, sign, 1)
- writeMultiple(s, prefix, 1)
- writeMultiple(s, "0", zeroes)
- writeMultiple(s, digits, 1)
- writeMultiple(s, " ", right)
-}
-
-// scan sets z to the integer value corresponding to the longest possible prefix
-// read from r representing a signed integer number in a given conversion base.
-// It returns z, the actual conversion base used, and an error, if any. In the
-// error case, the value of z is undefined but the returned value is nil. The
-// syntax follows the syntax of integer literals in Go.
-//
-// The base argument must be 0 or a value from 2 through MaxBase. If the base
-// is 0, the string prefix determines the actual conversion base. A prefix of
-// ``0x'' or ``0X'' selects base 16; the ``0'' prefix selects base 8, and a
-// ``0b'' or ``0B'' prefix selects base 2. Otherwise the selected base is 10.
-//
-func (z *Int) scan(r io.RuneScanner, base int) (*Int, int, error) {
- // determine sign
- ch, _, err := r.ReadRune()
- if err != nil {
- return nil, 0, err
- }
- neg := false
- switch ch {
- case '-':
- neg = true
- case '+': // nothing to do
- default:
- r.UnreadRune()
- }
-
- // determine mantissa
- z.abs, base, err = z.abs.scan(r, base)
- if err != nil {
- return nil, base, err
- }
- z.neg = len(z.abs) > 0 && neg // 0 has no sign
-
- return z, base, nil
-}
-
-// Scan is a support routine for fmt.Scanner; it sets z to the value of
-// the scanned number. It accepts the formats 'b' (binary), 'o' (octal),
-// 'd' (decimal), 'x' (lowercase hexadecimal), and 'X' (uppercase hexadecimal).
-func (z *Int) Scan(s fmt.ScanState, ch rune) error {
- s.SkipSpace() // skip leading space characters
- base := 0
- switch ch {
- case 'b':
- base = 2
- case 'o':
- base = 8
- case 'd':
- base = 10
- case 'x', 'X':
- base = 16
- case 's', 'v':
- // let scan determine the base
- default:
- return errors.New("Int.Scan: invalid verb")
- }
- _, _, err := z.scan(s, base)
- return err
-}
-
-// Int64 returns the int64 representation of x.
-// If x cannot be represented in an int64, the result is undefined.
-func (x *Int) Int64() int64 {
- v := int64(x.Uint64())
- if x.neg {
- v = -v
- }
- return v
-}
-
-// Uint64 returns the uint64 representation of x.
-// If x cannot be represented in a uint64, the result is undefined.
-func (x *Int) Uint64() uint64 {
- if len(x.abs) == 0 {
- return 0
- }
- v := uint64(x.abs[0])
- if _W == 32 && len(x.abs) > 1 {
- v |= uint64(x.abs[1]) << 32
- }
- return v
-}
-
-// SetString sets z to the value of s, interpreted in the given base,
-// and returns z and a boolean indicating success. If SetString fails,
-// the value of z is undefined but the returned value is nil.
-//
-// The base argument must be 0 or a value from 2 through MaxBase. If the base
-// is 0, the string prefix determines the actual conversion base. A prefix of
-// ``0x'' or ``0X'' selects base 16; the ``0'' prefix selects base 8, and a
-// ``0b'' or ``0B'' prefix selects base 2. Otherwise the selected base is 10.
-//
-func (z *Int) SetString(s string, base int) (*Int, bool) {
- r := strings.NewReader(s)
- _, _, err := z.scan(r, base)
- if err != nil {
- return nil, false
- }
- _, _, err = r.ReadRune()
- if err != io.EOF {
- return nil, false
- }
- return z, true // err == io.EOF => scan consumed all of s
-}
-
-// SetBytes interprets buf as the bytes of a big-endian unsigned
-// integer, sets z to that value, and returns z.
-func (z *Int) SetBytes(buf []byte) *Int {
- z.abs = z.abs.setBytes(buf)
- z.neg = false
- return z
-}
-
-// Bytes returns the absolute value of x as a big-endian byte slice.
-func (x *Int) Bytes() []byte {
- buf := make([]byte, len(x.abs)*_S)
- return buf[x.abs.bytes(buf):]
-}
-
-// BitLen returns the length of the absolute value of x in bits.
-// The bit length of 0 is 0.
-func (x *Int) BitLen() int {
- return x.abs.bitLen()
-}
-
-// Exp sets z = x**y mod |m| (i.e. the sign of m is ignored), and returns z.
-// If y <= 0, the result is 1 mod |m|; if m == nil or m == 0, z = x**y.
-// See Knuth, volume 2, section 4.6.3.
-func (z *Int) Exp(x, y, m *Int) *Int {
- var yWords nat
- if !y.neg {
- yWords = y.abs
- }
- // y >= 0
-
- var mWords nat
- if m != nil {
- mWords = m.abs // m.abs may be nil for m == 0
- }
-
- z.abs = z.abs.expNN(x.abs, yWords, mWords)
- z.neg = len(z.abs) > 0 && x.neg && len(yWords) > 0 && yWords[0]&1 == 1 // 0 has no sign
- return z
-}
-
-// GCD sets z to the greatest common divisor of a and b, which both must
-// be > 0, and returns z.
-// If x and y are not nil, GCD sets x and y such that z = a*x + b*y.
-// If either a or b is <= 0, GCD sets z = x = y = 0.
-func (z *Int) GCD(x, y, a, b *Int) *Int {
- if a.Sign() <= 0 || b.Sign() <= 0 {
- z.SetInt64(0)
- if x != nil {
- x.SetInt64(0)
- }
- if y != nil {
- y.SetInt64(0)
- }
- return z
- }
- if x == nil && y == nil {
- return z.binaryGCD(a, b)
- }
-
- A := new(Int).Set(a)
- B := new(Int).Set(b)
-
- X := new(Int)
- Y := new(Int).SetInt64(1)
-
- lastX := new(Int).SetInt64(1)
- lastY := new(Int)
-
- q := new(Int)
- temp := new(Int)
-
- for len(B.abs) > 0 {
- r := new(Int)
- q, r = q.QuoRem(A, B, r)
-
- A, B = B, r
-
- temp.Set(X)
- X.Mul(X, q)
- X.neg = !X.neg
- X.Add(X, lastX)
- lastX.Set(temp)
-
- temp.Set(Y)
- Y.Mul(Y, q)
- Y.neg = !Y.neg
- Y.Add(Y, lastY)
- lastY.Set(temp)
- }
-
- if x != nil {
- *x = *lastX
- }
-
- if y != nil {
- *y = *lastY
- }
-
- *z = *A
- return z
-}
-
-// binaryGCD sets z to the greatest common divisor of a and b, which both must
-// be > 0, and returns z.
-// See Knuth, The Art of Computer Programming, Vol. 2, Section 4.5.2, Algorithm B.
-func (z *Int) binaryGCD(a, b *Int) *Int {
- u := z
- v := new(Int)
-
- // use one Euclidean iteration to ensure that u and v are approx. the same size
- switch {
- case len(a.abs) > len(b.abs):
- u.Set(b)
- v.Rem(a, b)
- case len(a.abs) < len(b.abs):
- u.Set(a)
- v.Rem(b, a)
- default:
- u.Set(a)
- v.Set(b)
- }
-
- // v might be 0 now
- if len(v.abs) == 0 {
- return u
- }
- // u > 0 && v > 0
-
- // determine largest k such that u = u' << k, v = v' << k
- k := u.abs.trailingZeroBits()
- if vk := v.abs.trailingZeroBits(); vk < k {
- k = vk
- }
- u.Rsh(u, k)
- v.Rsh(v, k)
-
- // determine t (we know that u > 0)
- t := new(Int)
- if u.abs[0]&1 != 0 {
- // u is odd
- t.Neg(v)
- } else {
- t.Set(u)
- }
-
- for len(t.abs) > 0 {
- // reduce t
- t.Rsh(t, t.abs.trailingZeroBits())
- if t.neg {
- v, t = t, v
- v.neg = len(v.abs) > 0 && !v.neg // 0 has no sign
- } else {
- u, t = t, u
- }
- t.Sub(u, v)
- }
-
- return z.Lsh(u, k)
-}
-
-// ProbablyPrime performs n Miller-Rabin tests to check whether x is prime.
-// If it returns true, x is prime with probability 1 - 1/4^n.
-// If it returns false, x is not prime.
-func (x *Int) ProbablyPrime(n int) bool {
- return !x.neg && x.abs.probablyPrime(n)
-}
-
-// Rand sets z to a pseudo-random number in [0, n) and returns z.
-func (z *Int) Rand(rnd *rand.Rand, n *Int) *Int {
- z.neg = false
- if n.neg == true || len(n.abs) == 0 {
- z.abs = nil
- return z
- }
- z.abs = z.abs.random(rnd, n.abs, n.abs.bitLen())
- return z
-}
-
-// ModInverse sets z to the multiplicative inverse of g in the group ℤ/pℤ (where
-// p is a prime) and returns z.
-func (z *Int) ModInverse(g, p *Int) *Int {
- var d Int
- d.GCD(z, nil, g, p)
- // x and y are such that g*x + p*y = d. Since p is prime, d = 1. Taking
- // that modulo p results in g*x = 1, therefore x is the inverse element.
- if z.neg {
- z.Add(z, p)
- }
- return z
-}
-
-// Lsh sets z = x << n and returns z.
-func (z *Int) Lsh(x *Int, n uint) *Int {
- z.abs = z.abs.shl(x.abs, n)
- z.neg = x.neg
- return z
-}
-
-// Rsh sets z = x >> n and returns z.
-func (z *Int) Rsh(x *Int, n uint) *Int {
- if x.neg {
- // (-x) >> s == ^(x-1) >> s == ^((x-1) >> s) == -(((x-1) >> s) + 1)
- t := z.abs.sub(x.abs, natOne) // no underflow because |x| > 0
- t = t.shr(t, n)
- z.abs = t.add(t, natOne)
- z.neg = true // z cannot be zero if x is negative
- return z
- }
-
- z.abs = z.abs.shr(x.abs, n)
- z.neg = false
- return z
-}
-
-// Bit returns the value of the i'th bit of x. That is, it
-// returns (x>>i)&1. The bit index i must be >= 0.
-func (x *Int) Bit(i int) uint {
- if i == 0 {
- // optimization for common case: odd/even test of x
- if len(x.abs) > 0 {
- return uint(x.abs[0] & 1) // bit 0 is same for -x
- }
- return 0
- }
- if i < 0 {
- panic("negative bit index")
- }
- if x.neg {
- t := nat(nil).sub(x.abs, natOne)
- return t.bit(uint(i)) ^ 1
- }
-
- return x.abs.bit(uint(i))
-}
-
-// SetBit sets z to x, with x's i'th bit set to b (0 or 1).
-// That is, if b is 1 SetBit sets z = x | (1 << i);
-// if b is 0 SetBit sets z = x &^ (1 << i). If b is not 0 or 1,
-// SetBit will panic.
-func (z *Int) SetBit(x *Int, i int, b uint) *Int {
- if i < 0 {
- panic("negative bit index")
- }
- if x.neg {
- t := z.abs.sub(x.abs, natOne)
- t = t.setBit(t, uint(i), b^1)
- z.abs = t.add(t, natOne)
- z.neg = len(z.abs) > 0
- return z
- }
- z.abs = z.abs.setBit(x.abs, uint(i), b)
- z.neg = false
- return z
-}
-
-// And sets z = x & y and returns z.
-func (z *Int) And(x, y *Int) *Int {
- if x.neg == y.neg {
- if x.neg {
- // (-x) & (-y) == ^(x-1) & ^(y-1) == ^((x-1) | (y-1)) == -(((x-1) | (y-1)) + 1)
- x1 := nat(nil).sub(x.abs, natOne)
- y1 := nat(nil).sub(y.abs, natOne)
- z.abs = z.abs.add(z.abs.or(x1, y1), natOne)
- z.neg = true // z cannot be zero if x and y are negative
- return z
- }
-
- // x & y == x & y
- z.abs = z.abs.and(x.abs, y.abs)
- z.neg = false
- return z
- }
-
- // x.neg != y.neg
- if x.neg {
- x, y = y, x // & is symmetric
- }
-
- // x & (-y) == x & ^(y-1) == x &^ (y-1)
- y1 := nat(nil).sub(y.abs, natOne)
- z.abs = z.abs.andNot(x.abs, y1)
- z.neg = false
- return z
-}
-
-// AndNot sets z = x &^ y and returns z.
-func (z *Int) AndNot(x, y *Int) *Int {
- if x.neg == y.neg {
- if x.neg {
- // (-x) &^ (-y) == ^(x-1) &^ ^(y-1) == ^(x-1) & (y-1) == (y-1) &^ (x-1)
- x1 := nat(nil).sub(x.abs, natOne)
- y1 := nat(nil).sub(y.abs, natOne)
- z.abs = z.abs.andNot(y1, x1)
- z.neg = false
- return z
- }
-
- // x &^ y == x &^ y
- z.abs = z.abs.andNot(x.abs, y.abs)
- z.neg = false
- return z
- }
-
- if x.neg {
- // (-x) &^ y == ^(x-1) &^ y == ^(x-1) & ^y == ^((x-1) | y) == -(((x-1) | y) + 1)
- x1 := nat(nil).sub(x.abs, natOne)
- z.abs = z.abs.add(z.abs.or(x1, y.abs), natOne)
- z.neg = true // z cannot be zero if x is negative and y is positive
- return z
- }
-
- // x &^ (-y) == x &^ ^(y-1) == x & (y-1)
- y1 := nat(nil).add(y.abs, natOne)
- z.abs = z.abs.and(x.abs, y1)
- z.neg = false
- return z
-}
-
-// Or sets z = x | y and returns z.
-func (z *Int) Or(x, y *Int) *Int {
- if x.neg == y.neg {
- if x.neg {
- // (-x) | (-y) == ^(x-1) | ^(y-1) == ^((x-1) & (y-1)) == -(((x-1) & (y-1)) + 1)
- x1 := nat(nil).sub(x.abs, natOne)
- y1 := nat(nil).sub(y.abs, natOne)
- z.abs = z.abs.add(z.abs.and(x1, y1), natOne)
- z.neg = true // z cannot be zero if x and y are negative
- return z
- }
-
- // x | y == x | y
- z.abs = z.abs.or(x.abs, y.abs)
- z.neg = false
- return z
- }
-
- // x.neg != y.neg
- if x.neg {
- x, y = y, x // | is symmetric
- }
-
- // x | (-y) == x | ^(y-1) == ^((y-1) &^ x) == -(^((y-1) &^ x) + 1)
- y1 := nat(nil).sub(y.abs, natOne)
- z.abs = z.abs.add(z.abs.andNot(y1, x.abs), natOne)
- z.neg = true // z cannot be zero if one of x or y is negative
- return z
-}
-
-// Xor sets z = x ^ y and returns z.
-func (z *Int) Xor(x, y *Int) *Int {
- if x.neg == y.neg {
- if x.neg {
- // (-x) ^ (-y) == ^(x-1) ^ ^(y-1) == (x-1) ^ (y-1)
- x1 := nat(nil).sub(x.abs, natOne)
- y1 := nat(nil).sub(y.abs, natOne)
- z.abs = z.abs.xor(x1, y1)
- z.neg = false
- return z
- }
-
- // x ^ y == x ^ y
- z.abs = z.abs.xor(x.abs, y.abs)
- z.neg = false
- return z
- }
-
- // x.neg != y.neg
- if x.neg {
- x, y = y, x // ^ is symmetric
- }
-
- // x ^ (-y) == x ^ ^(y-1) == ^(x ^ (y-1)) == -((x ^ (y-1)) + 1)
- y1 := nat(nil).sub(y.abs, natOne)
- z.abs = z.abs.add(z.abs.xor(x.abs, y1), natOne)
- z.neg = true // z cannot be zero if only one of x or y is negative
- return z
-}
-
-// Not sets z = ^x and returns z.
-func (z *Int) Not(x *Int) *Int {
- if x.neg {
- // ^(-x) == ^(^(x-1)) == x-1
- z.abs = z.abs.sub(x.abs, natOne)
- z.neg = false
- return z
- }
-
- // ^x == -x-1 == -(x+1)
- z.abs = z.abs.add(x.abs, natOne)
- z.neg = true // z cannot be zero if x is positive
- return z
-}
-
-// Gob codec version. Permits backward-compatible changes to the encoding.
-const intGobVersion byte = 1
-
-// GobEncode implements the gob.GobEncoder interface.
-func (x *Int) GobEncode() ([]byte, error) {
- if x == nil {
- return nil, nil
- }
- buf := make([]byte, 1+len(x.abs)*_S) // extra byte for version and sign bit
- i := x.abs.bytes(buf) - 1 // i >= 0
- b := intGobVersion << 1 // make space for sign bit
- if x.neg {
- b |= 1
- }
- buf[i] = b
- return buf[i:], nil
-}
-
-// GobDecode implements the gob.GobDecoder interface.
-func (z *Int) GobDecode(buf []byte) error {
- if len(buf) == 0 {
- // Other side sent a nil or default value.
- *z = Int{}
- return nil
- }
- b := buf[0]
- if b>>1 != intGobVersion {
- return errors.New(fmt.Sprintf("Int.GobDecode: encoding version %d not supported", b>>1))
- }
- z.neg = b&1 != 0
- z.abs = z.abs.setBytes(buf[1:])
- return nil
-}
-
-// MarshalJSON implements the json.Marshaler interface.
-func (z *Int) MarshalJSON() ([]byte, error) {
- // TODO(gri): get rid of the []byte/string conversions
- return []byte(z.String()), nil
-}
-
-// UnmarshalJSON implements the json.Unmarshaler interface.
-func (z *Int) UnmarshalJSON(text []byte) error {
- // TODO(gri): get rid of the []byte/string conversions
- if _, ok := z.SetString(string(text), 0); !ok {
- return fmt.Errorf("math/big: cannot unmarshal %q into a *big.Int", text)
- }
- return nil
-}
-
-// MarshalText implements the encoding.TextMarshaler interface
-func (z *Int) MarshalText() (text []byte, err error) {
- return []byte(z.String()), nil
-}
-
-// UnmarshalText implements the encoding.TextUnmarshaler interface
-func (z *Int) UnmarshalText(text []byte) error {
- if _, ok := z.SetString(string(text), 0); !ok {
- return fmt.Errorf("math/big: cannot unmarshal %q into a *big.Int", text)
- }
- return nil
-}
diff --git a/src/pkg/math/big/int_test.go b/src/pkg/math/big/int_test.go
deleted file mode 100644
index 299dc72fb..000000000
--- a/src/pkg/math/big/int_test.go
+++ /dev/null
@@ -1,1601 +0,0 @@
-// Copyright 2009 The Go Authors. All rights reserved.
-// Use of this source code is governed by a BSD-style
-// license that can be found in the LICENSE file.
-
-package big
-
-import (
- "bytes"
- "encoding/gob"
- "encoding/hex"
- "encoding/json"
- "encoding/xml"
- "fmt"
- "math/rand"
- "testing"
- "testing/quick"
-)
-
-func isNormalized(x *Int) bool {
- if len(x.abs) == 0 {
- return !x.neg
- }
- // len(x.abs) > 0
- return x.abs[len(x.abs)-1] != 0
-}
-
-type funZZ func(z, x, y *Int) *Int
-type argZZ struct {
- z, x, y *Int
-}
-
-var sumZZ = []argZZ{
- {NewInt(0), NewInt(0), NewInt(0)},
- {NewInt(1), NewInt(1), NewInt(0)},
- {NewInt(1111111110), NewInt(123456789), NewInt(987654321)},
- {NewInt(-1), NewInt(-1), NewInt(0)},
- {NewInt(864197532), NewInt(-123456789), NewInt(987654321)},
- {NewInt(-1111111110), NewInt(-123456789), NewInt(-987654321)},
-}
-
-var prodZZ = []argZZ{
- {NewInt(0), NewInt(0), NewInt(0)},
- {NewInt(0), NewInt(1), NewInt(0)},
- {NewInt(1), NewInt(1), NewInt(1)},
- {NewInt(-991 * 991), NewInt(991), NewInt(-991)},
- // TODO(gri) add larger products
-}
-
-func TestSignZ(t *testing.T) {
- var zero Int
- for _, a := range sumZZ {
- s := a.z.Sign()
- e := a.z.Cmp(&zero)
- if s != e {
- t.Errorf("got %d; want %d for z = %v", s, e, a.z)
- }
- }
-}
-
-func TestSetZ(t *testing.T) {
- for _, a := range sumZZ {
- var z Int
- z.Set(a.z)
- if !isNormalized(&z) {
- t.Errorf("%v is not normalized", z)
- }
- if (&z).Cmp(a.z) != 0 {
- t.Errorf("got z = %v; want %v", z, a.z)
- }
- }
-}
-
-func TestAbsZ(t *testing.T) {
- var zero Int
- for _, a := range sumZZ {
- var z Int
- z.Abs(a.z)
- var e Int
- e.Set(a.z)
- if e.Cmp(&zero) < 0 {
- e.Sub(&zero, &e)
- }
- if z.Cmp(&e) != 0 {
- t.Errorf("got z = %v; want %v", z, e)
- }
- }
-}
-
-func testFunZZ(t *testing.T, msg string, f funZZ, a argZZ) {
- var z Int
- f(&z, a.x, a.y)
- if !isNormalized(&z) {
- t.Errorf("%s%v is not normalized", msg, z)
- }
- if (&z).Cmp(a.z) != 0 {
- t.Errorf("%s%+v\n\tgot z = %v; want %v", msg, a, &z, a.z)
- }
-}
-
-func TestSumZZ(t *testing.T) {
- AddZZ := func(z, x, y *Int) *Int { return z.Add(x, y) }
- SubZZ := func(z, x, y *Int) *Int { return z.Sub(x, y) }
- for _, a := range sumZZ {
- arg := a
- testFunZZ(t, "AddZZ", AddZZ, arg)
-
- arg = argZZ{a.z, a.y, a.x}
- testFunZZ(t, "AddZZ symmetric", AddZZ, arg)
-
- arg = argZZ{a.x, a.z, a.y}
- testFunZZ(t, "SubZZ", SubZZ, arg)
-
- arg = argZZ{a.y, a.z, a.x}
- testFunZZ(t, "SubZZ symmetric", SubZZ, arg)
- }
-}
-
-func TestProdZZ(t *testing.T) {
- MulZZ := func(z, x, y *Int) *Int { return z.Mul(x, y) }
- for _, a := range prodZZ {
- arg := a
- testFunZZ(t, "MulZZ", MulZZ, arg)
-
- arg = argZZ{a.z, a.y, a.x}
- testFunZZ(t, "MulZZ symmetric", MulZZ, arg)
- }
-}
-
-// mulBytes returns x*y via grade school multiplication. Both inputs
-// and the result are assumed to be in big-endian representation (to
-// match the semantics of Int.Bytes and Int.SetBytes).
-func mulBytes(x, y []byte) []byte {
- z := make([]byte, len(x)+len(y))
-
- // multiply
- k0 := len(z) - 1
- for j := len(y) - 1; j >= 0; j-- {
- d := int(y[j])
- if d != 0 {
- k := k0
- carry := 0
- for i := len(x) - 1; i >= 0; i-- {
- t := int(z[k]) + int(x[i])*d + carry
- z[k], carry = byte(t), t>>8
- k--
- }
- z[k] = byte(carry)
- }
- k0--
- }
-
- // normalize (remove leading 0's)
- i := 0
- for i < len(z) && z[i] == 0 {
- i++
- }
-
- return z[i:]
-}
-
-func checkMul(a, b []byte) bool {
- var x, y, z1 Int
- x.SetBytes(a)
- y.SetBytes(b)
- z1.Mul(&x, &y)
-
- var z2 Int
- z2.SetBytes(mulBytes(a, b))
-
- return z1.Cmp(&z2) == 0
-}
-
-func TestMul(t *testing.T) {
- if err := quick.Check(checkMul, nil); err != nil {
- t.Error(err)
- }
-}
-
-var mulRangesZ = []struct {
- a, b int64
- prod string
-}{
- // entirely positive ranges are covered by mulRangesN
- {-1, 1, "0"},
- {-2, -1, "2"},
- {-3, -2, "6"},
- {-3, -1, "-6"},
- {1, 3, "6"},
- {-10, -10, "-10"},
- {0, -1, "1"}, // empty range
- {-1, -100, "1"}, // empty range
- {-1, 1, "0"}, // range includes 0
- {-1e9, 0, "0"}, // range includes 0
- {-1e9, 1e9, "0"}, // range includes 0
- {-10, -1, "3628800"}, // 10!
- {-20, -2, "-2432902008176640000"}, // -20!
- {-99, -1,
- "-933262154439441526816992388562667004907159682643816214685929" +
- "638952175999932299156089414639761565182862536979208272237582" +
- "511852109168640000000000000000000000", // -99!
