mirror of git://gcc.gnu.org/git/gcc.git
623 lines
16 KiB
Go
623 lines
16 KiB
Go
// Copyright 2010 The Go Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package big
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import (
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"math"
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"testing"
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)
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func TestZeroRat(t *testing.T) {
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var x, y, z Rat
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y.SetFrac64(0, 42)
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if x.Cmp(&y) != 0 {
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t.Errorf("x and y should be both equal and zero")
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}
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if s := x.String(); s != "0/1" {
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t.Errorf("got x = %s, want 0/1", s)
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}
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if s := x.RatString(); s != "0" {
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t.Errorf("got x = %s, want 0", s)
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}
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z.Add(&x, &y)
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if s := z.RatString(); s != "0" {
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t.Errorf("got x+y = %s, want 0", s)
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}
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z.Sub(&x, &y)
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if s := z.RatString(); s != "0" {
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t.Errorf("got x-y = %s, want 0", s)
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}
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z.Mul(&x, &y)
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if s := z.RatString(); s != "0" {
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t.Errorf("got x*y = %s, want 0", s)
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}
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// check for division by zero
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defer func() {
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if s := recover(); s == nil || s.(string) != "division by zero" {
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panic(s)
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}
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}()
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z.Quo(&x, &y)
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}
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func TestRatSign(t *testing.T) {
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zero := NewRat(0, 1)
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for _, a := range setStringTests {
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x, ok := new(Rat).SetString(a.in)
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if !ok {
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continue
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}
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s := x.Sign()
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e := x.Cmp(zero)
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if s != e {
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t.Errorf("got %d; want %d for z = %v", s, e, &x)
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}
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}
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}
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var ratCmpTests = []struct {
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rat1, rat2 string
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out int
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}{
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{"0", "0/1", 0},
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{"1/1", "1", 0},
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{"-1", "-2/2", 0},
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{"1", "0", 1},
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{"0/1", "1/1", -1},
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{"-5/1434770811533343057144", "-5/1434770811533343057145", -1},
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{"49832350382626108453/8964749413", "49832350382626108454/8964749413", -1},
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{"-37414950961700930/7204075375675961", "37414950961700930/7204075375675961", -1},
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{"37414950961700930/7204075375675961", "74829901923401860/14408150751351922", 0},
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}
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func TestRatCmp(t *testing.T) {
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for i, test := range ratCmpTests {
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x, _ := new(Rat).SetString(test.rat1)
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y, _ := new(Rat).SetString(test.rat2)
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out := x.Cmp(y)
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if out != test.out {
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t.Errorf("#%d got out = %v; want %v", i, out, test.out)
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}
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}
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}
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func TestIsInt(t *testing.T) {
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one := NewInt(1)
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for _, a := range setStringTests {
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x, ok := new(Rat).SetString(a.in)
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if !ok {
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continue
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}
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i := x.IsInt()
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e := x.Denom().Cmp(one) == 0
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if i != e {
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t.Errorf("got IsInt(%v) == %v; want %v", x, i, e)
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}
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}
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}
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func TestRatAbs(t *testing.T) {
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zero := new(Rat)
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for _, a := range setStringTests {
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x, ok := new(Rat).SetString(a.in)
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if !ok {
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continue
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}
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e := new(Rat).Set(x)
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if e.Cmp(zero) < 0 {
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e.Sub(zero, e)
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}
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z := new(Rat).Abs(x)
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if z.Cmp(e) != 0 {
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t.Errorf("got Abs(%v) = %v; want %v", x, z, e)
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}
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}
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}
