github.com/bgentry/go@v0.0.0-20150121062915-6cf5a733d54d/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 (
	"io"
	"runtime"
	"strings"
	"testing"
)

var cmpTests = []struct {
	x, y nat
	r    int
}{
	{nil, nil, 0},
	{nil, nat(nil), 0},
	{nat(nil), nil, 0},
	{nat(nil), nat(nil), 0},
	{nat{0}, nat{0}, 0},
	{nat{0}, nat{1}, -1},
	{nat{1}, nat{0}, 1},
	{nat{1}, nat{1}, 0},
	{nat{0, _M}, nat{1}, 1},
	{nat{1}, nat{0, _M}, -1},
	{nat{1, _M}, nat{0, _M}, 1},
	{nat{0, _M}, nat{1, _M}, -1},
	{nat{16, 571956, 8794, 68}, nat{837, 9146, 1, 754489}, -1},
	{nat{34986, 41, 105, 1957}, nat{56, 7458, 104, 1957}, 1},
}

func TestCmp(t *testing.T) {
	for i, a := range cmpTests {
		r := a.x.cmp(a.y)
		if r != a.r {
			t.Errorf("#%d got r = %v; want %v", i, r, a.r)
		}
	}
}

type funNN func(z, x, y nat) nat
type argNN struct {
	z, x, y nat
}

var sumNN = []argNN{
	{},
	{nat{1}, nil, nat{1}},
	{nat{1111111110}, nat{123456789}, nat{987654321}},
	{nat{0, 0, 0, 1}, nil, nat{0, 0, 0, 1}},
	{nat{0, 0, 0, 1111111110}, nat{0, 0, 0, 123456789}, nat{0, 0, 0, 987654321}},
	{nat{0, 0, 0, 1}, nat{0, 0, _M}, nat{0, 0, 1}},
}

var prodNN = []argNN{
	{},
	{nil, nil, nil},
	{nil, nat{991}, nil},
	{nat{991}, nat{991}, nat{1}},
	{nat{991 * 991}, nat{991}, nat{991}},
	{nat{0, 0, 991 * 991}, nat{0, 991}, nat{0, 991}},
	{nat{1 * 991, 2 * 991, 3 * 991, 4 * 991}, nat{1, 2, 3, 4}, nat{991}},
	{nat{4, 11, 20, 30, 20, 11, 4}, nat{1, 2, 3, 4}, nat{4, 3, 2, 1}},
	// 3^100 * 3^28 = 3^128
	{
		natFromString("11790184577738583171520872861412518665678211592275841109096961"),
		natFromString("515377520732011331036461129765621272702107522001"),
		natFromString("22876792454961"),
	},
	// z = 111....1 (70000 digits)
	// x = 10^(99*700) + ... + 10^1400 + 10^700 + 1
	// y = 111....1 (700 digits, larger than Karatsuba threshold on 32-bit and 64-bit)
	{
		natFromString(strings.Repeat("1", 70000)),
		natFromString("1" + strings.Repeat(strings.Repeat("0", 699)+"1", 99)),
		natFromString(strings.Repeat("1", 700)),
	},
	// z = 111....1 (20000 digits)
	// x = 10^10000 + 1
	// y = 111....1 (10000 digits)
	{
		natFromString(strings.Repeat("1", 20000)),
		natFromString("1" + strings.Repeat("0", 9999) + "1"),
		natFromString(strings.Repeat("1", 10000)),
	},
}

func natFromString(s string) nat {
	x, _, _, err := nat(nil).scan(strings.NewReader(s), 0)
	if err != nil {
		panic(err)
	}
	return x
}

func TestSet(t *testing.T) {
	for _, a := range sumNN {
		z := nat(nil).set(a.z)
		if z.cmp(a.z) != 0 {
			t.Errorf("got z = %v; want %v", z, a.z)
		}
	}
}

func testFunNN(t *testing.T, msg string, f funNN, a argNN) {
	z := f(nil, a.x, a.y)
	if z.cmp(a.z) != 0 {
		t.Errorf("%s%+v\n\tgot z = %v; want %v", msg, a, z, a.z)
	}
}

func TestFunNN(t *testing.T) {
	for _, a := range sumNN {
		arg := a
		testFunNN(t, "add", nat.add, arg)

