gcc/libgo/go/math/big/rat_test.go
2013-11-06 19:49:01 +00:00

930 lines
23 KiB
Go

// Copyright 2010 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 (
"bytes"
"encoding/gob"
"fmt"
"math"
"strconv"
"strings"
"testing"
)
func TestZeroRat(t *testing.T) {
var x, y, z Rat
y.SetFrac64(0, 42)
if x.Cmp(&y) != 0 {
t.Errorf("x and y should be both equal and zero")
}
if s := x.String(); s != "0/1" {
t.Errorf("got x = %s, want 0/1", s)
}
if s := x.RatString(); s != "0" {
t.Errorf("got x = %s, want 0", s)
}
z.Add(&x, &y)
if s := z.RatString(); s != "0" {
t.Errorf("got x+y = %s, want 0", s)
}
z.Sub(&x, &y)
if s := z.RatString(); s != "0" {
t.Errorf("got x-y = %s, want 0", s)
}
z.Mul(&x, &y)
if s := z.RatString(); s != "0" {
t.Errorf("got x*y = %s, want 0", s)
}
// check for division by zero
defer func() {
if s := recover(); s == nil || s.(string) != "division by zero" {
panic(s)
}
}()
z.Quo(&x, &y)
}
var setStringTests = []struct {
in, out string
ok bool
}{
{"0", "0", true},
{"-0", "0", true},
{"1", "1", true},
{"-1", "-1", true},
{"1.", "1", true},
{"1e0", "1", true},
{"1.e1", "10", true},
{in: "1e", ok: false},
{in: "1.e", ok: false},
{in: "1e+14e-5", ok: false},
{in: "1e4.5", ok: false},
{in: "r", ok: false},
{in: "a/b", ok: false},
{in: "a.b", ok: false},
{"-0.1", "-1/10", true},
{"-.1", "-1/10", true},
{"2/4", "1/2", true},
{".25", "1/4", true},
{"-1/5", "-1/5", true},
{"8129567.7690E14", "812956776900000000000", true},
{"78189e+4", "781890000", true},
{"553019.8935e+8", "55301989350000", true},
{"98765432109876543210987654321e-10", "98765432109876543210987654321/10000000000", true},
{"9877861857500000E-7", "3951144743/4", true},
{"2169378.417e-3", "2169378417/1000000", true},
{"884243222337379604041632732738665534", "884243222337379604041632732738665534", true},
{"53/70893980658822810696", "53/70893980658822810696", true},
{"106/141787961317645621392", "53/70893980658822810696", true},
{"204211327800791583.81095", "4084226556015831676219/20000", true},
}
func TestRatSetString(t *testing.T) {
for i, test := range setStringTests {
x, ok := new(Rat).SetString(test.in)
if ok {
if !test.ok {
t.Errorf("#%d SetString(%q) expected failure", i, test.in)
} else if x.RatString() != test.out {
t.Errorf("#%d SetString(%q) got %s want %s", i, test.in, x.RatString(), test.out)
}
} else if x != nil {
t.Errorf("#%d SetString(%q) got %p want nil", i, test.in, x)
}
}
}
func TestRatScan(t *testing.T) {
var buf bytes.Buffer
for i, test := range setStringTests {
x := new(Rat)
buf.Reset()
buf.WriteString(test.in)
_, err := fmt.Fscanf(&buf, "%v", x)
if err == nil != test.ok {
if test.ok {
t.Errorf("#%d error: %s", i, err)
} else {
t.Errorf("#%d expected error", i)
}
continue
}
if err == nil && x.RatString() != test.out {
t.Errorf("#%d got %s want %s", i, x.RatString(), test.out)
}
}
}
var floatStringTests = []struct {
in string
prec int
out string
}{
{"0", 0, "0"},
{"0", 4, "0.0000"},
{"1", 0, "1"},
{"1", 2, "1.00"},
{"-1", 0, "-1"},
{".25", 2, "0.25"},
{".25", 1, "0.3"},
{".25", 3, "0.250"},
{"-1/3", 3, "-0.333"},
{"-2/3", 4, "-0.6667"},
{"0.96", 1, "1.0"},
{"0.999", 2, "1.00"},
{"0.9", 0, "1"},
{".25", -1, "0"},
{".55", -1, "1"},
}
func TestFloatString(t *testing.T) {
for i, test := range floatStringTests {
x, _ := new(Rat).SetString(test.in)
if x.FloatString(test.prec) != test.out {
t.Errorf("#%d got %s want %s", i, x.FloatString(test.prec), test.out)