- },
-}
-
-func TestMulRangeZ(t *testing.T) {
- var tmp Int
- // test entirely positive ranges
- for i, r := range mulRangesN {
- prod := tmp.MulRange(int64(r.a), int64(r.b)).String()
- if prod != r.prod {
- t.Errorf("#%da: got %s; want %s", i, prod, r.prod)
- }
- }
- // test other ranges
- for i, r := range mulRangesZ {
- prod := tmp.MulRange(r.a, r.b).String()
- if prod != r.prod {
- t.Errorf("#%db: got %s; want %s", i, prod, r.prod)
- }
- }
-}
-
-var stringTests = []struct {
- in string
- out string
- base int
- val int64
- ok bool
-}{
- {in: "", ok: false},
- {in: "a", ok: false},
- {in: "z", ok: false},
- {in: "+", ok: false},
- {in: "-", ok: false},
- {in: "0b", ok: false},
- {in: "0x", ok: false},
- {in: "2", base: 2, ok: false},
- {in: "0b2", base: 0, ok: false},
- {in: "08", ok: false},
- {in: "8", base: 8, ok: false},
- {in: "0xg", base: 0, ok: false},
- {in: "g", base: 16, ok: false},
- {"0", "0", 0, 0, true},
- {"0", "0", 10, 0, true},
- {"0", "0", 16, 0, true},
- {"+0", "0", 0, 0, true},
- {"-0", "0", 0, 0, true},
- {"10", "10", 0, 10, true},
- {"10", "10", 10, 10, true},
- {"10", "10", 16, 16, true},
- {"-10", "-10", 16, -16, true},
- {"+10", "10", 16, 16, true},
- {"0x10", "16", 0, 16, true},
- {in: "0x10", base: 16, ok: false},
- {"-0x10", "-16", 0, -16, true},
- {"+0x10", "16", 0, 16, true},
- {"00", "0", 0, 0, true},
- {"0", "0", 8, 0, true},
- {"07", "7", 0, 7, true},
- {"7", "7", 8, 7, true},
- {"023", "19", 0, 19, true},
- {"23", "23", 8, 19, true},
- {"cafebabe", "cafebabe", 16, 0xcafebabe, true},
- {"0b0", "0", 0, 0, true},
- {"-111", "-111", 2, -7, true},
- {"-0b111", "-7", 0, -7, true},
- {"0b1001010111", "599", 0, 0x257, true},
- {"1001010111", "1001010111", 2, 0x257, true},
-}
-
-func format(base int) string {
- switch base {
- case 2:
- return "%b"
- case 8:
- return "%o"
- case 16:
- return "%x"
- }
- return "%d"
-}
-
-func TestGetString(t *testing.T) {
- z := new(Int)
- for i, test := range stringTests {
- if !test.ok {
- continue
- }
- z.SetInt64(test.val)
-
- if test.base == 10 {
- s := z.String()
- if s != test.out {
- t.Errorf("#%da got %s; want %s", i, s, test.out)
- }
- }
-
- s := fmt.Sprintf(format(test.base), z)
- if s != test.out {
- t.Errorf("#%db got %s; want %s", i, s, test.out)
- }
- }
-}
-
-func TestSetString(t *testing.T) {
- tmp := new(Int)
- for i, test := range stringTests {
- // initialize to a non-zero value so that issues with parsing
- // 0 are detected
- tmp.SetInt64(1234567890)
- n1, ok1 := new(Int).SetString(test.in, test.base)
- n2, ok2 := tmp.SetString(test.in, test.base)
- expected := NewInt(test.val)
- if ok1 != test.ok || ok2 != test.ok {
- t.Errorf("#%d (input '%s') ok incorrect (should be %t)", i, test.in, test.ok)
- continue
- }
- if !ok1 {
- if n1 != nil {
- t.Errorf("#%d (input '%s') n1 != nil", i, test.in)
- }
- continue
- }
- if !ok2 {
- if n2 != nil {
- t.Errorf("#%d (input '%s') n2 != nil", i, test.in)
- }
- continue
- }
-
- if ok1 && !isNormalized(n1) {
- t.Errorf("#%d (input '%s'): %v is not normalized", i, test.in, *n1)
- }
- if ok2 && !isNormalized(n2) {
- t.Errorf("#%d (input '%s'): %v is not normalized", i, test.in, *n2)
- }
-
- if n1.Cmp(expected) != 0 {
- t.Errorf("#%d (input '%s') got: %s want: %d", i, test.in, n1, test.val)
- }
- if n2.Cmp(expected) != 0 {
- t.Errorf("#%d (input '%s') got: %s want: %d", i, test.in, n2, test.val)
- }
- }
-}
-
-var formatTests = []struct {
- input string
- format string
- output string
-}{
- {"<nil>", "%x", "<nil>"},
- {"<nil>", "%#x", "<nil>"},
- {"<nil>", "%#y", "%!y(big.Int=<nil>)"},
-
- {"10", "%b", "1010"},
- {"10", "%o", "12"},
- {"10", "%d", "10"},
- {"10", "%v", "10"},
- {"10", "%x", "a"},
- {"10", "%X", "A"},
- {"-10", "%X", "-A"},
- {"10", "%y", "%!y(big.Int=10)"},
- {"-10", "%y", "%!y(big.Int=-10)"},
-
- {"10", "%#b", "1010"},
- {"10", "%#o", "012"},
- {"10", "%#d", "10"},
- {"10", "%#v", "10"},
- {"10", "%#x", "0xa"},
- {"10", "%#X", "0XA"},
- {"-10", "%#X", "-0XA"},
- {"10", "%#y", "%!y(big.Int=10)"},
- {"-10", "%#y", "%!y(big.Int=-10)"},
-
- {"1234", "%d", "1234"},
- {"1234", "%3d", "1234"},
- {"1234", "%4d", "1234"},
- {"-1234", "%d", "-1234"},
- {"1234", "% 5d", " 1234"},
- {"1234", "%+5d", "+1234"},
- {"1234", "%-5d", "1234 "},
- {"1234", "%x", "4d2"},
- {"1234", "%X", "4D2"},
- {"-1234", "%3x", "-4d2"},
- {"-1234", "%4x", "-4d2"},
- {"-1234", "%5x", " -4d2"},
- {"-1234", "%-5x", "-4d2 "},
- {"1234", "%03d", "1234"},
- {"1234", "%04d", "1234"},
- {"1234", "%05d", "01234"},
- {"1234", "%06d", "001234"},
- {"-1234", "%06d", "-01234"},
- {"1234", "%+06d", "+01234"},
- {"1234", "% 06d", " 01234"},
- {"1234", "%-6d", "1234 "},
- {"1234", "%-06d", "1234 "},
- {"-1234", "%-06d", "-1234 "},
-
- {"1234", "%.3d", "1234"},
- {"1234", "%.4d", "1234"},
- {"1234", "%.5d", "01234"},
- {"1234", "%.6d", "001234"},
- {"-1234", "%.3d", "-1234"},
- {"-1234", "%.4d", "-1234"},
- {"-1234", "%.5d", "-01234"},
- {"-1234", "%.6d", "-001234"},
-
- {"1234", "%8.3d", " 1234"},
- {"1234", "%8.4d", " 1234"},
- {"1234", "%8.5d", " 01234"},
- {"1234", "%8.6d", " 001234"},
- {"-1234", "%8.3d", " -1234"},
- {"-1234", "%8.4d", " -1234"},
- {"-1234", "%8.5d", " -01234"},
- {"-1234", "%8.6d", " -001234"},
-
- {"1234", "%+8.3d", " +1234"},
- {"1234", "%+8.4d", " +1234"},
- {"1234", "%+8.5d", " +01234"},
- {"1234", "%+8.6d", " +001234"},
- {"-1234", "%+8.3d", " -1234"},
- {"-1234", "%+8.4d", " -1234"},
- {"-1234", "%+8.5d", " -01234"},
- {"-1234", "%+8.6d", " -001234"},
-
- {"1234", "% 8.3d", " 1234"},
- {"1234", "% 8.4d", " 1234"},
- {"1234", "% 8.5d", " 01234"},
- {"1234", "% 8.6d", " 001234"},
- {"-1234", "% 8.3d", " -1234"},
- {"-1234", "% 8.4d", " -1234"},
- {"-1234", "% 8.5d", " -01234"},
- {"-1234", "% 8.6d", " -001234"},
-
- {"1234", "%.3x", "4d2"},
- {"1234", "%.4x", "04d2"},
- {"1234", "%.5x", "004d2"},
- {"1234", "%.6x", "0004d2"},
- {"-1234", "%.3x", "-4d2"},
- {"-1234", "%.4x", "-04d2"},
- {"-1234", "%.5x", "-004d2"},
- {"-1234", "%.6x", "-0004d2"},
-
- {"1234", "%8.3x", " 4d2"},
- {"1234", "%8.4x", " 04d2"},
- {"1234", "%8.5x", " 004d2"},
- {"1234", "%8.6x", " 0004d2"},
- {"-1234", "%8.3x", " -4d2"},
- {"-1234", "%8.4x", " -04d2"},
- {"-1234", "%8.5x", " -004d2"},
- {"-1234", "%8.6x", " -0004d2"},
-
- {"1234", "%+8.3x", " +4d2"},
- {"1234", "%+8.4x", " +04d2"},
- {"1234", "%+8.5x", " +004d2"},
- {"1234", "%+8.6x", " +0004d2"},
- {"-1234", "%+8.3x", " -4d2"},
- {"-1234", "%+8.4x", " -04d2"},
- {"-1234", "%+8.5x", " -004d2"},
- {"-1234", "%+8.6x", " -0004d2"},
-
- {"1234", "% 8.3x", " 4d2"},
- {"1234", "% 8.4x", " 04d2"},
- {"1234", "% 8.5x", " 004d2"},
- {"1234", "% 8.6x", " 0004d2"},
- {"1234", "% 8.7x", " 00004d2"},
- {"1234", "% 8.8x", " 000004d2"},
- {"-1234", "% 8.3x", " -4d2"},
- {"-1234", "% 8.4x", " -04d2"},
- {"-1234", "% 8.5x", " -004d2"},
- {"-1234", "% 8.6x", " -0004d2"},
- {"-1234", "% 8.7x", "-00004d2"},
- {"-1234", "% 8.8x", "-000004d2"},
-
- {"1234", "%-8.3d", "1234 "},
- {"1234", "%-8.4d", "1234 "},
- {"1234", "%-8.5d", "01234 "},
- {"1234", "%-8.6d", "001234 "},
- {"1234", "%-8.7d", "0001234 "},
- {"1234", "%-8.8d", "00001234"},
- {"-1234", "%-8.3d", "-1234 "},
- {"-1234", "%-8.4d", "-1234 "},
- {"-1234", "%-8.5d", "-01234 "},
- {"-1234", "%-8.6d", "-001234 "},
- {"-1234", "%-8.7d", "-0001234"},
- {"-1234", "%-8.8d", "-00001234"},
-
- {"16777215", "%b", "111111111111111111111111"}, // 2**24 - 1
-
- {"0", "%.d", ""},
- {"0", "%.0d", ""},
- {"0", "%3.d", ""},
-}
-
-func TestFormat(t *testing.T) {
- for i, test := range formatTests {
- var x *Int
- if test.input != "<nil>" {
- var ok bool
- x, ok = new(Int).SetString(test.input, 0)
- if !ok {
- t.Errorf("#%d failed reading input %s", i, test.input)
- }
- }
- output := fmt.Sprintf(test.format, x)
- if output != test.output {
- t.Errorf("#%d got %q; want %q, {%q, %q, %q}", i, output, test.output, test.input, test.format, test.output)
- }
- }
-}
-
-var scanTests = []struct {
- input string
- format string
- output string
- remaining int
-}{
- {"1010", "%b", "10", 0},
- {"0b1010", "%v", "10", 0},
- {"12", "%o", "10", 0},
- {"012", "%v", "10", 0},
- {"10", "%d", "10", 0},
- {"10", "%v", "10", 0},
- {"a", "%x", "10", 0},
- {"0xa", "%v", "10", 0},
- {"A", "%X", "10", 0},
- {"-A", "%X", "-10", 0},
- {"+0b1011001", "%v", "89", 0},
- {"0xA", "%v", "10", 0},
- {"0 ", "%v", "0", 1},
- {"2+3", "%v", "2", 2},
- {"0XABC 12", "%v", "2748", 3},
-}
-
-func TestScan(t *testing.T) {
- var buf bytes.Buffer
- for i, test := range scanTests {
- x := new(Int)
- buf.Reset()
- buf.WriteString(test.input)
- if _, err := fmt.Fscanf(&buf, test.format, x); err != nil {
- t.Errorf("#%d error: %s", i, err)
- }
- if x.String() != test.output {
- t.Errorf("#%d got %s; want %s", i, x.String(), test.output)
- }
- if buf.Len() != test.remaining {
- t.Errorf("#%d got %d bytes remaining; want %d", i, buf.Len(), test.remaining)
- }
- }
-}
-
-// Examples from the Go Language Spec, section "Arithmetic operators"
-var divisionSignsTests = []struct {
- x, y int64
- q, r int64 // T-division
- d, m int64 // Euclidian division
-}{
- {5, 3, 1, 2, 1, 2},
- {-5, 3, -1, -2, -2, 1},
- {5, -3, -1, 2, -1, 2},
- {-5, -3, 1, -2, 2, 1},
- {1, 2, 0, 1, 0, 1},
- {8, 4, 2, 0, 2, 0},
-}
-
-func TestDivisionSigns(t *testing.T) {
- for i, test := range divisionSignsTests {
- x := NewInt(test.x)
- y := NewInt(test.y)
- q := NewInt(test.q)
- r := NewInt(test.r)
- d := NewInt(test.d)
- m := NewInt(test.m)
-
- q1 := new(Int).Quo(x, y)
- r1 := new(Int).Rem(x, y)
- if !isNormalized(q1) {
- t.Errorf("#%d Quo: %v is not normalized", i, *q1)
- }
- if !isNormalized(r1) {
- t.Errorf("#%d Rem: %v is not normalized", i, *r1)
- }
- if q1.Cmp(q) != 0 || r1.Cmp(r) != 0 {
- t.Errorf("#%d QuoRem: got (%s, %s), want (%s, %s)", i, q1, r1, q, r)
- }
-
- q2, r2 := new(Int).QuoRem(x, y, new(Int))
- if !isNormalized(q2) {
- t.Errorf("#%d Quo: %v is not normalized", i, *q2)
- }
- if !isNormalized(r2) {
- t.Errorf("#%d Rem: %v is not normalized", i, *r2)
- }
- if q2.Cmp(q) != 0 || r2.Cmp(r) != 0 {
- t.Errorf("#%d QuoRem: got (%s, %s), want (%s, %s)", i, q2, r2, q, r)
- }
-
- d1 := new(Int).Div(x, y)
- m1 := new(Int).Mod(x, y)
- if !isNormalized(d1) {
- t.Errorf("#%d Div: %v is not normalized", i, *d1)
- }
- if !isNormalized(m1) {
- t.Errorf("#%d Mod: %v is not normalized", i, *m1)
- }
- if d1.Cmp(d) != 0 || m1.Cmp(m) != 0 {
- t.Errorf("#%d DivMod: got (%s, %s), want (%s, %s)", i, d1, m1, d, m)
- }
-
- d2, m2 := new(Int).DivMod(x, y, new(Int))
- if !isNormalized(d2) {
- t.Errorf("#%d Div: %v is not normalized", i, *d2)
- }
- if !isNormalized(m2) {
- t.Errorf("#%d Mod: %v is not normalized", i, *m2)
- }
- if d2.Cmp(d) != 0 || m2.Cmp(m) != 0 {
- t.Errorf("#%d DivMod: got (%s, %s), want (%s, %s)", i, d2, m2, d, m)
- }
- }
-}
-
-func checkSetBytes(b []byte) bool {
- hex1 := hex.EncodeToString(new(Int).SetBytes(b).Bytes())
- hex2 := hex.EncodeToString(b)
-
- for len(hex1) < len(hex2) {
- hex1 = "0" + hex1
- }
-
- for len(hex1) > len(hex2) {
- hex2 = "0" + hex2
- }
-
- return hex1 == hex2
-}
-
-func TestSetBytes(t *testing.T) {
- if err := quick.Check(checkSetBytes, nil); err != nil {
- t.Error(err)
- }
-}
-
-func checkBytes(b []byte) bool {
- b2 := new(Int).SetBytes(b).Bytes()
- return bytes.Equal(b, b2)
-}
-
-func TestBytes(t *testing.T) {
- if err := quick.Check(checkSetBytes, nil); err != nil {
- t.Error(err)
- }
-}
-
-func checkQuo(x, y []byte) bool {
- u := new(Int).SetBytes(x)
- v := new(Int).SetBytes(y)
-
- if len(v.abs) == 0 {
- return true
- }
-
- r := new(Int)
- q, r := new(Int).QuoRem(u, v, r)
-
- if r.Cmp(v) >= 0 {
- return false
- }
-
- uprime := new(Int).Set(q)
- uprime.Mul(uprime, v)
- uprime.Add(uprime, r)
-
- return uprime.Cmp(u) == 0
-}
-
-var quoTests = []struct {
- x, y string
- q, r string
-}{
- {
- "476217953993950760840509444250624797097991362735329973741718102894495832294430498335824897858659711275234906400899559094370964723884706254265559534144986498357",
- "9353930466774385905609975137998169297361893554149986716853295022578535724979483772383667534691121982974895531435241089241440253066816724367338287092081996",
- "50911",
- "1",
- },
- {
- "11510768301994997771168",
- "1328165573307167369775",
- "8",
- "885443715537658812968",
- },
-}
-
-func TestQuo(t *testing.T) {
- if err := quick.Check(checkQuo, nil); err != nil {
- t.Error(err)
- }
-
- for i, test := range quoTests {
- x, _ := new(Int).SetString(test.x, 10)
- y, _ := new(Int).SetString(test.y, 10)
- expectedQ, _ := new(Int).SetString(test.q, 10)
- expectedR, _ := new(Int).SetString(test.r, 10)
-
- r := new(Int)
- q, r := new(Int).QuoRem(x, y, r)
-
- if q.Cmp(expectedQ) != 0 || r.Cmp(expectedR) != 0 {
- t.Errorf("#%d got (%s, %s) want (%s, %s)", i, q, r, expectedQ, expectedR)
- }
- }
-}
-
-func TestQuoStepD6(t *testing.T) {
- // See Knuth, Volume 2, section 4.3.1, exercise 21. This code exercises
- // a code path which only triggers 1 in 10^{-19} cases.