		arg = argNN{a.z, a.y, a.x}
		testFunNN(t, "add symmetric", nat.add, arg)

		arg = argNN{a.x, a.z, a.y}
		testFunNN(t, "sub", nat.sub, arg)

		arg = argNN{a.y, a.z, a.x}
		testFunNN(t, "sub symmetric", nat.sub, arg)
	}

	for _, a := range prodNN {
		arg := a
		testFunNN(t, "mul", nat.mul, arg)

		arg = argNN{a.z, a.y, a.x}
		testFunNN(t, "mul symmetric", nat.mul, arg)
	}
}

var mulRangesN = []struct {
	a, b uint64
	prod string
}{
	{0, 0, "0"},
	{1, 1, "1"},
	{1, 2, "2"},
	{1, 3, "6"},
	{10, 10, "10"},
	{0, 100, "0"},
	{0, 1e9, "0"},
	{1, 0, "1"},                    // empty range
	{100, 1, "1"},                  // empty range
	{1, 10, "3628800"},             // 10!
	{1, 20, "2432902008176640000"}, // 20!
	{1, 100,
		"933262154439441526816992388562667004907159682643816214685929" +
			"638952175999932299156089414639761565182862536979208272237582" +
			"51185210916864000000000000000000000000", // 100!
	},
}

func TestMulRangeN(t *testing.T) {
	for i, r := range mulRangesN {
		prod := nat(nil).mulRange(r.a, r.b).decimalString()
		if prod != r.prod {
			t.Errorf("#%d: got %s; want %s", i, prod, r.prod)
		}
	}
}

// allocBytes returns the number of bytes allocated by invoking f.
func allocBytes(f func()) uint64 {
	var stats runtime.MemStats
	runtime.ReadMemStats(&stats)
	t := stats.TotalAlloc
	f()
	runtime.ReadMemStats(&stats)
	return stats.TotalAlloc - t
}

// TestMulUnbalanced tests that multiplying numbers of different lengths
// does not cause deep recursion and in turn allocate too much memory.
// Test case for issue 3807.
func TestMulUnbalanced(t *testing.T) {
	defer runtime.GOMAXPROCS(runtime.GOMAXPROCS(1))
	x := rndNat(50000)
	y := rndNat(40)
	allocSize := allocBytes(func() {
		nat(nil).mul(x, y)
	})
	inputSize := uint64(len(x)+len(y)) * _S
	if ratio := allocSize / uint64(inputSize); ratio > 10 {
		t.Errorf("multiplication uses too much memory (%d > %d times the size of inputs)", allocSize, ratio)
	}
}

func rndNat(n int) nat {
	return nat(rndV(n)).norm()
}

func BenchmarkMul(b *testing.B) {
	mulx := rndNat(1e4)
	muly := rndNat(1e4)
	b.ResetTimer()
	for i := 0; i < b.N; i++ {
		var z nat
		z.mul(mulx, muly)
	}
}

func toString(x nat, charset string) string {
	base := len(charset)

	// special cases
	switch {
	case base < 2:
		panic("illegal base")
	case len(x) == 0:
		return string(charset[0])
	}

	// allocate buffer for conversion
	i := x.bitLen()/log2(Word(base)) + 1 // +1: round up
	s := make([]byte, i)

	// don't destroy x
	q := nat(nil).set(x)

	// convert
	for len(q) > 0 {
		i--
		var r Word
		q, r = q.divW(q, Word(base))
		s[i] = charset[r]
	}

	return string(s[i:])
}

var strTests = []struct {
	x nat    // nat value to be converted
	c string // conversion charset
	s string // expected result
}{
	{nil, "01", "0"},
	{nat{1}, "01", "1"},
	{nat{0xc5}, "01", "11000101"},
	{nat{03271}, lowercaseDigits[:8], "3271"},
	{nat{10}, lowercaseDigits[:10], "10"},
	{nat{1234567890}, uppercaseDigits[:10], "1234567890"},
	{nat{0xdeadbeef}, lowercaseDigits[:16], "deadbeef"},
	{nat{0xdeadbeef}, uppercaseDigits[:16], "DEADBEEF"},
	{nat{0x229be7}, lowercaseDigits[:17], "1a2b3c"},
	{nat{0x309663e6}, uppercaseDigits[:32], "O9COV6"},
}

