2014-04-11 Marc Glisse <marc.glisse@inria.fr>

[official-gcc.git] / libgo / go / 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[0:8], "3271"},
        {nat{10}, lowercaseDigits[0:10], "10"},
        {nat{1234567890}, uppercaseDigits[0:10], "1234567890"},
        {nat{0xdeadbeef}, lowercaseDigits[0:16], "deadbeef"},
        {nat{0xdeadbeef}, uppercaseDigits[0:16], "DEADBEEF"},
        {nat{0x229be7}, lowercaseDigits[0:17], "1a2b3c"},
        {nat{0x309663e6}, uppercaseDigits[0:32], "O9COV6"},
}

func TestString(t *testing.T) {
        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
        ok   bool   // expected success
        next rune   // next character (or 0, if at EOF)
}{
        // error: illegal base
        {base: -1},
        {base: 1},
        {base: 37},

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

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

func TestScanBase(t *testing.T) {
        for _, a := range natScanTests {
                r := strings.NewReader(a.s)
                x, b, 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)
                }
                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")
        }
        n := runtime.GOMAXPROCS(0)
        m := b.N / n // n*m <= b.N due to flooring, but the error is neglibible (n is not very large)
        c := make(chan int, n)
        for i := 0; i < n; i++ {
                go func() {
                        for j := 0; j < m; j++ {
                                x.decimalString()
                        }
                        c <- 0
                }()
        }
        for i := 0; i < n; i++ {
                <-c
        }
}

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[0:base])
        if t := toString(z, lowercaseDigits[0: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[0:base]) // warm divisor cache
        b.StartTimer()

        for i := 0; i < b.N; i++ {
                _ = z.string(lowercaseDigits[0: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[0:base]) // warm divisor cache
                b.StartTimer()

                for i := 0; i < b.N; i++ {
                        _ = z.string(lowercaseDigits[0: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[0:b])
                        xs2 := toString(x, lowercaseDigits[0: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) {
        x := Word(1)
        for i := uint(0); i <= _W; i++ {
                n := trailingZeroBits(x)
                if n != i%_W {
                        t.Errorf("got trailingZeroBits(%#x) = %d; want %d", x, n, i%_W)
                }
                x <<= 1
        }

        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.string(lowercaseDigits[0:16]), n, i)
                }
                y = y.shl(y, 1)
        }
}

var expNNTests = []struct {
        x, y, m string
        out     string
}{
        {"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, _, _ := nat(nil).scan(strings.NewReader(test.x), 0)
                y, _, _ := nat(nil).scan(strings.NewReader(test.y), 0)
                out, _, _ := nat(nil).scan(strings.NewReader(test.out), 0)

                var m nat

                if len(test.m) > 0 {
                        m, _, _ = nat(nil).scan(strings.NewReader(test.m), 0)
                }

                z := nat(nil).expNN(x, y, m)
                if z.cmp(out) != 0 {
                        t.Errorf("#%d got %v want %v", i, z, out)
                }
        }
}

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) }