-
- u := &Int{false, nat{0, 0, 1 + 1<<(_W-1), _M ^ (1 << (_W - 1))}}
- v := &Int{false, nat{5, 2 + 1<<(_W-1), 1 << (_W - 1)}}
-
- r := new(Int)
- q, r := new(Int).QuoRem(u, v, r)
- const expectedQ64 = "18446744073709551613"
- const expectedR64 = "3138550867693340382088035895064302439801311770021610913807"
- const expectedQ32 = "4294967293"
- const expectedR32 = "39614081266355540837921718287"
- if q.String() != expectedQ64 && q.String() != expectedQ32 ||
- r.String() != expectedR64 && r.String() != expectedR32 {
- t.Errorf("got (%s, %s) want (%s, %s) or (%s, %s)", q, r, expectedQ64, expectedR64, expectedQ32, expectedR32)
- }
-}
-
-var bitLenTests = []struct {
- in string
- out int
-}{
- {"-1", 1},
- {"0", 0},
- {"1", 1},
- {"2", 2},
- {"4", 3},
- {"0xabc", 12},
- {"0x8000", 16},
- {"0x80000000", 32},
- {"0x800000000000", 48},
- {"0x8000000000000000", 64},
- {"0x80000000000000000000", 80},
- {"-0x4000000000000000000000", 87},
-}
-
-func TestBitLen(t *testing.T) {
- for i, test := range bitLenTests {
- x, ok := new(Int).SetString(test.in, 0)
- if !ok {
- t.Errorf("#%d test input invalid: %s", i, test.in)
- continue
- }
-
- if n := x.BitLen(); n != test.out {
- t.Errorf("#%d got %d want %d", i, n, test.out)
- }
- }
-}
-
-var expTests = []struct {
- x, y, m string
- out string
-}{
- // y <= 0
- {"0", "0", "", "1"},
- {"1", "0", "", "1"},
- {"-10", "0", "", "1"},
- {"1234", "-1", "", "1"},
-
- // m == 1
- {"0", "0", "1", "0"},
- {"1", "0", "1", "0"},
- {"-10", "0", "1", "0"},
- {"1234", "-1", "1", "0"},
-
- // misc
- {"5", "-7", "", "1"},
- {"-5", "-7", "", "1"},
- {"5", "0", "", "1"},
- {"-5", "0", "", "1"},
- {"5", "1", "", "5"},
- {"-5", "1", "", "-5"},
- {"-2", "3", "2", "0"},
- {"5", "2", "", "25"},
- {"1", "65537", "2", "1"},
- {"0x8000000000000000", "2", "", "0x40000000000000000000000000000000"},
- {"0x8000000000000000", "2", "6719", "4944"},
- {"0x8000000000000000", "3", "6719", "5447"},
- {"0x8000000000000000", "1000", "6719", "1603"},
- {"0x8000000000000000", "1000000", "6719", "3199"},
- {"0x8000000000000000", "-1000000", "6719", "1"},
- {
- "2938462938472983472983659726349017249287491026512746239764525612965293865296239471239874193284792387498274256129746192347",
- "298472983472983471903246121093472394872319615612417471234712061",
- "29834729834729834729347290846729561262544958723956495615629569234729836259263598127342374289365912465901365498236492183464",
- "23537740700184054162508175125554701713153216681790245129157191391322321508055833908509185839069455749219131480588829346291",
- },
-}
-
-func TestExp(t *testing.T) {
- for i, test := range expTests {
- x, ok1 := new(Int).SetString(test.x, 0)
- y, ok2 := new(Int).SetString(test.y, 0)
- out, ok3 := new(Int).SetString(test.out, 0)
-
- var ok4 bool
- var m *Int
-
- if len(test.m) == 0 {
- m, ok4 = nil, true
- } else {
- m, ok4 = new(Int).SetString(test.m, 0)
- }
-
- if !ok1 || !ok2 || !ok3 || !ok4 {
- t.Errorf("#%d: error in input", i)
- continue
- }
-
- z1 := new(Int).Exp(x, y, m)
- if !isNormalized(z1) {
- t.Errorf("#%d: %v is not normalized", i, *z1)
- }
- if z1.Cmp(out) != 0 {
- t.Errorf("#%d: got %s want %s", i, z1, out)
- }
-
- if m == nil {
- // the result should be the same as for m == 0;
- // specifically, there should be no div-zero panic
- m = &Int{abs: nat{}} // m != nil && len(m.abs) == 0
- z2 := new(Int).Exp(x, y, m)
- if z2.Cmp(z1) != 0 {
- t.Errorf("#%d: got %s want %s", i, z1, z2)
- }
- }
- }
-}
-
-func checkGcd(aBytes, bBytes []byte) bool {
- x := new(Int)
- y := new(Int)
- a := new(Int).SetBytes(aBytes)
- b := new(Int).SetBytes(bBytes)
-
- d := new(Int).GCD(x, y, a, b)
- x.Mul(x, a)
- y.Mul(y, b)
- x.Add(x, y)
-
- return x.Cmp(d) == 0
-}
-
-var gcdTests = []struct {
- d, x, y, a, b string
-}{
- // a <= 0 || b <= 0
- {"0", "0", "0", "0", "0"},
- {"0", "0", "0", "0", "7"},
- {"0", "0", "0", "11", "0"},
- {"0", "0", "0", "-77", "35"},
- {"0", "0", "0", "64515", "-24310"},
- {"0", "0", "0", "-64515", "-24310"},
-
- {"1", "-9", "47", "120", "23"},
- {"7", "1", "-2", "77", "35"},
- {"935", "-3", "8", "64515", "24310"},
- {"935000000000000000", "-3", "8", "64515000000000000000", "24310000000000000000"},
- {"1", "-221", "22059940471369027483332068679400581064239780177629666810348940098015901108344", "98920366548084643601728869055592650835572950932266967461790948584315647051443", "991"},
-
- // test early exit (after one Euclidean iteration) in binaryGCD
- {"1", "", "", "1", "98920366548084643601728869055592650835572950932266967461790948584315647051443"},
-}
-
-func testGcd(t *testing.T, d, x, y, a, b *Int) {
- var X *Int
- if x != nil {
- X = new(Int)
- }
- var Y *Int
- if y != nil {
- Y = new(Int)
- }
-
- D := new(Int).GCD(X, Y, a, b)
- if D.Cmp(d) != 0 {
- t.Errorf("GCD(%s, %s): got d = %s, want %s", a, b, D, d)
- }
- if x != nil && X.Cmp(x) != 0 {
- t.Errorf("GCD(%s, %s): got x = %s, want %s", a, b, X, x)
- }
- if y != nil && Y.Cmp(y) != 0 {
- t.Errorf("GCD(%s, %s): got y = %s, want %s", a, b, Y, y)
- }
-
- // binaryGCD requires a > 0 && b > 0
- if a.Sign() <= 0 || b.Sign() <= 0 {
- return
- }
-
- D.binaryGCD(a, b)
- if D.Cmp(d) != 0 {
- t.Errorf("binaryGcd(%s, %s): got d = %s, want %s", a, b, D, d)
- }
-}
-
-func TestGcd(t *testing.T) {
- for _, test := range gcdTests {
- d, _ := new(Int).SetString(test.d, 0)
- x, _ := new(Int).SetString(test.x, 0)
- y, _ := new(Int).SetString(test.y, 0)
- a, _ := new(Int).SetString(test.a, 0)
- b, _ := new(Int).SetString(test.b, 0)
-
- testGcd(t, d, nil, nil, a, b)
- testGcd(t, d, x, nil, a, b)
- testGcd(t, d, nil, y, a, b)
- testGcd(t, d, x, y, a, b)
- }
-
- quick.Check(checkGcd, nil)
-}
-
-var primes = []string{
- "2",
- "3",
- "5",
- "7",
- "11",
-
- "13756265695458089029",
- "13496181268022124907",
- "10953742525620032441",
- "17908251027575790097",
-
- // http://code.google.com/p/go/issues/detail?id=638
- "18699199384836356663",
-
- "98920366548084643601728869055592650835572950932266967461790948584315647051443",
- "94560208308847015747498523884063394671606671904944666360068158221458669711639",
-
- // http://primes.utm.edu/lists/small/small3.html
- "449417999055441493994709297093108513015373787049558499205492347871729927573118262811508386655998299074566974373711472560655026288668094291699357843464363003144674940345912431129144354948751003607115263071543163",
- "230975859993204150666423538988557839555560243929065415434980904258310530753006723857139742334640122533598517597674807096648905501653461687601339782814316124971547968912893214002992086353183070342498989426570593",
- "5521712099665906221540423207019333379125265462121169655563495403888449493493629943498064604536961775110765377745550377067893607246020694972959780839151452457728855382113555867743022746090187341871655890805971735385789993",
- "203956878356401977405765866929034577280193993314348263094772646453283062722701277632936616063144088173312372882677123879538709400158306567338328279154499698366071906766440037074217117805690872792848149112022286332144876183376326512083574821647933992961249917319836219304274280243803104015000563790123",
-}
-
-var composites = []string{
- "21284175091214687912771199898307297748211672914763848041968395774954376176754",
- "6084766654921918907427900243509372380954290099172559290432744450051395395951",
- "84594350493221918389213352992032324280367711247940675652888030554255915464401",
- "82793403787388584738507275144194252681",
-}
-
-func TestProbablyPrime(t *testing.T) {
- nreps := 20
- if testing.Short() {
- nreps = 1
- }
- for i, s := range primes {
- p, _ := new(Int).SetString(s, 10)
- if !p.ProbablyPrime(nreps) {
- t.Errorf("#%d prime found to be non-prime (%s)", i, s)
- }
- }
-
- for i, s := range composites {
- c, _ := new(Int).SetString(s, 10)
- if c.ProbablyPrime(nreps) {
- t.Errorf("#%d composite found to be prime (%s)", i, s)
- }
- if testing.Short() {
- break
- }
- }
-}
-
-type intShiftTest struct {
- in string
- shift uint
- out string
-}
-
-var rshTests = []intShiftTest{
- {"0", 0, "0"},
- {"-0", 0, "0"},
- {"0", 1, "0"},
- {"0", 2, "0"},
- {"1", 0, "1"},
- {"1", 1, "0"},
- {"1", 2, "0"},
- {"2", 0, "2"},
- {"2", 1, "1"},
- {"-1", 0, "-1"},
- {"-1", 1, "-1"},
- {"-1", 10, "-1"},
- {"-100", 2, "-25"},
- {"-100", 3, "-13"},
- {"-100", 100, "-1"},
- {"4294967296", 0, "4294967296"},
- {"4294967296", 1, "2147483648"},
- {"4294967296", 2, "1073741824"},
- {"18446744073709551616", 0, "18446744073709551616"},
- {"18446744073709551616", 1, "9223372036854775808"},
- {"18446744073709551616", 2, "4611686018427387904"},
- {"18446744073709551616", 64, "1"},
- {"340282366920938463463374607431768211456", 64, "18446744073709551616"},
- {"340282366920938463463374607431768211456", 128, "1"},
-}
-
-func TestRsh(t *testing.T) {
- for i, test := range rshTests {
- in, _ := new(Int).SetString(test.in, 10)
- expected, _ := new(Int).SetString(test.out, 10)
- out := new(Int).Rsh(in, test.shift)
-
- if !isNormalized(out) {
- t.Errorf("#%d: %v is not normalized", i, *out)
- }
- if out.Cmp(expected) != 0 {
- t.Errorf("#%d: got %s want %s", i, out, expected)
- }
- }
-}
-
-func TestRshSelf(t *testing.T) {
- for i, test := range rshTests {
- z, _ := new(Int).SetString(test.in, 10)
- expected, _ := new(Int).SetString(test.out, 10)
- z.Rsh(z, test.shift)
-
- if !isNormalized(z) {
- t.Errorf("#%d: %v is not normalized", i, *z)
- }
- if z.Cmp(expected) != 0 {
- t.Errorf("#%d: got %s want %s", i, z, expected)
- }
- }
-}
-
-var lshTests = []intShiftTest{
- {"0", 0, "0"},
- {"0", 1, "0"},
- {"0", 2, "0"},
- {"1", 0, "1"},
- {"1", 1, "2"},
- {"1", 2, "4"},
- {"2", 0, "2"},
- {"2", 1, "4"},
- {"2", 2, "8"},
- {"-87", 1, "-174"},
- {"4294967296", 0, "4294967296"},
- {"4294967296", 1, "8589934592"},
- {"4294967296", 2, "17179869184"},
- {"18446744073709551616", 0, "18446744073709551616"},
- {"9223372036854775808", 1, "18446744073709551616"},
- {"4611686018427387904", 2, "18446744073709551616"},
- {"1", 64, "18446744073709551616"},
- {"18446744073709551616", 64, "340282366920938463463374607431768211456"},
- {"1", 128, "340282366920938463463374607431768211456"},
-}
-
-func TestLsh(t *testing.T) {
- for i, test := range lshTests {
- in, _ := new(Int).SetString(test.in, 10)
- expected, _ := new(Int).SetString(test.out, 10)
- out := new(Int).Lsh(in, test.shift)
-
- if !isNormalized(out) {
- t.Errorf("#%d: %v is not normalized", i, *out)
- }
- if out.Cmp(expected) != 0 {
- t.Errorf("#%d: got %s want %s", i, out, expected)
- }
- }
-}
-
-func TestLshSelf(t *testing.T) {
- for i, test := range lshTests {
- z, _ := new(Int).SetString(test.in, 10)
- expected, _ := new(Int).SetString(test.out, 10)
- z.Lsh(z, test.shift)
-
- if !isNormalized(z) {
- t.Errorf("#%d: %v is not normalized", i, *z)
- }
- if z.Cmp(expected) != 0 {
- t.Errorf("#%d: got %s want %s", i, z, expected)
- }
- }
-}
-
-func TestLshRsh(t *testing.T) {
- for i, test := range rshTests {
- in, _ := new(Int).SetString(test.in, 10)
- out := new(Int).Lsh(in, test.shift)
- out = out.Rsh(out, test.shift)
-
- if !isNormalized(out) {
- t.Errorf("#%d: %v is not normalized", i, *out)
- }
- if in.Cmp(out) != 0 {
- t.Errorf("#%d: got %s want %s", i, out, in)
- }
- }
- for i, test := range lshTests {
- in, _ := new(Int).SetString(test.in, 10)
- out := new(Int).Lsh(in, test.shift)
- out.Rsh(out, test.shift)
-
- if !isNormalized(out) {
- t.Errorf("#%d: %v is not normalized", i, *out)
- }
- if in.Cmp(out) != 0 {
- t.Errorf("#%d: got %s want %s", i, out, in)
- }
- }
-}
-
-var int64Tests = []int64{
- 0,
- 1,
- -1,
- 4294967295,
- -4294967295,
- 4294967296,
- -4294967296,
- 9223372036854775807,
- -9223372036854775807,
- -9223372036854775808,
-}
-
-func TestInt64(t *testing.T) {
- for i, testVal := range int64Tests {
- in := NewInt(testVal)
- out := in.Int64()
-
- if out != testVal {
- t.Errorf("#%d got %d want %d", i, out, testVal)
- }
- }
-}
-
-var uint64Tests = []uint64{
- 0,
- 1,
- 4294967295,
- 4294967296,
- 8589934591,
- 8589934592,
- 9223372036854775807,
- 9223372036854775808,
- 18446744073709551615, // 1<<64 - 1
-}
-
-func TestUint64(t *testing.T) {
- in := new(Int)
- for i, testVal := range uint64Tests {
- in.SetUint64(testVal)
- out := in.Uint64()
-
- if out != testVal {
- t.Errorf("#%d got %d want %d", i, out, testVal)
- }
-
- str := fmt.Sprint(testVal)
- strOut := in.String()
- if strOut != str {
- t.Errorf("#%d.String got %s want %s", i, strOut, str)
- }
- }
-}
-
-var bitwiseTests = []struct {
- x, y string
- and, or, xor, andNot string
-}{
- {"0x00", "0x00", "0x00", "0x00", "0x00", "0x00"},
- {"0x00", "0x01", "0x00", "0x01", "0x01", "0x00"},
- {"0x01", "0x00", "0x00", "0x01", "0x01", "0x01"},
- {"-0x01", "0x00", "0x00", "-0x01", "-0x01", "-0x01"},
- {"-0xaf", "-0x50", "-0xf0", "-0x0f", "0xe1", "0x41"},
- {"0x00", "-0x01", "0x00", "-0x01", "-0x01", "0x00"},
- {"0x01", "0x01", "0x01", "0x01", "0x00", "0x00"},
- {"-0x01", "-0x01", "-0x01", "-0x01", "0x00", "0x00"},
- {"0x07", "0x08", "0x00", "0x0f", "0x0f", "0x07"},
- {"0x05", "0x0f", "0x05", "0x0f", "0x0a", "0x00"},
- {"0x013ff6", "0x9a4e", "0x1a46", "0x01bffe", "0x01a5b8", "0x0125b0"},
- {"-0x013ff6", "0x9a4e", "0x800a", "-0x0125b2", "-0x01a5bc", "-0x01c000"},
- {"-0x013ff6", "-0x9a4e", "-0x01bffe", "-0x1a46", "0x01a5b8", "0x8008"},
- {
- "0x1000009dc6e3d9822cba04129bcbe3401",
- "0xb9bd7d543685789d57cb918e833af352559021483cdb05cc21fd",
- "0x1000001186210100001000009048c2001",
- "0xb9bd7d543685789d57cb918e8bfeff7fddb2ebe87dfbbdfe35fd",
- "0xb9bd7d543685789d57ca918e8ae69d6fcdb2eae87df2b97215fc",
- "0x8c40c2d8822caa04120b8321400",
- },
- {
- "0x1000009dc6e3d9822cba04129bcbe3401",
- "-0xb9bd7d543685789d57cb918e833af352559021483cdb05cc21fd",
- "0x8c40c2d8822caa04120b8321401",
- "-0xb9bd7d543685789d57ca918e82229142459020483cd2014001fd",
- "-0xb9bd7d543685789d57ca918e8ae69d6fcdb2eae87df2b97215fe",
- "0x1000001186210100001000009048c2000",
- },
- {
- "-0x1000009dc6e3d9822cba04129bcbe3401",
- "-0xb9bd7d543685789d57cb918e833af352559021483cdb05cc21fd",
- "-0xb9bd7d543685789d57cb918e8bfeff7fddb2ebe87dfbbdfe35fd",
- "-0x1000001186210100001000009048c2001",
- "0xb9bd7d543685789d57ca918e8ae69d6fcdb2eae87df2b97215fc",
- "0xb9bd7d543685789d57ca918e82229142459020483cd2014001fc",
- },
-}
-
-type bitFun func(z, x, y *Int) *Int
-
-func testBitFun(t *testing.T, msg string, f bitFun, x, y *Int, exp string) {
- expected := new(Int)
- expected.SetString(exp, 0)
-
- out := f(new(Int), x, y)
- if out.Cmp(expected) != 0 {
- t.Errorf("%s: got %s want %s", msg, out, expected)
- }
-}
-
-func testBitFunSelf(t *testing.T, msg string, f bitFun, x, y *Int, exp string) {
- self := new(Int)
- self.Set(x)
- expected := new(Int)
- expected.SetString(exp, 0)
-
- self = f(self, self, y)
- if self.Cmp(expected) != 0 {
- t.Errorf("%s: got %s want %s", msg, self, expected)
- }
-}
-
-func altBit(x *Int, i int) uint {
- z := new(Int).Rsh(x, uint(i))
- z = z.And(z, NewInt(1))
- if z.Cmp(new(Int)) != 0 {
- return 1
- }
- return 0
-}
-
-func altSetBit(z *Int, x *Int, i int, b uint) *Int {
- one := NewInt(1)
- m := one.Lsh(one, uint(i))
- switch b {
- case 1:
- return z.Or(x, m)
- case 0:
- return z.AndNot(x, m)
- }
- panic("set bit is not 0 or 1")
-}
-
-func testBitset(t *testing.T, x *Int) {
- n := x.BitLen()
- z := new(Int).Set(x)
- z1 := new(Int).Set(x)
- for i := 0; i < n+10; i++ {
- old := z.Bit(i)
- old1 := altBit(z1, i)
- if old != old1 {
- t.Errorf("bitset: inconsistent value for Bit(%s, %d), got %v want %v", z1, i, old, old1)
- }
- z := new(Int).SetBit(z, i, 1)
- z1 := altSetBit(new(Int), z1, i, 1)
- if z.Bit(i) == 0 {
- t.Errorf("bitset: bit %d of %s got 0 want 1", i, x)
- }
- if z.Cmp(z1) != 0 {
- t.Errorf("bitset: inconsistent value after SetBit 1, got %s want %s", z, z1)
- }
- z.SetBit(z, i, 0)
- altSetBit(z1, z1, i, 0)
- if z.Bit(i) != 0 {
- t.Errorf("bitset: bit %d of %s got 1 want 0", i, x)
- }
- if z.Cmp(z1) != 0 {
- t.Errorf("bitset: inconsistent value after SetBit 0, got %s want %s", z, z1)
- }
- altSetBit(z1, z1, i, old)
- z.SetBit(z, i, old)
- if z.Cmp(z1) != 0 {
- t.Errorf("bitset: inconsistent value after SetBit old, got %s want %s", z, z1)
- }
- }
- if z.Cmp(x) != 0 {
- t.Errorf("bitset: got %s want %s", z, x)
- }
-}
-
-var bitsetTests = []struct {
- x string
- i int
- b uint
-}{
- {"0", 0, 0},
- {"0", 200, 0},
- {"1", 0, 1},
- {"1", 1, 0},
- {"-1", 0, 1},
- {"-1", 200, 1},
- {"0x2000000000000000000000000000", 108, 0},
- {"0x2000000000000000000000000000", 109, 1},
- {"0x2000000000000000000000000000", 110, 0},
- {"-0x2000000000000000000000000001", 108, 1},
- {"-0x2000000000000000000000000001", 109, 0},
- {"-0x2000000000000000000000000001", 110, 1},
-}
-
-func TestBitSet(t *testing.T) {
- for _, test := range bitwiseTests {
- x := new(Int)
- x.SetString(test.x, 0)
- testBitset(t, x)
- x = new(Int)
- x.SetString(test.y, 0)
- testBitset(t, x)
- }
- for i, test := range bitsetTests {
- x := new(Int)
- x.SetString(test.x, 0)
- b := x.Bit(test.i)
- if b != test.b {
- t.Errorf("#%d got %v want %v", i, b, test.b)
- }
- }
- z := NewInt(1)
- z.SetBit(NewInt(0), 2, 1)
- if z.Cmp(NewInt(4)) != 0 {
- t.Errorf("destination leaked into result; got %s want 4", z)
- }
-}
-
-func BenchmarkBitset(b *testing.B) {
- z := new(Int)
- z.SetBit(z, 512, 1)
- b.ResetTimer()
- b.StartTimer()
- for i := b.N - 1; i >= 0; i-- {
- z.SetBit(z, i&512, 1)
- }
-}
-
-func BenchmarkBitsetNeg(b *testing.B) {
- z := NewInt(-1)
- z.SetBit(z, 512, 0)
- b.ResetTimer()
- b.StartTimer()
- for i := b.N - 1; i >= 0; i-- {
- z.SetBit(z, i&512, 0)
- }
-}
-
-func BenchmarkBitsetOrig(b *testing.B) {
- z := new(Int)
- altSetBit(z, z, 512, 1)
- b.ResetTimer()
- b.StartTimer()
- for i := b.N - 1; i >= 0; i-- {
- altSetBit(z, z, i&512, 1)
- }
-}
-
-func BenchmarkBitsetNegOrig(b *testing.B) {
- z := NewInt(-1)
- altSetBit(z, z, 512, 0)
- b.ResetTimer()
- b.StartTimer()
- for i := b.N - 1; i >= 0; i-- {
- altSetBit(z, z, i&512, 0)
- }
-}
-
-func TestBitwise(t *testing.T) {
- x := new(Int)
- y := new(Int)
- for _, test := range bitwiseTests {
- x.SetString(test.x, 0)
- y.SetString(test.y, 0)
-
- testBitFun(t, "and", (*Int).And, x, y, test.and)
- testBitFunSelf(t, "and", (*Int).And, x, y, test.and)
- testBitFun(t, "andNot", (*Int).AndNot, x, y, test.andNot)
- testBitFunSelf(t, "andNot", (*Int).AndNot, x, y, test.andNot)
- testBitFun(t, "or", (*Int).Or, x, y, test.or)
- testBitFunSelf(t, "or", (*Int).Or, x, y, test.or)
- testBitFun(t, "xor", (*Int).Xor, x, y, test.xor)
- testBitFunSelf(t, "xor", (*Int).Xor, x, y, test.xor)
- }
-}
-
-var notTests = []struct {
- in string
- out string
-}{
- {"0", "-1"},
- {"1", "-2"},
- {"7", "-8"},
- {"0", "-1"},
- {"-81910", "81909"},
- {
- "298472983472983471903246121093472394872319615612417471234712061",
- "-298472983472983471903246121093472394872319615612417471234712062",
- },
-}
-
-func TestNot(t *testing.T) {
- in := new(Int)
- out := new(Int)
- expected := new(Int)
- for i, test := range notTests {
- in.SetString(test.in, 10)
- expected.SetString(test.out, 10)
- out = out.Not(in)
- if out.Cmp(expected) != 0 {
- t.Errorf("#%d: got %s want %s", i, out, expected)
- }
- out = out.Not(out)
- if out.Cmp(in) != 0 {
- t.Errorf("#%d: got %s want %s", i, out, in)
- }
- }
-}
-
-var modInverseTests = []struct {
- element string
- prime string
-}{
- {"1", "7"},
- {"1", "13"},
- {"239487239847", "2410312426921032588552076022197566074856950548502459942654116941958108831682612228890093858261341614673227141477904012196503648957050582631942730706805009223062734745341073406696246014589361659774041027169249453200378729434170325843778659198143763193776859869524088940195577346119843545301547043747207749969763750084308926339295559968882457872412993810129130294592999947926365264059284647209730384947211681434464714438488520940127459844288859336526896320919633919"},
-}
-
-func TestModInverse(t *testing.T) {
- var element, prime Int
- one := NewInt(1)
- for i, test := range modInverseTests {
- (&element).SetString(test.element, 10)
- (&prime).SetString(test.prime, 10)
- inverse := new(Int).ModInverse(&element, &prime)
- inverse.Mul(inverse, &element)
- inverse.Mod(inverse, &prime)
- if inverse.Cmp(one) != 0 {
- t.Errorf("#%d: failed (e·e^(-1)=%s)", i, inverse)
- }
- }
-}
-
-var encodingTests = []string{
- "-539345864568634858364538753846587364875430589374589",
- "-678645873",
- "-100",
- "-2",
- "-1",
- "0",
- "1",
- "2",
- "10",
- "42",
- "1234567890",
- "298472983472983471903246121093472394872319615612417471234712061",
-}
-
-func TestIntGobEncoding(t *testing.T) {
- var medium bytes.Buffer
- enc := gob.NewEncoder(&medium)
- dec := gob.NewDecoder(&medium)
- for _, test := range encodingTests {
- medium.Reset() // empty buffer for each test case (in case of failures)
- var tx Int
- tx.SetString(test, 10)
- if err := enc.Encode(&tx); err != nil {
- t.Errorf("encoding of %s failed: %s", &tx, err)
- }
- var rx Int
- if err := dec.Decode(&rx); err != nil {
- t.Errorf("decoding of %s failed: %s", &tx, err)
- }
- if rx.Cmp(&tx) != 0 {
- t.Errorf("transmission of %s failed: got %s want %s", &tx, &rx, &tx)
- }
- }
-}
-
-// Sending a nil Int pointer (inside a slice) on a round trip through gob should yield a zero.
-// TODO: top-level nils.
-func TestGobEncodingNilIntInSlice(t *testing.T) {
- buf := new(bytes.Buffer)
- enc := gob.NewEncoder(buf)
- dec := gob.NewDecoder(buf)
-
- var in = make([]*Int, 1)
- err := enc.Encode(&in)
- if err != nil {
- t.Errorf("gob encode failed: %q", err)
- }
- var out []*Int
- err = dec.Decode(&out)
- if err != nil {
- t.Fatalf("gob decode failed: %q", err)
- }
- if len(out) != 1 {
- t.Fatalf("wrong len; want 1 got %d", len(out))
- }
- var zero Int
- if out[0].Cmp(&zero) != 0 {
- t.Errorf("transmission of (*Int)(nill) failed: got %s want 0", out)
- }
-}
-
-func TestIntJSONEncoding(t *testing.T) {
- for _, test := range encodingTests {
- var tx Int
- tx.SetString(test, 10)
- b, err := json.Marshal(&tx)
- if err != nil {
- t.Errorf("marshaling of %s failed: %s", &tx, err)
- }
- var rx Int
- if err := json.Unmarshal(b, &rx); err != nil {
- t.Errorf("unmarshaling of %s failed: %s", &tx, err)
- }
- if rx.Cmp(&tx) != 0 {
- t.Errorf("JSON encoding of %s failed: got %s want %s", &tx, &rx, &tx)
- }
- }
-}
-
-var intVals = []string{
- "-141592653589793238462643383279502884197169399375105820974944592307816406286",
- "-1415926535897932384626433832795028841971",
- "-141592653589793",
- "-1",
- "0",
- "1",
- "141592653589793",
- "1415926535897932384626433832795028841971",
- "141592653589793238462643383279502884197169399375105820974944592307816406286",
-}
-
-func TestIntJSONEncodingTextMarshaller(t *testing.T) {
- for _, num := range intVals {
- var tx Int
- tx.SetString(num, 0)
- b, err := json.Marshal(&tx)
- if err != nil {
- t.Errorf("marshaling of %s failed: %s", &tx, err)
- continue
- }
- var rx Int
- if err := json.Unmarshal(b, &rx); err != nil {
- t.Errorf("unmarshaling of %s failed: %s", &tx, err)
- continue
- }
- if rx.Cmp(&tx) != 0 {
- t.Errorf("JSON encoding of %s failed: got %s want %s", &tx, &rx, &tx)
- }
- }
-}
-
-func TestIntXMLEncodingTextMarshaller(t *testing.T) {
- for _, num := range intVals {
- var tx Int
- tx.SetString(num, 0)
- b, err := xml.Marshal(&tx)
- if err != nil {
- t.Errorf("marshaling of %s failed: %s", &tx, err)
- continue
- }
- var rx Int
- if err := xml.Unmarshal(b, &rx); err != nil {
- t.Errorf("unmarshaling of %s failed: %s", &tx, err)
- continue
- }
- if rx.Cmp(&tx) != 0 {
- t.Errorf("XML encoding of %s failed: got %s want %s", &tx, &rx, &tx)
- }
- }
-}
-
-func TestIssue2607(t *testing.T) {
- // This code sequence used to hang.
- n := NewInt(10)
- n.Rand(rand.New(rand.NewSource(9)), n)
-}
diff --git a/src/pkg/math/big/nat.go b/src/pkg/math/big/nat.go
deleted file mode 100644
index 16a87f5c5..000000000
--- a/src/pkg/math/big/nat.go
+++ /dev/null
@@ -1,1508 +0,0 @@
-// Copyright 2009 The Go Authors. All rights reserved.
-// Use of this source code is governed by a BSD-style
-// license that can be found in the LICENSE file.
-
-// Package big implements multi-precision arithmetic (big numbers).
-// The following numeric types are supported:
-//
-// - Int signed integers
-// - Rat rational numbers
-//
-// Methods are typically of the form:
-//
-// func (z *Int) Op(x, y *Int) *Int (similar for *Rat)
-//
-// and implement operations z = x Op y with the result as receiver; if it
-// is one of the operands it may be overwritten (and its memory reused).
-// To enable chaining of operations, the result is also returned. Methods
-// returning a result other than *Int or *Rat take one of the operands as
-// the receiver.
-//
-package big
-
-// This file contains operations on unsigned multi-precision integers.
-// These are the building blocks for the operations on signed integers
-// and rationals.
-
-import (
- "errors"
- "io"
- "math"
- "math/rand"
- "sync"
-)
-
-// An unsigned integer x of the form
-//
-// x = x[n-1]*_B^(n-1) + x[n-2]*_B^(n-2) + ... + x[1]*_B + x[0]
-//
-// with 0 <= x[i] < _B and 0 <= i < n is stored in a slice of length n,
-// with the digits x[i] as the slice elements.
-//
-// A number is normalized if the slice contains no leading 0 digits.
-// During arithmetic operations, denormalized values may occur but are
-// always normalized before returning the final result. The normalized
-// representation of 0 is the empty or nil slice (length = 0).
