Source file src/math/big/rat_test.go

Documentation: math/big

     1  // Copyright 2010 The Go Authors. All rights reserved.
     2  // Use of this source code is governed by a BSD-style
     3  // license that can be found in the LICENSE file.
     4  
     5  package big
     6  
     7  import (
     8  	"math"
     9  	"testing"
    10  )
    11  
    12  func TestZeroRat(t *testing.T) {
    13  	var x, y, z Rat
    14  	y.SetFrac64(0, 42)
    15  
    16  	if x.Cmp(&y) != 0 {
    17  		t.Errorf("x and y should be both equal and zero")
    18  	}
    19  
    20  	if s := x.String(); s != "0/1" {
    21  		t.Errorf("got x = %s, want 0/1", s)
    22  	}
    23  
    24  	if s := x.RatString(); s != "0" {
    25  		t.Errorf("got x = %s, want 0", s)
    26  	}
    27  
    28  	z.Add(&x, &y)
    29  	if s := z.RatString(); s != "0" {
    30  		t.Errorf("got x+y = %s, want 0", s)
    31  	}
    32  
    33  	z.Sub(&x, &y)
    34  	if s := z.RatString(); s != "0" {
    35  		t.Errorf("got x-y = %s, want 0", s)
    36  	}
    37  
    38  	z.Mul(&x, &y)
    39  	if s := z.RatString(); s != "0" {
    40  		t.Errorf("got x*y = %s, want 0", s)
    41  	}
    42  
    43  	// check for division by zero
    44  	defer func() {
    45  		if s := recover(); s == nil || s.(string) != "division by zero" {
    46  			panic(s)
    47  		}
    48  	}()
    49  	z.Quo(&x, &y)
    50  }
    51  
    52  func TestRatSign(t *testing.T) {
    53  	zero := NewRat(0, 1)
    54  	for _, a := range setStringTests {
    55  		x, ok := new(Rat).SetString(a.in)
    56  		if !ok {
    57  			continue
    58  		}
    59  		s := x.Sign()
    60  		e := x.Cmp(zero)
    61  		if s != e {
    62  			t.Errorf("got %d; want %d for z = %v", s, e, &x)
    63  		}
    64  	}
    65  }
    66  
    67  var ratCmpTests = []struct {
    68  	rat1, rat2 string
    69  	out        int
    70  }{
    71  	{"0", "0/1", 0},
    72  	{"1/1", "1", 0},
    73  	{"-1", "-2/2", 0},
    74  	{"1", "0", 1},
    75  	{"0/1", "1/1", -1},
    76  	{"-5/1434770811533343057144", "-5/1434770811533343057145", -1},
    77  	{"49832350382626108453/8964749413", "49832350382626108454/8964749413", -1},
    78  	{"-37414950961700930/7204075375675961", "37414950961700930/7204075375675961", -1},
    79  	{"37414950961700930/7204075375675961", "74829901923401860/14408150751351922", 0},
    80  }
    81  
    82  func TestRatCmp(t *testing.T) {
    83  	for i, test := range ratCmpTests {
    84  		x, _ := new(Rat).SetString(test.rat1)
    85  		y, _ := new(Rat).SetString(test.rat2)
    86  
    87  		out := x.Cmp(y)
    88  		if out != test.out {
    89  			t.Errorf("#%d got out = %v; want %v", i, out, test.out)
    90  		}
    91  	}
    92  }
    93  
    94  func TestIsInt(t *testing.T) {
    95  	one := NewInt(1)
    96  	for _, a := range setStringTests {
    97  		x, ok := new(Rat).SetString(a.in)
    98  		if !ok {
    99  			continue
   100  		}
   101  		i := x.IsInt()
   102  		e := x.Denom().Cmp(one) == 0
   103  		if i != e {
   104  			t.Errorf("got IsInt(%v) == %v; want %v", x, i, e)
   105  		}
   106  	}
   107  }
   108  
   109  func TestRatAbs(t *testing.T) {