}
}
}
func TestRatSign(t *testing.T) {
zero := NewRat(0, 1)
for _, a := range setStringTests {
x, ok := new(Rat).SetString(a.in)
if !ok {
continue
}
s := x.Sign()
e := x.Cmp(zero)
if s != e {
t.Errorf("got %d; want %d for z = %v", s, e, &x)
}
}
}
var ratCmpTests = []struct {
rat1, rat2 string
out int
}{
{"0", "0/1", 0},
{"1/1", "1", 0},
{"-1", "-2/2", 0},
{"1", "0", 1},
{"0/1", "1/1", -1},
{"-5/1434770811533343057144", "-5/1434770811533343057145", -1},
{"49832350382626108453/8964749413", "49832350382626108454/8964749413", -1},
{"-37414950961700930/7204075375675961", "37414950961700930/7204075375675961", -1},
{"37414950961700930/7204075375675961", "74829901923401860/14408150751351922", 0},
}
func TestRatCmp(t *testing.T) {
for i, test := range ratCmpTests {
x, _ := new(Rat).SetString(test.rat1)
y, _ := new(Rat).SetString(test.rat2)
out := x.Cmp(y)
if out != test.out {
t.Errorf("#%d got out = %v; want %v", i, out, test.out)
}
}
}
func TestIsInt(t *testing.T) {
one := NewInt(1)
for _, a := range setStringTests {
x, ok := new(Rat).SetString(a.in)
if !ok {
continue
}
i := x.IsInt()
e := x.Denom().Cmp(one) == 0
if i != e {
t.Errorf("got IsInt(%v) == %v; want %v", x, i, e)
}
}
}
func TestRatAbs(t *testing.T) {
zero := new(Rat)
for _, a := range setStringTests {
x, ok := new(Rat).SetString(a.in)
if !ok {
continue
}
e := new(Rat).Set(x)
if e.Cmp(zero) < 0 {
e.Sub(zero, e)
}
z := new(Rat).Abs(x)
if z.Cmp(e) != 0 {
t.Errorf("got Abs(%v) = %v; want %v", x, z, e)
}
}
}
func TestRatNeg(t *testing.T) {
zero := new(Rat)
for _, a := range setStringTests {
x, ok := new(Rat).SetString(a.in)
if !ok {
continue
}
e := new(Rat).Sub(zero, x)
z := new(Rat).Neg(x)
if z.Cmp(e) != 0 {
t.Errorf("got Neg(%v) = %v; want %v", x, z, e)
}
}
}
func TestRatInv(t *testing.T) {
zero := new(Rat)
for _, a := range setStringTests {
x, ok := new(Rat).SetString(a.in)
if !ok {
continue
}
if x.Cmp(zero) == 0 {
continue // avoid division by zero
}
e := new(Rat).SetFrac(x.Denom(), x.Num())
z := new(Rat).Inv(x)
if z.Cmp(e) != 0 {
t.Errorf("got Inv(%v) = %v; want %v", x, z, e)
}
}
}
type ratBinFun func(z, x, y *Rat) *Rat
type ratBinArg struct {
x, y, z string
}
func testRatBin(t *testing.T, i int, name string, f ratBinFun, a ratBinArg) {
x, _ := new(Rat).SetString(a.x)
y, _ := new(Rat).SetString(a.y)
z, _ := new(Rat).SetString(a.z)
out := f(new(Rat), x, y)
if out.Cmp(z) != 0 {
t.Errorf("%s #%d got %s want %s", name, i, out, z)
}
}
var ratBinTests = []struct {
x, y string
sum, prod string
}{
{"0", "0", "0", "0"},
{"0", "1", "1", "0"},
{"-1", "0", "-1", "0"},
{"-1", "1", "0", "-1"},
{"1", "1", "2", "1"},
{"1/2", "1/2", "1", "1/4"},
{"1/4", "1/3", "7/12", "1/12"},
{"2/5", "-14/3", "-64/15", "-28/15"},
{"4707/49292519774798173060", "-3367/70976135186689855734", "84058377121001851123459/1749296273614329067191168098769082663020", "-1760941/388732505247628681598037355282018369560"},
{"-61204110018146728334/3", "-31052192278051565633/2", "-215564796870448153567/6", "950260896245257153059642991192710872711/3"},
{"-854857841473707320655/4237645934602118692642972629634714039", "-18/31750379913563777419", "-27/133467566250814981", "15387441146526731771790/134546868362786310073779084329032722548987800600710485341"},
{"618575745270541348005638912139/19198433543745179392300736", "-19948846211000086/637313996471", "27674141753240653/30123979153216", "-6169936206128396568797607742807090270137721977/6117715203873571641674006593837351328"},