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func TestRatNeg(t *testing.T) {
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zero := new(Rat)
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for _, a := range setStringTests {
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x, ok := new(Rat).SetString(a.in)
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if !ok {
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continue
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}
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e := new(Rat).Sub(zero, x)
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z := new(Rat).Neg(x)
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if z.Cmp(e) != 0 {
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t.Errorf("got Neg(%v) = %v; want %v", x, z, e)
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}
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}
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}
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func TestRatInv(t *testing.T) {
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zero := new(Rat)
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for _, a := range setStringTests {
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x, ok := new(Rat).SetString(a.in)
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if !ok {
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continue
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}
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if x.Cmp(zero) == 0 {
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continue // avoid division by zero
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}
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e := new(Rat).SetFrac(x.Denom(), x.Num())
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z := new(Rat).Inv(x)
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if z.Cmp(e) != 0 {
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t.Errorf("got Inv(%v) = %v; want %v", x, z, e)
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}
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}
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}
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type ratBinFun func(z, x, y *Rat) *Rat
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type ratBinArg struct {
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x, y, z string
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}
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func testRatBin(t *testing.T, i int, name string, f ratBinFun, a ratBinArg) {
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x, _ := new(Rat).SetString(a.x)
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y, _ := new(Rat).SetString(a.y)
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z, _ := new(Rat).SetString(a.z)
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out := f(new(Rat), x, y)
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if out.Cmp(z) != 0 {
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t.Errorf("%s #%d got %s want %s", name, i, out, z)
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}
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}
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var ratBinTests = []struct {
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x, y string
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sum, prod string
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}{
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{"0", "0", "0", "0"},
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{"0", "1", "1", "0"},
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{"-1", "0", "-1", "0"},
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{"-1", "1", "0", "-1"},
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{"1", "1", "2", "1"},
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{"1/2", "1/2", "1", "1/4"},
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{"1/4", "1/3", "7/12", "1/12"},
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{"2/5", "-14/3", "-64/15", "-28/15"},
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{"4707/49292519774798173060", "-3367/70976135186689855734", "84058377121001851123459/1749296273614329067191168098769082663020", "-1760941/388732505247628681598037355282018369560"},
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{"-61204110018146728334/3", "-31052192278051565633/2", "-215564796870448153567/6", "950260896245257153059642991192710872711/3"},
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{"-854857841473707320655/4237645934602118692642972629634714039", "-18/31750379913563777419", "-27/133467566250814981", "15387441146526731771790/134546868362786310073779084329032722548987800600710485341"},
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{"618575745270541348005638912139/19198433543745179392300736", "-19948846211000086/637313996471", "27674141753240653/30123979153216", "-6169936206128396568797607742807090270137721977/6117715203873571641674006593837351328"},
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{"-3/26206484091896184128", "5/2848423294177090248", "15310893822118706237/9330894968229805033368778458685147968", "-5/24882386581946146755650075889827061248"},
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{"26946729/330400702820", "41563965/225583428284", "1238218672302860271/4658307703098666660055", "224002580204097/14906584649915733312176"},
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{"-8259900599013409474/7", "-84829337473700364773/56707961321161574960", "-468402123685491748914621885145127724451/396955729248131024720", "350340947706464153265156004876107029701/198477864624065512360"},
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{"575775209696864/1320203974639986246357", "29/712593081308", "410331716733912717985762465/940768218243776489278275419794956", "808/45524274987585732633"},
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{"1786597389946320496771/2066653520653241", "6269770/1992362624741777", "3559549865190272133656109052308126637/4117523232840525481453983149257", "8967230/3296219033"},
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{"-36459180403360509753/32150500941194292113930", "9381566963714/9633539", "301622077145533298008420642898530153/309723104686531919656937098270", "-3784609207827/3426986245"},
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}
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func TestRatBin(t *testing.T) {
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for i, test := range ratBinTests {
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arg := ratBinArg{test.x, test.y, test.sum}
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testRatBin(t, i, "Add", (*Rat).Add, arg)
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arg = ratBinArg{test.y, test.x, test.sum}
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testRatBin(t, i, "Add symmetric", (*Rat).Add, arg)
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arg = ratBinArg{test.sum, test.x, test.y}
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testRatBin(t, i, "Sub", (*Rat).Sub, arg)
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arg = ratBinArg{test.sum, test.y, test.x}
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testRatBin(t, i, "Sub symmetric", (*Rat).Sub, arg)
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arg = ratBinArg{test.x, test.y, test.prod}
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testRatBin(t, i, "Mul", (*Rat).Mul, arg)
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arg = ratBinArg{test.y, test.x, test.prod}
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testRatBin(t, i, "Mul symmetric", (*Rat).Mul, arg)
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if test.x != "0" {