-//
-type nat []Word
-
-var (
- natOne = nat{1}
- natTwo = nat{2}
- natTen = nat{10}
-)
-
-func (z nat) clear() {
- for i := range z {
- z[i] = 0
- }
-}
-
-func (z nat) norm() nat {
- i := len(z)
- for i > 0 && z[i-1] == 0 {
- i--
- }
- return z[0:i]
-}
-
-func (z nat) make(n int) nat {
- if n <= cap(z) {
- return z[0:n] // reuse z
- }
- // 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)
-}
-
-func (z nat) setWord(x Word) nat {
- if x == 0 {
- return z.make(0)
- }
- z = z.make(1)
- z[0] = x
- return z
-}
-
-func (z nat) setUint64(x uint64) nat {
- // single-digit values
- if w := Word(x); uint64(w) == x {
- return z.setWord(w)
- }
-
- // compute number of words n required to represent x
- n := 0
- for t := x; t > 0; t >>= _W {
- n++
- }
-
- // split x into n words
- z = z.make(n)
- for i := range z {
- z[i] = Word(x & _M)
- x >>= _W
- }
-
- return z
-}
-
-func (z nat) set(x nat) nat {
- z = z.make(len(x))
- copy(z, x)
- return z
-}
-
-func (z nat) add(x, y nat) nat {
- m := len(x)
- n := len(y)
-
- switch {
- case m < n:
- return z.add(y, x)
- case m == 0:
- // n == 0 because m >= n; result is 0
- return z.make(0)
- case n == 0:
- // result is x
- return z.set(x)
- }
- // m > 0
-
- z = z.make(m + 1)
- c := addVV(z[0:n], x, y)
- if m > n {
- c = addVW(z[n:m], x[n:], c)
- }
- z[m] = c
-
- return z.norm()
-}
-
-func (z nat) sub(x, y nat) nat {
- m := len(x)
- n := len(y)
-
- switch {
- case m < n:
- panic("underflow")
- case m == 0:
- // n == 0 because m >= n; result is 0
- return z.make(0)
- case n == 0:
- // result is x
- return z.set(x)
- }
- // m > 0
-
- z = z.make(m)
- c := subVV(z[0:n], x, y)
- if m > n {
- c = subVW(z[n:], x[n:], c)
- }
- if c != 0 {
- panic("underflow")
- }
-
- return z.norm()
-}
-
-func (x nat) cmp(y nat) (r int) {
- m := len(x)
- n := len(y)
- if m != n || m == 0 {
- switch {
- case m < n:
- r = -1
- case m > n:
- r = 1
- }
- return
- }
-
- i := m - 1
- for i > 0 && x[i] == y[i] {
- i--
- }
-
- switch {
- case x[i] < y[i]:
- r = -1
- case x[i] > y[i]:
- r = 1
- }
- return
-}
-
-func (z nat) mulAddWW(x nat, y, r Word) nat {
- m := len(x)
- if m == 0 || y == 0 {
- return z.setWord(r) // result is r
- }
- // m > 0
-
- z = z.make(m + 1)
- z[m] = mulAddVWW(z[0:m], x, y, r)
-
- return z.norm()
-}
-
-// basicMul multiplies x and y and leaves the result in z.
-// The (non-normalized) result is placed in z[0 : len(x) + len(y)].
-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:i+len(x)], x, d)
- }
- }
-}
-
-// 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[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[0:n], z, x); c != 0 {
- subVW(z[n:n+n>>1], z[n:], c)
- }
-}
-
-// Operands that are shorter than karatsubaThreshold are multiplied using
-// "grade school" multiplication; for longer operands the Karatsuba algorithm
-// is used.
-var karatsubaThreshold int = 40 // computed by calibrate.go
-
-// karatsuba multiplies x and y and leaves the result in z.
-// Both x and y must have the same length n and n must be a
-// power of 2. The result vector z must have len(z) >= 6*n.
-// The (non-normalized) result is placed in z[0 : 2*n].
-func karatsuba(z, x, y nat) {
- n := len(y)
-
- // Switch to basic multiplication if numbers are odd or small.
- // (n is always even if karatsubaThreshold is even, but be
- // conservative)
- if n&1 != 0 || n < karatsubaThreshold || n < 2 {
- basicMul(z, x, y)
- return
- }
- // n&1 == 0 && n >= karatsubaThreshold && n >= 2
-
- // Karatsuba multiplication is based on the observation that
- // for two numbers x and y with:
- //
- // x = x1*b + x0
- // y = y1*b + y0
- //
- // the product x*y can be obtained with 3 products z2, z1, z0
- // instead of 4:
- //
- // x*y = x1*y1*b*b + (x1*y0 + x0*y1)*b + x0*y0
- // = z2*b*b + z1*b + z0
- //
- // with:
- //
- // xd = x1 - x0
- // yd = y0 - y1
- //
- // z1 = xd*yd + z2 + z0
- // = (x1-x0)*(y0 - y1) + z2 + z0
- // = x1*y0 - x1*y1 - x0*y0 + x0*y1 + z2 + z0
- // = x1*y0 - z2 - z0 + x0*y1 + z2 + z0
- // = x1*y0 + x0*y1
-
- // split x, y into "digits"
- n2 := n >> 1 // n2 >= 1
- x1, x0 := x[n2:], x[0:n2] // x = x1*b + y0
- y1, y0 := y[n2:], y[0:n2] // y = y1*b + y0
-
- // z is used for the result and temporary storage:
- //
- // 6*n 5*n 4*n 3*n 2*n 1*n 0*n
- // z = [z2 copy|z0 copy| xd*yd | yd:xd | x1*y1 | x0*y0 ]
- //
- // For each recursive call of karatsuba, an unused slice of
- // z is passed in that has (at least) half the length of the
- // caller's z.
-
- // compute z0 and z2 with the result "in place" in z
- karatsuba(z, x0, y0) // z0 = x0*y0
- karatsuba(z[n:], x1, y1) // z2 = x1*y1
-
- // 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) != 0 { // x1-x0
- s = -s
- 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) != 0 { // y0-y1
- s = -s
- subVV(yd, y1, y0) // y1-y0
- }
-
- // p = (x1-x0)*(y0-y1) == x1*y0 - x1*y1 - x0*y0 + x0*y1 for s > 0
- // p = (x0-x1)*(y0-y1) == x0*y0 - x0*y1 - x1*y0 + x1*y1 for s < 0
- p := z[n*3:]
- karatsuba(p, xd, yd)
-
- // save original z2:z0
- // (ok to use upper half of z since we're done recursing)
- r := z[n*4:]
- copy(r, z[:n*2])
-
- // add up all partial products
- //
- // 2*n n 0
- // z = [ z2 | z0 ]
- // + [ z0 ]
- // + [ z2 ]
- // + [ p ]
- //
- karatsubaAdd(z[n2:], r, n)
- karatsubaAdd(z[n2:], r[n:], n)
- if s > 0 {
- karatsubaAdd(z[n2:], p, n)
- } else {
- karatsubaSub(z[n2:], p, n)
- }
-}
-
-// alias returns true if x and y share the same base array.
-func alias(x, y nat) bool {
- return cap(x) > 0 && cap(y) > 0 && &x[0:cap(x)][cap(x)-1] == &y[0:cap(y)][cap(y)-1]
-}
-
-// addAt implements z += x<<(_W*i); z must be long enough.
-// (we don't use nat.add because we need z to stay the same
-// 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:i+n], z[i:], x); c != 0 {
- j := i + n
- if j < len(z) {
- addVW(z[j:], z[j:], c)
- }
- }
- }
-}
-
-func max(x, y int) int {
- if x > y {
- return x
- }
- return y
-}
-
-// karatsubaLen computes an approximation to the maximum k <= n such that
-// k = p<<i for a number p <= karatsubaThreshold and an i >= 0. Thus, the
-// result is the largest number that can be divided repeatedly by 2 before
-// becoming about the value of karatsubaThreshold.
-func karatsubaLen(n int) int {
- i := uint(0)
- for n > karatsubaThreshold {
- n >>= 1
- i++
- }
- return n << i
-}
-
-func (z nat) mul(x, y nat) nat {
- m := len(x)
- n := len(y)
-
- switch {
- case m < n:
- return z.mul(y, x)
- case m == 0 || n == 0:
- return z.make(0)
- case n == 1:
- return z.mulAddWW(x, y[0], 0)
- }
- // m >= n > 1
-
- // determine if z can be reused
- if alias(z, x) || alias(z, y) {
- z = nil // z is an alias for x or y - cannot reuse
- }
-
- // use basic multiplication if the numbers are small
- if n < karatsubaThreshold {
- z = z.make(m + n)
- basicMul(z, x, y)
- return z.norm()
- }
- // m >= n && n >= karatsubaThreshold && n >= 2
-
- // determine Karatsuba length k such that
- //
- // x = xh*b + x0 (0 <= x0 < b)
- // y = yh*b + y0 (0 <= y0 < b)
- // b = 1<<(_W*k) ("base" of digits xi, yi)
- //
- k := karatsubaLen(n)
- // k <= n
-
- // multiply x0 and y0 via Karatsuba
- x0 := x[0:k] // x0 is not normalized
- y0 := y[0:k] // y0 is not normalized
- z = z.make(max(6*k, m+n)) // enough space for karatsuba of x0*y0 and full result of x*y
- karatsuba(z, x0, y0)
- z = z[0 : m+n] // z has final length but may be incomplete
- z[2*k:].clear() // upper portion of z is garbage (and 2*k <= m+n since k <= n <= m)
-
- // If xh != 0 or yh != 0, add the missing terms to z. For
- //
- // xh = xi*b^i + ... + x2*b^2 + x1*b (0 <= xi < b)
- // yh = y1*b (0 <= y1 < b)
- //
- // the missing terms are
- //
- // x0*y1*b and xi*y0*b^i, xi*y1*b^(i+1) for i > 0
- //
- // since all the yi for i > 1 are 0 by choice of k: If any of them
- // were > 0, then yh >= b^2 and thus y >= b^2. Then k' = k*2 would
- // be a larger valid threshold contradicting the assumption about k.
- //
- if k < n || m != n {
- var t nat
-
- // add x0*y1*b
- x0 := x0.norm()
- y1 := y[k:] // y1 is normalized because y is
- t = t.mul(x0, y1) // update t so we don't lose t's underlying array
- addAt(z, t, k)
-
- // add xi*y0<<i, xi*y1*b<<(i+k)
- y0 := y0.norm()
- for i := k; i < len(x); i += k {
- xi := x[i:]
- if len(xi) > k {
- xi = xi[:k]
- }
- xi = xi.norm()
- t = t.mul(xi, y0)
- addAt(z, t, i)
- t = t.mul(xi, y1)
- addAt(z, t, i+k)
- }
- }
-
- return z.norm()
-}
-
-// mulRange computes the product of all the unsigned integers in the
-// range [a, b] inclusively. If a > b (empty range), the result is 1.
-func (z nat) mulRange(a, b uint64) nat {
- switch {
- case a == 0:
- // cut long ranges short (optimization)
- return z.setUint64(0)
- case a > b:
- return z.setUint64(1)
- case a == b:
- return z.setUint64(a)
- case a+1 == b:
- return z.mul(nat(nil).setUint64(a), nat(nil).setUint64(b))
- }
- m := (a + b) / 2
- return z.mul(nat(nil).mulRange(a, m), nat(nil).mulRange(m+1, b))
-}
-
-// q = (x-r)/y, with 0 <= r < y
-func (z nat) divW(x nat, y Word) (q nat, r Word) {
- m := len(x)
- switch {
- case y == 0:
- panic("division by zero")
- case y == 1:
- q = z.set(x) // result is x
- return
- case m == 0:
- q = z.make(0) // result is 0
- return
- }
- // m > 0
- z = z.make(m)
- r = divWVW(z, 0, x, y)
- q = z.norm()
- return
-}
-
-func (z nat) div(z2, u, v nat) (q, r nat) {
- if len(v) == 0 {
- panic("division by zero")
- }
-
- if u.cmp(v) < 0 {
- q = z.make(0)
- r = z2.set(u)
- return
- }
-
- if len(v) == 1 {
- var r2 Word
- q, r2 = z.divW(u, v[0])
- r = z2.setWord(r2)
- return
- }
-
- q, r = z.divLarge(z2, u, v)
- return
-}
-
-// q = (uIn-r)/v, with 0 <= r < y
-// Uses z as storage for q, and u as storage for r if possible.
-// See Knuth, Volume 2, section 4.3.1, Algorithm D.
-// Preconditions:
-// len(v) >= 2
-// len(uIn) >= len(v)
-func (z nat) divLarge(u, uIn, v nat) (q, r nat) {
- n := len(v)
- m := len(uIn) - n
-
- // determine if z can be reused
- // TODO(gri) should find a better solution - this if statement
- // is very costly (see e.g. time pidigits -s -n 10000)
- if alias(z, uIn) || alias(z, v) {
- z = nil // z is an alias for uIn or v - cannot reuse
- }
- q = z.make(m + 1)
-
- qhatv := make(nat, n+1)
- if alias(u, uIn) || alias(u, v) {
- u = nil // u is an alias for uIn or v - cannot reuse
- }
- u = u.make(len(uIn) + 1)
- u.clear()
-
- // D1.
- shift := leadingZeros(v[n-1])
- if shift > 0 {
- // do not modify v, it may be used by another goroutine simultaneously
- v1 := make(nat, n)
- shlVU(v1, v, shift)
- v = v1
- }
- u[len(uIn)] = shlVU(u[0:len(uIn)], uIn, shift)
-
- // D2.
- for j := m; j >= 0; j-- {
- // D3.
- qhat := Word(_M)
- if u[j+n] != v[n-1] {
- var rhat Word
- qhat, rhat = divWW(u[j+n], u[j+n-1], v[n-1])
-
- // x1 | x2 = q̂v_{n-2}
- x1, x2 := mulWW(qhat, v[n-2])
- // test if q̂v_{n-2} > br̂ + u_{j+n-2}
- for greaterThan(x1, x2, rhat, u[j+n-2]) {
- qhat--
- prevRhat := rhat
- rhat += v[n-1]
- // v[n-1] >= 0, so this tests for overflow.
- if rhat < prevRhat {
- break
- }
- x1, x2 = mulWW(qhat, v[n-2])
- }
- }
-
- // D4.
- qhatv[n] = mulAddVWW(qhatv[0:n], v, qhat, 0)
-
- c := subVV(u[j:j+len(qhatv)], u[j:], qhatv)
- if c != 0 {
- c := addVV(u[j:j+n], u[j:], v)
- u[j+n] += c
- qhat--
- }
-
- q[j] = qhat
- }
-
- q = q.norm()
- shrVU(u, u, shift)
- r = u.norm()
-
- return q, r
-}
-
-// Length of x in bits. x must be normalized.
-func (x nat) bitLen() int {
- if i := len(x) - 1; i >= 0 {
- return i*_W + bitLen(x[i])
- }
- return 0
-}
-
-// MaxBase is the largest number base accepted for string conversions.
-const MaxBase = 'z' - 'a' + 10 + 1 // = hexValue('z') + 1
-
-func hexValue(ch rune) Word {
- d := int(MaxBase + 1) // illegal base
- switch {
- case '0' <= ch && ch <= '9':
- d = int(ch - '0')
- case 'a' <= ch && ch <= 'z':
- d = int(ch - 'a' + 10)
- case 'A' <= ch && ch <= 'Z':
- d = int(ch - 'A' + 10)
- }
- return Word(d)
-}
-
-// scan sets z to the natural number corresponding to the longest possible prefix
-// read from r representing an unsigned integer in a given conversion base.
-// It returns z, the actual conversion base used, and an error, if any. In the
-// error case, the value of z is undefined. The syntax follows the syntax of
-// unsigned integer literals in Go.
-//
-// The base argument must be 0 or a value from 2 through MaxBase. If the base
-// is 0, the string prefix determines the actual conversion base. A prefix of
-// ``0x'' or ``0X'' selects base 16; the ``0'' prefix selects base 8, and a
-// ``0b'' or ``0B'' prefix selects base 2. Otherwise the selected base is 10.
-//
-func (z nat) scan(r io.RuneScanner, base int) (nat, int, error) {
- // reject illegal bases
- if base < 0 || base == 1 || MaxBase < base {
- return z, 0, errors.New("illegal number base")
- }
-
- // one char look-ahead
- ch, _, err := r.ReadRune()
- if err != nil {
- return z, 0, err
- }
-
- // determine base if necessary
- b := Word(base)
- if base == 0 {
- b = 10
- if ch == '0' {
- switch ch, _, err = r.ReadRune(); err {
- case nil:
- b = 8
- switch ch {
- case 'x', 'X':
- b = 16
- case 'b', 'B':
- b = 2
- }
- if b == 2 || b == 16 {
- if ch, _, err = r.ReadRune(); err != nil {
- return z, 0, err
- }
- }
- case io.EOF:
- return z.make(0), 10, nil
- default:
- return z, 10, err
- }
- }
- }
-
- // convert string
- // - group as many digits d as possible together into a "super-digit" dd with "super-base" bb
- // - only when bb does not fit into a word anymore, do a full number mulAddWW using bb and dd
- z = z.make(0)
- bb := Word(1)
- dd := Word(0)
- for max := _M / b; ; {
- d := hexValue(ch)
- if d >= b {
- r.UnreadRune() // ch does not belong to number anymore
- break
- }
-
- if bb <= max {
- bb *= b
- dd = dd*b + d
- } else {
- // bb * b would overflow
- z = z.mulAddWW(z, bb, dd)
- bb = b
- dd = d
- }
-
- if ch, _, err = r.ReadRune(); err != nil {
- if err != io.EOF {
- return z, int(b), err
- }
- break
- }
- }
-
- switch {
- case bb > 1:
- // there was at least one mantissa digit
- z = z.mulAddWW(z, bb, dd)
- case base == 0 && b == 8:
- // there was only the octal prefix 0 (possibly followed by digits > 7);
- // return base 10, not 8
- return z, 10, nil
- case base != 0 || b != 8:
- // there was neither a mantissa digit nor the octal prefix 0
- return z, int(b), errors.New("syntax error scanning number")
- }
-
- return z.norm(), int(b), nil
-}
-
-// Character sets for string conversion.
-const (
- lowercaseDigits = "0123456789abcdefghijklmnopqrstuvwxyz"
- uppercaseDigits = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"
-)
-
-// decimalString returns a decimal representation of x.
-// It calls x.string with the charset "0123456789".
-func (x nat) decimalString() string {
- return x.string(lowercaseDigits[0:10])
-}
-
-// string converts x to a string using digits from a charset; a digit with
-// value d is represented by charset[d]. The conversion base is determined
-// by len(charset), which must be >= 2 and <= 256.
-func (x nat) string(charset string) string {
- b := Word(len(charset))
-
- // special cases
- switch {
- case b < 2 || MaxBase > 256:
- panic("illegal base")
- case len(x) == 0:
- return string(charset[0])
- }
-
- // allocate buffer for conversion
- i := int(float64(x.bitLen())/math.Log2(float64(b))) + 1 // off by one at most
- s := make([]byte, i)
-
- // convert power of two and non power of two bases separately
- if b == b&-b {
- // shift is base-b digit size in bits
- shift := trailingZeroBits(b) // shift > 0 because b >= 2
- mask := Word(1)<<shift - 1
- w := x[0]
- nbits := uint(_W) // number of unprocessed bits in w
-
- // convert less-significant words
- for k := 1; k < len(x); k++ {
- // convert full digits
- for nbits >= shift {
- i--
- s[i] = charset[w&mask]
- w >>= shift
- nbits -= shift
- }
-
- // convert any partial leading digit and advance to next word
- if nbits == 0 {
- // no partial digit remaining, just advance
- w = x[k]
- nbits = _W
- } else {
- // partial digit in current (k-1) and next (k) word
- w |= x[k] << nbits
- i--
- s[i] = charset[w&mask]
-
- // advance
- w = x[k] >> (shift - nbits)
- nbits = _W - (shift - nbits)
- }
- }
-
- // convert digits of most-significant word (omit leading zeros)
- for nbits >= 0 && w != 0 {
- i--
- s[i] = charset[w&mask]
- w >>= shift
- nbits -= shift
- }
-
- } else {
- // determine "big base"; i.e., the largest possible value bb
- // that is a power of base b and still fits into a Word
- // (as in 10^19 for 19 decimal digits in a 64bit Word)
- bb := b // big base is b**ndigits
- ndigits := 1 // number of base b digits
- for max := Word(_M / b); bb <= max; bb *= b {
- ndigits++ // maximize ndigits where bb = b**ndigits, bb <= _M
- }
-
- // construct table of successive squares of bb*leafSize to use in subdivisions
- // result (table != nil) <=> (len(x) > leafSize > 0)
- table := divisors(len(x), b, ndigits, bb)
-
- // preserve x, create local copy for use by convertWords
- q := nat(nil).set(x)
-
- // convert q to string s in base b
- q.convertWords(s, charset, b, ndigits, bb, table)
-
- // strip leading zeros
- // (x != 0; thus s must contain at least one non-zero digit
- // and the loop will terminate)
- i = 0
- for zero := charset[0]; s[i] == zero; {
- i++
- }
- }
-
- return string(s[i:])
-}
-
-// Convert words of q to base b digits in s. If q is large, it is recursively "split in half"
-// by nat/nat division using tabulated divisors. Otherwise, it is converted iteratively using
-// repeated nat/Word division.
-//
-// The iterative method processes n Words by n divW() calls, each of which visits every Word in the
-// incrementally shortened q for a total of n + (n-1) + (n-2) ... + 2 + 1, or n(n+1)/2 divW()'s.
-// Recursive conversion divides q by its approximate square root, yielding two parts, each half
-// the size of q. Using the iterative method on both halves means 2 * (n/2)(n/2 + 1)/2 divW()'s
-// plus the expensive long div(). Asymptotically, the ratio is favorable at 1/2 the divW()'s, and
-// is made better by splitting the subblocks recursively. Best is to split blocks until one more
-// split would take longer (because of the nat/nat div()) than the twice as many divW()'s of the
-// iterative approach. This threshold is represented by leafSize. Benchmarking of leafSize in the
-// range 2..64 shows that values of 8 and 16 work well, with a 4x speedup at medium lengths and
-// ~30x for 20000 digits. Use nat_test.go's BenchmarkLeafSize tests to optimize leafSize for
-// specific hardware.
-//
-func (q nat) convertWords(s []byte, charset string, b Word, ndigits int, bb Word, table []divisor) {
- // split larger blocks recursively
- if table != nil {
- // len(q) > leafSize > 0
- var r nat
- index := len(table) - 1
- for len(q) > leafSize {
- // find divisor close to sqrt(q) if possible, but in any case < q
- maxLength := q.bitLen() // ~= log2 q, or at of least largest possible q of this bit length
- minLength := maxLength >> 1 // ~= log2 sqrt(q)
- for index > 0 && table[index-1].nbits > minLength {
- index-- // desired
- }
- if table[index].nbits >= maxLength && table[index].bbb.cmp(q) >= 0 {
- index--
- if index < 0 {
- panic("internal inconsistency")
- }
- }
-
- // split q into the two digit number (q'*bbb + r) to form independent subblocks
- q, r = q.div(r, q, table[index].bbb)
-
- // convert subblocks and collect results in s[:h] and s[h:]
- h := len(s) - table[index].ndigits
- r.convertWords(s[h:], charset, b, ndigits, bb, table[0:index])
- s = s[:h] // == q.convertWords(s, charset, b, ndigits, bb, table[0:index+1])
- }
- }
-
- // having split any large blocks now process the remaining (small) block iteratively
- i := len(s)
- var r Word
- if b == 10 {
- // hard-coding for 10 here speeds this up by 1.25x (allows for / and % by constants)
- for len(q) > 0 {
- // extract least significant, base bb "digit"
- q, r = q.divW(q, bb)
- for j := 0; j < ndigits && i > 0; j++ {
- i--
- // avoid % computation since r%10 == r - int(r/10)*10;
- // this appears to be faster for BenchmarkString10000Base10
- // and smaller strings (but a bit slower for larger ones)
- t := r / 10
- s[i] = charset[r-t<<3-t-t] // TODO(gri) replace w/ t*10 once compiler produces better code
- r = t
- }
- }
- } else {
- for len(q) > 0 {
- // extract least significant, base bb "digit"
- q, r = q.divW(q, bb)
- for j := 0; j < ndigits && i > 0; j++ {
- i--
- s[i] = charset[r%b]
- r /= b
- }
- }
- }
-
- // prepend high-order zeroes
- zero := charset[0]
- for i > 0 { // while need more leading zeroes
- i--
- s[i] = zero
- }
-}
-
-// Split blocks greater than leafSize Words (or set to 0 to disable recursive conversion)
-// Benchmark and configure leafSize using: go test -bench="Leaf"
-// 8 and 16 effective on 3.0 GHz Xeon "Clovertown" CPU (128 byte cache lines)
-// 8 and 16 effective on 2.66 GHz Core 2 Duo "Penryn" CPU
-var leafSize int = 8 // number of Word-size binary values treat as a monolithic block
-
-type divisor struct {
- bbb nat // divisor
- nbits int // bit length of divisor (discounting leading zeroes) ~= log2(bbb)
- ndigits int // digit length of divisor in terms of output base digits
-}
-
-var cacheBase10 struct {
- sync.Mutex
- table [64]divisor // cached divisors for base 10
-}
-
-// expWW computes x**y
-func (z nat) expWW(x, y Word) nat {
- return z.expNN(nat(nil).setWord(x), nat(nil).setWord(y), nil)
-}
-
-// construct table of powers of bb*leafSize to use in subdivisions
-func divisors(m int, b Word, ndigits int, bb Word) []divisor {
- // only compute table when recursive conversion is enabled and x is large
- if leafSize == 0 || m <= leafSize {
- return nil
- }
-
- // determine k where (bb**leafSize)**(2**k) >= sqrt(x)
- k := 1
- for words := leafSize; words < m>>1 && k < len(cacheBase10.table); words <<= 1 {
- k++
- }
-
- // reuse and extend existing table of divisors or create new table as appropriate
- var table []divisor // for b == 10, table overlaps with cacheBase10.table
- if b == 10 {
- cacheBase10.Lock()
- table = cacheBase10.table[0:k] // reuse old table for this conversion
- } else {
- table = make([]divisor, k) // create new table for this conversion
- }
-
- // extend table
- if table[k-1].ndigits == 0 {
- // add new entries as needed
- var larger nat
- for i := 0; i < k; i++ {
- if table[i].ndigits == 0 {
- if i == 0 {
- table[0].bbb = nat(nil).expWW(bb, Word(leafSize))
- table[0].ndigits = ndigits * leafSize
- } else {
- table[i].bbb = nat(nil).mul(table[i-1].bbb, table[i-1].bbb)
- table[i].ndigits = 2 * table[i-1].ndigits
- }
-
- // optimization: exploit aggregated extra bits in macro blocks
- larger = nat(nil).set(table[i].bbb)
- for mulAddVWW(larger, larger, b, 0) == 0 {
- table[i].bbb = table[i].bbb.set(larger)
- table[i].ndigits++
- }
-
- table[i].nbits = table[i].bbb.bitLen()
- }
- }
- }
-
- if b == 10 {
- cacheBase10.Unlock()
- }
-
- return table
-}
-
-const deBruijn32 = 0x077CB531
-
-var deBruijn32Lookup = []byte{
- 0, 1, 28, 2, 29, 14, 24, 3, 30, 22, 20, 15, 25, 17, 4, 8,
- 31, 27, 13, 23, 21, 19, 16, 7, 26, 12, 18, 6, 11, 5, 10, 9,
-}
-
-const deBruijn64 = 0x03f79d71b4ca8b09
-
-var deBruijn64Lookup = []byte{
- 0, 1, 56, 2, 57, 49, 28, 3, 61, 58, 42, 50, 38, 29, 17, 4,
- 62, 47, 59, 36, 45, 43, 51, 22, 53, 39, 33, 30, 24, 18, 12, 5,
- 63, 55, 48, 27, 60, 41, 37, 16, 46, 35, 44, 21, 52, 32, 23, 11,
- 54, 26, 40, 15, 34, 20, 31, 10, 25, 14, 19, 9, 13, 8, 7, 6,
-}
-
-// trailingZeroBits returns the number of consecutive least significant zero
-// bits of x.
