1102 lines
26 KiB
Go
1102 lines
26 KiB
Go
// Copyright 2009 The Go Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package big
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import (
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"bytes"
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"encoding/hex"
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"fmt"
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"gob"
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"testing"
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"testing/quick"
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)
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func isNormalized(x *Int) bool {
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if len(x.abs) == 0 {
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return !x.neg
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}
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// len(x.abs) > 0
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return x.abs[len(x.abs)-1] != 0
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}
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type funZZ func(z, x, y *Int) *Int
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type argZZ struct {
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z, x, y *Int
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}
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var sumZZ = []argZZ{
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{NewInt(0), NewInt(0), NewInt(0)},
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{NewInt(1), NewInt(1), NewInt(0)},
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{NewInt(1111111110), NewInt(123456789), NewInt(987654321)},
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{NewInt(-1), NewInt(-1), NewInt(0)},
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{NewInt(864197532), NewInt(-123456789), NewInt(987654321)},
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{NewInt(-1111111110), NewInt(-123456789), NewInt(-987654321)},
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}
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var prodZZ = []argZZ{
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{NewInt(0), NewInt(0), NewInt(0)},
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{NewInt(0), NewInt(1), NewInt(0)},
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{NewInt(1), NewInt(1), NewInt(1)},
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{NewInt(-991 * 991), NewInt(991), NewInt(-991)},
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// TODO(gri) add larger products
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}
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func TestSignZ(t *testing.T) {
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var zero Int
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for _, a := range sumZZ {
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s := a.z.Sign()
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e := a.z.Cmp(&zero)
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if s != e {
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t.Errorf("got %d; want %d for z = %v", s, e, a.z)
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}
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}
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}
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func TestSetZ(t *testing.T) {
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for _, a := range sumZZ {
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var z Int
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z.Set(a.z)
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if !isNormalized(&z) {
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t.Errorf("%v is not normalized", z)
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}
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if (&z).Cmp(a.z) != 0 {
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t.Errorf("got z = %v; want %v", z, a.z)
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}
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}
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}
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func TestAbsZ(t *testing.T) {
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var zero Int
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for _, a := range sumZZ {
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var z Int
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z.Abs(a.z)
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var e Int
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e.Set(a.z)
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if e.Cmp(&zero) < 0 {
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e.Sub(&zero, &e)
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}
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if z.Cmp(&e) != 0 {
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t.Errorf("got z = %v; want %v", z, e)
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}
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}
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}
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func testFunZZ(t *testing.T, msg string, f funZZ, a argZZ) {
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var z Int
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f(&z, a.x, a.y)
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if !isNormalized(&z) {
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t.Errorf("%s%v is not normalized", z, msg)
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}
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if (&z).Cmp(a.z) != 0 {
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t.Errorf("%s%+v\n\tgot z = %v; want %v", msg, a, &z, a.z)
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}
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}
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func TestSumZZ(t *testing.T) {
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AddZZ := func(z, x, y *Int) *Int { return z.Add(x, y) }
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SubZZ := func(z, x, y *Int) *Int { return z.Sub(x, y) }
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for _, a := range sumZZ {
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arg := a
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testFunZZ(t, "AddZZ", AddZZ, arg)
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arg = argZZ{a.z, a.y, a.x}
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testFunZZ(t, "AddZZ symmetric", AddZZ, arg)
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arg = argZZ{a.x, a.z, a.y}
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testFunZZ(t, "SubZZ", SubZZ, arg)
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arg = argZZ{a.y, a.z, a.x}
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testFunZZ(t, "SubZZ symmetric", SubZZ, arg)
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}
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}
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func TestProdZZ(t *testing.T) {
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MulZZ := func(z, x, y *Int) *Int { return z.Mul(x, y) }
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for _, a := range prodZZ {
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arg := a
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testFunZZ(t, "MulZZ", MulZZ, arg)
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arg = argZZ{a.z, a.y, a.x}
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testFunZZ(t, "MulZZ symmetric", MulZZ, arg)
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}
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}
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// mulBytes returns x*y via grade school multiplication. Both inputs
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// and the result are assumed to be in big-endian representation (to
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// match the semantics of Int.Bytes and Int.SetBytes).