{"-3/26206484091896184128", "5/2848423294177090248", "15310893822118706237/9330894968229805033368778458685147968", "-5/24882386581946146755650075889827061248"},
{"26946729/330400702820", "41563965/225583428284", "1238218672302860271/4658307703098666660055", "224002580204097/14906584649915733312176"},
{"-8259900599013409474/7", "-84829337473700364773/56707961321161574960", "-468402123685491748914621885145127724451/396955729248131024720", "350340947706464153265156004876107029701/198477864624065512360"},
{"575775209696864/1320203974639986246357", "29/712593081308", "410331716733912717985762465/940768218243776489278275419794956", "808/45524274987585732633"},
{"1786597389946320496771/2066653520653241", "6269770/1992362624741777", "3559549865190272133656109052308126637/4117523232840525481453983149257", "8967230/3296219033"},
{"-36459180403360509753/32150500941194292113930", "9381566963714/9633539", "301622077145533298008420642898530153/309723104686531919656937098270", "-3784609207827/3426986245"},
}
func TestRatBin(t *testing.T) {
for i, test := range ratBinTests {
arg := ratBinArg{test.x, test.y, test.sum}
testRatBin(t, i, "Add", (*Rat).Add, arg)
arg = ratBinArg{test.y, test.x, test.sum}
testRatBin(t, i, "Add symmetric", (*Rat).Add, arg)
arg = ratBinArg{test.sum, test.x, test.y}
testRatBin(t, i, "Sub", (*Rat).Sub, arg)
arg = ratBinArg{test.sum, test.y, test.x}
testRatBin(t, i, "Sub symmetric", (*Rat).Sub, arg)
arg = ratBinArg{test.x, test.y, test.prod}
testRatBin(t, i, "Mul", (*Rat).Mul, arg)
arg = ratBinArg{test.y, test.x, test.prod}
testRatBin(t, i, "Mul symmetric", (*Rat).Mul, arg)
if test.x != "0" {
arg = ratBinArg{test.prod, test.x, test.y}
testRatBin(t, i, "Quo", (*Rat).Quo, arg)
}
if test.y != "0" {
arg = ratBinArg{test.prod, test.y, test.x}
testRatBin(t, i, "Quo symmetric", (*Rat).Quo, arg)
}
}
}
func TestIssue820(t *testing.T) {
x := NewRat(3, 1)
y := NewRat(2, 1)
z := y.Quo(x, y)
q := NewRat(3, 2)
if z.Cmp(q) != 0 {
t.Errorf("got %s want %s", z, q)
}
y = NewRat(3, 1)
x = NewRat(2, 1)
z = y.Quo(x, y)
q = NewRat(2, 3)
if z.Cmp(q) != 0 {
t.Errorf("got %s want %s", z, q)
}
x = NewRat(3, 1)
z = x.Quo(x, x)
q = NewRat(3, 3)
if z.Cmp(q) != 0 {
t.Errorf("got %s want %s", z, q)
}
}
var setFrac64Tests = []struct {
a, b int64
out string
}{
{0, 1, "0"},
{0, -1, "0"},
{1, 1, "1"},
{-1, 1, "-1"},
{1, -1, "-1"},
{-1, -1, "1"},
{-9223372036854775808, -9223372036854775808, "1"},
}
func TestRatSetFrac64Rat(t *testing.T) {
for i, test := range setFrac64Tests {
x := new(Rat).SetFrac64(test.a, test.b)
if x.RatString() != test.out {
t.Errorf("#%d got %s want %s", i, x.RatString(), test.out)
}
}
}
func TestRatGobEncoding(t *testing.T) {
var medium bytes.Buffer
enc := gob.NewEncoder(&medium)
dec := gob.NewDecoder(&medium)
for _, test := range encodingTests {
medium.Reset() // empty buffer for each test case (in case of failures)
var tx Rat
tx.SetString(test + ".14159265")
if err := enc.Encode(&tx); err != nil {
t.Errorf("encoding of %s failed: %s", &tx, err)
}
var rx Rat
if err := dec.Decode(&rx); err != nil {
t.Errorf("decoding of %s failed: %s", &tx, err)
}
if rx.Cmp(&tx) != 0 {
t.Errorf("transmission of %s failed: got %s want %s", &tx, &rx, &tx)
}
}
}
// Sending a nil Rat pointer (inside a slice) on a round trip through gob should yield a zero.
