rat_test.go

Documentation: math/big

  // 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)
  		}
  	}
  }
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