func TestString(t *testing.T) {
	// test invalid character set explicitly
	var panicStr string
	func() {
		defer func() {
			panicStr = recover().(string)
		}()
		natOne.string("0")
	}()
	if panicStr != "invalid character set length" {
		t.Errorf("expected panic for invalid character set")
	}

	for _, a := range strTests {
		s := a.x.string(a.c)
		if s != a.s {
			t.Errorf("string%+v\n\tgot s = %s; want %s", a, s, a.s)
		}

		x, b, _, err := nat(nil).scan(strings.NewReader(a.s), len(a.c))
		if x.cmp(a.x) != 0 {
			t.Errorf("scan%+v\n\tgot z = %v; want %v", a, x, a.x)
		}
		if b != len(a.c) {
			t.Errorf("scan%+v\n\tgot b = %d; want %d", a, b, len(a.c))
		}
		if err != nil {
			t.Errorf("scan%+v\n\tgot error = %s", a, err)
		}
	}
}

var natScanTests = []struct {
	s     string // string to be scanned
	base  int    // input base
	x     nat    // expected nat
	b     int    // expected base
	count int    // expected digit count
	ok    bool   // expected success
	next  rune   // next character (or 0, if at EOF)
}{
	// error: illegal base
	{base: -1},
	{base: 37},

	// error: no mantissa
	{},
	{s: "?"},
	{base: 10},
	{base: 36},
	{s: "?", base: 10},
	{s: "0x"},
	{s: "345", base: 2},

	// error: incorrect use of decimal point
	{s: ".0"},
	{s: ".0", base: 10},
	{s: ".", base: 1},
	{s: "0x.0"},

	// no errors
	{"0", 0, nil, 10, 1, true, 0},
	{"0", 10, nil, 10, 1, true, 0},
	{"0", 36, nil, 36, 1, true, 0},
	{"1", 0, nat{1}, 10, 1, true, 0},
	{"1", 10, nat{1}, 10, 1, true, 0},
	{"0 ", 0, nil, 10, 1, true, ' '},
	{"08", 0, nil, 10, 1, true, '8'},
	{"08", 10, nat{8}, 10, 2, true, 0},
	{"018", 0, nat{1}, 8, 1, true, '8'},
	{"0b1", 0, nat{1}, 2, 1, true, 0},
	{"0b11000101", 0, nat{0xc5}, 2, 8, true, 0},
	{"03271", 0, nat{03271}, 8, 4, true, 0},
	{"10ab", 0, nat{10}, 10, 2, true, 'a'},
	{"1234567890", 0, nat{1234567890}, 10, 10, true, 0},
	{"xyz", 36, nat{(33*36+34)*36 + 35}, 36, 3, true, 0},
	{"xyz?", 36, nat{(33*36+34)*36 + 35}, 36, 3, true, '?'},
	{"0x", 16, nil, 16, 1, true, 'x'},
	{"0xdeadbeef", 0, nat{0xdeadbeef}, 16, 8, true, 0},
	{"0XDEADBEEF", 0, nat{0xdeadbeef}, 16, 8, true, 0},

	// no errors, decimal point
	{"0.", 0, nil, 10, 1, true, '.'},
	{"0.", 1, nil, 10, 0, true, 0},
	{"0.1.2", 1, nat{1}, 10, -1, true, '.'},
	{".000", 1, nil, 10, -3, true, 0},
	{"12.3", 1, nat{123}, 10, -1, true, 0},
	{"012.345", 1, nat{12345}, 10, -3, true, 0},
}

func TestScanBase(t *testing.T) {
	for _, a := range natScanTests {
		r := strings.NewReader(a.s)
		x, b, count, err := nat(nil).scan(r, a.base)
		if err == nil && !a.ok {
			t.Errorf("scan%+v\n\texpected error", a)
		}
		if err != nil {
			if a.ok {
				t.Errorf("scan%+v\n\tgot error = %s", a, err)
			}
			continue
		}
		if x.cmp(a.x) != 0 {
			t.Errorf("scan%+v\n\tgot z = %v; want %v", a, x, a.x)
		}
		if b != a.b {
			t.Errorf("scan%+v\n\tgot b = %d; want %d", a, b, a.base)
		}
		if count != a.count {
			t.Errorf("scan%+v\n\tgot count = %d; want %d", a, count, a.count)
		}
		next, _, err := r.ReadRune()
		if err == io.EOF {
			next = 0
			err = nil
		}
		if err == nil && next != a.next {
			t.Errorf("scan%+v\n\tgot next = %q; want %q", a, next, a.next)
		}
	}
}