// TODO: top-level nils.
func TestGobEncodingNilRatInSlice(t *testing.T) {
buf := new(bytes.Buffer)
enc := gob.NewEncoder(buf)
dec := gob.NewDecoder(buf)
var in = make([]*Rat, 1)
err := enc.Encode(&in)
if err != nil {
t.Errorf("gob encode failed: %q", err)
}
var out []*Rat
err = dec.Decode(&out)
if err != nil {
t.Fatalf("gob decode failed: %q", err)
}
if len(out) != 1 {
t.Fatalf("wrong len; want 1 got %d", len(out))
}
var zero Rat
if out[0].Cmp(&zero) != 0 {
t.Errorf("transmission of (*Int)(nill) failed: got %s want 0", out)
}
}
func TestIssue2379(t *testing.T) {
// 1) no aliasing
q := NewRat(3, 2)
x := new(Rat)
x.SetFrac(NewInt(3), NewInt(2))
if x.Cmp(q) != 0 {
t.Errorf("1) got %s want %s", x, q)
}
// 2) aliasing of numerator
x = NewRat(2, 3)
x.SetFrac(NewInt(3), x.Num())
if x.Cmp(q) != 0 {
t.Errorf("2) got %s want %s", x, q)
}
// 3) aliasing of denominator
x = NewRat(2, 3)
x.SetFrac(x.Denom(), NewInt(2))
if x.Cmp(q) != 0 {
t.Errorf("3) got %s want %s", x, q)
}
// 4) aliasing of numerator and denominator
x = NewRat(2, 3)
x.SetFrac(x.Denom(), x.Num())
if x.Cmp(q) != 0 {
t.Errorf("4) got %s want %s", x, q)
}
// 5) numerator and denominator are the same
q = NewRat(1, 1)
x = new(Rat)
n := NewInt(7)
x.SetFrac(n, n)
if x.Cmp(q) != 0 {
t.Errorf("5) got %s want %s", x, q)
}
}
func TestIssue3521(t *testing.T) {
a := new(Int)
b := new(Int)
a.SetString("64375784358435883458348587", 0)
b.SetString("4789759874531", 0)
// 0) a raw zero value has 1 as denominator
zero := new(Rat)
one := NewInt(1)
if zero.Denom().Cmp(one) != 0 {
t.Errorf("0) got %s want %s", zero.Denom(), one)
}
// 1a) a zero value remains zero independent of denominator
x := new(Rat)
x.Denom().Set(new(Int).Neg(b))
if x.Cmp(zero) != 0 {
t.Errorf("1a) got %s want %s", x, zero)
}
// 1b) a zero value may have a denominator != 0 and != 1
x.Num().Set(a)
qab := new(Rat).SetFrac(a, b)
if x.Cmp(qab) != 0 {
t.Errorf("1b) got %s want %s", x, qab)
}
// 2a) an integral value becomes a fraction depending on denominator
x.SetFrac64(10, 2)
x.Denom().SetInt64(3)
q53 := NewRat(5, 3)
if x.Cmp(q53) != 0 {
t.Errorf("2a) got %s want %s", x, q53)
}
// 2b) an integral value becomes a fraction depending on denominator
x = NewRat(10, 2)
x.Denom().SetInt64(3)
if x.Cmp(q53) != 0 {
t.Errorf("2b) got %s want %s", x, q53)
}
// 3) changing the numerator/denominator of a Rat changes the Rat
x.SetFrac(a, b)
a = x.Num()
b = x.Denom()
a.SetInt64(5)
b.SetInt64(3)
if x.Cmp(q53) != 0 {
t.Errorf("3) got %s want %s", x, q53)
}
}
// Test inputs to Rat.SetString. The prefix "long:" causes the test
// to be skipped in --test.short mode. (The threshold is about 500us.)
var float64inputs = []string{
// Constants plundered from strconv/testfp.txt.