-func trailingZeroBits(x Word) uint {
- // x & -x leaves only the right-most bit set in the word. Let k be the
- // index of that bit. Since only a single bit is set, the value is two
- // to the power of k. Multiplying by a power of two is equivalent to
- // left shifting, in this case by k bits. The de Bruijn constant is
- // such that all six bit, consecutive substrings are distinct.
- // Therefore, if we have a left shifted version of this constant we can
- // find by how many bits it was shifted by looking at which six bit
- // substring ended up at the top of the word.
- // (Knuth, volume 4, section 7.3.1)
- switch _W {
- case 32:
- return uint(deBruijn32Lookup[((x&-x)*deBruijn32)>>27])
- case 64:
- return uint(deBruijn64Lookup[((x&-x)*(deBruijn64&_M))>>58])
- default:
- panic("unknown word size")
- }
-}
-
-// trailingZeroBits returns the number of consecutive least significant zero
-// bits of x.
-func (x nat) trailingZeroBits() uint {
- if len(x) == 0 {
- return 0
- }
- var i uint
- for x[i] == 0 {
- i++
- }
- // x[i] != 0
- return i*_W + trailingZeroBits(x[i])
-}
-
-// z = x << s
-func (z nat) shl(x nat, s uint) nat {
- m := len(x)
- if m == 0 {
- return z.make(0)
- }
- // m > 0
-
- n := m + int(s/_W)
- z = z.make(n + 1)
- z[n] = shlVU(z[n-m:n], x, s%_W)
- z[0 : n-m].clear()
-
- return z.norm()
-}
-
-// z = x >> s
-func (z nat) shr(x nat, s uint) nat {
- m := len(x)
- n := m - int(s/_W)
- if n <= 0 {
- return z.make(0)
- }
- // n > 0
-
- z = z.make(n)
- shrVU(z, x[m-n:], s%_W)
-
- return z.norm()
-}
-
-func (z nat) setBit(x nat, i uint, b uint) nat {
- j := int(i / _W)
- m := Word(1) << (i % _W)
- n := len(x)
- switch b {
- case 0:
- z = z.make(n)
- copy(z, x)
- if j >= n {
- // no need to grow
- return z
- }
- z[j] &^= m
- return z.norm()
- case 1:
- if j >= n {
- z = z.make(j + 1)
- z[n:].clear()
- } else {
- z = z.make(n)
- }
- copy(z, x)
- z[j] |= m
- // no need to normalize
- return z
- }
- panic("set bit is not 0 or 1")
-}
-
-func (z nat) bit(i uint) uint {
- j := int(i / _W)
- if j >= len(z) {
- return 0
- }
- return uint(z[j] >> (i % _W) & 1)
-}
-
-func (z nat) and(x, y nat) nat {
- m := len(x)
- n := len(y)
- if m > n {
- m = n
- }
- // m <= n
-
- z = z.make(m)
- for i := 0; i < m; i++ {
- z[i] = x[i] & y[i]
- }
-
- return z.norm()
-}
-
-func (z nat) andNot(x, y nat) nat {
- m := len(x)
- n := len(y)
- if n > m {
- n = m
- }
- // m >= n
-
- z = z.make(m)
- for i := 0; i < n; i++ {
- z[i] = x[i] &^ y[i]
- }
- copy(z[n:m], x[n:m])
-
- return z.norm()
-}
-
-func (z nat) or(x, y nat) nat {
- m := len(x)
- n := len(y)
- s := x
- if m < n {
- n, m = m, n
- s = y
- }
- // m >= n
-
- z = z.make(m)
- for i := 0; i < n; i++ {
- z[i] = x[i] | y[i]
- }
- copy(z[n:m], s[n:m])
-
- return z.norm()
-}
-
-func (z nat) xor(x, y nat) nat {
- m := len(x)
- n := len(y)
- s := x
- if m < n {
- n, m = m, n
- s = y
- }
- // m >= n
-
- z = z.make(m)
- for i := 0; i < n; i++ {
- z[i] = x[i] ^ y[i]
- }
- copy(z[n:m], s[n:m])
-
- return z.norm()
-}
-
-// greaterThan returns true iff (x1<<_W + x2) > (y1<<_W + y2)
-func greaterThan(x1, x2, y1, y2 Word) bool {
- return x1 > y1 || x1 == y1 && x2 > y2
-}
-
-// modW returns x % d.
-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)
-}
-
-// random creates a random integer in [0..limit), using the space in z if
-// possible. n is the bit length of limit.
-func (z nat) random(rand *rand.Rand, limit nat, n int) nat {
- if alias(z, limit) {
- z = nil // z is an alias for limit - cannot reuse
- }
- z = z.make(len(limit))
-
- bitLengthOfMSW := uint(n % _W)
- if bitLengthOfMSW == 0 {
- bitLengthOfMSW = _W
- }
- mask := Word((1 << bitLengthOfMSW) - 1)
-
- for {
- switch _W {
- case 32:
- for i := range z {
- z[i] = Word(rand.Uint32())
- }
- case 64:
- for i := range z {
- z[i] = Word(rand.Uint32()) | Word(rand.Uint32())<<32
- }
- default:
- panic("unknown word size")
- }
- z[len(limit)-1] &= mask
- if z.cmp(limit) < 0 {
- break
- }
- }
-
- return z.norm()
-}
-
-// If m != 0 (i.e., len(m) != 0), expNN sets z to x**y mod m;
-// otherwise it sets z to x**y. The result is the value of z.
-func (z nat) expNN(x, y, m nat) nat {
- if alias(z, x) || alias(z, y) {
- // We cannot allow in-place modification of x or y.
- z = nil
- }
-
- // x**y mod 1 == 0
- if len(m) == 1 && m[0] == 1 {
- return z.setWord(0)
- }
- // m == 0 || m > 1
-
- // x**0 == 1
- if len(y) == 0 {
- return z.setWord(1)
- }
- // y > 0
-
- if len(m) != 0 {
- // We likely end up being as long as the modulus.
- z = z.make(len(m))
- }
- z = z.set(x)
-
- // If the base is non-trivial and the exponent is large, we use
- // 4-bit, windowed exponentiation. This involves precomputing 14 values
- // (x^2...x^15) but then reduces the number of multiply-reduces by a
- // third. Even for a 32-bit exponent, this reduces the number of
- // operations.
- if len(x) > 1 && len(y) > 1 && len(m) > 0 {
- return z.expNNWindowed(x, y, m)
- }
-
- v := y[len(y)-1] // v > 0 because y is normalized and y > 0
- shift := leadingZeros(v) + 1
- v <<= shift
- var q nat
-
- const mask = 1 << (_W - 1)
-
- // We walk through the bits of the exponent one by one. Each time we
- // see a bit, we square, thus doubling the power. If the bit is a one,
- // we also multiply by x, thus adding one to the power.
-
- w := _W - int(shift)
- // zz and r are used to avoid allocating in mul and div as
- // otherwise the arguments would alias.
- var zz, r nat
- for j := 0; j < w; j++ {
- zz = zz.mul(z, z)
- zz, z = z, zz
-
- if v&mask != 0 {
- zz = zz.mul(z, x)
- zz, z = z, zz
- }
-
- if len(m) != 0 {
- zz, r = zz.div(r, z, m)
- zz, r, q, z = q, z, zz, r
- }
-
- v <<= 1
- }
-
- for i := len(y) - 2; i >= 0; i-- {
- v = y[i]
-
- for j := 0; j < _W; j++ {
- zz = zz.mul(z, z)
- zz, z = z, zz
-
- if v&mask != 0 {
- zz = zz.mul(z, x)
- zz, z = z, zz
- }
-
- if len(m) != 0 {
- zz, r = zz.div(r, z, m)
- zz, r, q, z = q, z, zz, r
- }
-
- v <<= 1
- }
- }
-
- return z.norm()
-}
-
-// expNNWindowed calculates x**y mod m using a fixed, 4-bit window.
-func (z nat) expNNWindowed(x, y, m nat) nat {
- // zz and r are used to avoid allocating in mul and div as otherwise
- // the arguments would alias.
- var zz, r nat
-
- const n = 4
- // powers[i] contains x^i.
- var powers [1 << n]nat
- powers[0] = natOne
- powers[1] = x
- for i := 2; i < 1<<n; i += 2 {
- p2, p, p1 := &powers[i/2], &powers[i], &powers[i+1]
- *p = p.mul(*p2, *p2)
- zz, r = zz.div(r, *p, m)
- *p, r = r, *p
- *p1 = p1.mul(*p, x)
- zz, r = zz.div(r, *p1, m)
- *p1, r = r, *p1
- }
-
- z = z.setWord(1)
-
- for i := len(y) - 1; i >= 0; i-- {
- yi := y[i]
- for j := 0; j < _W; j += n {
- if i != len(y)-1 || j != 0 {
- // Unrolled loop for significant performance
- // gain. Use go test -bench=".*" in crypto/rsa
- // to check performance before making changes.
- zz = zz.mul(z, z)
- zz, z = z, zz
- zz, r = zz.div(r, z, m)
- z, r = r, z
-
- zz = zz.mul(z, z)
- zz, z = z, zz
- zz, r = zz.div(r, z, m)
- z, r = r, z
-
- zz = zz.mul(z, z)
- zz, z = z, zz
- zz, r = zz.div(r, z, m)
- z, r = r, z
-
- zz = zz.mul(z, z)
- zz, z = z, zz
- zz, r = zz.div(r, z, m)
- z, r = r, z
- }
-
- zz = zz.mul(z, powers[yi>>(_W-n)])
- zz, z = z, zz
- zz, r = zz.div(r, z, m)
- z, r = r, z
-
- yi <<= n
- }
- }
-
- return z.norm()
-}
-
-// probablyPrime performs reps Miller-Rabin tests to check whether n is prime.
-// If it returns true, n is prime with probability 1 - 1/4^reps.
-// If it returns false, n is not prime.
-func (n nat) probablyPrime(reps int) bool {
- if len(n) == 0 {
- return false
- }
-
- if len(n) == 1 {
- if n[0] < 2 {
- return false
- }
-
- if n[0]%2 == 0 {
- return n[0] == 2
- }
-
- // We have to exclude these cases because we reject all
- // multiples of these numbers below.
- switch n[0] {
- case 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53:
- return true
- }
- }
-
- const primesProduct32 = 0xC0CFD797 // Π {p ∈ primes, 2 < p <= 29}
- const primesProduct64 = 0xE221F97C30E94E1D // Π {p ∈ primes, 2 < p <= 53}
-
- var r Word
- switch _W {
- case 32:
- r = n.modW(primesProduct32)
- case 64:
- r = n.modW(primesProduct64 & _M)
- default:
- panic("Unknown word size")
- }
-
- if r%3 == 0 || r%5 == 0 || r%7 == 0 || r%11 == 0 ||
- r%13 == 0 || r%17 == 0 || r%19 == 0 || r%23 == 0 || r%29 == 0 {
- return false
- }
-
- if _W == 64 && (r%31 == 0 || r%37 == 0 || r%41 == 0 ||
- r%43 == 0 || r%47 == 0 || r%53 == 0) {
- return false
- }
-
- nm1 := nat(nil).sub(n, natOne)
- // determine q, k such that nm1 = q << k
- k := nm1.trailingZeroBits()
- q := nat(nil).shr(nm1, k)
-
- nm3 := nat(nil).sub(nm1, natTwo)
- rand := rand.New(rand.NewSource(int64(n[0])))
-
- var x, y, quotient nat
- nm3Len := nm3.bitLen()
-
-NextRandom:
- for i := 0; i < reps; i++ {
- x = x.random(rand, nm3, nm3Len)
- x = x.add(x, natTwo)
- y = y.expNN(x, q, n)
- if y.cmp(natOne) == 0 || y.cmp(nm1) == 0 {
- continue
- }
- for j := uint(1); j < k; j++ {
- y = y.mul(y, y)
- quotient, y = quotient.div(y, y, n)
- if y.cmp(nm1) == 0 {
- continue NextRandom
- }
- if y.cmp(natOne) == 0 {
- return false
- }
- }
- return false
- }
-
- return true
-}
-
-// bytes writes the value of z into buf using big-endian encoding.
-// len(buf) must be >= len(z)*_S. The value of z is encoded in the
-// slice buf[i:]. The number i of unused bytes at the beginning of
-// buf is returned as result.
-func (z nat) bytes(buf []byte) (i int) {
- i = len(buf)
- for _, d := range z {
- for j := 0; j < _S; j++ {
- i--
- buf[i] = byte(d)
- d >>= 8
- }
- }
-
- for i < len(buf) && buf[i] == 0 {
- i++
- }
-
- return
-}
-
-// setBytes interprets buf as the bytes of a big-endian unsigned
-// integer, sets z to that value, and returns z.
-func (z nat) setBytes(buf []byte) nat {
- z = z.make((len(buf) + _S - 1) / _S)
-
- k := 0
- s := uint(0)
- var d Word
- for i := len(buf); i > 0; i-- {
- d |= Word(buf[i-1]) << s
- if s += 8; s == _S*8 {
- z[k] = d
- k++
- s = 0
- d = 0
- }
- }
- if k < len(z) {
- z[k] = d
- }
-
- return z.norm()
-}
diff --git a/src/pkg/math/big/nat_test.go b/src/pkg/math/big/nat_test.go
deleted file mode 100644
index a2ae53385..000000000
--- a/src/pkg/math/big/nat_test.go
+++ /dev/null
@@ -1,771 +0,0 @@
-// Copyright 2009 The Go Authors. All rights reserved.
-// Use of this source code is governed by a BSD-style
-// license that can be found in the LICENSE file.
-
-package big
-
-import (
- "io"
- "runtime"
- "strings"
- "testing"
-)
-
-var cmpTests = []struct {
- x, y nat
- r int
-}{
- {nil, nil, 0},
- {nil, nat(nil), 0},
- {nat(nil), nil, 0},
- {nat(nil), nat(nil), 0},
- {nat{0}, nat{0}, 0},
- {nat{0}, nat{1}, -1},
- {nat{1}, nat{0}, 1},
- {nat{1}, nat{1}, 0},
- {nat{0, _M}, nat{1}, 1},
- {nat{1}, nat{0, _M}, -1},
- {nat{1, _M}, nat{0, _M}, 1},
- {nat{0, _M}, nat{1, _M}, -1},
- {nat{16, 571956, 8794, 68}, nat{837, 9146, 1, 754489}, -1},
- {nat{34986, 41, 105, 1957}, nat{56, 7458, 104, 1957}, 1},
-}
-
-func TestCmp(t *testing.T) {
- for i, a := range cmpTests {
- r := a.x.cmp(a.y)
- if r != a.r {
- t.Errorf("#%d got r = %v; want %v", i, r, a.r)
- }
- }
-}
-
-type funNN func(z, x, y nat) nat
-type argNN struct {
- z, x, y nat
-}
-
-var sumNN = []argNN{
- {},
- {nat{1}, nil, nat{1}},
- {nat{1111111110}, nat{123456789}, nat{987654321}},
- {nat{0, 0, 0, 1}, nil, nat{0, 0, 0, 1}},
- {nat{0, 0, 0, 1111111110}, nat{0, 0, 0, 123456789}, nat{0, 0, 0, 987654321}},
- {nat{0, 0, 0, 1}, nat{0, 0, _M}, nat{0, 0, 1}},
-}
-
-var prodNN = []argNN{
- {},
- {nil, nil, nil},
- {nil, nat{991}, nil},
- {nat{991}, nat{991}, nat{1}},
- {nat{991 * 991}, nat{991}, nat{991}},
- {nat{0, 0, 991 * 991}, nat{0, 991}, nat{0, 991}},
- {nat{1 * 991, 2 * 991, 3 * 991, 4 * 991}, nat{1, 2, 3, 4}, nat{991}},
- {nat{4, 11, 20, 30, 20, 11, 4}, nat{1, 2, 3, 4}, nat{4, 3, 2, 1}},
- // 3^100 * 3^28 = 3^128
- {
- natFromString("11790184577738583171520872861412518665678211592275841109096961"),
- natFromString("515377520732011331036461129765621272702107522001"),
- natFromString("22876792454961"),
- },
- // z = 111....1 (70000 digits)
- // x = 10^(99*700) + ... + 10^1400 + 10^700 + 1
- // y = 111....1 (700 digits, larger than Karatsuba threshold on 32-bit and 64-bit)
- {
- natFromString(strings.Repeat("1", 70000)),
- natFromString("1" + strings.Repeat(strings.Repeat("0", 699)+"1", 99)),
- natFromString(strings.Repeat("1", 700)),
- },
- // z = 111....1 (20000 digits)
- // x = 10^10000 + 1
- // y = 111....1 (10000 digits)
- {
- natFromString(strings.Repeat("1", 20000)),
- natFromString("1" + strings.Repeat("0", 9999) + "1"),
- natFromString(strings.Repeat("1", 10000)),
- },
-}
-
-func natFromString(s string) nat {
- x, _, err := nat(nil).scan(strings.NewReader(s), 0)
- if err != nil {
- panic(err)
- }
- return x
-}
-
-func TestSet(t *testing.T) {
- for _, a := range sumNN {
- z := nat(nil).set(a.z)
- if z.cmp(a.z) != 0 {
- t.Errorf("got z = %v; want %v", z, a.z)
- }
- }
-}
-
-func testFunNN(t *testing.T, msg string, f funNN, a argNN) {
- z := f(nil, a.x, a.y)
- if z.cmp(a.z) != 0 {
- t.Errorf("%s%+v\n\tgot z = %v; want %v", msg, a, z, a.z)
- }
-}
-
-func TestFunNN(t *testing.T) {
- for _, a := range sumNN {
- arg := a
- testFunNN(t, "add", nat.add, arg)
-
- arg = argNN{a.z, a.y, a.x}
- testFunNN(t, "add symmetric", nat.add, arg)
-
- arg = argNN{a.x, a.z, a.y}
- testFunNN(t, "sub", nat.sub, arg)
-
- arg = argNN{a.y, a.z, a.x}
- testFunNN(t, "sub symmetric", nat.sub, arg)
- }
-
- for _, a := range prodNN {
- arg := a
- testFunNN(t, "mul", nat.mul, arg)
-
- arg = argNN{a.z, a.y, a.x}
- testFunNN(t, "mul symmetric", nat.mul, arg)
- }
-}
-
-var mulRangesN = []struct {
- a, b uint64
- prod string
-}{
- {0, 0, "0"},
- {1, 1, "1"},
- {1, 2, "2"},
- {1, 3, "6"},
- {10, 10, "10"},
- {0, 100, "0"},
- {0, 1e9, "0"},
- {1, 0, "1"}, // empty range
- {100, 1, "1"}, // empty range
- {1, 10, "3628800"}, // 10!
- {1, 20, "2432902008176640000"}, // 20!
- {1, 100,
- "933262154439441526816992388562667004907159682643816214685929" +
- "638952175999932299156089414639761565182862536979208272237582" +
- "51185210916864000000000000000000000000", // 100!
- },
-}
-
-func TestMulRangeN(t *testing.T) {
- for i, r := range mulRangesN {
- prod := nat(nil).mulRange(r.a, r.b).decimalString()
- if prod != r.prod {
- t.Errorf("#%d: got %s; want %s", i, prod, r.prod)
- }
- }
-}
-
-// allocBytes returns the number of bytes allocated by invoking f.
-func allocBytes(f func()) uint64 {
- var stats runtime.MemStats
- runtime.ReadMemStats(&stats)
- t := stats.TotalAlloc
- f()
- runtime.ReadMemStats(&stats)
- return stats.TotalAlloc - t
-}
-
-// TestMulUnbalanced tests that multiplying numbers of different lengths
-// does not cause deep recursion and in turn allocate too much memory.
-// Test case for issue 3807.