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arg = ratBinArg{test.prod, test.x, test.y}
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testRatBin(t, i, "Quo", (*Rat).Quo, arg)
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}
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if test.y != "0" {
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arg = ratBinArg{test.prod, test.y, test.x}
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testRatBin(t, i, "Quo symmetric", (*Rat).Quo, arg)
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}
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}
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}
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func TestIssue820(t *testing.T) {
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x := NewRat(3, 1)
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y := NewRat(2, 1)
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z := y.Quo(x, y)
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q := NewRat(3, 2)
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if z.Cmp(q) != 0 {
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t.Errorf("got %s want %s", z, q)
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}
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y = NewRat(3, 1)
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x = NewRat(2, 1)
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z = y.Quo(x, y)
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q = NewRat(2, 3)
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if z.Cmp(q) != 0 {
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t.Errorf("got %s want %s", z, q)
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}
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x = NewRat(3, 1)
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z = x.Quo(x, x)
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q = NewRat(3, 3)
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if z.Cmp(q) != 0 {
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t.Errorf("got %s want %s", z, q)
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}
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}
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var setFrac64Tests = []struct {
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a, b int64
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out string
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}{
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{0, 1, "0"},
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{0, -1, "0"},
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{1, 1, "1"},
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{-1, 1, "-1"},
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{1, -1, "-1"},
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{-1, -1, "1"},
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{-9223372036854775808, -9223372036854775808, "1"},
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}
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func TestRatSetFrac64Rat(t *testing.T) {
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for i, test := range setFrac64Tests {
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x := new(Rat).SetFrac64(test.a, test.b)
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if x.RatString() != test.out {
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t.Errorf("#%d got %s want %s", i, x.RatString(), test.out)
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}
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}
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}
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func TestIssue2379(t *testing.T) {
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// 1) no aliasing
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q := NewRat(3, 2)
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x := new(Rat)
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x.SetFrac(NewInt(3), NewInt(2))
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if x.Cmp(q) != 0 {
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t.Errorf("1) got %s want %s", x, q)
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}
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// 2) aliasing of numerator
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x = NewRat(2, 3)
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x.SetFrac(NewInt(3), x.Num())
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if x.Cmp(q) != 0 {
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t.Errorf("2) got %s want %s", x, q)
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}
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// 3) aliasing of denominator
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x = NewRat(2, 3)
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x.SetFrac(x.Denom(), NewInt(2))
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if x.Cmp(q) != 0 {
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t.Errorf("3) got %s want %s", x, q)
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}
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// 4) aliasing of numerator and denominator
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x = NewRat(2, 3)
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x.SetFrac(x.Denom(), x.Num())
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if x.Cmp(q) != 0 {
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t.Errorf("4) got %s want %s", x, q)
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}
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// 5) numerator and denominator are the same
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q = NewRat(1, 1)
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x = new(Rat)
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n := NewInt(7)
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x.SetFrac(n, n)
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if x.Cmp(q) != 0 {
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t.Errorf("5) got %s want %s", x, q)
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}
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}
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func TestIssue3521(t *testing.T) {
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a := new(Int)
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b := new(Int)
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a.SetString("64375784358435883458348587", 0)
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b.SetString("4789759874531", 0)
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// 0) a raw zero value has 1 as denominator
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zero := new(Rat)
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one := NewInt(1)
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if zero.Denom().Cmp(one) != 0 {
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t.Errorf("0) got %s want %s", zero.Denom(), one)
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}
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// 1a) a zero value remains zero independent of denominator
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x := new(Rat)
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x.Denom().Set(new(Int).Neg(b))
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if x.Cmp(zero) != 0 {
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t.Errorf("1a) got %s want %s", x, zero)
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}
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// 1b) a zero value may have a denominator != 0 and != 1
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x.Num().Set(a)
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qab := new(Rat).SetFrac(a, b)