// Table 1: Stress Inputs for Conversion to 53-bit Binary, < 1/2 ULP
"5e+125",
"69e+267",
"999e-026",
"7861e-034",
"75569e-254",
"928609e-261",
"9210917e+080",
"84863171e+114",
"653777767e+273",
"5232604057e-298",
"27235667517e-109",
"653532977297e-123",
"3142213164987e-294",
"46202199371337e-072",
"231010996856685e-073",
"9324754620109615e+212",
"78459735791271921e+049",
"272104041512242479e+200",
"6802601037806061975e+198",
"20505426358836677347e-221",
"836168422905420598437e-234",
"4891559871276714924261e+222",
// Table 2: Stress Inputs for Conversion to 53-bit Binary, > 1/2 ULP
"9e-265",
"85e-037",
"623e+100",
"3571e+263",
"81661e+153",
"920657e-023",
"4603285e-024",
"87575437e-309",
"245540327e+122",
"6138508175e+120",
"83356057653e+193",
"619534293513e+124",
"2335141086879e+218",
"36167929443327e-159",
"609610927149051e-255",
"3743626360493413e-165",
"94080055902682397e-242",
"899810892172646163e+283",
"7120190517612959703e+120",
"25188282901709339043e-252",
"308984926168550152811e-052",
"6372891218502368041059e+064",
// Table 14: Stress Inputs for Conversion to 24-bit Binary, <1/2 ULP
"5e-20",
"67e+14",
"985e+15",
"7693e-42",
"55895e-16",
"996622e-44",
"7038531e-32",
"60419369e-46",
"702990899e-20",
"6930161142e-48",
"25933168707e+13",
"596428896559e+20",
// Table 15: Stress Inputs for Conversion to 24-bit Binary, >1/2 ULP
"3e-23",
"57e+18",
"789e-35",
"2539e-18",
"76173e+28",
"887745e-11",
"5382571e-37",
"82381273e-35",
"750486563e-38",
"3752432815e-39",
"75224575729e-45",
"459926601011e+15",
// Constants plundered from strconv/atof_test.go.
"0",
"1",
"+1",
"1e23",
"1E23",
"100000000000000000000000",
"1e-100",
"123456700",
"99999999999999974834176",
"100000000000000000000001",
"100000000000000008388608",
"100000000000000016777215",
"100000000000000016777216",
"-1",
"-0.1",
"-0", // NB: exception made for this input
"1e-20",
"625e-3",
// largest float64
"1.7976931348623157e308",
"-1.7976931348623157e308",
// next float64 - too large
"1.7976931348623159e308",
"-1.7976931348623159e308",
// the border is ...158079
// borderline - okay
"1.7976931348623158e308",
"-1.7976931348623158e308",
// borderline - too large
"1.797693134862315808e308",
"-1.797693134862315808e308",
// a little too large
"1e308",
"2e308",
"1e309",
// way too large
"1e310",
"-1e310",
"1e400",
"-1e400",
"long:1e400000",
"long:-1e400000",
// denormalized
"1e-305",
"1e-306",
"1e-307",
"1e-308",
"1e-309",
"1e-310",
"1e-322",
// smallest denormal
"5e-324",
"4e-324",
"3e-324",
// too small
"2e-324",
// way too small
"1e-350",
"long:1e-400000",
// way too small, negative
"-1e-350",
"long:-1e-400000",
// try to overflow exponent
// [Disabled: too slow and memory-hungry with rationals.]
// "1e-4294967296",
// "1e+4294967296",
// "1e-18446744073709551616",
// "1e+18446744073709551616",
// http://www.exploringbinary.com/java-hangs-when-converting-2-2250738585072012e-308/
"2.2250738585072012e-308",
// http://www.exploringbinary.com/php-hangs-on-numeric-value-2-2250738585072011e-308/
"2.2250738585072011e-308",
// A very large number (initially wrongly parsed by the fast algorithm).
"4.630813248087435e+307",
// A different kind of very large number.
"22.222222222222222",
"long:2." + strings.Repeat("2", 4000) + "e+1",
// Exactly halfway between 1 and math.Nextafter(1, 2).
// Round to even (down).
"1.00000000000000011102230246251565404236316680908203125",
// Slightly lower; still round down.
"1.00000000000000011102230246251565404236316680908203124",
// Slightly higher; round up.
"1.00000000000000011102230246251565404236316680908203126",
// Slightly higher, but you have to read all the way to the end.