var pi = "3" +
	"14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651" +
	"32823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461" +
	"28475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920" +
	"96282925409171536436789259036001133053054882046652138414695194151160943305727036575959195309218611738193261179" +
	"31051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798" +
	"60943702770539217176293176752384674818467669405132000568127145263560827785771342757789609173637178721468440901" +
	"22495343014654958537105079227968925892354201995611212902196086403441815981362977477130996051870721134999999837" +
	"29780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083" +
	"81420617177669147303598253490428755468731159562863882353787593751957781857780532171226806613001927876611195909" +
	"21642019893809525720106548586327886593615338182796823030195203530185296899577362259941389124972177528347913151" +
	"55748572424541506959508295331168617278558890750983817546374649393192550604009277016711390098488240128583616035" +
	"63707660104710181942955596198946767837449448255379774726847104047534646208046684259069491293313677028989152104" +
	"75216205696602405803815019351125338243003558764024749647326391419927260426992279678235478163600934172164121992" +
	"45863150302861829745557067498385054945885869269956909272107975093029553211653449872027559602364806654991198818" +
	"34797753566369807426542527862551818417574672890977772793800081647060016145249192173217214772350141441973568548" +
	"16136115735255213347574184946843852332390739414333454776241686251898356948556209921922218427255025425688767179" +
	"04946016534668049886272327917860857843838279679766814541009538837863609506800642251252051173929848960841284886" +
	"26945604241965285022210661186306744278622039194945047123713786960956364371917287467764657573962413890865832645" +
	"99581339047802759009946576407895126946839835259570982582262052248940772671947826848260147699090264013639443745" +
	"53050682034962524517493996514314298091906592509372216964615157098583874105978859597729754989301617539284681382" +
	"68683868942774155991855925245953959431049972524680845987273644695848653836736222626099124608051243884390451244" +
	"13654976278079771569143599770012961608944169486855584840635342207222582848864815845602850601684273945226746767" +
	"88952521385225499546667278239864565961163548862305774564980355936345681743241125150760694794510965960940252288" +
	"79710893145669136867228748940560101503308617928680920874760917824938589009714909675985261365549781893129784821" +
	"68299894872265880485756401427047755513237964145152374623436454285844479526586782105114135473573952311342716610" +
	"21359695362314429524849371871101457654035902799344037420073105785390621983874478084784896833214457138687519435" +
	"06430218453191048481005370614680674919278191197939952061419663428754440643745123718192179998391015919561814675" +
	"14269123974894090718649423196156794520809514655022523160388193014209376213785595663893778708303906979207734672" +
	"21825625996615014215030680384477345492026054146659252014974428507325186660021324340881907104863317346496514539" +
	"05796268561005508106658796998163574736384052571459102897064140110971206280439039759515677157700420337869936007" +
	"23055876317635942187312514712053292819182618612586732157919841484882916447060957527069572209175671167229109816" +
	"90915280173506712748583222871835209353965725121083579151369882091444210067510334671103141267111369908658516398" +
	"31501970165151168517143765761835155650884909989859982387345528331635507647918535893226185489632132933089857064" +
	"20467525907091548141654985946163718027098199430992448895757128289059232332609729971208443357326548938239119325" +
	"97463667305836041428138830320382490375898524374417029132765618093773444030707469211201913020330380197621101100" +
	"44929321516084244485963766983895228684783123552658213144957685726243344189303968642624341077322697802807318915" +
	"44110104468232527162010526522721116603966655730925471105578537634668206531098965269186205647693125705863566201" +
	"85581007293606598764861179104533488503461136576867532494416680396265797877185560845529654126654085306143444318" +
	"58676975145661406800700237877659134401712749470420562230538994561314071127000407854733269939081454664645880797" +
	"27082668306343285878569830523580893306575740679545716377525420211495576158140025012622859413021647155097925923" +
	"09907965473761255176567513575178296664547791745011299614890304639947132962107340437518957359614589019389713111" +
	"79042978285647503203198691514028708085990480109412147221317947647772622414254854540332157185306142288137585043" +
	"06332175182979866223717215916077166925474873898665494945011465406284336639379003976926567214638530673609657120" +
	"91807638327166416274888800786925602902284721040317211860820419000422966171196377921337575114959501566049631862" +
	"94726547364252308177036751590673502350728354056704038674351362222477158915049530984448933309634087807693259939" +
	"78054193414473774418426312986080998886874132604721569516239658645730216315981931951673538129741677294786724229" +
	"24654366800980676928238280689964004824354037014163149658979409243237896907069779422362508221688957383798623001" +
	"59377647165122893578601588161755782973523344604281512627203734314653197777416031990665541876397929334419521541" +
	"34189948544473456738316249934191318148092777710386387734317720754565453220777092120190516609628049092636019759" +
	"88281613323166636528619326686336062735676303544776280350450777235547105859548702790814356240145171806246436267" +
	"94561275318134078330336254232783944975382437205835311477119926063813346776879695970309833913077109870408591337"

