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Retro68/gcc/libgo/go/math/big/int_test.go
Wolfgang Thaller 449227a01f upgrade to gcc 4.9.1
2014-09-21 19:33:12 +02:00

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// 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"
"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
}{
{"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)
}
}
}
func TestIssue2607(t *testing.T) {
// This code sequence used to hang.
n := NewInt(10)
n.Rand(rand.New(rand.NewSource(9)), n)
}
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