-func TestMulUnbalanced(t *testing.T) {
- defer runtime.GOMAXPROCS(runtime.GOMAXPROCS(1))
- x := rndNat(50000)
- y := rndNat(40)
- allocSize := allocBytes(func() {
- nat(nil).mul(x, y)
- })
- inputSize := uint64(len(x)+len(y)) * _S
- if ratio := allocSize / uint64(inputSize); ratio > 10 {
- t.Errorf("multiplication uses too much memory (%d > %d times the size of inputs)", allocSize, ratio)
- }
-}
-
-func rndNat(n int) nat {
- return nat(rndV(n)).norm()
-}
-
-func BenchmarkMul(b *testing.B) {
- mulx := rndNat(1e4)
- muly := rndNat(1e4)
- b.ResetTimer()
- for i := 0; i < b.N; i++ {
- var z nat
- z.mul(mulx, muly)
- }
-}
-
-func toString(x nat, charset string) string {
- base := len(charset)
-
- // special cases
- switch {
- case base < 2:
- panic("illegal base")
- case len(x) == 0:
- return string(charset[0])
- }
-
- // allocate buffer for conversion
- i := x.bitLen()/log2(Word(base)) + 1 // +1: round up
- s := make([]byte, i)
-
- // don't destroy x
- q := nat(nil).set(x)
-
- // convert
- for len(q) > 0 {
- i--
- var r Word
- q, r = q.divW(q, Word(base))
- s[i] = charset[r]
- }
-
- return string(s[i:])
-}
-
-var strTests = []struct {
- x nat // nat value to be converted
- c string // conversion charset
- s string // expected result
-}{
- {nil, "01", "0"},
- {nat{1}, "01", "1"},
- {nat{0xc5}, "01", "11000101"},
- {nat{03271}, lowercaseDigits[0:8], "3271"},
- {nat{10}, lowercaseDigits[0:10], "10"},
- {nat{1234567890}, uppercaseDigits[0:10], "1234567890"},
- {nat{0xdeadbeef}, lowercaseDigits[0:16], "deadbeef"},
- {nat{0xdeadbeef}, uppercaseDigits[0:16], "DEADBEEF"},
- {nat{0x229be7}, lowercaseDigits[0:17], "1a2b3c"},
- {nat{0x309663e6}, uppercaseDigits[0:32], "O9COV6"},
-}
-
-func TestString(t *testing.T) {
- for _, a := range strTests {
- s := a.x.string(a.c)
- if s != a.s {
- t.Errorf("string%+v\n\tgot s = %s; want %s", a, s, a.s)
- }
-
- x, b, err := nat(nil).scan(strings.NewReader(a.s), len(a.c))
- if x.cmp(a.x) != 0 {
- t.Errorf("scan%+v\n\tgot z = %v; want %v", a, x, a.x)
- }
- if b != len(a.c) {
- t.Errorf("scan%+v\n\tgot b = %d; want %d", a, b, len(a.c))
- }
- if err != nil {
- t.Errorf("scan%+v\n\tgot error = %s", a, err)
- }
- }
-}
-
-var natScanTests = []struct {
- s string // string to be scanned
- base int // input base
- x nat // expected nat
- b int // expected base
- ok bool // expected success
- next rune // next character (or 0, if at EOF)
-}{
- // error: illegal base
- {base: -1},
- {base: 1},
- {base: 37},
-
- // error: no mantissa
- {},
- {s: "?"},
- {base: 10},
- {base: 36},
- {s: "?", base: 10},
- {s: "0x"},
- {s: "345", base: 2},
-
- // no errors
- {"0", 0, nil, 10, true, 0},
- {"0", 10, nil, 10, true, 0},
- {"0", 36, nil, 36, true, 0},
- {"1", 0, nat{1}, 10, true, 0},
- {"1", 10, nat{1}, 10, true, 0},
- {"0 ", 0, nil, 10, true, ' '},
- {"08", 0, nil, 10, true, '8'},
- {"018", 0, nat{1}, 8, true, '8'},
- {"0b1", 0, nat{1}, 2, true, 0},
- {"0b11000101", 0, nat{0xc5}, 2, true, 0},
- {"03271", 0, nat{03271}, 8, true, 0},
- {"10ab", 0, nat{10}, 10, true, 'a'},
- {"1234567890", 0, nat{1234567890}, 10, true, 0},
- {"xyz", 36, nat{(33*36+34)*36 + 35}, 36, true, 0},
- {"xyz?", 36, nat{(33*36+34)*36 + 35}, 36, true, '?'},
- {"0x", 16, nil, 16, true, 'x'},
- {"0xdeadbeef", 0, nat{0xdeadbeef}, 16, true, 0},
- {"0XDEADBEEF", 0, nat{0xdeadbeef}, 16, true, 0},
-}
-
-func TestScanBase(t *testing.T) {
- for _, a := range natScanTests {
- r := strings.NewReader(a.s)
- x, b, err := nat(nil).scan(r, a.base)
- if err == nil && !a.ok {
- t.Errorf("scan%+v\n\texpected error", a)
- }
- if err != nil {
- if a.ok {
- t.Errorf("scan%+v\n\tgot error = %s", a, err)
- }
- continue
- }
- if x.cmp(a.x) != 0 {
- t.Errorf("scan%+v\n\tgot z = %v; want %v", a, x, a.x)
- }
- if b != a.b {
- t.Errorf("scan%+v\n\tgot b = %d; want %d", a, b, a.base)
- }
- next, _, err := r.ReadRune()
- if err == io.EOF {
- next = 0
- err = nil
- }
- if err == nil && next != a.next {
- t.Errorf("scan%+v\n\tgot next = %q; want %q", a, next, a.next)
- }
- }
-}
-
-var pi = "3" +
- "14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651" +
- "32823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461" +
- "28475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920" +
- "96282925409171536436789259036001133053054882046652138414695194151160943305727036575959195309218611738193261179" +
- "31051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798" +
- "60943702770539217176293176752384674818467669405132000568127145263560827785771342757789609173637178721468440901" +
- "22495343014654958537105079227968925892354201995611212902196086403441815981362977477130996051870721134999999837" +
- "29780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083" +
- "81420617177669147303598253490428755468731159562863882353787593751957781857780532171226806613001927876611195909" +
- "21642019893809525720106548586327886593615338182796823030195203530185296899577362259941389124972177528347913151" +
- "55748572424541506959508295331168617278558890750983817546374649393192550604009277016711390098488240128583616035" +
- "63707660104710181942955596198946767837449448255379774726847104047534646208046684259069491293313677028989152104" +
- "75216205696602405803815019351125338243003558764024749647326391419927260426992279678235478163600934172164121992" +
- "45863150302861829745557067498385054945885869269956909272107975093029553211653449872027559602364806654991198818" +
- "34797753566369807426542527862551818417574672890977772793800081647060016145249192173217214772350141441973568548" +
- "16136115735255213347574184946843852332390739414333454776241686251898356948556209921922218427255025425688767179" +
- "04946016534668049886272327917860857843838279679766814541009538837863609506800642251252051173929848960841284886" +
- "26945604241965285022210661186306744278622039194945047123713786960956364371917287467764657573962413890865832645" +
- "99581339047802759009946576407895126946839835259570982582262052248940772671947826848260147699090264013639443745" +
- "53050682034962524517493996514314298091906592509372216964615157098583874105978859597729754989301617539284681382" +
- "68683868942774155991855925245953959431049972524680845987273644695848653836736222626099124608051243884390451244" +
- "13654976278079771569143599770012961608944169486855584840635342207222582848864815845602850601684273945226746767" +
- "88952521385225499546667278239864565961163548862305774564980355936345681743241125150760694794510965960940252288" +
- "79710893145669136867228748940560101503308617928680920874760917824938589009714909675985261365549781893129784821" +
- "68299894872265880485756401427047755513237964145152374623436454285844479526586782105114135473573952311342716610" +
- "21359695362314429524849371871101457654035902799344037420073105785390621983874478084784896833214457138687519435" +
- "06430218453191048481005370614680674919278191197939952061419663428754440643745123718192179998391015919561814675" +
- "14269123974894090718649423196156794520809514655022523160388193014209376213785595663893778708303906979207734672" +
- "21825625996615014215030680384477345492026054146659252014974428507325186660021324340881907104863317346496514539" +
- "05796268561005508106658796998163574736384052571459102897064140110971206280439039759515677157700420337869936007" +
- "23055876317635942187312514712053292819182618612586732157919841484882916447060957527069572209175671167229109816" +
- "90915280173506712748583222871835209353965725121083579151369882091444210067510334671103141267111369908658516398" +
- "31501970165151168517143765761835155650884909989859982387345528331635507647918535893226185489632132933089857064" +
- "20467525907091548141654985946163718027098199430992448895757128289059232332609729971208443357326548938239119325" +
- "97463667305836041428138830320382490375898524374417029132765618093773444030707469211201913020330380197621101100" +
- "44929321516084244485963766983895228684783123552658213144957685726243344189303968642624341077322697802807318915" +
- "44110104468232527162010526522721116603966655730925471105578537634668206531098965269186205647693125705863566201" +
- "85581007293606598764861179104533488503461136576867532494416680396265797877185560845529654126654085306143444318" +
- "58676975145661406800700237877659134401712749470420562230538994561314071127000407854733269939081454664645880797" +
- "27082668306343285878569830523580893306575740679545716377525420211495576158140025012622859413021647155097925923" +
- "09907965473761255176567513575178296664547791745011299614890304639947132962107340437518957359614589019389713111" +
- "79042978285647503203198691514028708085990480109412147221317947647772622414254854540332157185306142288137585043" +
- "06332175182979866223717215916077166925474873898665494945011465406284336639379003976926567214638530673609657120" +
- "91807638327166416274888800786925602902284721040317211860820419000422966171196377921337575114959501566049631862" +
- "94726547364252308177036751590673502350728354056704038674351362222477158915049530984448933309634087807693259939" +
- "78054193414473774418426312986080998886874132604721569516239658645730216315981931951673538129741677294786724229" +
- "24654366800980676928238280689964004824354037014163149658979409243237896907069779422362508221688957383798623001" +
- "59377647165122893578601588161755782973523344604281512627203734314653197777416031990665541876397929334419521541" +
- "34189948544473456738316249934191318148092777710386387734317720754565453220777092120190516609628049092636019759" +
- "88281613323166636528619326686336062735676303544776280350450777235547105859548702790814356240145171806246436267" +
- "94561275318134078330336254232783944975382437205835311477119926063813346776879695970309833913077109870408591337"
-
-// Test case for BenchmarkScanPi.
-func TestScanPi(t *testing.T) {
- var x nat
- z, _, err := x.scan(strings.NewReader(pi), 10)
- if err != nil {
- t.Errorf("scanning pi: %s", err)
- }
- if s := z.decimalString(); s != pi {
- t.Errorf("scanning pi: got %s", s)
- }
-}
-
-func TestScanPiParallel(t *testing.T) {
- const n = 2
- c := make(chan int)
- for i := 0; i < n; i++ {
- go func() {
- TestScanPi(t)
- c <- 0
- }()
- }
- for i := 0; i < n; i++ {
- <-c
- }
-}
-
-func BenchmarkScanPi(b *testing.B) {
- for i := 0; i < b.N; i++ {
- var x nat
- x.scan(strings.NewReader(pi), 10)
- }
-}
-
-func BenchmarkStringPiParallel(b *testing.B) {
- var x nat
- x, _, _ = x.scan(strings.NewReader(pi), 0)
- if x.decimalString() != pi {
- panic("benchmark incorrect: conversion failed")
- }
- b.RunParallel(func(pb *testing.PB) {
- for pb.Next() {
- x.decimalString()
- }
- })
-}
-
-func BenchmarkScan10Base2(b *testing.B) { ScanHelper(b, 2, 10, 10) }
-func BenchmarkScan100Base2(b *testing.B) { ScanHelper(b, 2, 10, 100) }
-func BenchmarkScan1000Base2(b *testing.B) { ScanHelper(b, 2, 10, 1000) }
-func BenchmarkScan10000Base2(b *testing.B) { ScanHelper(b, 2, 10, 10000) }
-func BenchmarkScan100000Base2(b *testing.B) { ScanHelper(b, 2, 10, 100000) }
-
-func BenchmarkScan10Base8(b *testing.B) { ScanHelper(b, 8, 10, 10) }
-func BenchmarkScan100Base8(b *testing.B) { ScanHelper(b, 8, 10, 100) }
-func BenchmarkScan1000Base8(b *testing.B) { ScanHelper(b, 8, 10, 1000) }
-func BenchmarkScan10000Base8(b *testing.B) { ScanHelper(b, 8, 10, 10000) }
-func BenchmarkScan100000Base8(b *testing.B) { ScanHelper(b, 8, 10, 100000) }
-
-func BenchmarkScan10Base10(b *testing.B) { ScanHelper(b, 10, 10, 10) }
-func BenchmarkScan100Base10(b *testing.B) { ScanHelper(b, 10, 10, 100) }
-func BenchmarkScan1000Base10(b *testing.B) { ScanHelper(b, 10, 10, 1000) }
-func BenchmarkScan10000Base10(b *testing.B) { ScanHelper(b, 10, 10, 10000) }
-func BenchmarkScan100000Base10(b *testing.B) { ScanHelper(b, 10, 10, 100000) }
-
-func BenchmarkScan10Base16(b *testing.B) { ScanHelper(b, 16, 10, 10) }
-func BenchmarkScan100Base16(b *testing.B) { ScanHelper(b, 16, 10, 100) }
-func BenchmarkScan1000Base16(b *testing.B) { ScanHelper(b, 16, 10, 1000) }
-func BenchmarkScan10000Base16(b *testing.B) { ScanHelper(b, 16, 10, 10000) }
-func BenchmarkScan100000Base16(b *testing.B) { ScanHelper(b, 16, 10, 100000) }
-
-func ScanHelper(b *testing.B, base int, x, y Word) {
- b.StopTimer()
- var z nat
- z = z.expWW(x, y)
-
- var s string
- s = z.string(lowercaseDigits[0:base])
- if t := toString(z, lowercaseDigits[0:base]); t != s {
- b.Fatalf("scanning: got %s; want %s", s, t)
- }
- b.StartTimer()
-
- for i := 0; i < b.N; i++ {
- z.scan(strings.NewReader(s), base)
- }
-}
-
-func BenchmarkString10Base2(b *testing.B) { StringHelper(b, 2, 10, 10) }
-func BenchmarkString100Base2(b *testing.B) { StringHelper(b, 2, 10, 100) }
-func BenchmarkString1000Base2(b *testing.B) { StringHelper(b, 2, 10, 1000) }
-func BenchmarkString10000Base2(b *testing.B) { StringHelper(b, 2, 10, 10000) }
-func BenchmarkString100000Base2(b *testing.B) { StringHelper(b, 2, 10, 100000) }
-
-func BenchmarkString10Base8(b *testing.B) { StringHelper(b, 8, 10, 10) }
-func BenchmarkString100Base8(b *testing.B) { StringHelper(b, 8, 10, 100) }
-func BenchmarkString1000Base8(b *testing.B) { StringHelper(b, 8, 10, 1000) }
-func BenchmarkString10000Base8(b *testing.B) { StringHelper(b, 8, 10, 10000) }
-func BenchmarkString100000Base8(b *testing.B) { StringHelper(b, 8, 10, 100000) }
-
-func BenchmarkString10Base10(b *testing.B) { StringHelper(b, 10, 10, 10) }
-func BenchmarkString100Base10(b *testing.B) { StringHelper(b, 10, 10, 100) }
-func BenchmarkString1000Base10(b *testing.B) { StringHelper(b, 10, 10, 1000) }
-func BenchmarkString10000Base10(b *testing.B) { StringHelper(b, 10, 10, 10000) }
-func BenchmarkString100000Base10(b *testing.B) { StringHelper(b, 10, 10, 100000) }
-
-func BenchmarkString10Base16(b *testing.B) { StringHelper(b, 16, 10, 10) }
-func BenchmarkString100Base16(b *testing.B) { StringHelper(b, 16, 10, 100) }
-func BenchmarkString1000Base16(b *testing.B) { StringHelper(b, 16, 10, 1000) }
-func BenchmarkString10000Base16(b *testing.B) { StringHelper(b, 16, 10, 10000) }
-func BenchmarkString100000Base16(b *testing.B) { StringHelper(b, 16, 10, 100000) }
-
-func StringHelper(b *testing.B, base int, x, y Word) {
- b.StopTimer()
- var z nat
- z = z.expWW(x, y)
- z.string(lowercaseDigits[0:base]) // warm divisor cache
- b.StartTimer()
-
- for i := 0; i < b.N; i++ {
- _ = z.string(lowercaseDigits[0:base])
- }
-}
-
-func BenchmarkLeafSize0(b *testing.B) { LeafSizeHelper(b, 10, 0) } // test without splitting
-func BenchmarkLeafSize1(b *testing.B) { LeafSizeHelper(b, 10, 1) }
-func BenchmarkLeafSize2(b *testing.B) { LeafSizeHelper(b, 10, 2) }
-func BenchmarkLeafSize3(b *testing.B) { LeafSizeHelper(b, 10, 3) }
-func BenchmarkLeafSize4(b *testing.B) { LeafSizeHelper(b, 10, 4) }
-func BenchmarkLeafSize5(b *testing.B) { LeafSizeHelper(b, 10, 5) }
-func BenchmarkLeafSize6(b *testing.B) { LeafSizeHelper(b, 10, 6) }
-func BenchmarkLeafSize7(b *testing.B) { LeafSizeHelper(b, 10, 7) }
-func BenchmarkLeafSize8(b *testing.B) { LeafSizeHelper(b, 10, 8) }
-func BenchmarkLeafSize9(b *testing.B) { LeafSizeHelper(b, 10, 9) }
-func BenchmarkLeafSize10(b *testing.B) { LeafSizeHelper(b, 10, 10) }
-func BenchmarkLeafSize11(b *testing.B) { LeafSizeHelper(b, 10, 11) }
-func BenchmarkLeafSize12(b *testing.B) { LeafSizeHelper(b, 10, 12) }
-func BenchmarkLeafSize13(b *testing.B) { LeafSizeHelper(b, 10, 13) }
-func BenchmarkLeafSize14(b *testing.B) { LeafSizeHelper(b, 10, 14) }
-func BenchmarkLeafSize15(b *testing.B) { LeafSizeHelper(b, 10, 15) }
-func BenchmarkLeafSize16(b *testing.B) { LeafSizeHelper(b, 10, 16) }
-func BenchmarkLeafSize32(b *testing.B) { LeafSizeHelper(b, 10, 32) } // try some large lengths
-func BenchmarkLeafSize64(b *testing.B) { LeafSizeHelper(b, 10, 64) }
-
-func LeafSizeHelper(b *testing.B, base Word, size int) {
- b.StopTimer()
- originalLeafSize := leafSize
- resetTable(cacheBase10.table[:])
- leafSize = size
- b.StartTimer()
-
- for d := 1; d <= 10000; d *= 10 {
- b.StopTimer()
- var z nat
- z = z.expWW(base, Word(d)) // build target number
- _ = z.string(lowercaseDigits[0:base]) // warm divisor cache
- b.StartTimer()
-
- for i := 0; i < b.N; i++ {
- _ = z.string(lowercaseDigits[0:base])
- }
- }
-
- b.StopTimer()
- resetTable(cacheBase10.table[:])
- leafSize = originalLeafSize
- b.StartTimer()
-}
-
-func resetTable(table []divisor) {
- if table != nil && table[0].bbb != nil {
- for i := 0; i < len(table); i++ {
- table[i].bbb = nil
- table[i].nbits = 0
- table[i].ndigits = 0
- }
- }
-}
-
-func TestStringPowers(t *testing.T) {
- var b, p Word
- for b = 2; b <= 16; b++ {
- for p = 0; p <= 512; p++ {
- x := nat(nil).expWW(b, p)
- xs := x.string(lowercaseDigits[0:b])
- xs2 := toString(x, lowercaseDigits[0:b])
- if xs != xs2 {
- t.Errorf("failed at %d ** %d in base %d: %s != %s", b, p, b, xs, xs2)
- }
- }
- if b >= 3 && testing.Short() {
- break
- }
- }
-}
-
-func TestLeadingZeros(t *testing.T) {
- var x Word = _B >> 1
- for i := 0; i <= _W; i++ {
- if int(leadingZeros(x)) != i {
- t.Errorf("failed at %x: got %d want %d", x, leadingZeros(x), i)
- }
- x >>= 1
- }
-}
-
-type shiftTest struct {
- in nat
- shift uint
- out nat
-}
-
-var leftShiftTests = []shiftTest{
- {nil, 0, nil},
- {nil, 1, nil},
- {natOne, 0, natOne},
- {natOne, 1, natTwo},
- {nat{1 << (_W - 1)}, 1, nat{0}},
- {nat{1 << (_W - 1), 0}, 1, nat{0, 1}},
-}
-
-func TestShiftLeft(t *testing.T) {
- for i, test := range leftShiftTests {
- var z nat
- z = z.shl(test.in, test.shift)
- for j, d := range test.out {
- if j >= len(z) || z[j] != d {
- t.Errorf("#%d: got: %v want: %v", i, z, test.out)
- break
- }
- }
- }
-}
-
-var rightShiftTests = []shiftTest{
- {nil, 0, nil},
- {nil, 1, nil},
- {natOne, 0, natOne},
- {natOne, 1, nil},
- {natTwo, 1, natOne},
- {nat{0, 1}, 1, nat{1 << (_W - 1)}},
- {nat{2, 1, 1}, 1, nat{1<<(_W-1) + 1, 1 << (_W - 1)}},
-}
-
-func TestShiftRight(t *testing.T) {
- for i, test := range rightShiftTests {
- var z nat
- z = z.shr(test.in, test.shift)
- for j, d := range test.out {
- if j >= len(z) || z[j] != d {
- t.Errorf("#%d: got: %v want: %v", i, z, test.out)
- break
- }
- }
- }
-}
-
-type modWTest struct {
- in string
- dividend string
- out string
-}
-
-var modWTests32 = []modWTest{
- {"23492635982634928349238759823742", "252341", "220170"},
-}
-
-var modWTests64 = []modWTest{
- {"6527895462947293856291561095690465243862946", "524326975699234", "375066989628668"},
-}
-
-func runModWTests(t *testing.T, tests []modWTest) {
- for i, test := range tests {
- in, _ := new(Int).SetString(test.in, 10)
- d, _ := new(Int).SetString(test.dividend, 10)
- out, _ := new(Int).SetString(test.out, 10)
-
- r := in.abs.modW(d.abs[0])
- if r != out.abs[0] {
- t.Errorf("#%d failed: got %d want %s", i, r, out)
- }
- }
-}
-
-func TestModW(t *testing.T) {
- if _W >= 32 {
- runModWTests(t, modWTests32)
- }
- if _W >= 64 {
- runModWTests(t, modWTests64)
- }
-}
-
-func TestTrailingZeroBits(t *testing.T) {
- x := Word(1)
- for i := uint(0); i <= _W; i++ {
- n := trailingZeroBits(x)
- if n != i%_W {
- t.Errorf("got trailingZeroBits(%#x) = %d; want %d", x, n, i%_W)
- }
- x <<= 1
- }
-
- y := nat(nil).set(natOne)
- for i := uint(0); i <= 3*_W; i++ {
- n := y.trailingZeroBits()
- if n != i {
- t.Errorf("got 0x%s.trailingZeroBits() = %d; want %d", y.string(lowercaseDigits[0:16]), n, i)
- }
- y = y.shl(y, 1)
- }
-}
-
-var expNNTests = []struct {
- x, y, m string
- out string
-}{
- {"0", "0", "0", "1"},
- {"0", "0", "1", "0"},
- {"1", "1", "1", "0"},
- {"2", "1", "1", "0"},
- {"2", "2", "1", "0"},
- {"10", "100000000000", "1", "0"},
- {"0x8000000000000000", "2", "", "0x40000000000000000000000000000000"},
- {"0x8000000000000000", "2", "6719", "4944"},
- {"0x8000000000000000", "3", "6719", "5447"},
- {"0x8000000000000000", "1000", "6719", "1603"},
- {"0x8000000000000000", "1000000", "6719", "3199"},
- {
- "2938462938472983472983659726349017249287491026512746239764525612965293865296239471239874193284792387498274256129746192347",
- "298472983472983471903246121093472394872319615612417471234712061",
- "29834729834729834729347290846729561262544958723956495615629569234729836259263598127342374289365912465901365498236492183464",
- "23537740700184054162508175125554701713153216681790245129157191391322321508055833908509185839069455749219131480588829346291",
- },
-}
-
-func TestExpNN(t *testing.T) {
- for i, test := range expNNTests {
- x, _, _ := nat(nil).scan(strings.NewReader(test.x), 0)
- y, _, _ := nat(nil).scan(strings.NewReader(test.y), 0)
- out, _, _ := nat(nil).scan(strings.NewReader(test.out), 0)
-
- var m nat
-
- if len(test.m) > 0 {
- m, _, _ = nat(nil).scan(strings.NewReader(test.m), 0)
- }
-
- z := nat(nil).expNN(x, y, m)
- if z.cmp(out) != 0 {
- t.Errorf("#%d got %s want %s", i, z.decimalString(), out.decimalString())
- }
- }
-}
-
-func ExpHelper(b *testing.B, x, y Word) {
- var z nat
- for i := 0; i < b.N; i++ {
- z.expWW(x, y)
- }
-}
-
-func BenchmarkExp3Power0x10(b *testing.B) { ExpHelper(b, 3, 0x10) }
-func BenchmarkExp3Power0x40(b *testing.B) { ExpHelper(b, 3, 0x40) }
-func BenchmarkExp3Power0x100(b *testing.B) { ExpHelper(b, 3, 0x100) }
-func BenchmarkExp3Power0x400(b *testing.B) { ExpHelper(b, 3, 0x400) }
-func BenchmarkExp3Power0x1000(b *testing.B) { ExpHelper(b, 3, 0x1000) }
-func BenchmarkExp3Power0x4000(b *testing.B) { ExpHelper(b, 3, 0x4000) }
-func BenchmarkExp3Power0x10000(b *testing.B) { ExpHelper(b, 3, 0x10000) }
-func BenchmarkExp3Power0x40000(b *testing.B) { ExpHelper(b, 3, 0x40000) }
-func BenchmarkExp3Power0x100000(b *testing.B) { ExpHelper(b, 3, 0x100000) }
-func BenchmarkExp3Power0x400000(b *testing.B) { ExpHelper(b, 3, 0x400000) }
diff --git a/src/pkg/math/big/rat.go b/src/pkg/math/big/rat.go
deleted file mode 100644
index f0973b390..000000000
--- a/src/pkg/math/big/rat.go
+++ /dev/null
@@ -1,600 +0,0 @@
-// Copyright 2010 The Go Authors. All rights reserved.
-// Use of this source code is governed by a BSD-style
-// license that can be found in the LICENSE file.
-
-// This file implements multi-precision rational numbers.
-
-package big
-
-import (
- "encoding/binary"
- "errors"
- "fmt"
- "math"
- "strings"
-)
-
-// A Rat represents a quotient a/b of arbitrary precision.
-// The zero value for a Rat represents the value 0.
-type Rat struct {
- // To make zero values for Rat work w/o initialization,
- // a zero value of b (len(b) == 0) acts like b == 1.
- // a.neg determines the sign of the Rat, b.neg is ignored.
- a, b Int
-}
-
-// NewRat creates a new Rat with numerator a and denominator b.
-func NewRat(a, b int64) *Rat {
- return new(Rat).SetFrac64(a, b)
-}
-
-// SetFloat64 sets z to exactly f and returns z.
-// If f is not finite, SetFloat returns nil.
-func (z *Rat) SetFloat64(f float64) *Rat {
- const expMask = 1<<11 - 1
- bits := math.Float64bits(f)
- mantissa := bits & (1<<52 - 1)
- exp := int((bits >> 52) & expMask)
- switch exp {
- case expMask: // non-finite
- return nil
- case 0: // denormal
- exp -= 1022
- default: // normal
- mantissa |= 1 << 52
- exp -= 1023
- }
-
- shift := 52 - exp
-
- // Optimization (?): partially pre-normalise.
