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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 (
"fmt"
"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, false)
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 := string(nat(nil).mulRange(r.a, r.b).utoa(10))
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 TestNLZ(t *testing.T) {
var x Word = _B >> 1
for i := 0; i <= _W; i++ {
if int(nlz(x)) != i {
t.Errorf("failed at %x: got %d want %d", x, nlz(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
}
}
}
}
func BenchmarkZeroShifts(b *testing.B) {
x := rndNat(800)
b.Run("Shl", func(b *testing.B) {
for i := 0; i < b.N; i++ {
var z nat
z.shl(x, 0)
}
})
b.Run("ShlSame", func(b *testing.B) {
for i := 0; i < b.N; i++ {
x.shl(x, 0)
}
})
b.Run("Shr", func(b *testing.B) {
for i := 0; i < b.N; i++ {
var z nat
z.shr(x, 0)
}
})
b.Run("ShrSame", func(b *testing.B) {
for i := 0; i < b.N; i++ {
x.shr(x, 0)
}
})
}
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)
}
}
var montgomeryTests = []struct {
x, y, m string
k0 uint64
out32, out64 string
}{
{
"0xffffffffffffffffffffffffffffffffffffffffffffffffe",
"0xffffffffffffffffffffffffffffffffffffffffffffffffe",
"0xfffffffffffffffffffffffffffffffffffffffffffffffff",
1,
"0x1000000000000000000000000000000000000000000",
"0x10000000000000000000000000000000000",
},
{
"0x000000000ffffff5",
"0x000000000ffffff0",
"0x0000000010000001",
0xff0000000fffffff,
"0x000000000bfffff4",
"0x0000000003400001",
},
{
"0x0000000080000000",
"0x00000000ffffffff",
"0x1000000000000001",
0xfffffffffffffff,
"0x0800000008000001",
"0x0800000008000001",
},
{
"0x0000000080000000",
"0x0000000080000000",
"0xffffffff00000001",
0xfffffffeffffffff,
"0xbfffffff40000001",
"0xbfffffff40000001",
},
{
"0x0000000080000000",
"0x0000000080000000",
"0x00ffffff00000001",
0xfffffeffffffff,
"0xbfffff40000001",
"0xbfffff40000001",
},
{
"0x0000000080000000",
"0x0000000080000000",
"0x0000ffff00000001",
0xfffeffffffff,
"0xbfff40000001",
"0xbfff40000001",
},
{
"0x3321ffffffffffffffffffffffffffff00000000000022222623333333332bbbb888c0",
"0x3321ffffffffffffffffffffffffffff00000000000022222623333333332bbbb888c0",
"0x33377fffffffffffffffffffffffffffffffffffffffffffff0000000000022222eee1",
0xdecc8f1249812adf,
"0x04eb0e11d72329dc0915f86784820fc403275bf2f6620a20e0dd344c5cd0875e50deb5",
"0x0d7144739a7d8e11d72329dc0915f86784820fc403275bf2f61ed96f35dd34dbb3d6a0",
},
{
"0x10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffffffffffff00000000000022222223333333333444444444",
"0x10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffffffffffffffffffffff999999999999999aaabbbbbbbbcccccccccccc",
"0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff33377fffffffffffffffffffffffffffffffffffffffffffff0000000000022222eee1",
0xdecc8f1249812adf,
"0x5c0d52f451aec609b15da8e5e5626c4eaa88723bdeac9d25ca9b961269400410ca208a16af9c2fb07d7a11c7772cba02c22f9711078d51a3797eb18e691295293284d988e349fa6deba46b25a4ecd9f715",