"long:1.00000000000000011102230246251565404236316680908203125" + strings.Repeat("0", 10000) + "1",
// Smallest denormal, 2^(-1022-52)
"4.940656458412465441765687928682213723651e-324",
// Half of smallest denormal, 2^(-1022-53)
"2.470328229206232720882843964341106861825e-324",
// A little more than the exact half of smallest denormal
// 2^-1075 + 2^-1100. (Rounds to 1p-1074.)
"2.470328302827751011111470718709768633275e-324",
// The exact halfway between smallest normal and largest denormal:
// 2^-1022 - 2^-1075. (Rounds to 2^-1022.)
"2.225073858507201136057409796709131975935e-308",
"1152921504606846975", // 1<<60 - 1
"-1152921504606846975", // -(1<<60 - 1)
"1152921504606846977", // 1<<60 + 1
"-1152921504606846977", // -(1<<60 + 1)
"1/3",
}
func TestFloat64SpecialCases(t *testing.T) {
for _, input := range float64inputs {
if strings.HasPrefix(input, "long:") {
if testing.Short() {
continue
}
input = input[len("long:"):]
}
r, ok := new(Rat).SetString(input)
if !ok {
t.Errorf("Rat.SetString(%q) failed", input)
continue
}
f, exact := r.Float64()
// 1. Check string -> Rat -> float64 conversions are
// consistent with strconv.ParseFloat.
// Skip this check if the input uses "a/b" rational syntax.
if !strings.Contains(input, "/") {
e, _ := strconv.ParseFloat(input, 64)
// Careful: negative Rats too small for
// float64 become -0, but Rat obviously cannot
// preserve the sign from SetString("-0").
switch {
case math.Float64bits(e) == math.Float64bits(f):
// Ok: bitwise equal.
case f == 0 && r.Num().BitLen() == 0:
// Ok: Rat(0) is equivalent to both +/- float64(0).
default:
t.Errorf("strconv.ParseFloat(%q) = %g (%b), want %g (%b); delta = %g", input, e, e, f, f, f-e)
}
}
if !isFinite(f) {
continue
}
// 2. Check f is best approximation to r.
if !checkIsBestApprox(t, f, r) {
// Append context information.
t.Errorf("(input was %q)", input)
}
// 3. Check f->R->f roundtrip is non-lossy.
checkNonLossyRoundtrip(t, f)
// 4. Check exactness using slow algorithm.
if wasExact := new(Rat).SetFloat64(f).Cmp(r) == 0; wasExact != exact {
t.Errorf("Rat.SetString(%q).Float64().exact = %t, want %t", input, exact, wasExact)
}
}
}
func TestFloat64Distribution(t *testing.T) {
// Generate a distribution of (sign, mantissa, exp) values
// broader than the float64 range, and check Rat.Float64()
// always picks the closest float64 approximation.
var add = []int64{
0,
1,
3,
5,
7,
9,
11,
}
var winc, einc = uint64(1), int(1) // soak test (~75s on x86-64)
if testing.Short() {
winc, einc = 10, 500 // quick test (~12ms on x86-64)
}
for _, sign := range "+-" {
for _, a := range add {
for wid := uint64(0); wid < 60; wid += winc {
b := int64(1<<wid + a)
if sign == '-' {
b = -b
}
for exp := -1100; exp < 1100; exp += einc {
num, den := NewInt(b), NewInt(1)
if exp > 0 {
num.Lsh(num, uint(exp))
} else {
den.Lsh(den, uint(-exp))
}
r := new(Rat).SetFrac(num, den)
f, _ := r.Float64()
if !checkIsBestApprox(t, f, r) {
// Append context information.
t.Errorf("(input was mantissa %#x, exp %d; f = %g (%b); f ~ %g; r = %v)",
b, exp, f, f, math.Ldexp(float64(b), exp), r)
}
checkNonLossyRoundtrip(t, f)
}
}
}
}
}
// TestFloat64NonFinite 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)
}
}
}
// checkNonLossyRoundtrip checks that a float->Rat->float roundtrip is
// non-lossy for finite f.
func checkNonLossyRoundtrip(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)
}
// checkIsBestApprox checks that f is the best possible float64
// approximation of r.
// Returns true on success.
func checkIsBestApprox(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 && !isEven(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 && !isEven(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 isEven(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)
}
}
}