- for mantissa&1 == 0 && shift > 0 {
- mantissa >>= 1
- shift--
- }
-
- z.a.SetUint64(mantissa)
- z.a.neg = f < 0
- z.b.Set(intOne)
- if shift > 0 {
- z.b.Lsh(&z.b, uint(shift))
- } else {
- z.a.Lsh(&z.a, uint(-shift))
- }
- return z.norm()
-}
-
-// isFinite reports whether f represents a finite rational value.
-// It is equivalent to !math.IsNan(f) && !math.IsInf(f, 0).
-func isFinite(f float64) bool {
- return math.Abs(f) <= math.MaxFloat64
-}
-
-// low64 returns the least significant 64 bits of natural number z.
-func low64(z nat) uint64 {
- if len(z) == 0 {
- return 0
- }
- if _W == 32 && len(z) > 1 {
- return uint64(z[1])<<32 | uint64(z[0])
- }
- return uint64(z[0])
-}
-
-// quotToFloat returns the non-negative IEEE 754 double-precision
-// value nearest to the quotient a/b, using round-to-even in halfway
-// cases. It does not mutate its arguments.
-// Preconditions: b is non-zero; a and b have no common factors.
-func quotToFloat(a, b nat) (f float64, exact bool) {
- // TODO(adonovan): specialize common degenerate cases: 1.0, integers.
- alen := a.bitLen()
- if alen == 0 {
- return 0, true
- }
- blen := b.bitLen()
- if blen == 0 {
- panic("division by zero")
- }
-
- // 1. Left-shift A or B such that quotient A/B is in [1<<53, 1<<55).
- // (54 bits if A<B when they are left-aligned, 55 bits if A>=B.)
- // This is 2 or 3 more than the float64 mantissa field width of 52:
- // - the optional extra bit is shifted away in step 3 below.
- // - the high-order 1 is omitted in float64 "normal" representation;
- // - the low-order 1 will be used during rounding then discarded.
- exp := alen - blen
- var a2, b2 nat
- a2 = a2.set(a)
- b2 = b2.set(b)
- if shift := 54 - exp; shift > 0 {
- a2 = a2.shl(a2, uint(shift))
- } else if shift < 0 {
- b2 = b2.shl(b2, uint(-shift))
- }
-
- // 2. Compute quotient and remainder (q, r). NB: due to the
- // extra shift, the low-order bit of q is logically the
- // high-order bit of r.
- var q nat
- q, r := q.div(a2, a2, b2) // (recycle a2)
- mantissa := low64(q)
- haveRem := len(r) > 0 // mantissa&1 && !haveRem => remainder is exactly half
-
- // 3. If quotient didn't fit in 54 bits, re-do division by b2<<1
- // (in effect---we accomplish this incrementally).
- if mantissa>>54 == 1 {
- if mantissa&1 == 1 {
- haveRem = true
- }
- mantissa >>= 1
- exp++
- }
- if mantissa>>53 != 1 {
- panic("expected exactly 54 bits of result")
- }
-
- // 4. Rounding.
- if -1022-52 <= exp && exp <= -1022 {
- // Denormal case; lose 'shift' bits of precision.
- shift := uint64(-1022 - (exp - 1)) // [1..53)
- lostbits := mantissa & (1<<shift - 1)
- haveRem = haveRem || lostbits != 0
- mantissa >>= shift
- exp = -1023 + 2
- }
- // Round q using round-half-to-even.
- exact = !haveRem
- if mantissa&1 != 0 {
- exact = false
- if haveRem || mantissa&2 != 0 {
- if mantissa++; mantissa >= 1<<54 {
- // Complete rollover 11...1 => 100...0, so shift is safe
- mantissa >>= 1
- exp++
- }
- }
- }
- mantissa >>= 1 // discard rounding bit. Mantissa now scaled by 2^53.
-
- f = math.Ldexp(float64(mantissa), exp-53)
- if math.IsInf(f, 0) {
- exact = false
- }
- return
-}
-
-// Float64 returns the nearest float64 value for x and a bool indicating
-// whether f represents x exactly. If the magnitude of x is too large to
-// be represented by a float64, f is an infinity and exact is false.
-// The sign of f always matches the sign of x, even if f == 0.
-func (x *Rat) Float64() (f float64, exact bool) {
- b := x.b.abs
- if len(b) == 0 {
- b = b.set(natOne) // materialize denominator
- }
- f, exact = quotToFloat(x.a.abs, b)
- if x.a.neg {
- f = -f
- }
- return
-}
-
-// SetFrac sets z to a/b and returns z.
-func (z *Rat) SetFrac(a, b *Int) *Rat {
- z.a.neg = a.neg != b.neg
- babs := b.abs
- if len(babs) == 0 {
- panic("division by zero")
- }
- if &z.a == b || alias(z.a.abs, babs) {
- babs = nat(nil).set(babs) // make a copy
- }
- z.a.abs = z.a.abs.set(a.abs)
- z.b.abs = z.b.abs.set(babs)
- return z.norm()
-}
-
-// SetFrac64 sets z to a/b and returns z.
-func (z *Rat) SetFrac64(a, b int64) *Rat {
- z.a.SetInt64(a)
- if b == 0 {
- panic("division by zero")
- }
- if b < 0 {
- b = -b
- z.a.neg = !z.a.neg
- }
- z.b.abs = z.b.abs.setUint64(uint64(b))
- return z.norm()
-}
-
-// SetInt sets z to x (by making a copy of x) and returns z.
-func (z *Rat) SetInt(x *Int) *Rat {
- z.a.Set(x)
- z.b.abs = z.b.abs.make(0)
- return z
-}
-
-// SetInt64 sets z to x and returns z.
-func (z *Rat) SetInt64(x int64) *Rat {
- z.a.SetInt64(x)
- z.b.abs = z.b.abs.make(0)
- return z
-}
-
-// Set sets z to x (by making a copy of x) and returns z.
-func (z *Rat) Set(x *Rat) *Rat {
- if z != x {
- z.a.Set(&x.a)
- z.b.Set(&x.b)
- }
- return z
-}
-
-// Abs sets z to |x| (the absolute value of x) and returns z.
-func (z *Rat) Abs(x *Rat) *Rat {
- z.Set(x)
- z.a.neg = false
- return z
-}
-
-// Neg sets z to -x and returns z.
-func (z *Rat) Neg(x *Rat) *Rat {
- z.Set(x)
- z.a.neg = len(z.a.abs) > 0 && !z.a.neg // 0 has no sign
- return z
-}
-
-// Inv sets z to 1/x and returns z.
-func (z *Rat) Inv(x *Rat) *Rat {
- if len(x.a.abs) == 0 {
- panic("division by zero")
- }
- z.Set(x)
- a := z.b.abs
- if len(a) == 0 {
- a = a.set(natOne) // materialize numerator
- }
- b := z.a.abs
- if b.cmp(natOne) == 0 {
- b = b.make(0) // normalize denominator
- }
- z.a.abs, z.b.abs = a, b // sign doesn't change
- return z
-}
-
-// Sign returns:
-//
-// -1 if x < 0
-// 0 if x == 0
-// +1 if x > 0
-//
-func (x *Rat) Sign() int {
- return x.a.Sign()
-}
-
-// IsInt returns true if the denominator of x is 1.
-func (x *Rat) IsInt() bool {
- return len(x.b.abs) == 0 || x.b.abs.cmp(natOne) == 0
-}
-
-// Num returns the numerator of x; it may be <= 0.
-// The result is a reference to x's numerator; it
-// may change if a new value is assigned to x, and vice versa.
-// The sign of the numerator corresponds to the sign of x.
-func (x *Rat) Num() *Int {
- return &x.a
-}
-
-// Denom returns the denominator of x; it is always > 0.
-// The result is a reference to x's denominator; it
-// may change if a new value is assigned to x, and vice versa.
-func (x *Rat) Denom() *Int {
- x.b.neg = false // the result is always >= 0
- if len(x.b.abs) == 0 {
- x.b.abs = x.b.abs.set(natOne) // materialize denominator
- }
- return &x.b
-}
-
-func (z *Rat) norm() *Rat {
- switch {
- case len(z.a.abs) == 0:
- // z == 0 - normalize sign and denominator
- z.a.neg = false
- z.b.abs = z.b.abs.make(0)
- case len(z.b.abs) == 0:
- // z is normalized int - nothing to do
- case z.b.abs.cmp(natOne) == 0:
- // z is int - normalize denominator
- z.b.abs = z.b.abs.make(0)
- default:
- neg := z.a.neg
- z.a.neg = false
- z.b.neg = false
- if f := NewInt(0).binaryGCD(&z.a, &z.b); f.Cmp(intOne) != 0 {
- z.a.abs, _ = z.a.abs.div(nil, z.a.abs, f.abs)
- z.b.abs, _ = z.b.abs.div(nil, z.b.abs, f.abs)
- if z.b.abs.cmp(natOne) == 0 {
- // z is int - normalize denominator
- z.b.abs = z.b.abs.make(0)
- }
- }
- z.a.neg = neg
- }
- return z
-}
-
-// mulDenom sets z to the denominator product x*y (by taking into
-// account that 0 values for x or y must be interpreted as 1) and
-// returns z.
-func mulDenom(z, x, y nat) nat {
- switch {
- case len(x) == 0:
- return z.set(y)
- case len(y) == 0:
- return z.set(x)
- }
- return z.mul(x, y)
-}
-
-// scaleDenom computes x*f.
-// If f == 0 (zero value of denominator), the result is (a copy of) x.
-func scaleDenom(x *Int, f nat) *Int {
- var z Int
- if len(f) == 0 {
- return z.Set(x)
- }
- z.abs = z.abs.mul(x.abs, f)
- z.neg = x.neg
- return &z
-}
-
-// Cmp compares x and y and returns:
-//
-// -1 if x < y
-// 0 if x == y
-// +1 if x > y
-//
-func (x *Rat) Cmp(y *Rat) int {
- return scaleDenom(&x.a, y.b.abs).Cmp(scaleDenom(&y.a, x.b.abs))
-}
-
-// Add sets z to the sum x+y and returns z.
-func (z *Rat) Add(x, y *Rat) *Rat {
- a1 := scaleDenom(&x.a, y.b.abs)
- a2 := scaleDenom(&y.a, x.b.abs)
- z.a.Add(a1, a2)
- z.b.abs = mulDenom(z.b.abs, x.b.abs, y.b.abs)
- return z.norm()
-}
-
-// Sub sets z to the difference x-y and returns z.
-func (z *Rat) Sub(x, y *Rat) *Rat {
- a1 := scaleDenom(&x.a, y.b.abs)
- a2 := scaleDenom(&y.a, x.b.abs)
- z.a.Sub(a1, a2)
- z.b.abs = mulDenom(z.b.abs, x.b.abs, y.b.abs)
- return z.norm()
-}
-
-// Mul sets z to the product x*y and returns z.
-func (z *Rat) Mul(x, y *Rat) *Rat {
- z.a.Mul(&x.a, &y.a)
- z.b.abs = mulDenom(z.b.abs, x.b.abs, y.b.abs)
- return z.norm()
-}
-
-// Quo sets z to the quotient x/y and returns z.
-// If y == 0, a division-by-zero run-time panic occurs.
-func (z *Rat) Quo(x, y *Rat) *Rat {
- if len(y.a.abs) == 0 {
- panic("division by zero")
- }
- a := scaleDenom(&x.a, y.b.abs)
- b := scaleDenom(&y.a, x.b.abs)
- z.a.abs = a.abs
- z.b.abs = b.abs
- z.a.neg = a.neg != b.neg
- return z.norm()
-}
-
-func ratTok(ch rune) bool {
- return strings.IndexRune("+-/0123456789.eE", ch) >= 0
-}
-
-// Scan is a support routine for fmt.Scanner. It accepts the formats
-// 'e', 'E', 'f', 'F', 'g', 'G', and 'v'. All formats are equivalent.
-func (z *Rat) Scan(s fmt.ScanState, ch rune) error {
- tok, err := s.Token(true, ratTok)
- if err != nil {
- return err
- }
- if strings.IndexRune("efgEFGv", ch) < 0 {
- return errors.New("Rat.Scan: invalid verb")
- }
- if _, ok := z.SetString(string(tok)); !ok {
- return errors.New("Rat.Scan: invalid syntax")
- }
- return nil
-}
-
-// SetString sets z to the value of s and returns z and a boolean indicating
-// success. s can be given as a fraction "a/b" or as a floating-point number
-// optionally followed by an exponent. If the operation failed, the value of
-// z is undefined but the returned value is nil.
-func (z *Rat) SetString(s string) (*Rat, bool) {
- if len(s) == 0 {
- return nil, false
- }
-
- // check for a quotient
- sep := strings.Index(s, "/")
- if sep >= 0 {
- if _, ok := z.a.SetString(s[0:sep], 10); !ok {
- return nil, false
- }
- s = s[sep+1:]
- var err error
- if z.b.abs, _, err = z.b.abs.scan(strings.NewReader(s), 10); err != nil {
- return nil, false
- }
- return z.norm(), true
- }
-
- // check for a decimal point
- sep = strings.Index(s, ".")
- // check for an exponent
- e := strings.IndexAny(s, "eE")
- var exp Int
- if e >= 0 {
- if e < sep {
- // The E must come after the decimal point.
- return nil, false
- }
- if _, ok := exp.SetString(s[e+1:], 10); !ok {
- return nil, false
- }
- s = s[0:e]
- }
- if sep >= 0 {
- s = s[0:sep] + s[sep+1:]
- exp.Sub(&exp, NewInt(int64(len(s)-sep)))
- }
-
- if _, ok := z.a.SetString(s, 10); !ok {
- return nil, false
- }
- powTen := nat(nil).expNN(natTen, exp.abs, nil)
- if exp.neg {
- z.b.abs = powTen
- z.norm()
- } else {
- z.a.abs = z.a.abs.mul(z.a.abs, powTen)
- z.b.abs = z.b.abs.make(0)
- }
-
- return z, true
-}
-
-// String returns a string representation of x in the form "a/b" (even if b == 1).
-func (x *Rat) String() string {
- s := "/1"
- if len(x.b.abs) != 0 {
- s = "/" + x.b.abs.decimalString()
- }
- return x.a.String() + s
-}
-
-// RatString returns a string representation of x in the form "a/b" if b != 1,
-// and in the form "a" if b == 1.
-func (x *Rat) RatString() string {
- if x.IsInt() {
- return x.a.String()
- }
- return x.String()
-}
-
-// FloatString returns a string representation of x in decimal form with prec
-// digits of precision after the decimal point and the last digit rounded.
-func (x *Rat) FloatString(prec int) string {
- if x.IsInt() {
- s := x.a.String()
- if prec > 0 {
- s += "." + strings.Repeat("0", prec)
- }
- return s
- }
- // x.b.abs != 0
-
- q, r := nat(nil).div(nat(nil), x.a.abs, x.b.abs)
-
- p := natOne
- if prec > 0 {
- p = nat(nil).expNN(natTen, nat(nil).setUint64(uint64(prec)), nil)
- }
-
- r = r.mul(r, p)
- r, r2 := r.div(nat(nil), r, x.b.abs)
-
- // see if we need to round up
- r2 = r2.add(r2, r2)
- if x.b.abs.cmp(r2) <= 0 {
- r = r.add(r, natOne)
- if r.cmp(p) >= 0 {
- q = nat(nil).add(q, natOne)
- r = nat(nil).sub(r, p)
- }
- }
-
- s := q.decimalString()
- if x.a.neg {
- s = "-" + s
- }
-
- if prec > 0 {
- rs := r.decimalString()
- leadingZeros := prec - len(rs)
- s += "." + strings.Repeat("0", leadingZeros) + rs
- }
-
- return s
-}
-
-// Gob codec version. Permits backward-compatible changes to the encoding.
-const ratGobVersion byte = 1
-
-// GobEncode implements the gob.GobEncoder interface.
-func (x *Rat) GobEncode() ([]byte, error) {
- if x == nil {
- return nil, nil
- }
- buf := make([]byte, 1+4+(len(x.a.abs)+len(x.b.abs))*_S) // extra bytes for version and sign bit (1), and numerator length (4)
- i := x.b.abs.bytes(buf)
- j := x.a.abs.bytes(buf[0:i])
- n := i - j
- if int(uint32(n)) != n {
- // this should never happen
- return nil, errors.New("Rat.GobEncode: numerator too large")
- }
- binary.BigEndian.PutUint32(buf[j-4:j], uint32(n))
- j -= 1 + 4
- b := ratGobVersion << 1 // make space for sign bit
- if x.a.neg {
- b |= 1
- }
- buf[j] = b
- return buf[j:], nil
-}
-
-// GobDecode implements the gob.GobDecoder interface.
-func (z *Rat) GobDecode(buf []byte) error {
- if len(buf) == 0 {
- // Other side sent a nil or default value.
- *z = Rat{}
- return nil
- }
- b := buf[0]
- if b>>1 != ratGobVersion {
- return errors.New(fmt.Sprintf("Rat.GobDecode: encoding version %d not supported", b>>1))
- }
- const j = 1 + 4
- i := j + binary.BigEndian.Uint32(buf[j-4:j])
- z.a.neg = b&1 != 0
- z.a.abs = z.a.abs.setBytes(buf[j:i])
- z.b.abs = z.b.abs.setBytes(buf[i:])
- return nil
-}
-
-// MarshalText implements the encoding.TextMarshaler interface
-func (r *Rat) MarshalText() (text []byte, err error) {
- return []byte(r.RatString()), nil
-}
-
-// UnmarshalText implements the encoding.TextUnmarshaler interface
-func (r *Rat) UnmarshalText(text []byte) error {
- if _, ok := r.SetString(string(text)); !ok {
- return fmt.Errorf("math/big: cannot unmarshal %q into a *big.Rat", text)
- }
- return nil
-}
diff --git a/src/pkg/math/big/rat_test.go b/src/pkg/math/big/rat_test.go
deleted file mode 100644
index 414a67d41..000000000
--- a/src/pkg/math/big/rat_test.go
+++ /dev/null
@@ -1,994 +0,0 @@
-// Copyright 2010 The Go Authors. All rights reserved.
-// Use of this source code is governed by a BSD-style
-// license that can be found in the LICENSE file.
-
-package big
-
-import (
- "bytes"
- "encoding/gob"
- "encoding/json"
- "encoding/xml"
- "fmt"
- "math"
- "strconv"
- "strings"
- "testing"
-)
-
-func TestZeroRat(t *testing.T) {
- var x, y, z Rat
- y.SetFrac64(0, 42)
-
- if x.Cmp(&y) != 0 {
- t.Errorf("x and y should be both equal and zero")
- }
-
- if s := x.String(); s != "0/1" {
- t.Errorf("got x = %s, want 0/1", s)
- }
-
- if s := x.RatString(); s != "0" {
- t.Errorf("got x = %s, want 0", s)
- }
-
- z.Add(&x, &y)
- if s := z.RatString(); s != "0" {
- t.Errorf("got x+y = %s, want 0", s)
- }
-
- z.Sub(&x, &y)
- if s := z.RatString(); s != "0" {
- t.Errorf("got x-y = %s, want 0", s)
- }
-
- z.Mul(&x, &y)
- if s := z.RatString(); s != "0" {
- t.Errorf("got x*y = %s, want 0", s)
- }
-
- // check for division by zero
- defer func() {
- if s := recover(); s == nil || s.(string) != "division by zero" {
- panic(s)
- }
- }()
- z.Quo(&x, &y)
-}
-
-var setStringTests = []struct {
- in, out string
- ok bool
-}{
- {"0", "0", true},
- {"-0", "0", true},
- {"1", "1", true},
- {"-1", "-1", true},
- {"1.", "1", true},
- {"1e0", "1", true},
- {"1.e1", "10", true},
- {in: "1e", ok: false},
- {in: "1.e", ok: false},
- {in: "1e+14e-5", ok: false},
- {in: "1e4.5", ok: false},
- {in: "r", ok: false},
- {in: "a/b", ok: false},
- {in: "a.b", ok: false},
- {"-0.1", "-1/10", true},
- {"-.1", "-1/10", true},
- {"2/4", "1/2", true},
- {".25", "1/4", true},
- {"-1/5", "-1/5", true},
- {"8129567.7690E14", "812956776900000000000", true},
- {"78189e+4", "781890000", true},
- {"553019.8935e+8", "55301989350000", true},
- {"98765432109876543210987654321e-10", "98765432109876543210987654321/10000000000", true},
- {"9877861857500000E-7", "3951144743/4", true},
- {"2169378.417e-3", "2169378417/1000000", true},
- {"884243222337379604041632732738665534", "884243222337379604041632732738665534", true},
- {"53/70893980658822810696", "53/70893980658822810696", true},
- {"106/141787961317645621392", "53/70893980658822810696", true},
- {"204211327800791583.81095", "4084226556015831676219/20000", true},
-}
-
-func TestRatSetString(t *testing.T) {
- for i, test := range setStringTests {
- x, ok := new(Rat).SetString(test.in)
-
- if ok {
- if !test.ok {
- t.Errorf("#%d SetString(%q) expected failure", i, test.in)
- } else if x.RatString() != test.out {
- t.Errorf("#%d SetString(%q) got %s want %s", i, test.in, x.RatString(), test.out)
- }
- } else if x != nil {
- t.Errorf("#%d SetString(%q) got %p want nil", i, test.in, x)
- }
- }
-}
-
-func TestRatScan(t *testing.T) {
- var buf bytes.Buffer
- for i, test := range setStringTests {
- x := new(Rat)
- buf.Reset()
- buf.WriteString(test.in)
-
- _, err := fmt.Fscanf(&buf, "%v", x)
- if err == nil != test.ok {
- if test.ok {
- t.Errorf("#%d error: %s", i, err)
- } else {
- t.Errorf("#%d expected error", i)
- }
- continue
- }
- if err == nil && x.RatString() != test.out {
- t.Errorf("#%d got %s want %s", i, x.RatString(), test.out)
- }
- }
-}
-
-var floatStringTests = []struct {
- in string
- prec int
- out string
-}{
- {"0", 0, "0"},
- {"0", 4, "0.0000"},
- {"1", 0, "1"},
- {"1", 2, "1.00"},
- {"-1", 0, "-1"},
- {".25", 2, "0.25"},
- {".25", 1, "0.3"},
- {".25", 3, "0.250"},
- {"-1/3", 3, "-0.333"},
- {"-2/3", 4, "-0.6667"},
- {"0.96", 1, "1.0"},
- {"0.999", 2, "1.00"},
- {"0.9", 0, "1"},
- {".25", -1, "0"},
- {".55", -1, "1"},
-}
-
-func TestFloatString(t *testing.T) {
- for i, test := range floatStringTests {
- x, _ := new(Rat).SetString(test.in)
-
- if x.FloatString(test.prec) != test.out {
- t.Errorf("#%d got %s want %s", i, x.FloatString(test.prec), test.out)
- }
- }
-}
-
-func TestRatSign(t *testing.T) {
- zero := NewRat(0, 1)
- for _, a := range setStringTests {
- x, ok := new(Rat).SetString(a.in)
- if !ok {
- continue
- }
- s := x.Sign()
- e := x.Cmp(zero)
- if s != e {
- t.Errorf("got %d; want %d for z = %v", s, e, &x)
- }
- }
-}
-
-var ratCmpTests = []struct {
- rat1, rat2 string
- out int
-}{
- {"0", "0/1", 0},
- {"1/1", "1", 0},
- {"-1", "-2/2", 0},
- {"1", "0", 1},
- {"0/1", "1/1", -1},
- {"-5/1434770811533343057144", "-5/1434770811533343057145", -1},
- {"49832350382626108453/8964749413", "49832350382626108454/8964749413", -1},
- {"-37414950961700930/7204075375675961", "37414950961700930/7204075375675961", -1},
- {"37414950961700930/7204075375675961", "74829901923401860/14408150751351922", 0},
-}
-
-func TestRatCmp(t *testing.T) {
- for i, test := range ratCmpTests {
- x, _ := new(Rat).SetString(test.rat1)
- y, _ := new(Rat).SetString(test.rat2)
-
- out := x.Cmp(y)
- if out != test.out {
- t.Errorf("#%d got out = %v; want %v", i, out, test.out)
- }
- }
-}
-
-func TestIsInt(t *testing.T) {
- one := NewInt(1)
- for _, a := range setStringTests {
- x, ok := new(Rat).SetString(a.in)
- if !ok {
- continue
- }
- i := x.IsInt()
- e := x.Denom().Cmp(one) == 0
- if i != e {
- t.Errorf("got IsInt(%v) == %v; want %v", x, i, e)
- }
- }
-}
-
-func TestRatAbs(t *testing.T) {
- zero := new(Rat)
- for _, a := range setStringTests {
- x, ok := new(Rat).SetString(a.in)
- if !ok {
- continue
- }
- e := new(Rat).Set(x)
- if e.Cmp(zero) < 0 {
- e.Sub(zero, e)
- }
- z := new(Rat).Abs(x)
- if z.Cmp(e) != 0 {
- t.Errorf("got Abs(%v) = %v; want %v", x, z, e)
- }
- }
-}
-
-func TestRatNeg(t *testing.T) {
- zero := new(Rat)
- for _, a := range setStringTests {
- x, ok := new(Rat).SetString(a.in)
- if !ok {
- continue
- }
- e := new(Rat).Sub(zero, x)
- z := new(Rat).Neg(x)
- if z.Cmp(e) != 0 {
- t.Errorf("got Neg(%v) = %v; want %v", x, z, e)
- }
- }
-}
-
-func TestRatInv(t *testing.T) {
- zero := new(Rat)
- for _, a := range setStringTests {
- x, ok := new(Rat).SetString(a.in)
- if !ok {
- continue
- }
- if x.Cmp(zero) == 0 {
- continue // avoid division by zero
- }
- e := new(Rat).SetFrac(x.Denom(), x.Num())
- z := new(Rat).Inv(x)
- if z.Cmp(e) != 0 {
- t.Errorf("got Inv(%v) = %v; want %v", x, z, e)
- }
- }
-}
-
-type ratBinFun func(z, x, y *Rat) *Rat
-type ratBinArg struct {
- x, y, z string
-}
-
-func testRatBin(t *testing.T, i int, name string, f ratBinFun, a ratBinArg) {
- x, _ := new(Rat).SetString(a.x)
- y, _ := new(Rat).SetString(a.y)
- z, _ := new(Rat).SetString(a.z)
- out := f(new(Rat), x, y)
-
- if out.Cmp(z) != 0 {
- t.Errorf("%s #%d got %s want %s", name, i, out, z)
- }
-}
-
-var ratBinTests = []struct {
- x, y string
- sum, prod string
-}{
- {"0", "0", "0", "0"},
- {"0", "1", "1", "0"},
- {"-1", "0", "-1", "0"},
- {"-1", "1", "0", "-1"},
- {"1", "1", "2", "1"},
- {"1/2", "1/2", "1", "1/4"},
- {"1/4", "1/3", "7/12", "1/12"},
- {"2/5", "-14/3", "-64/15", "-28/15"},
- {"4707/49292519774798173060", "-3367/70976135186689855734", "84058377121001851123459/1749296273614329067191168098769082663020", "-1760941/388732505247628681598037355282018369560"},
- {"-61204110018146728334/3", "-31052192278051565633/2", "-215564796870448153567/6", "950260896245257153059642991192710872711/3"},
- {"-854857841473707320655/4237645934602118692642972629634714039", "-18/31750379913563777419", "-27/133467566250814981", "15387441146526731771790/134546868362786310073779084329032722548987800600710485341"},
- {"618575745270541348005638912139/19198433543745179392300736", "-19948846211000086/637313996471", "27674141753240653/30123979153216", "-6169936206128396568797607742807090270137721977/6117715203873571641674006593837351328"},
- {"-3/26206484091896184128", "5/2848423294177090248", "15310893822118706237/9330894968229805033368778458685147968", "-5/24882386581946146755650075889827061248"},
- {"26946729/330400702820", "41563965/225583428284", "1238218672302860271/4658307703098666660055", "224002580204097/14906584649915733312176"},
- {"-8259900599013409474/7", "-84829337473700364773/56707961321161574960", "-468402123685491748914621885145127724451/396955729248131024720", "350340947706464153265156004876107029701/198477864624065512360"},
- {"575775209696864/1320203974639986246357", "29/712593081308", "410331716733912717985762465/940768218243776489278275419794956", "808/45524274987585732633"},
- {"1786597389946320496771/2066653520653241", "6269770/1992362624741777", "3559549865190272133656109052308126637/4117523232840525481453983149257", "8967230/3296219033"},
- {"-36459180403360509753/32150500941194292113930", "9381566963714/9633539", "301622077145533298008420642898530153/309723104686531919656937098270", "-3784609207827/3426986245"},
-}
-
-func TestRatBin(t *testing.T) {
- for i, test := range ratBinTests {
- arg := ratBinArg{test.x, test.y, test.sum}
- testRatBin(t, i, "Add", (*Rat).Add, arg)
-
- arg = ratBinArg{test.y, test.x, test.sum}
- testRatBin(t, i, "Add symmetric", (*Rat).Add, arg)
-
- arg = ratBinArg{test.sum, test.x, test.y}
- testRatBin(t, i, "Sub", (*Rat).Sub, arg)
-
- arg = ratBinArg{test.sum, test.y, test.x}
- testRatBin(t, i, "Sub symmetric", (*Rat).Sub, arg)
-
- arg = ratBinArg{test.x, test.y, test.prod}
- testRatBin(t, i, "Mul", (*Rat).Mul, arg)
-
- arg = ratBinArg{test.y, test.x, test.prod}
- testRatBin(t, i, "Mul symmetric", (*Rat).Mul, arg)
-
- if test.x != "0" {
- arg = ratBinArg{test.prod, test.x, test.y}
- testRatBin(t, i, "Quo", (*Rat).Quo, arg)
- }
-
- if test.y != "0" {
- arg = ratBinArg{test.prod, test.y, test.x}
- testRatBin(t, i, "Quo symmetric", (*Rat).Quo, arg)
- }
- }
-}
-
-func TestIssue820(t *testing.T) {
- x := NewRat(3, 1)
- y := NewRat(2, 1)
- z := y.Quo(x, y)
- q := NewRat(3, 2)
- if z.Cmp(q) != 0 {
- t.Errorf("got %s want %s", z, q)
- }
-
- y = NewRat(3, 1)
- x = NewRat(2, 1)
- z = y.Quo(x, y)
- q = NewRat(2, 3)
- if z.Cmp(q) != 0 {
- t.Errorf("got %s want %s", z, q)
- }
-
- x = NewRat(3, 1)
- z = x.Quo(x, x)
- q = NewRat(3, 3)
- if z.Cmp(q) != 0 {
- t.Errorf("got %s want %s", z, q)
- }
-}
-
-var setFrac64Tests = []struct {
- a, b int64
- out string
-}{
- {0, 1, "0"},
- {0, -1, "0"},
- {1, 1, "1"},
- {-1, 1, "-1"},
- {1, -1, "-1"},
- {-1, -1, "1"},
- {-9223372036854775808, -9223372036854775808, "1"},
-}
-
-func TestRatSetFrac64Rat(t *testing.T) {
- for i, test := range setFrac64Tests {
- x := new(Rat).SetFrac64(test.a, test.b)
- if x.RatString() != test.out {
- t.Errorf("#%d got %s want %s", i, x.RatString(), test.out)
- }
- }
-}
-
-func TestRatGobEncoding(t *testing.T) {
- var medium bytes.Buffer
- enc := gob.NewEncoder(&medium)
- dec := gob.NewDecoder(&medium)
- for _, test := range encodingTests {
- medium.Reset() // empty buffer for each test case (in case of failures)
- var tx Rat
- tx.SetString(test + ".14159265")
- if err := enc.Encode(&tx); err != nil {
- t.Errorf("encoding of %s failed: %s", &tx, err)
- }
- var rx Rat
- if err := dec.Decode(&rx); err != nil {
- t.Errorf("decoding of %s failed: %s", &tx, err)
- }
- if rx.Cmp(&tx) != 0 {
- t.Errorf("transmission of %s failed: got %s want %s", &tx, &rx, &tx)
- }
- }
-}
-
-// Sending a nil Rat pointer (inside a slice) on a round trip through gob should yield a zero.
