src/math/big/nat_test.go

// 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])
			}
		})
	}
}