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if x.Cmp(qab) != 0 {
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t.Errorf("1b) got %s want %s", x, qab)
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}
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// 2a) an integral value becomes a fraction depending on denominator
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x.SetFrac64(10, 2)
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x.Denom().SetInt64(3)
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q53 := NewRat(5, 3)
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if x.Cmp(q53) != 0 {
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t.Errorf("2a) got %s want %s", x, q53)
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}
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// 2b) an integral value becomes a fraction depending on denominator
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x = NewRat(10, 2)
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x.Denom().SetInt64(3)
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if x.Cmp(q53) != 0 {
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t.Errorf("2b) got %s want %s", x, q53)
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}
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// 3) changing the numerator/denominator of a Rat changes the Rat
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x.SetFrac(a, b)
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a = x.Num()
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b = x.Denom()
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a.SetInt64(5)
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b.SetInt64(3)
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if x.Cmp(q53) != 0 {
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t.Errorf("3) got %s want %s", x, q53)
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}
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}
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func TestFloat32Distribution(t *testing.T) {
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// Generate a distribution of (sign, mantissa, exp) values
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// broader than the float32 range, and check Rat.Float32()
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// always picks the closest float32 approximation.
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var add = []int64{
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0,
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1,
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3,
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5,
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7,
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9,
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11,
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}
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var winc, einc = uint64(5), 15 // quick test (~60ms on x86-64)
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if *long {
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winc, einc = uint64(1), 1 // soak test (~1.5s on x86-64)
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}
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for _, sign := range "+-" {
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for _, a := range add {
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for wid := uint64(0); wid < 30; wid += winc {
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b := 1<<wid + a
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if sign == '-' {
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b = -b
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}
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for exp := -150; exp < 150; exp += einc {
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num, den := NewInt(b), NewInt(1)
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if exp > 0 {
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num.Lsh(num, uint(exp))
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} else {
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den.Lsh(den, uint(-exp))
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}
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r := new(Rat).SetFrac(num, den)
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f, _ := r.Float32()
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if !checkIsBestApprox32(t, f, r) {
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// Append context information.
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t.Errorf("(input was mantissa %#x, exp %d; f = %g (%b); f ~ %g; r = %v)",
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b, exp, f, f, math.Ldexp(float64(b), exp), r)
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}
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checkNonLossyRoundtrip32(t, f)
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}
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}
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}
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}
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}
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func TestFloat64Distribution(t *testing.T) {
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// Generate a distribution of (sign, mantissa, exp) values
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// broader than the float64 range, and check Rat.Float64()
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// always picks the closest float64 approximation.
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var add = []int64{
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0,
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1,
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3,
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5,
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7,
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9,
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11,
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}
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var winc, einc = uint64(10), 500 // quick test (~12ms on x86-64)
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if *long {
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winc, einc = uint64(1), 1 // soak test (~75s on x86-64)
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}
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for _, sign := range "+-" {
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for _, a := range add {
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for wid := uint64(0); wid < 60; wid += winc {
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b := 1<<wid + a
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if sign == '-' {
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b = -b
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}
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for exp := -1100; exp < 1100; exp += einc {
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num, den := NewInt(b), NewInt(1)
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if exp > 0 {
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num.Lsh(num, uint(exp))
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} else {
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den.Lsh(den, uint(-exp))
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}
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r := new(Rat).SetFrac(num, den)
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f, _ := r.Float64()
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if !checkIsBestApprox64(t, f, r) {
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// Append context information.