   110  	zero := new(Rat)
   111  	for _, a := range setStringTests {
   112  		x, ok := new(Rat).SetString(a.in)
   113  		if !ok {
   114  			continue
   115  		}
   116  		e := new(Rat).Set(x)
   117  		if e.Cmp(zero) < 0 {
   118  			e.Sub(zero, e)
   119  		}
   120  		z := new(Rat).Abs(x)
   121  		if z.Cmp(e) != 0 {
   122  			t.Errorf("got Abs(%v) = %v; want %v", x, z, e)
   123  		}
   124  	}
   125  }
   126  
   127  func TestRatNeg(t *testing.T) {
   128  	zero := new(Rat)
   129  	for _, a := range setStringTests {
   130  		x, ok := new(Rat).SetString(a.in)
   131  		if !ok {
   132  			continue
   133  		}
   134  		e := new(Rat).Sub(zero, x)
   135  		z := new(Rat).Neg(x)
   136  		if z.Cmp(e) != 0 {
   137  			t.Errorf("got Neg(%v) = %v; want %v", x, z, e)
   138  		}
   139  	}
   140  }
   141  
   142  func TestRatInv(t *testing.T) {
   143  	zero := new(Rat)
   144  	for _, a := range setStringTests {
   145  		x, ok := new(Rat).SetString(a.in)
   146  		if !ok {
   147  			continue
   148  		}
   149  		if x.Cmp(zero) == 0 {
   150  			continue // avoid division by zero
   151  		}
   152  		e := new(Rat).SetFrac(x.Denom(), x.Num())
   153  		z := new(Rat).Inv(x)
   154  		if z.Cmp(e) != 0 {
   155  			t.Errorf("got Inv(%v) = %v; want %v", x, z, e)
   156  		}
   157  	}
   158  }
   159  
   160  type ratBinFun func(z, x, y *Rat) *Rat
   161  type ratBinArg struct {
   162  	x, y, z string
   163  }
   164  
   165  func testRatBin(t *testing.T, i int, name string, f ratBinFun, a ratBinArg) {
   166  	x, _ := new(Rat).SetString(a.x)
   167  	y, _ := new(Rat).SetString(a.y)
   168  	z, _ := new(Rat).SetString(a.z)
   169  	out := f(new(Rat), x, y)
   170  
   171  	if out.Cmp(z) != 0 {
   172  		t.Errorf("%s #%d got %s want %s", name, i, out, z)
   173  	}
   174  }
   175  
   176  var ratBinTests = []struct {
   177  	x, y      string
   178  	sum, prod string
   179  }{
   180  	{"0", "0", "0", "0"},
   181  	{"0", "1", "1", "0"},
   182  	{"-1", "0", "-1", "0"},
   183  	{"-1", "1", "0", "-1"},
   184  	{"1", "1", "2", "1"},
   185  	{"1/2", "1/2", "1", "1/4"},
   186  	{"1/4", "1/3", "7/12", "1/12"},
   187  	{"2/5", "-14/3", "-64/15", "-28/15"},
   188  	{"4707/49292519774798173060", "-3367/70976135186689855734", "84058377121001851123459/1749296273614329067191168098769082663020", "-1760941/388732505247628681598037355282018369560"},
   189  	{"-61204110018146728334/3", "-31052192278051565633/2", "-215564796870448153567/6", "950260896245257153059642991192710872711/3"},
   190  	{"-854857841473707320655/4237645934602118692642972629634714039", "-18/31750379913563777419", "-27/133467566250814981", "15387441146526731771790/134546868362786310073779084329032722548987800600710485341"},
   191  	{"618575745270541348005638912139/19198433543745179392300736", "-19948846211000086/637313996471", "27674141753240653/30123979153216", "-6169936206128396568797607742807090270137721977/6117715203873571641674006593837351328"},
   192  	{"-3/26206484091896184128", "5/2848423294177090248", "15310893822118706237/9330894968229805033368778458685147968", "-5/24882386581946146755650075889827061248"},