// Test case for BenchmarkScanPi.
func TestScanPi(t *testing.T) {
	var x nat
	z, _, _, err := x.scan(strings.NewReader(pi), 10)
	if err != nil {
		t.Errorf("scanning pi: %s", err)
	}
	if s := z.decimalString(); s != pi {
		t.Errorf("scanning pi: got %s", s)
	}
}

func TestScanPiParallel(t *testing.T) {
	const n = 2
	c := make(chan int)
	for i := 0; i < n; i++ {
		go func() {
			TestScanPi(t)
			c <- 0
		}()
	}
	for i := 0; i < n; i++ {
		<-c
	}
}

func BenchmarkScanPi(b *testing.B) {
	for i := 0; i < b.N; i++ {
		var x nat
		x.scan(strings.NewReader(pi), 10)
	}
}

func BenchmarkStringPiParallel(b *testing.B) {
	var x nat
	x, _, _, _ = x.scan(strings.NewReader(pi), 0)
	if x.decimalString() != pi {
		panic("benchmark incorrect: conversion failed")
	}
	b.RunParallel(func(pb *testing.PB) {
		for pb.Next() {
			x.decimalString()
		}
	})
}

func BenchmarkScan10Base2(b *testing.B)     { ScanHelper(b, 2, 10, 10) }
func BenchmarkScan100Base2(b *testing.B)    { ScanHelper(b, 2, 10, 100) }
func BenchmarkScan1000Base2(b *testing.B)   { ScanHelper(b, 2, 10, 1000) }
func BenchmarkScan10000Base2(b *testing.B)  { ScanHelper(b, 2, 10, 10000) }
func BenchmarkScan100000Base2(b *testing.B) { ScanHelper(b, 2, 10, 100000) }

func BenchmarkScan10Base8(b *testing.B)     { ScanHelper(b, 8, 10, 10) }
func BenchmarkScan100Base8(b *testing.B)    { ScanHelper(b, 8, 10, 100) }
func BenchmarkScan1000Base8(b *testing.B)   { ScanHelper(b, 8, 10, 1000) }
func BenchmarkScan10000Base8(b *testing.B)  { ScanHelper(b, 8, 10, 10000) }
func BenchmarkScan100000Base8(b *testing.B) { ScanHelper(b, 8, 10, 100000) }

func BenchmarkScan10Base10(b *testing.B)     { ScanHelper(b, 10, 10, 10) }
func BenchmarkScan100Base10(b *testing.B)    { ScanHelper(b, 10, 10, 100) }
func BenchmarkScan1000Base10(b *testing.B)   { ScanHelper(b, 10, 10, 1000) }
func BenchmarkScan10000Base10(b *testing.B)  { ScanHelper(b, 10, 10, 10000) }
func BenchmarkScan100000Base10(b *testing.B) { ScanHelper(b, 10, 10, 100000) }

func BenchmarkScan10Base16(b *testing.B)     { ScanHelper(b, 16, 10, 10) }
func BenchmarkScan100Base16(b *testing.B)    { ScanHelper(b, 16, 10, 100) }
func BenchmarkScan1000Base16(b *testing.B)   { ScanHelper(b, 16, 10, 1000) }
func BenchmarkScan10000Base16(b *testing.B)  { ScanHelper(b, 16, 10, 10000) }
func BenchmarkScan100000Base16(b *testing.B) { ScanHelper(b, 16, 10, 100000) }