"0x92fcad4b5c0d52f451aec609b15da8e5e5626c4eaa88723bdeac9d25ca9b961269400410ca208a16af9c2fb07d799c32fe2f3cc5422f9711078d51a3797eb18e691295293284d8f5e69caf6decddfe1df6",
},
}
func TestMontgomery(t *testing.T) {
one := NewInt(1)
_B := new(Int).Lsh(one, _W)
for i, test := range montgomeryTests {
x := natFromString(test.x)
y := natFromString(test.y)
m := natFromString(test.m)
for len(x) < len(m) {
x = append(x, 0)
}
for len(y) < len(m) {
y = append(y, 0)
}
if x.cmp(m) > 0 {
_, r := nat(nil).div(nil, x, m)
t.Errorf("#%d: x > m (0x%s > 0x%s; use 0x%s)", i, x.utoa(16), m.utoa(16), r.utoa(16))
}
if y.cmp(m) > 0 {
_, r := nat(nil).div(nil, x, m)
t.Errorf("#%d: y > m (0x%s > 0x%s; use 0x%s)", i, y.utoa(16), m.utoa(16), r.utoa(16))
}
var out nat
if _W == 32 {
out = natFromString(test.out32)
} else {
out = natFromString(test.out64)
}
// t.Logf("#%d: len=%d\n", i, len(m))
// check output in table
xi := &Int{abs: x}
yi := &Int{abs: y}
mi := &Int{abs: m}
p := new(Int).Mod(new(Int).Mul(xi, new(Int).Mul(yi, new(Int).ModInverse(new(Int).Lsh(one, uint(len(m))*_W), mi))), mi)
if out.cmp(p.abs.norm()) != 0 {
t.Errorf("#%d: out in table=0x%s, computed=0x%s", i, out.utoa(16), p.abs.norm().utoa(16))
}
// check k0 in table
k := new(Int).Mod(&Int{abs: m}, _B)
k = new(Int).Sub(_B, k)
k = new(Int).Mod(k, _B)
k0 := Word(new(Int).ModInverse(k, _B).Uint64())
if k0 != Word(test.k0) {
t.Errorf("#%d: k0 in table=%#x, computed=%#x\n", i, test.k0, k0)
}
// check montgomery with correct k0 produces correct output
z := nat(nil).montgomery(x, y, m, k0, len(m))
z = z.norm()
if z.cmp(out) != 0 {
t.Errorf("#%d: got 0x%s want 0x%s", i, z.utoa(16), out.utoa(16))
}
}
}
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",
},
{
"11521922904531591643048817447554701904414021819823889996244743037378330903763518501116638828335352811871131385129455853417360623007349090150042001944696604737499160174391019030572483602867266711107136838523916077674888297896995042968746762200926853379",
"426343618817810911523",
"444747819283133684179",
"42",
},
}
func TestExpNN(t *testing.T) {
for i, test := range expNNTests {
x := natFromString(test.x)
y := natFromString(test.y)
out := natFromString(test.out)
var m nat
if len(test.m) > 0 {
m = natFromString(test.m)
}
z := nat(nil).expNN(x, y, m)
if z.cmp(out) != 0 {
t.Errorf("#%d got %s want %s", i, z.utoa(10), out.utoa(10))
}
}
}
func BenchmarkExp3Power(b *testing.B) {
const x = 3
for _, y := range []Word{
0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000,
} {
b.Run(fmt.Sprintf("%#x", y), func(b *testing.B) {
var z nat
for i := 0; i < b.N; i++ {
z.expWW(x, y)
}
})
}
}
func fibo(n int) nat {
switch n {
case 0:
return nil
case 1:
return nat{1}
}
f0 := fibo(0)
f1 := fibo(1)
var f2 nat
for i := 1; i < n; i++ {
f2 = f2.add(f0, f1)
f0, f1, f2 = f1, f2, f0
}
return f1
}
var fiboNums = []string{
"0",
"55",
"6765",
"832040",
"102334155",
"12586269025",
"1548008755920",
"190392490709135",
"23416728348467685",
"2880067194370816120",