   193  	{"26946729/330400702820", "41563965/225583428284", "1238218672302860271/4658307703098666660055", "224002580204097/14906584649915733312176"},
   194  	{"-8259900599013409474/7", "-84829337473700364773/56707961321161574960", "-468402123685491748914621885145127724451/396955729248131024720", "350340947706464153265156004876107029701/198477864624065512360"},
   195  	{"575775209696864/1320203974639986246357", "29/712593081308", "410331716733912717985762465/940768218243776489278275419794956", "808/45524274987585732633"},
   196  	{"1786597389946320496771/2066653520653241", "6269770/1992362624741777", "3559549865190272133656109052308126637/4117523232840525481453983149257", "8967230/3296219033"},
   197  	{"-36459180403360509753/32150500941194292113930", "9381566963714/9633539", "301622077145533298008420642898530153/309723104686531919656937098270", "-3784609207827/3426986245"},
   198  }
   199  
   200  func TestRatBin(t *testing.T) {
   201  	for i, test := range ratBinTests {
   202  		arg := ratBinArg{test.x, test.y, test.sum}
   203  		testRatBin(t, i, "Add", (*Rat).Add, arg)
   204  
   205  		arg = ratBinArg{test.y, test.x, test.sum}
   206  		testRatBin(t, i, "Add symmetric", (*Rat).Add, arg)
   207  
   208  		arg = ratBinArg{test.sum, test.x, test.y}
   209  		testRatBin(t, i, "Sub", (*Rat).Sub, arg)
   210  
   211  		arg = ratBinArg{test.sum, test.y, test.x}
   212  		testRatBin(t, i, "Sub symmetric", (*Rat).Sub, arg)
   213  
   214  		arg = ratBinArg{test.x, test.y, test.prod}
   215  		testRatBin(t, i, "Mul", (*Rat).Mul, arg)
   216  
   217  		arg = ratBinArg{test.y, test.x, test.prod}
   218  		testRatBin(t, i, "Mul symmetric", (*Rat).Mul, arg)
   219  
   220  		if test.x != "0" {
   221  			arg = ratBinArg{test.prod, test.x, test.y}
   222  			testRatBin(t, i, "Quo", (*Rat).Quo, arg)
   223  		}
   224  
   225  		if test.y != "0" {
   226  			arg = ratBinArg{test.prod, test.y, test.x}
   227  			testRatBin(t, i, "Quo symmetric", (*Rat).Quo, arg)
   228  		}
   229  	}
   230  }
   231  
   232  func TestIssue820(t *testing.T) {
   233  	x := NewRat(3, 1)
   234  	y := NewRat(2, 1)
   235  	z := y.Quo(x, y)
   236  	q := NewRat(3, 2)
   237  	if z.Cmp(q) != 0 {
   238  		t.Errorf("got %s want %s", z, q)
   239  	}
   240  
   241  	y = NewRat(3, 1)
   242  	x = NewRat(2, 1)
   243  	z = y.Quo(x, y)
   244  	q = NewRat(2, 3)
   245  	if z.Cmp(q) != 0 {
   246  		t.Errorf("got %s want %s", z, q)
   247  	}
   248  
   249  	x = NewRat(3, 1)
   250  	z = x.Quo(x, x)
   251  	q = NewRat(3, 3)
   252  	if z.Cmp(q) != 0 {
   253  		t.Errorf("got %s want %s", z, q)
   254  	}
   255  }
   256  
   257  var setFrac64Tests = []struct {
   258  	a, b int64
   259  	out  string
   260  }{
   261  	{0, 1, "0"},
   262  	{0, -1, "0"},
   263  	{1, 1, "1"},
   264  	{-1, 1, "-1"},
   265  	{1, -1, "-1"},
   266  	{-1, -1, "1"},
   267  	{-9223372036854775808, -9223372036854775808, "1"},
   268  }
   269  
   270  func TestRatSetFrac64Rat(t *testing.T) {
   271  	for i, test := range setFrac64Tests {
   272  		x := new(Rat).SetFrac64(test.a, test.b)
   273  		if x.RatString() != test.out {