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func mulBytes(x, y []byte) []byte {
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z := make([]byte, len(x)+len(y))
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// multiply
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k0 := len(z) - 1
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for j := len(y) - 1; j >= 0; j-- {
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d := int(y[j])
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if d != 0 {
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k := k0
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carry := 0
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for i := len(x) - 1; i >= 0; i-- {
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t := int(z[k]) + int(x[i])*d + carry
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z[k], carry = byte(t), t>>8
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k--
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}
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z[k] = byte(carry)
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}
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k0--
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}
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// normalize (remove leading 0's)
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i := 0
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for i < len(z) && z[i] == 0 {
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i++
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}
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return z[i:]
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}
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func checkMul(a, b []byte) bool {
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var x, y, z1 Int
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x.SetBytes(a)
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y.SetBytes(b)
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z1.Mul(&x, &y)
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var z2 Int
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z2.SetBytes(mulBytes(a, b))
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return z1.Cmp(&z2) == 0
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}
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func TestMul(t *testing.T) {
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if err := quick.Check(checkMul, nil); err != nil {
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t.Error(err)
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}
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}
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var mulRangesZ = []struct {
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a, b int64
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prod string
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}{
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// entirely positive ranges are covered by mulRangesN
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{-1, 1, "0"},
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{-2, -1, "2"},
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{-3, -2, "6"},
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{-3, -1, "-6"},
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{1, 3, "6"},
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{-10, -10, "-10"},
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{0, -1, "1"}, // empty range
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{-1, -100, "1"}, // empty range
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{-1, 1, "0"}, // range includes 0
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{-1e9, 0, "0"}, // range includes 0
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{-1e9, 1e9, "0"}, // range includes 0
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{-10, -1, "3628800"}, // 10!
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{-20, -2, "-2432902008176640000"}, // -20!
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{-99, -1,
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"-933262154439441526816992388562667004907159682643816214685929" +
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"638952175999932299156089414639761565182862536979208272237582" +
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"511852109168640000000000000000000000", // -99!
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},
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}
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func TestMulRangeZ(t *testing.T) {
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var tmp Int
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// test entirely positive ranges
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for i, r := range mulRangesN {
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prod := tmp.MulRange(int64(r.a), int64(r.b)).String()
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if prod != r.prod {
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t.Errorf("#%da: got %s; want %s", i, prod, r.prod)
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}
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}
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// test other ranges
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for i, r := range mulRangesZ {
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prod := tmp.MulRange(r.a, r.b).String()
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if prod != r.prod {
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t.Errorf("#%db: got %s; want %s", i, prod, r.prod)
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}
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}
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}
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var stringTests = []struct {
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in string
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out string
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base int
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val int64
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ok bool
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}{
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{in: "", ok: false},
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{in: "a", ok: false},
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{in: "z", ok: false},
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{in: "+", ok: false},
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{in: "-", ok: false},
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{in: "0b", ok: false},
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{in: "0x", ok: false},
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{in: "2", base: 2, ok: false},
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{in: "0b2", base: 0, ok: false},
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{in: "08", ok: false},
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{in: "8", base: 8, ok: false},
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{in: "0xg", base: 0, ok: false},
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{in: "g", base: 16, ok: false},
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{"0", "0", 0, 0, true},
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{"0", "0", 10, 0, true},
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{"0", "0", 16, 0, true},
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{"+0", "0", 0, 0, true},
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{"-0", "0", 0, 0, true},
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{"10", "10", 0, 10, true},
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{"10", "10", 10, 10, true},
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{"10", "10", 16, 16, true},
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{"-10", "-10", 16, -16, true},
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{"+10", "10", 16, 16, true},
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{"0x10", "16", 0, 16, true},
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{in: "0x10", base: 16, ok: false},
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{"-0x10", "-16", 0, -16, true},
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{"+0x10", "16", 0, 16, true},
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{"00", "0", 0, 0, true},
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{"0", "0", 8, 0, true},
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{"07", "7", 0, 7, true},
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{"7", "7", 8, 7, true},
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{"023", "19", 0, 19, true},
