// 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 (
"math"
"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)
}
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 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)
}
}
func TestFloat32Distribution(t *testing.T) {
// Generate a distribution of (sign, mantissa, exp) values
// broader than the float32 range, and check Rat.Float32()
// always picks the closest float32 approximation.
var add = []int64{
0,
1,
3,
5,
7,
9,
11,
}
var winc, einc = uint64(5), 15 // quick test (~60ms on x86-64)
if *long {
winc, einc = uint64(1), 1 // soak test (~1.5s on x86-64)
}
for _, sign := range "+-" {
for _, a := range add {
for wid := uint64(0); wid < 30; wid += winc {
b := 1<<wid + a
if sign == '-' {
b = -b
}
for exp := -150; exp < 150; 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.Float32()
if !checkIsBestApprox32(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)
}
checkNonLossyRoundtrip32(t, f)
}
}
}
}
}
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(10), 500 // quick test (~12ms on x86-64)
if *long {
winc, einc = uint64(1), 1 // soak test (~75s on x86-64)
}
for _, sign := range "+-" {
for _, a := range add {
for wid := uint64(0); wid < 60; wid += winc {
b := 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 !checkIsBestApprox64(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)
}
checkNonLossyRoundtrip64(t, f)
}
}
}
}
}
// 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)
}
}
}