src/cmd/internal/gc/big/rat_test.go - go - Git at Google

 // 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"
 	"encoding/json"
 	"encoding/xml"
 	"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 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)
 	}
 }

 var ratNums = []string{
 	"-141592653589793238462643383279502884197169399375105820974944592307816406286",
 	"-1415926535897932384626433832795028841971",
 	"-141592653589793",
 	"-1",
 	"0",
 	"1",
 	"141592653589793",
 	"1415926535897932384626433832795028841971",
 	"141592653589793238462643383279502884197169399375105820974944592307816406286",
 }

 var ratDenoms = []string{
 	"1",
 	"718281828459045",
 	"7182818284590452353602874713526624977572",
 	"718281828459045235360287471352662497757247093699959574966967627724076630353",
 }

 func TestRatJSONEncoding(t *testing.T) {
 	for _, num := range ratNums {
 		for _, denom := range ratDenoms {
 			var tx Rat
 			tx.SetString(num + "/" + denom)
 			b, err := json.Marshal(&tx)
 			if err != nil {
 				t.Errorf("marshaling of %s failed: %s", &tx, err)
 				continue
 			}
 			var rx Rat
 			if err := json.Unmarshal(b, &rx); err != nil {
 				t.Errorf("unmarshaling of %s failed: %s", &tx, err)
 				continue
 			}
 			if rx.Cmp(&tx) != 0 {
 				t.Errorf("JSON encoding of %s failed: got %s want %s", &tx, &rx, &tx)
 			}
 		}
 	}
 }

 func TestRatXMLEncoding(t *testing.T) {
 	for _, num := range ratNums {
 		for _, denom := range ratDenoms {
 			var tx Rat
 			tx.SetString(num + "/" + denom)
 			b, err := xml.Marshal(&tx)
 			if err != nil {
 				t.Errorf("marshaling of %s failed: %s", &tx, err)
 				continue
 			}
 			var rx Rat
 			if err := xml.Unmarshal(b, &rx); err != nil {
 				t.Errorf("unmarshaling of %s failed: %s", &tx, err)
 				continue
 			}
 			if rx.Cmp(&tx) != 0 {
 				t.Errorf("XML encoding of %s failed: got %s want %s", &tx, &rx, &tx)
 			}
 		}
 	}
 }

 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(1), 1 // soak test (~1.5s on x86-64)
 	if testing.Short() {
 		winc, einc = 5, 15 // quick test (~60ms 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(1), 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 := 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)
 		}
 	}
 }
	// 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"
	"encoding/json"
	"encoding/xml"
	"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 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)
	}
	}

	var ratNums = []string{
	"-141592653589793238462643383279502884197169399375105820974944592307816406286",
	"-1415926535897932384626433832795028841971",
	"-141592653589793",
	"-1",
	"0",
	"1",
	"141592653589793",
	"1415926535897932384626433832795028841971",
	"141592653589793238462643383279502884197169399375105820974944592307816406286",
	}

	var ratDenoms = []string{
	"1",
	"718281828459045",
	"7182818284590452353602874713526624977572",
	"718281828459045235360287471352662497757247093699959574966967627724076630353",
	}

	func TestRatJSONEncoding(t *testing.T) {
	for _, num := range ratNums {
	for _, denom := range ratDenoms {
	var tx Rat
	tx.SetString(num + "/" + denom)
	b, err := json.Marshal(&tx)
	if err != nil {
	t.Errorf("marshaling of %s failed: %s", &tx, err)
	continue
	}
	var rx Rat
	if err := json.Unmarshal(b, &rx); err != nil {
	t.Errorf("unmarshaling of %s failed: %s", &tx, err)
	continue
	}
	if rx.Cmp(&tx) != 0 {
	t.Errorf("JSON encoding of %s failed: got %s want %s", &tx, &rx, &tx)
	}
	}
	}
	}

	func TestRatXMLEncoding(t *testing.T) {
	for _, num := range ratNums {
	for _, denom := range ratDenoms {
	var tx Rat
	tx.SetString(num + "/" + denom)
	b, err := xml.Marshal(&tx)
	if err != nil {
	t.Errorf("marshaling of %s failed: %s", &tx, err)
	continue
	}
	var rx Rat
	if err := xml.Unmarshal(b, &rx); err != nil {
	t.Errorf("unmarshaling of %s failed: %s", &tx, err)
	continue
	}
	if rx.Cmp(&tx) != 0 {
	t.Errorf("XML encoding of %s failed: got %s want %s", &tx, &rx, &tx)
	}
	}
	}
	}

	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(1), 1 // soak test (~1.5s on x86-64)
	if testing.Short() {
	winc, einc = 5, 15 // quick test (~60ms 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(1), 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 := 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)
	}
	}
	}