-// TODO: top-level nils.
-func TestGobEncodingNilRatInSlice(t *testing.T) {
- buf := new(bytes.Buffer)
- enc := gob.NewEncoder(buf)
- dec := gob.NewDecoder(buf)
-
- var in = make([]*Rat, 1)
- err := enc.Encode(&in)
- if err != nil {
- t.Errorf("gob encode failed: %q", err)
- }
- var out []*Rat
- err = dec.Decode(&out)
- if err != nil {
- t.Fatalf("gob decode failed: %q", err)
- }
- if len(out) != 1 {
- t.Fatalf("wrong len; want 1 got %d", len(out))
- }
- var zero Rat
- if out[0].Cmp(&zero) != 0 {
- t.Errorf("transmission of (*Int)(nill) failed: got %s want 0", out)
- }
-}
-
-var ratNums = []string{
- "-141592653589793238462643383279502884197169399375105820974944592307816406286",
- "-1415926535897932384626433832795028841971",
- "-141592653589793",
- "-1",
- "0",
- "1",
- "141592653589793",
- "1415926535897932384626433832795028841971",
- "141592653589793238462643383279502884197169399375105820974944592307816406286",
-}
-
-var ratDenoms = []string{
- "1",
- "718281828459045",
- "7182818284590452353602874713526624977572",
- "718281828459045235360287471352662497757247093699959574966967627724076630353",
-}
-
-func TestRatJSONEncoding(t *testing.T) {
- for _, num := range ratNums {
- for _, denom := range ratDenoms {
- var tx Rat
- tx.SetString(num + "/" + denom)
- b, err := json.Marshal(&tx)
- if err != nil {
- t.Errorf("marshaling of %s failed: %s", &tx, err)
- continue
- }
- var rx Rat
- if err := json.Unmarshal(b, &rx); err != nil {
- t.Errorf("unmarshaling of %s failed: %s", &tx, err)
- continue
- }
- if rx.Cmp(&tx) != 0 {
- t.Errorf("JSON encoding of %s failed: got %s want %s", &tx, &rx, &tx)
- }
- }
- }
-}
-
-func TestRatXMLEncoding(t *testing.T) {
- for _, num := range ratNums {
- for _, denom := range ratDenoms {
- var tx Rat
- tx.SetString(num + "/" + denom)
- b, err := xml.Marshal(&tx)
- if err != nil {
- t.Errorf("marshaling of %s failed: %s", &tx, err)
- continue
- }
- var rx Rat
- if err := xml.Unmarshal(b, &rx); err != nil {
- t.Errorf("unmarshaling of %s failed: %s", &tx, err)
- continue
- }
- if rx.Cmp(&tx) != 0 {
- t.Errorf("XML encoding of %s failed: got %s want %s", &tx, &rx, &tx)
- }
- }
- }
-}
-
-func TestIssue2379(t *testing.T) {
- // 1) no aliasing
- q := NewRat(3, 2)
- x := new(Rat)
- x.SetFrac(NewInt(3), NewInt(2))
- if x.Cmp(q) != 0 {
- t.Errorf("1) got %s want %s", x, q)
- }
-
- // 2) aliasing of numerator
- x = NewRat(2, 3)
- x.SetFrac(NewInt(3), x.Num())
- if x.Cmp(q) != 0 {
- t.Errorf("2) got %s want %s", x, q)
- }
-
- // 3) aliasing of denominator
- x = NewRat(2, 3)
- x.SetFrac(x.Denom(), NewInt(2))
- if x.Cmp(q) != 0 {
- t.Errorf("3) got %s want %s", x, q)
- }
-
- // 4) aliasing of numerator and denominator
- x = NewRat(2, 3)
- x.SetFrac(x.Denom(), x.Num())
- if x.Cmp(q) != 0 {
- t.Errorf("4) got %s want %s", x, q)
- }
-
- // 5) numerator and denominator are the same
- q = NewRat(1, 1)
- x = new(Rat)
- n := NewInt(7)
- x.SetFrac(n, n)
- if x.Cmp(q) != 0 {
- t.Errorf("5) got %s want %s", x, q)
- }
-}
-
-func TestIssue3521(t *testing.T) {
- a := new(Int)
- b := new(Int)
- a.SetString("64375784358435883458348587", 0)
- b.SetString("4789759874531", 0)
-
- // 0) a raw zero value has 1 as denominator
- zero := new(Rat)
- one := NewInt(1)
- if zero.Denom().Cmp(one) != 0 {
- t.Errorf("0) got %s want %s", zero.Denom(), one)
- }
-
- // 1a) a zero value remains zero independent of denominator
- x := new(Rat)
- x.Denom().Set(new(Int).Neg(b))
- if x.Cmp(zero) != 0 {
- t.Errorf("1a) got %s want %s", x, zero)
- }
-
- // 1b) a zero value may have a denominator != 0 and != 1
- x.Num().Set(a)
- qab := new(Rat).SetFrac(a, b)
- if x.Cmp(qab) != 0 {
- t.Errorf("1b) got %s want %s", x, qab)
- }
-
- // 2a) an integral value becomes a fraction depending on denominator
- x.SetFrac64(10, 2)
- x.Denom().SetInt64(3)
- q53 := NewRat(5, 3)
- if x.Cmp(q53) != 0 {
- t.Errorf("2a) got %s want %s", x, q53)
- }
-
- // 2b) an integral value becomes a fraction depending on denominator
- x = NewRat(10, 2)
- x.Denom().SetInt64(3)
- if x.Cmp(q53) != 0 {
- t.Errorf("2b) got %s want %s", x, q53)
- }
-
- // 3) changing the numerator/denominator of a Rat changes the Rat
- x.SetFrac(a, b)
- a = x.Num()
- b = x.Denom()
- a.SetInt64(5)
- b.SetInt64(3)
- if x.Cmp(q53) != 0 {
- t.Errorf("3) got %s want %s", x, q53)
- }
-}
-
-// Test inputs to Rat.SetString. The prefix "long:" causes the test
-// to be skipped in --test.short mode. (The threshold is about 500us.)
-var float64inputs = []string{
- // Constants plundered from strconv/testfp.txt.
-
- // Table 1: Stress Inputs for Conversion to 53-bit Binary, < 1/2 ULP
- "5e+125",
- "69e+267",
- "999e-026",
- "7861e-034",
- "75569e-254",
- "928609e-261",
- "9210917e+080",
- "84863171e+114",
- "653777767e+273",
- "5232604057e-298",
- "27235667517e-109",
- "653532977297e-123",
- "3142213164987e-294",
- "46202199371337e-072",
- "231010996856685e-073",
- "9324754620109615e+212",
- "78459735791271921e+049",
- "272104041512242479e+200",
- "6802601037806061975e+198",
- "20505426358836677347e-221",
- "836168422905420598437e-234",
- "4891559871276714924261e+222",
-
- // Table 2: Stress Inputs for Conversion to 53-bit Binary, > 1/2 ULP
- "9e-265",
- "85e-037",
- "623e+100",
- "3571e+263",
- "81661e+153",
- "920657e-023",
- "4603285e-024",
- "87575437e-309",
- "245540327e+122",
- "6138508175e+120",
- "83356057653e+193",
- "619534293513e+124",
- "2335141086879e+218",
- "36167929443327e-159",
- "609610927149051e-255",
- "3743626360493413e-165",
- "94080055902682397e-242",
- "899810892172646163e+283",
- "7120190517612959703e+120",
- "25188282901709339043e-252",
- "308984926168550152811e-052",
- "6372891218502368041059e+064",
-
- // Table 14: Stress Inputs for Conversion to 24-bit Binary, <1/2 ULP
- "5e-20",
- "67e+14",
- "985e+15",
- "7693e-42",
- "55895e-16",
- "996622e-44",
- "7038531e-32",
- "60419369e-46",
- "702990899e-20",
- "6930161142e-48",
- "25933168707e+13",
- "596428896559e+20",
-
- // Table 15: Stress Inputs for Conversion to 24-bit Binary, >1/2 ULP
- "3e-23",
- "57e+18",
- "789e-35",
- "2539e-18",
- "76173e+28",
- "887745e-11",
- "5382571e-37",
- "82381273e-35",
- "750486563e-38",
- "3752432815e-39",
- "75224575729e-45",
- "459926601011e+15",
-
- // Constants plundered from strconv/atof_test.go.
-
- "0",
- "1",
- "+1",
- "1e23",
- "1E23",
- "100000000000000000000000",
- "1e-100",
- "123456700",
- "99999999999999974834176",
- "100000000000000000000001",
- "100000000000000008388608",
- "100000000000000016777215",
- "100000000000000016777216",
- "-1",
- "-0.1",
- "-0", // NB: exception made for this input
- "1e-20",
- "625e-3",
-
- // largest float64
- "1.7976931348623157e308",
- "-1.7976931348623157e308",
- // next float64 - too large
- "1.7976931348623159e308",
- "-1.7976931348623159e308",
- // the border is ...158079
- // borderline - okay
- "1.7976931348623158e308",
- "-1.7976931348623158e308",
- // borderline - too large
- "1.797693134862315808e308",
- "-1.797693134862315808e308",
-
- // a little too large
- "1e308",
- "2e308",
- "1e309",
-
- // way too large
- "1e310",
- "-1e310",
- "1e400",
- "-1e400",
- "long:1e400000",
- "long:-1e400000",
-
- // denormalized
- "1e-305",
- "1e-306",
- "1e-307",
- "1e-308",
- "1e-309",
- "1e-310",
- "1e-322",
- // smallest denormal
- "5e-324",
- "4e-324",
- "3e-324",
- // too small
- "2e-324",
- // way too small
- "1e-350",
- "long:1e-400000",
- // way too small, negative
- "-1e-350",
- "long:-1e-400000",
-
- // try to overflow exponent
- // [Disabled: too slow and memory-hungry with rationals.]
- // "1e-4294967296",
- // "1e+4294967296",
- // "1e-18446744073709551616",
- // "1e+18446744073709551616",
-
- // http://www.exploringbinary.com/java-hangs-when-converting-2-2250738585072012e-308/
- "2.2250738585072012e-308",
- // http://www.exploringbinary.com/php-hangs-on-numeric-value-2-2250738585072011e-308/
-
- "2.2250738585072011e-308",
-
- // A very large number (initially wrongly parsed by the fast algorithm).
- "4.630813248087435e+307",
-
- // A different kind of very large number.
- "22.222222222222222",
- "long:2." + strings.Repeat("2", 4000) + "e+1",
-
- // Exactly halfway between 1 and math.Nextafter(1, 2).
- // Round to even (down).
- "1.00000000000000011102230246251565404236316680908203125",
- // Slightly lower; still round down.
- "1.00000000000000011102230246251565404236316680908203124",
- // Slightly higher; round up.
- "1.00000000000000011102230246251565404236316680908203126",
- // Slightly higher, but you have to read all the way to the end.
- "long:1.00000000000000011102230246251565404236316680908203125" + strings.Repeat("0", 10000) + "1",
-
- // Smallest denormal, 2^(-1022-52)
- "4.940656458412465441765687928682213723651e-324",
- // Half of smallest denormal, 2^(-1022-53)
- "2.470328229206232720882843964341106861825e-324",
- // A little more than the exact half of smallest denormal
- // 2^-1075 + 2^-1100. (Rounds to 1p-1074.)
- "2.470328302827751011111470718709768633275e-324",
- // The exact halfway between smallest normal and largest denormal:
- // 2^-1022 - 2^-1075. (Rounds to 2^-1022.)
- "2.225073858507201136057409796709131975935e-308",
-
- "1152921504606846975", // 1<<60 - 1
- "-1152921504606846975", // -(1<<60 - 1)
- "1152921504606846977", // 1<<60 + 1
- "-1152921504606846977", // -(1<<60 + 1)
-
- "1/3",
-}
-
-func TestFloat64SpecialCases(t *testing.T) {
- for _, input := range float64inputs {
- if strings.HasPrefix(input, "long:") {
- if testing.Short() {
- continue
- }
- input = input[len("long:"):]
- }
-
- r, ok := new(Rat).SetString(input)
- if !ok {
- t.Errorf("Rat.SetString(%q) failed", input)
- continue
- }
- f, exact := r.Float64()
-
- // 1. Check string -> Rat -> float64 conversions are
- // consistent with strconv.ParseFloat.
- // Skip this check if the input uses "a/b" rational syntax.
- if !strings.Contains(input, "/") {
- e, _ := strconv.ParseFloat(input, 64)
-
- // Careful: negative Rats too small for
- // float64 become -0, but Rat obviously cannot
- // preserve the sign from SetString("-0").
- switch {
- case math.Float64bits(e) == math.Float64bits(f):
- // Ok: bitwise equal.
- case f == 0 && r.Num().BitLen() == 0:
- // Ok: Rat(0) is equivalent to both +/- float64(0).
- default:
- t.Errorf("strconv.ParseFloat(%q) = %g (%b), want %g (%b); delta = %g", input, e, e, f, f, f-e)
- }
- }
-
- if !isFinite(f) {
- continue
- }
-
- // 2. Check f is best approximation to r.
- if !checkIsBestApprox(t, f, r) {
- // Append context information.
- t.Errorf("(input was %q)", input)
- }
-
- // 3. Check f->R->f roundtrip is non-lossy.
- checkNonLossyRoundtrip(t, f)
-
- // 4. Check exactness using slow algorithm.
- if wasExact := new(Rat).SetFloat64(f).Cmp(r) == 0; wasExact != exact {
- t.Errorf("Rat.SetString(%q).Float64().exact = %t, want %t", input, exact, wasExact)
- }
- }
-}
-
-func TestFloat64Distribution(t *testing.T) {
- // Generate a distribution of (sign, mantissa, exp) values
- // broader than the float64 range, and check Rat.Float64()
- // always picks the closest float64 approximation.
- var add = []int64{
- 0,
- 1,
- 3,
- 5,
- 7,
- 9,
- 11,
- }
- var winc, einc = uint64(1), int(1) // soak test (~75s on x86-64)
- if testing.Short() {
- winc, einc = 10, 500 // quick test (~12ms on x86-64)
- }
-
- for _, sign := range "+-" {
- for _, a := range add {
- for wid := uint64(0); wid < 60; wid += winc {
- b := int64(1<<wid + a)
- if sign == '-' {
- b = -b
- }
- for exp := -1100; exp < 1100; exp += einc {
- num, den := NewInt(b), NewInt(1)
- if exp > 0 {
- num.Lsh(num, uint(exp))
- } else {
- den.Lsh(den, uint(-exp))
- }
- r := new(Rat).SetFrac(num, den)
- f, _ := r.Float64()
-
- if !checkIsBestApprox(t, f, r) {
- // Append context information.
- t.Errorf("(input was mantissa %#x, exp %d; f = %g (%b); f ~ %g; r = %v)",
- b, exp, f, f, math.Ldexp(float64(b), exp), r)
- }
-
- checkNonLossyRoundtrip(t, f)
- }
- }
- }
- }
-}
-
-// TestFloat64NonFinite checks that SetFloat64 of a non-finite value
-// returns nil.
-func TestSetFloat64NonFinite(t *testing.T) {
- for _, f := range []float64{math.NaN(), math.Inf(+1), math.Inf(-1)} {
- var r Rat
- if r2 := r.SetFloat64(f); r2 != nil {
- t.Errorf("SetFloat64(%g) was %v, want nil", f, r2)
- }
- }
-}
-
-// checkNonLossyRoundtrip checks that a float->Rat->float roundtrip is
-// non-lossy for finite f.
-func checkNonLossyRoundtrip(t *testing.T, f float64) {
- if !isFinite(f) {
- return
- }
- r := new(Rat).SetFloat64(f)
- if r == nil {
- t.Errorf("Rat.SetFloat64(%g (%b)) == nil", f, f)
- return
- }
- f2, exact := r.Float64()
- if f != f2 || !exact {
- t.Errorf("Rat.SetFloat64(%g).Float64() = %g (%b), %v, want %g (%b), %v; delta = %b",
- f, f2, f2, exact, f, f, true, f2-f)
- }
-}
-
-// delta returns the absolute difference between r and f.
-func delta(r *Rat, f float64) *Rat {
- d := new(Rat).Sub(r, new(Rat).SetFloat64(f))
- return d.Abs(d)
-}
-
-// checkIsBestApprox checks that f is the best possible float64
-// approximation of r.
-// Returns true on success.
-func checkIsBestApprox(t *testing.T, f float64, r *Rat) bool {
- if math.Abs(f) >= math.MaxFloat64 {
- // Cannot check +Inf, -Inf, nor the float next to them (MaxFloat64).
- // But we have tests for these special cases.
- return true
- }
-
- // r must be strictly between f0 and f1, the floats bracketing f.
- f0 := math.Nextafter(f, math.Inf(-1))
- f1 := math.Nextafter(f, math.Inf(+1))
-
- // For f to be correct, r must be closer to f than to f0 or f1.
- df := delta(r, f)
- df0 := delta(r, f0)
- df1 := delta(r, f1)
- if df.Cmp(df0) > 0 {
- t.Errorf("Rat(%v).Float64() = %g (%b), but previous float64 %g (%b) is closer", r, f, f, f0, f0)
- return false
- }
- if df.Cmp(df1) > 0 {
- t.Errorf("Rat(%v).Float64() = %g (%b), but next float64 %g (%b) is closer", r, f, f, f1, f1)
- return false
- }
- if df.Cmp(df0) == 0 && !isEven(f) {
- t.Errorf("Rat(%v).Float64() = %g (%b); halfway should have rounded to %g (%b) instead", r, f, f, f0, f0)
- return false
- }
- if df.Cmp(df1) == 0 && !isEven(f) {
- t.Errorf("Rat(%v).Float64() = %g (%b); halfway should have rounded to %g (%b) instead", r, f, f, f1, f1)
- return false
- }
- return true
-}
-
-func isEven(f float64) bool { return math.Float64bits(f)&1 == 0 }
-
-func TestIsFinite(t *testing.T) {
- finites := []float64{
- 1.0 / 3,
- 4891559871276714924261e+222,
- math.MaxFloat64,
- math.SmallestNonzeroFloat64,
- -math.MaxFloat64,
- -math.SmallestNonzeroFloat64,
- }
- for _, f := range finites {
- if !isFinite(f) {
- t.Errorf("!IsFinite(%g (%b))", f, f)
- }
- }
- nonfinites := []float64{
- math.NaN(),
- math.Inf(-1),
- math.Inf(+1),
- }
- for _, f := range nonfinites {
- if isFinite(f) {
- t.Errorf("IsFinite(%g, (%b))", f, f)
- }
- }
-}
generated by cgit v1.2.3 (git 2.39.1) at 2025-07-07 19:59:40 +0000