"354224848179261915075",
}
func TestFibo(t *testing.T) {
for i, want := range fiboNums {
n := i * 10
got := string(fibo(n).utoa(10))
if got != want {
t.Errorf("fibo(%d) failed: got %s want %s", n, got, want)
}
}
}
func BenchmarkFibo(b *testing.B) {
for i := 0; i < b.N; i++ {
fibo(1e0)
fibo(1e1)
fibo(1e2)
fibo(1e3)
fibo(1e4)
fibo(1e5)
}
}
var bitTests = []struct {
x string
i uint
want uint
}{
{"0", 0, 0},
{"0", 1, 0},
{"0", 1000, 0},
{"0x1", 0, 1},
{"0x10", 0, 0},
{"0x10", 3, 0},
{"0x10", 4, 1},
{"0x10", 5, 0},
{"0x8000000000000000", 62, 0},
{"0x8000000000000000", 63, 1},
{"0x8000000000000000", 64, 0},
{"0x3" + strings.Repeat("0", 32), 127, 0},
{"0x3" + strings.Repeat("0", 32), 128, 1},
{"0x3" + strings.Repeat("0", 32), 129, 1},
{"0x3" + strings.Repeat("0", 32), 130, 0},
}
func TestBit(t *testing.T) {
for i, test := range bitTests {
x := natFromString(test.x)
if got := x.bit(test.i); got != test.want {
t.Errorf("#%d: %s.bit(%d) = %v; want %v", i, test.x, test.i, got, test.want)
}
}
}
var stickyTests = []struct {
x string
i uint
want uint
}{
{"0", 0, 0},
{"0", 1, 0},
{"0", 1000, 0},
{"0x1", 0, 0},
{"0x1", 1, 1},
{"0x1350", 0, 0},
{"0x1350", 4, 0},
{"0x1350", 5, 1},
{"0x8000000000000000", 63, 0},
{"0x8000000000000000", 64, 1},
{"0x1" + strings.Repeat("0", 100), 400, 0},
{"0x1" + strings.Repeat("0", 100), 401, 1},
}
func TestSticky(t *testing.T) {
for i, test := range stickyTests {
x := natFromString(test.x)
if got := x.sticky(test.i); got != test.want {
t.Errorf("#%d: %s.sticky(%d) = %v; want %v", i, test.x, test.i, got, test.want)
}
if test.want == 1 {
// all subsequent i's should also return 1
for d := uint(1); d <= 3; d++ {
if got := x.sticky(test.i + d); got != 1 {
t.Errorf("#%d: %s.sticky(%d) = %v; want %v", i, test.x, test.i+d, got, 1)
}
}
}
}
}
func testSqr(t *testing.T, x nat) {
got := make(nat, 2*len(x))
want := make(nat, 2*len(x))
got = got.sqr(x)
want = want.mul(x, x)
if got.cmp(want) != 0 {
t.Errorf("basicSqr(%v), got %v, want %v", x, got, want)
}
}
func TestSqr(t *testing.T) {
for _, a := range prodNN {
if a.x != nil {
testSqr(t, a.x)
}
if a.y != nil {
testSqr(t, a.y)
}
if a.z != nil {
testSqr(t, a.z)
}
}
}
func benchmarkNatSqr(b *testing.B, nwords int) {
x := rndNat(nwords)
var z nat
b.ResetTimer()
for i := 0; i < b.N; i++ {
z.sqr(x)
}
}
var sqrBenchSizes = []int{1, 2, 3, 5, 8, 10, 20, 30, 50, 80, 100, 200, 300, 500, 800, 1000}
func BenchmarkNatSqr(b *testing.B) {
for _, n := range sqrBenchSizes {
if isRaceBuilder && n > 1e3 {
continue
}
b.Run(fmt.Sprintf("%d", n), func(b *testing.B) {
benchmarkNatSqr(b, n)
})
}
}
func BenchmarkNatSetBytes(b *testing.B) {
const maxLength = 128
lengths := []int{
// No remainder:
8, 24, maxLength,
// With remainder:
7, 23, maxLength - 1,
}
n := make(nat, maxLength/_W) // ensure n doesn't need to grow during the test
buf := make([]byte, maxLength)
for _, l := range lengths {
b.Run(fmt.Sprint(l), func(b *testing.B) {
for i := 0; i < b.N; i++ {
n.setBytes(buf[:l])
}
})
}
}