func ScanHelper(b *testing.B, base int, x, y Word) {
	b.StopTimer()
	var z nat
	z = z.expWW(x, y)

	var s string
	s = z.string(lowercaseDigits[:base])
	if t := toString(z, lowercaseDigits[:base]); t != s {
		b.Fatalf("scanning: got %s; want %s", s, t)
	}
	b.StartTimer()

	for i := 0; i < b.N; i++ {
		z.scan(strings.NewReader(s), base)
	}
}

func BenchmarkString10Base2(b *testing.B)     { StringHelper(b, 2, 10, 10) }
func BenchmarkString100Base2(b *testing.B)    { StringHelper(b, 2, 10, 100) }
func BenchmarkString1000Base2(b *testing.B)   { StringHelper(b, 2, 10, 1000) }
func BenchmarkString10000Base2(b *testing.B)  { StringHelper(b, 2, 10, 10000) }
func BenchmarkString100000Base2(b *testing.B) { StringHelper(b, 2, 10, 100000) }

func BenchmarkString10Base8(b *testing.B)     { StringHelper(b, 8, 10, 10) }
func BenchmarkString100Base8(b *testing.B)    { StringHelper(b, 8, 10, 100) }
func BenchmarkString1000Base8(b *testing.B)   { StringHelper(b, 8, 10, 1000) }
func BenchmarkString10000Base8(b *testing.B)  { StringHelper(b, 8, 10, 10000) }
func BenchmarkString100000Base8(b *testing.B) { StringHelper(b, 8, 10, 100000) }

func BenchmarkString10Base10(b *testing.B)     { StringHelper(b, 10, 10, 10) }
func BenchmarkString100Base10(b *testing.B)    { StringHelper(b, 10, 10, 100) }
func BenchmarkString1000Base10(b *testing.B)   { StringHelper(b, 10, 10, 1000) }
func BenchmarkString10000Base10(b *testing.B)  { StringHelper(b, 10, 10, 10000) }
func BenchmarkString100000Base10(b *testing.B) { StringHelper(b, 10, 10, 100000) }

func BenchmarkString10Base16(b *testing.B)     { StringHelper(b, 16, 10, 10) }
func BenchmarkString100Base16(b *testing.B)    { StringHelper(b, 16, 10, 100) }
func BenchmarkString1000Base16(b *testing.B)   { StringHelper(b, 16, 10, 1000) }
func BenchmarkString10000Base16(b *testing.B)  { StringHelper(b, 16, 10, 10000) }
func BenchmarkString100000Base16(b *testing.B) { StringHelper(b, 16, 10, 100000) }

func StringHelper(b *testing.B, base int, x, y Word) {
	b.StopTimer()
	var z nat
	z = z.expWW(x, y)
	z.string(lowercaseDigits[:base]) // warm divisor cache
	b.StartTimer()

	for i := 0; i < b.N; i++ {
		_ = z.string(lowercaseDigits[:base])
	}
}

func BenchmarkLeafSize0(b *testing.B)  { LeafSizeHelper(b, 10, 0) } // test without splitting
func BenchmarkLeafSize1(b *testing.B)  { LeafSizeHelper(b, 10, 1) }
func BenchmarkLeafSize2(b *testing.B)  { LeafSizeHelper(b, 10, 2) }
func BenchmarkLeafSize3(b *testing.B)  { LeafSizeHelper(b, 10, 3) }
func BenchmarkLeafSize4(b *testing.B)  { LeafSizeHelper(b, 10, 4) }
func BenchmarkLeafSize5(b *testing.B)  { LeafSizeHelper(b, 10, 5) }
func BenchmarkLeafSize6(b *testing.B)  { LeafSizeHelper(b, 10, 6) }
func BenchmarkLeafSize7(b *testing.B)  { LeafSizeHelper(b, 10, 7) }
func BenchmarkLeafSize8(b *testing.B)  { LeafSizeHelper(b, 10, 8) }
func BenchmarkLeafSize9(b *testing.B)  { LeafSizeHelper(b, 10, 9) }
func BenchmarkLeafSize10(b *testing.B) { LeafSizeHelper(b, 10, 10) }
func BenchmarkLeafSize11(b *testing.B) { LeafSizeHelper(b, 10, 11) }
func BenchmarkLeafSize12(b *testing.B) { LeafSizeHelper(b, 10, 12) }
func BenchmarkLeafSize13(b *testing.B) { LeafSizeHelper(b, 10, 13) }
func BenchmarkLeafSize14(b *testing.B) { LeafSizeHelper(b, 10, 14) }
func BenchmarkLeafSize15(b *testing.B) { LeafSizeHelper(b, 10, 15) }
func BenchmarkLeafSize16(b *testing.B) { LeafSizeHelper(b, 10, 16) }
func BenchmarkLeafSize32(b *testing.B) { LeafSizeHelper(b, 10, 32) } // try some large lengths
func BenchmarkLeafSize64(b *testing.B) { LeafSizeHelper(b, 10, 64) }