   274  			t.Errorf("#%d got %s want %s", i, x.RatString(), test.out)
   275  		}
   276  	}
   277  }
   278  
   279  func TestIssue2379(t *testing.T) {
   280  	// 1) no aliasing
   281  	q := NewRat(3, 2)
   282  	x := new(Rat)
   283  	x.SetFrac(NewInt(3), NewInt(2))
   284  	if x.Cmp(q) != 0 {
   285  		t.Errorf("1) got %s want %s", x, q)
   286  	}
   287  
   288  	// 2) aliasing of numerator
   289  	x = NewRat(2, 3)
   290  	x.SetFrac(NewInt(3), x.Num())
   291  	if x.Cmp(q) != 0 {
   292  		t.Errorf("2) got %s want %s", x, q)
   293  	}
   294  
   295  	// 3) aliasing of denominator
   296  	x = NewRat(2, 3)
   297  	x.SetFrac(x.Denom(), NewInt(2))
   298  	if x.Cmp(q) != 0 {
   299  		t.Errorf("3) got %s want %s", x, q)
   300  	}
   301  
   302  	// 4) aliasing of numerator and denominator
   303  	x = NewRat(2, 3)
   304  	x.SetFrac(x.Denom(), x.Num())
   305  	if x.Cmp(q) != 0 {
   306  		t.Errorf("4) got %s want %s", x, q)
   307  	}
   308  
   309  	// 5) numerator and denominator are the same
   310  	q = NewRat(1, 1)
   311  	x = new(Rat)
   312  	n := NewInt(7)
   313  	x.SetFrac(n, n)
   314  	if x.Cmp(q) != 0 {
   315  		t.Errorf("5) got %s want %s", x, q)
   316  	}
   317  }
   318  
   319  func TestIssue3521(t *testing.T) {
   320  	a := new(Int)
   321  	b := new(Int)
   322  	a.SetString("64375784358435883458348587", 0)
   323  	b.SetString("4789759874531", 0)
   324  
   325  	// 0) a raw zero value has 1 as denominator
   326  	zero := new(Rat)
   327  	one := NewInt(1)
   328  	if zero.Denom().Cmp(one) != 0 {
   329  		t.Errorf("0) got %s want %s", zero.Denom(), one)
   330  	}
   331  
   332  	// 1a) a zero value remains zero independent of denominator
   333  	x := new(Rat)
   334  	x.Denom().Set(new(Int).Neg(b))
   335  	if x.Cmp(zero) != 0 {
   336  		t.Errorf("1a) got %s want %s", x, zero)
   337  	}
   338  
   339  	// 1b) a zero value may have a denominator != 0 and != 1
   340  	x.Num().Set(a)
   341  	qab := new(Rat).SetFrac(a, b)
   342  	if x.Cmp(qab) != 0 {
   343  		t.Errorf("1b) got %s want %s", x, qab)
   344  	}
   345  
   346  	// 2a) an integral value becomes a fraction depending on denominator
   347  	x.SetFrac64(10, 2)
   348  	x.Denom().SetInt64(3)
   349  	q53 := NewRat(5, 3)
   350  	if x.Cmp(q53) != 0 {
   351  		t.Errorf("2a) got %s want %s", x, q53)
   352  	}
   353  
   354  	// 2b) an integral value becomes a fraction depending on denominator
   355  	x = NewRat(10, 2)
   356  	x.Denom().SetInt64(3)
   357  	if x.Cmp(q53) != 0 {
   358  		t.Errorf("2b) got %s want %s", x, q53)
   359  	}
   360  
   361  	// 3) changing the numerator/denominator of a Rat changes the Rat
   362  	x.SetFrac(a, b)
   363  	a = x.Num()
   364  	b = x.Denom()
   365  	a.SetInt64(5)
   366  	b.SetInt64(3)
   367  	if x.Cmp(q53) != 0 {
   368  		t.Errorf("3) got %s want %s", x, q53)
   369  	}
   370  }
   371  
   372  func TestFloat32Distribution(t *testing.T) {
   373  	// Generate a distribution of (sign, mantissa, exp) values
   374  	// broader than the float32 range, and check Rat.Float32()
   375  	// always picks the closest float32 approximation.