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t.Errorf("(input was mantissa %#x, exp %d; f = %g (%b); f ~ %g; r = %v)",
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b, exp, f, f, math.Ldexp(float64(b), exp), r)
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}
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checkNonLossyRoundtrip64(t, f)
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}
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}
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}
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}
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}
|
|
|
|
// TestSetFloat64NonFinite checks that SetFloat64 of a non-finite value
|
|
// returns nil.
|
|
func TestSetFloat64NonFinite(t *testing.T) {
|
|
for _, f := range []float64{math.NaN(), math.Inf(+1), math.Inf(-1)} {
|
|
var r Rat
|
|
if r2 := r.SetFloat64(f); r2 != nil {
|
|
t.Errorf("SetFloat64(%g) was %v, want nil", f, r2)
|
|
}
|
|
}
|
|
}
|
|
|
|
// checkNonLossyRoundtrip32 checks that a float->Rat->float roundtrip is
|
|
// non-lossy for finite f.
|
|
func checkNonLossyRoundtrip32(t *testing.T, f float32) {
|
|
if !isFinite(float64(f)) {
|
|
return
|
|
}
|
|
r := new(Rat).SetFloat64(float64(f))
|
|
if r == nil {
|
|
t.Errorf("Rat.SetFloat64(float64(%g) (%b)) == nil", f, f)
|
|
return
|
|
}
|
|
f2, exact := r.Float32()
|
|
if f != f2 || !exact {
|
|
t.Errorf("Rat.SetFloat64(float64(%g)).Float32() = %g (%b), %v, want %g (%b), %v; delta = %b",
|
|
f, f2, f2, exact, f, f, true, f2-f)
|
|
}
|
|
}
|
|
|
|
// checkNonLossyRoundtrip64 checks that a float->Rat->float roundtrip is
|
|
// non-lossy for finite f.
|
|
func checkNonLossyRoundtrip64(t *testing.T, f float64) {
|
|
if !isFinite(f) {
|
|
return
|
|
}
|
|
r := new(Rat).SetFloat64(f)
|
|
if r == nil {
|
|
t.Errorf("Rat.SetFloat64(%g (%b)) == nil", f, f)
|
|
return
|
|
}
|
|
f2, exact := r.Float64()
|
|
if f != f2 || !exact {
|
|
t.Errorf("Rat.SetFloat64(%g).Float64() = %g (%b), %v, want %g (%b), %v; delta = %b",
|
|
f, f2, f2, exact, f, f, true, f2-f)
|
|
}
|
|
}
|
|
|
|
// delta returns the absolute difference between r and f.
|
|
func delta(r *Rat, f float64) *Rat {
|
|
d := new(Rat).Sub(r, new(Rat).SetFloat64(f))
|
|
return d.Abs(d)
|
|
}
|
|
|
|
// checkIsBestApprox32 checks that f is the best possible float32
|
|
// approximation of r.
|
|
// Returns true on success.
|
|
func checkIsBestApprox32(t *testing.T, f float32, r *Rat) bool {
|
|
if math.Abs(float64(f)) >= math.MaxFloat32 {
|
|
// Cannot check +Inf, -Inf, nor the float next to them (MaxFloat32).
|
|
// But we have tests for these special cases.
|
|
return true
|
|
}
|
|
|
|
// r must be strictly between f0 and f1, the floats bracketing f.
|
|
f0 := math.Nextafter32(f, float32(math.Inf(-1)))
|
|
f1 := math.Nextafter32(f, float32(math.Inf(+1)))
|
|
|
|
// For f to be correct, r must be closer to f than to f0 or f1.