func LeafSizeHelper(b *testing.B, base Word, size int) {
	b.StopTimer()
	originalLeafSize := leafSize
	resetTable(cacheBase10.table[:])
	leafSize = size
	b.StartTimer()

	for d := 1; d <= 10000; d *= 10 {
		b.StopTimer()
		var z nat
		z = z.expWW(base, Word(d))           // build target number
		_ = z.string(lowercaseDigits[:base]) // warm divisor cache
		b.StartTimer()

		for i := 0; i < b.N; i++ {
			_ = z.string(lowercaseDigits[:base])
		}
	}

	b.StopTimer()
	resetTable(cacheBase10.table[:])
	leafSize = originalLeafSize
	b.StartTimer()
}

func resetTable(table []divisor) {
	if table != nil && table[0].bbb != nil {
		for i := 0; i < len(table); i++ {
			table[i].bbb = nil
			table[i].nbits = 0
			table[i].ndigits = 0
		}
	}
}

func TestStringPowers(t *testing.T) {
	var b, p Word
	for b = 2; b <= 16; b++ {
		for p = 0; p <= 512; p++ {
			x := nat(nil).expWW(b, p)
			xs := x.string(lowercaseDigits[:b])
			xs2 := toString(x, lowercaseDigits[:b])
			if xs != xs2 {
				t.Errorf("failed at %d ** %d in base %d: %s != %s", b, p, b, xs, xs2)
			}
		}
		if b >= 3 && testing.Short() {
			break
		}
	}
}

func TestLeadingZeros(t *testing.T) {
	var x Word = _B >> 1
	for i := 0; i <= _W; i++ {
		if int(leadingZeros(x)) != i {
			t.Errorf("failed at %x: got %d want %d", x, leadingZeros(x), i)
		}
		x >>= 1
	}
}

type shiftTest struct {
	in    nat
	shift uint
	out   nat
}

var leftShiftTests = []shiftTest{
	{nil, 0, nil},
	{nil, 1, nil},
	{natOne, 0, natOne},
	{natOne, 1, natTwo},
	{nat{1 << (_W - 1)}, 1, nat{0}},
	{nat{1 << (_W - 1), 0}, 1, nat{0, 1}},
}

func TestShiftLeft(t *testing.T) {
	for i, test := range leftShiftTests {
		var z nat
		z = z.shl(test.in, test.shift)
		for j, d := range test.out {
			if j >= len(z) || z[j] != d {
				t.Errorf("#%d: got: %v want: %v", i, z, test.out)
				break
			}
		}
	}
}

var rightShiftTests = []shiftTest{
	{nil, 0, nil},
	{nil, 1, nil},
	{natOne, 0, natOne},
	{natOne, 1, nil},
	{natTwo, 1, natOne},
	{nat{0, 1}, 1, nat{1 << (_W - 1)}},
	{nat{2, 1, 1}, 1, nat{1<<(_W-1) + 1, 1 << (_W - 1)}},
}

func TestShiftRight(t *testing.T) {
	for i, test := range rightShiftTests {
		var z nat
		z = z.shr(test.in, test.shift)
		for j, d := range test.out {
			if j >= len(z) || z[j] != d {
				t.Errorf("#%d: got: %v want: %v", i, z, test.out)
				break
			}
		}
	}
}

type modWTest struct {
	in       string
	dividend string
	out      string
}

var modWTests32 = []modWTest{
	{"23492635982634928349238759823742", "252341", "220170"},
}

var modWTests64 = []modWTest{
	{"6527895462947293856291561095690465243862946", "524326975699234", "375066989628668"},
}

