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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"
"os"
"strings"
"testing"
)
var cmpTests = []struct {
x, y nat
r int
}{
{nil, nil, 0},
{nil, nat{}, 0},
{nat{}, nil, 0},
{nat{}, nat{}, 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}},
}
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)
}
}
}
var mulArg, mulTmp nat
func init() {
const n = 1000
mulArg = make(nat, n)
for i := 0; i < n; i++ {
mulArg[i] = _M
}
}
func benchmarkMulLoad() {
for j := 1; j <= 10; j++ {
x := mulArg[0 : j*100]
mulTmp.mul(x, x)
}
}
func BenchmarkMul(b *testing.B) {
for i := 0; i < b.N; i++ {
benchmarkMulLoad()
}
}
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 int // 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 == os.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 BenchmarkScanPi(b *testing.B) {
for i := 0; i < b.N; i++ {
var x nat
x.scan(strings.NewReader(pi), 10)
}
}
const (
// 314**271
// base 2: 2249 digits
// base 8: 751 digits
// base 10: 678 digits
// base 16: 563 digits
shortBase = 314
shortExponent = 271
// 3141**2178
// base 2: 31577 digits
// base 8: 10527 digits
// base 10: 9507 digits
// base 16: 7895 digits
mediumBase = 3141
mediumExponent = 2718
// 3141**2178
// base 2: 406078 digits
// base 8: 135360 digits
// base 10: 122243 digits
// base 16: 101521 digits
longBase = 31415
longExponent = 27182
)
func BenchmarkScanShort2(b *testing.B) {
ScanHelper(b, 2, shortBase, shortExponent)
}
func BenchmarkScanShort8(b *testing.B) {
ScanHelper(b, 8, shortBase, shortExponent)
}
func BenchmarkScanSort10(b *testing.B) {
ScanHelper(b, 10, shortBase, shortExponent)
}
func BenchmarkScanShort16(b *testing.B) {
ScanHelper(b, 16, shortBase, shortExponent)
}
func BenchmarkScanMedium2(b *testing.B) {
ScanHelper(b, 2, mediumBase, mediumExponent)
}
func BenchmarkScanMedium8(b *testing.B) {
ScanHelper(b, 8, mediumBase, mediumExponent)
}
func BenchmarkScanMedium10(b *testing.B) {
ScanHelper(b, 10, mediumBase, mediumExponent)
}
func BenchmarkScanMedium16(b *testing.B) {
ScanHelper(b, 16, mediumBase, mediumExponent)
}
func BenchmarkScanLong2(b *testing.B) {
ScanHelper(b, 2, longBase, longExponent)
}
func BenchmarkScanLong8(b *testing.B) {
ScanHelper(b, 8, longBase, longExponent)
}
func BenchmarkScanLong10(b *testing.B) {
ScanHelper(b, 10, longBase, longExponent)
}
func BenchmarkScanLong16(b *testing.B) {
ScanHelper(b, 16, longBase, longExponent)
}
func ScanHelper(b *testing.B, base int, xv, yv Word) {
b.StopTimer()
var x, y, z nat
x = x.setWord(xv)
y = y.setWord(yv)
z = z.expNN(x, y, nil)
var s string
s = z.string(lowercaseDigits[0:base])
if t := toString(z, lowercaseDigits[0:base]); t != s {
panic(fmt.Sprintf("scanning: got %s; want %s", s, t))
}
b.StartTimer()
for i := 0; i < b.N; i++ {
x.scan(strings.NewReader(s), base)
}
}
func BenchmarkStringShort2(b *testing.B) {
StringHelper(b, 2, shortBase, shortExponent)
}
func BenchmarkStringShort8(b *testing.B) {
StringHelper(b, 8, shortBase, shortExponent)
}
func BenchmarkStringShort10(b *testing.B) {
StringHelper(b, 10, shortBase, shortExponent)
}
func BenchmarkStringShort16(b *testing.B) {
StringHelper(b, 16, shortBase, shortExponent)
}
func BenchmarkStringMedium2(b *testing.B) {
StringHelper(b, 2, mediumBase, mediumExponent)
}
func BenchmarkStringMedium8(b *testing.B) {
StringHelper(b, 8, mediumBase, mediumExponent)
}
func BenchmarkStringMedium10(b *testing.B) {
StringHelper(b, 10, mediumBase, mediumExponent)
}
func BenchmarkStringMedium16(b *testing.B) {
StringHelper(b, 16, mediumBase, mediumExponent)
}
func BenchmarkStringLong2(b *testing.B) {
StringHelper(b, 2, longBase, longExponent)
}
func BenchmarkStringLong8(b *testing.B) {
StringHelper(b, 8, longBase, longExponent)
}
func BenchmarkStringLong10(b *testing.B) {
StringHelper(b, 10, longBase, longExponent)
}
func BenchmarkStringLong16(b *testing.B) {
StringHelper(b, 16, longBase, longExponent)
}
func StringHelper(b *testing.B, base int, xv, yv Word) {
b.StopTimer()
var x, y, z nat
x = x.setWord(xv)
y = y.setWord(yv)
z = z.expNN(x, y, nil)
b.StartTimer()
for i := 0; i < b.N; i++ {
z.string(lowercaseDigits[0:base])
}
}
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 %s 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) {
var x Word
x--
for i := 0; i < _W; i++ {
if trailingZeroBits(x) != i {
t.Errorf("Failed at step %d: x: %x got: %d", i, x, trailingZeroBits(x))
}
x <<= 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)
}
}
}