|
|
df := delta(r, float64(f))
|
|
df0 := delta(r, float64(f0))
|
|
df1 := delta(r, float64(f1))
|
|
if df.Cmp(df0) > 0 {
|
|
t.Errorf("Rat(%v).Float32() = %g (%b), but previous float32 %g (%b) is closer", r, f, f, f0, f0)
|
|
return false
|
|
}
|
|
if df.Cmp(df1) > 0 {
|
|
t.Errorf("Rat(%v).Float32() = %g (%b), but next float32 %g (%b) is closer", r, f, f, f1, f1)
|
|
return false
|
|
}
|
|
if df.Cmp(df0) == 0 && !isEven32(f) {
|
|
t.Errorf("Rat(%v).Float32() = %g (%b); halfway should have rounded to %g (%b) instead", r, f, f, f0, f0)
|
|
return false
|
|
}
|
|
if df.Cmp(df1) == 0 && !isEven32(f) {
|
|
t.Errorf("Rat(%v).Float32() = %g (%b); halfway should have rounded to %g (%b) instead", r, f, f, f1, f1)
|
|
return false
|
|
}
|
|
return true
|
|
}
|
|
|
|
// checkIsBestApprox64 checks that f is the best possible float64
|
|
// approximation of r.
|
|
// Returns true on success.
|
|
func checkIsBestApprox64(t *testing.T, f float64, r *Rat) bool {
|
|
if math.Abs(f) >= math.MaxFloat64 {
|
|
// Cannot check +Inf, -Inf, nor the float next to them (MaxFloat64).
|
|
// But we have tests for these special cases.
|
|
return true
|
|
}
|
|
|
|
// r must be strictly between f0 and f1, the floats bracketing f.
|
|
f0 := math.Nextafter(f, math.Inf(-1))
|
|
f1 := math.Nextafter(f, math.Inf(+1))
|
|
|
|
// For f to be correct, r must be closer to f than to f0 or f1.
|
|
df := delta(r, f)
|
|
df0 := delta(r, f0)
|
|
df1 := delta(r, f1)
|
|
if df.Cmp(df0) > 0 {
|
|
t.Errorf("Rat(%v).Float64() = %g (%b), but previous float64 %g (%b) is closer", r, f, f, f0, f0)
|
|
return false
|
|
}
|
|
if df.Cmp(df1) > 0 {
|
|
t.Errorf("Rat(%v).Float64() = %g (%b), but next float64 %g (%b) is closer", r, f, f, f1, f1)
|
|
return false
|
|
}
|
|
if df.Cmp(df0) == 0 && !isEven64(f) {
|
|
t.Errorf("Rat(%v).Float64() = %g (%b); halfway should have rounded to %g (%b) instead", r, f, f, f0, f0)
|
|
return false
|
|
}
|
|
if df.Cmp(df1) == 0 && !isEven64(f) {
|
|
t.Errorf("Rat(%v).Float64() = %g (%b); halfway should have rounded to %g (%b) instead", r, f, f, f1, f1)
|
|
return false
|
|
}
|
|
return true
|
|
}
|
|
|
|
func isEven32(f float32) bool { return math.Float32bits(f)&1 == 0 }
|
|
func isEven64(f float64) bool { return math.Float64bits(f)&1 == 0 }
|
|
|
|
func TestIsFinite(t *testing.T) {
|
|
finites := []float64{
|
|
1.0 / 3,
|
|
4891559871276714924261e+222,
|
|
math.MaxFloat64,
|
|
math.SmallestNonzeroFloat64,
|
|
-math.MaxFloat64,
|
|
-math.SmallestNonzeroFloat64,
|
|
}
|
|
for _, f := range finites {
|
|
if !isFinite(f) {
|
|
t.Errorf("!IsFinite(%g (%b))", f, f)
|
|
}
|
|
}
|
|
nonfinites := []float64{
|
|
math.NaN(),
|
|
math.Inf(-1),
|
|
math.Inf(+1),
|
|
}
|
|
for _, f := range nonfinites {
|
|
if isFinite(f) {
|
|
t.Errorf("IsFinite(%g, (%b))", f, f)
|
|
}
|
|
}
|
|
}
|