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{"23", "23", 8, 19, true},
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{"cafebabe", "cafebabe", 16, 0xcafebabe, true},
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{"0b0", "0", 0, 0, true},
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{"-111", "-111", 2, -7, true},
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{"-0b111", "-7", 0, -7, true},
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{"0b1001010111", "599", 0, 0x257, true},
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{"1001010111", "1001010111", 2, 0x257, true},
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}
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func format(base int) string {
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switch base {
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case 2:
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return "%b"
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case 8:
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return "%o"
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case 16:
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return "%x"
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}
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return "%d"
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}
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func TestGetString(t *testing.T) {
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z := new(Int)
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for i, test := range stringTests {
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if !test.ok {
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continue
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}
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z.SetInt64(test.val)
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if test.base == 10 {
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s := z.String()
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if s != test.out {
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t.Errorf("#%da got %s; want %s", i, s, test.out)
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}
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}
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s := fmt.Sprintf(format(test.base), z)
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if s != test.out {
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t.Errorf("#%db got %s; want %s", i, s, test.out)
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}
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}
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}
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func TestSetString(t *testing.T) {
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tmp := new(Int)
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for i, test := range stringTests {
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n1, ok1 := new(Int).SetString(test.in, test.base)
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n2, ok2 := tmp.SetString(test.in, test.base)
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expected := NewInt(test.val)
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if ok1 != test.ok || ok2 != test.ok {
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t.Errorf("#%d (input '%s') ok incorrect (should be %t)", i, test.in, test.ok)
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continue
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}
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if !ok1 || !ok2 {
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continue
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}
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if ok1 && !isNormalized(n1) {
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t.Errorf("#%d (input '%s'): %v is not normalized", i, test.in, *n1)
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}
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if ok2 && !isNormalized(n2) {
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t.Errorf("#%d (input '%s'): %v is not normalized", i, test.in, *n2)
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}
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if n1.Cmp(expected) != 0 {
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t.Errorf("#%d (input '%s') got: %s want: %d", i, test.in, n1, test.val)
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}
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if n2.Cmp(expected) != 0 {
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t.Errorf("#%d (input '%s') got: %s want: %d", i, test.in, n2, test.val)
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}
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}
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}
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// Examples from the Go Language Spec, section "Arithmetic operators"
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var divisionSignsTests = []struct {
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x, y int64
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q, r int64 // T-division
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d, m int64 // Euclidian division
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}{
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{5, 3, 1, 2, 1, 2},
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{-5, 3, -1, -2, -2, 1},
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{5, -3, -1, 2, -1, 2},
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{-5, -3, 1, -2, 2, 1},
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{1, 2, 0, 1, 0, 1},
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{8, 4, 2, 0, 2, 0},
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}
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func TestDivisionSigns(t *testing.T) {
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for i, test := range divisionSignsTests {
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x := NewInt(test.x)
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y := NewInt(test.y)
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q := NewInt(test.q)
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r := NewInt(test.r)
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d := NewInt(test.d)
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m := NewInt(test.m)
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q1 := new(Int).Quo(x, y)
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r1 := new(Int).Rem(x, y)
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if !isNormalized(q1) {
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t.Errorf("#%d Quo: %v is not normalized", i, *q1)
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}
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if !isNormalized(r1) {
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t.Errorf("#%d Rem: %v is not normalized", i, *r1)
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}
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if q1.Cmp(q) != 0 || r1.Cmp(r) != 0 {
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t.Errorf("#%d QuoRem: got (%s, %s), want (%s, %s)", i, q1, r1, q, r)
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}
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q2, r2 := new(Int).QuoRem(x, y, new(Int))
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if !isNormalized(q2) {
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t.Errorf("#%d Quo: %v is not normalized", i, *q2)
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}
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if !isNormalized(r2) {
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t.Errorf("#%d Rem: %v is not normalized", i, *r2)
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}
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if q2.Cmp(q) != 0 || r2.Cmp(r) != 0 {
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t.Errorf("#%d QuoRem: got (%s, %s), want (%s, %s)", i, q2, r2, q, r)
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}
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d1 := new(Int).Div(x, y)
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m1 := new(Int).Mod(x, y)
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if !isNormalized(d1) {
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t.Errorf("#%d Div: %v is not normalized", i, *d1)
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}
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if !isNormalized(m1) {
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t.Errorf("#%d Mod: %v is not normalized", i, *m1)
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}
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if d1.Cmp(d) != 0 || m1.Cmp(m) != 0 {