func runModWTests(t *testing.T, tests []modWTest) {
	for i, test := range tests {
		in, _ := new(Int).SetString(test.in, 10)
		d, _ := new(Int).SetString(test.dividend, 10)
		out, _ := new(Int).SetString(test.out, 10)

		r := in.abs.modW(d.abs[0])
		if r != out.abs[0] {
			t.Errorf("#%d failed: got %d want %s", i, r, out)
		}
	}
}

func TestModW(t *testing.T) {
	if _W >= 32 {
		runModWTests(t, modWTests32)
	}
	if _W >= 64 {
		runModWTests(t, modWTests64)
	}
}

func TestTrailingZeroBits(t *testing.T) {
	// test 0 case explicitly
	if n := trailingZeroBits(0); n != 0 {
		t.Errorf("got trailingZeroBits(0) = %d; want 0", n)
	}

	x := Word(1)
	for i := uint(0); i < _W; i++ {
		n := trailingZeroBits(x)
		if n != i {
			t.Errorf("got trailingZeroBits(%#x) = %d; want %d", x, n, i%_W)
		}
		x <<= 1
	}

	// test 0 case explicitly
	if n := nat(nil).trailingZeroBits(); n != 0 {
		t.Errorf("got nat(nil).trailingZeroBits() = %d; want 0", n)
	}

	y := nat(nil).set(natOne)
	for i := uint(0); i <= 3*_W; i++ {
		n := y.trailingZeroBits()
		if n != i {
			t.Errorf("got 0x%s.trailingZeroBits() = %d; want %d", y.hexString(), n, i)
		}
		y = y.shl(y, 1)
	}
}

var expNNTests = []struct {
	x, y, m string
	out     string
}{
	{"0", "0", "0", "1"},
	{"0", "0", "1", "0"},
	{"1", "1", "1", "0"},
	{"2", "1", "1", "0"},
	{"2", "2", "1", "0"},
	{"10", "100000000000", "1", "0"},
	{"0x8000000000000000", "2", "", "0x40000000000000000000000000000000"},
	{"0x8000000000000000", "2", "6719", "4944"},
	{"0x8000000000000000", "3", "6719", "5447"},
	{"0x8000000000000000", "1000", "6719", "1603"},
	{"0x8000000000000000", "1000000", "6719", "3199"},
	{
		"2938462938472983472983659726349017249287491026512746239764525612965293865296239471239874193284792387498274256129746192347",
		"298472983472983471903246121093472394872319615612417471234712061",
		"29834729834729834729347290846729561262544958723956495615629569234729836259263598127342374289365912465901365498236492183464",
		"23537740700184054162508175125554701713153216681790245129157191391322321508055833908509185839069455749219131480588829346291",
	},
}

func TestExpNN(t *testing.T) {
	for i, test := range expNNTests {
		x := 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.decimalString(), out.decimalString())
		}
	}
}

func ExpHelper(b *testing.B, x, y Word) {
	var z nat
	for i := 0; i < b.N; i++ {
		z.expWW(x, y)
	}
}

func BenchmarkExp3Power0x10(b *testing.B)     { ExpHelper(b, 3, 0x10) }
func BenchmarkExp3Power0x40(b *testing.B)     { ExpHelper(b, 3, 0x40) }
func BenchmarkExp3Power0x100(b *testing.B)    { ExpHelper(b, 3, 0x100) }
func BenchmarkExp3Power0x400(b *testing.B)    { ExpHelper(b, 3, 0x400) }
func BenchmarkExp3Power0x1000(b *testing.B)   { ExpHelper(b, 3, 0x1000) }
func BenchmarkExp3Power0x4000(b *testing.B)   { ExpHelper(b, 3, 0x4000) }
func BenchmarkExp3Power0x10000(b *testing.B)  { ExpHelper(b, 3, 0x10000) }
func BenchmarkExp3Power0x40000(b *testing.B)  { ExpHelper(b, 3, 0x40000) }
func BenchmarkExp3Power0x100000(b *testing.B) { ExpHelper(b, 3, 0x100000) }
func BenchmarkExp3Power0x400000(b *testing.B) { ExpHelper(b, 3, 0x400000) }

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 := fibo(n).decimalString()
		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)
		}
	}
}