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t.Errorf("#%d DivMod: got (%s, %s), want (%s, %s)", i, d1, m1, d, m)
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}
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d2, m2 := new(Int).DivMod(x, y, new(Int))
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if !isNormalized(d2) {
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t.Errorf("#%d Div: %v is not normalized", i, *d2)
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}
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if !isNormalized(m2) {
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t.Errorf("#%d Mod: %v is not normalized", i, *m2)
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}
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if d2.Cmp(d) != 0 || m2.Cmp(m) != 0 {
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t.Errorf("#%d DivMod: got (%s, %s), want (%s, %s)", i, d2, m2, d, m)
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}
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}
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}
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func checkSetBytes(b []byte) bool {
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hex1 := hex.EncodeToString(new(Int).SetBytes(b).Bytes())
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hex2 := hex.EncodeToString(b)
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for len(hex1) < len(hex2) {
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hex1 = "0" + hex1
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}
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for len(hex1) > len(hex2) {
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hex2 = "0" + hex2
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}
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return hex1 == hex2
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}
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func TestSetBytes(t *testing.T) {
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if err := quick.Check(checkSetBytes, nil); err != nil {
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t.Error(err)
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}
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}
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func checkBytes(b []byte) bool {
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b2 := new(Int).SetBytes(b).Bytes()
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return bytes.Compare(b, b2) == 0
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}
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func TestBytes(t *testing.T) {
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if err := quick.Check(checkSetBytes, nil); err != nil {
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t.Error(err)
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}
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}
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func checkQuo(x, y []byte) bool {
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u := new(Int).SetBytes(x)
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v := new(Int).SetBytes(y)
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if len(v.abs) == 0 {
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return true
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}
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r := new(Int)
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q, r := new(Int).QuoRem(u, v, r)
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if r.Cmp(v) >= 0 {
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return false
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}
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uprime := new(Int).Set(q)
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uprime.Mul(uprime, v)
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uprime.Add(uprime, r)
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return uprime.Cmp(u) == 0
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}
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var quoTests = []struct {
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x, y string
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q, r string
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}{
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{
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"476217953993950760840509444250624797097991362735329973741718102894495832294430498335824897858659711275234906400899559094370964723884706254265559534144986498357",
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"9353930466774385905609975137998169297361893554149986716853295022578535724979483772383667534691121982974895531435241089241440253066816724367338287092081996",
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"50911",
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"1",
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},
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{
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"11510768301994997771168",
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"1328165573307167369775",
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"8",
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"885443715537658812968",
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},
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}
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func TestQuo(t *testing.T) {
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if err := quick.Check(checkQuo, nil); err != nil {
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t.Error(err)
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}
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for i, test := range quoTests {
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x, _ := new(Int).SetString(test.x, 10)
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y, _ := new(Int).SetString(test.y, 10)
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expectedQ, _ := new(Int).SetString(test.q, 10)
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expectedR, _ := new(Int).SetString(test.r, 10)
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|
|
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
|
|
}{
|
|
{"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"},
|
|
{
|
|
"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
|
|
}
|
|
|
|
z := y.Exp(x, y, m)
|
|
if !isNormalized(z) {
|
|
t.Errorf("#%d: %v is not normalized", i, *z)
|
|
}
|
|
if z.Cmp(out) != 0 {
|
|
t.Errorf("#%d: got %s want %s", i, z, out)
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
func checkGcd(aBytes, bBytes []byte) bool {
|
|
a := new(Int).SetBytes(aBytes)
|
|
b := new(Int).SetBytes(bBytes)
|
|
|
|
x := new(Int)
|
|
y := new(Int)
|
|
d := new(Int)
|
|
|
|
GcdInt(d, x, y, a, b)
|
|
x.Mul(x, a)
|
|
y.Mul(y, b)
|
|
x.Add(x, y)
|
|
|
|
return x.Cmp(d) == 0
|
|
}
|
|
|
|
|
|
var gcdTests = []struct {
|
|
a, b int64
|
|
d, x, y int64
|
|
}{
|
|
{120, 23, 1, -9, 47},
|
|
}
|
|
|
|
|
|
func TestGcd(t *testing.T) {
|
|
for i, test := range gcdTests {
|
|
a := NewInt(test.a)
|
|
b := NewInt(test.b)
|
|
|
|
x := new(Int)
|
|
y := new(Int)
|
|
d := new(Int)
|
|
|
|
expectedX := NewInt(test.x)
|
|
expectedY := NewInt(test.y)
|
|
expectedD := NewInt(test.d)
|
|
|
|
GcdInt(d, x, y, a, b)
|
|
|
|
if expectedX.Cmp(x) != 0 ||
|
|
expectedY.Cmp(y) != 0 ||
|
|
expectedD.Cmp(d) != 0 {
|
|
t.Errorf("#%d got (%s %s %s) want (%s %s %s)", i, x, y, d, expectedX, expectedY, expectedD)
|
|
}
|
|
}
|
|
|
|
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 !ProbablyPrime(p, 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 ProbablyPrime(c, 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 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 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 gobEncodingTests = []string{
|
|
"0",
|
|
"1",
|
|
"2",
|
|
"10",
|
|
"42",
|
|
"1234567890",
|
|
"298472983472983471903246121093472394872319615612417471234712061",
|
|
}
|
|
|
|
func TestGobEncoding(t *testing.T) {
|
|
var medium bytes.Buffer
|
|
enc := gob.NewEncoder(&medium)
|
|
dec := gob.NewDecoder(&medium)
|
|
for i, test := range gobEncodingTests {
|
|
for j := 0; j < 2; j++ {
|
|
medium.Reset() // empty buffer for each test case (in case of failures)
|
|
stest := test
|
|
if j == 0 {
|
|
stest = "-" + test
|
|
}
|
|
var tx Int
|
|
tx.SetString(stest, 10)
|
|
if err := enc.Encode(&tx); err != nil {
|
|
t.Errorf("#%d%c: encoding failed: %s", i, 'a'+j, err)
|
|
}
|
|
var rx Int
|
|
if err := dec.Decode(&rx); err != nil {
|
|
t.Errorf("#%d%c: decoding failed: %s", i, 'a'+j, err)
|
|
}
|
|
if rx.Cmp(&tx) != 0 {
|
|
t.Errorf("#%d%c: transmission failed: got %s want %s", i, 'a'+j, &rx, &tx)
|
|
}
|
|
}
|
|
}
|
|
}
|