   376  	var add = []int64{
   377  		0,
   378  		1,
   379  		3,
   380  		5,
   381  		7,
   382  		9,
   383  		11,
   384  	}
   385  	var winc, einc = uint64(5), 15 // quick test (~60ms on x86-64)
   386  	if *long {
   387  		winc, einc = uint64(1), 1 // soak test (~1.5s on x86-64)
   388  	}
   389  
   390  	for _, sign := range "+-" {
   391  		for _, a := range add {
   392  			for wid := uint64(0); wid < 30; wid += winc {
   393  				b := 1<<wid + a
   394  				if sign == '-' {
   395  					b = -b
   396  				}
   397  				for exp := -150; exp < 150; exp += einc {
   398  					num, den := NewInt(b), NewInt(1)
   399  					if exp > 0 {
   400  						num.Lsh(num, uint(exp))
   401  					} else {
   402  						den.Lsh(den, uint(-exp))
   403  					}
   404  					r := new(Rat).SetFrac(num, den)
   405  					f, _ := r.Float32()
   406  
   407  					if !checkIsBestApprox32(t, f, r) {
   408  						// Append context information.
   409  						t.Errorf("(input was mantissa %#x, exp %d; f = %g (%b); f ~ %g; r = %v)",
   410  							b, exp, f, f, math.Ldexp(float64(b), exp), r)
   411  					}
   412  
   413  					checkNonLossyRoundtrip32(t, f)
   414  				}
   415  			}
   416  		}
   417  	}
   418  }
   419  
   420  func TestFloat64Distribution(t *testing.T) {
   421  	// Generate a distribution of (sign, mantissa, exp) values
   422  	// broader than the float64 range, and check Rat.Float64()
   423  	// always picks the closest float64 approximation.
   424  	var add = []int64{
   425  		0,
   426  		1,
   427  		3,
   428  		5,
   429  		7,
   430  		9,
   431  		11,
   432  	}
   433  	var winc, einc = uint64(10), 500 // quick test (~12ms on x86-64)
   434  	if *long {
   435  		winc, einc = uint64(1), 1 // soak test (~75s on x86-64)
   436  	}
   437  
   438  	for _, sign := range "+-" {
   439  		for _, a := range add {
   440  			for wid := uint64(0); wid < 60; wid += winc {
   441  				b := 1<<wid + a
   442  				if sign == '-' {
   443  					b = -b
   444  				}
   445  				for exp := -1100; exp < 1100; exp += einc {
   446  					num, den := NewInt(b), NewInt(1)
   447  					if exp > 0 {
   448  						num.Lsh(num, uint(exp))
   449  					} else {
   450  						den.Lsh(den, uint(-exp))
   451  					}
   452  					r := new(Rat).SetFrac(num, den)
   453  					f, _ := r.Float64()
   454  
   455  					if !checkIsBestApprox64(t, f, r) {
   456  						// Append context information.
   457  						t.Errorf("(input was mantissa %#x, exp %d; f = %g (%b); f ~ %g; r = %v)",
   458  							b, exp, f, f, math.Ldexp(float64(b), exp), r)
   459  					}
   460  
   461  					checkNonLossyRoundtrip64(t, f)
   462  				}
   463  			}
   464  		}
   465  	}
   466  }
   467  
   468  // TestSetFloat64NonFinite checks that SetFloat64 of a non-finite value
   469  // returns nil.
   470  func TestSetFloat64NonFinite(t *testing.T) {
   471  	for _, f := range []float64{math.NaN(), math.Inf(+1), math.Inf(-1)} {
   472  		var r Rat
   473  		if r2 := r.SetFloat64(f); r2 != nil {
   474  			t.Errorf("SetFloat64(%g) was %v, want nil", f, r2)
   475  		}
   476  	}
   477  }
   478  
   479  // checkNonLossyRoundtrip32 checks that a float->Rat->float roundtrip is
   480  // non-lossy for finite f.
   481  func checkNonLossyRoundtrip32(t *testing.T, f float32) {
   482  	if !isFinite(float64(f)) {
   483  		return
   484  	}
   485  	r := new(Rat).SetFloat64(float64(f))
   486  	if r == nil {
   487  		t.Errorf("Rat.SetFloat64(float64(%g) (%b)) == nil", f, f)
   488  		return
   489  	}
   490  	f2, exact := r.Float32()
   491  	if f != f2 || !exact {
   492  		t.Errorf("Rat.SetFloat64(float64(%g)).Float32() = %g (%b), %v, want %g (%b), %v; delta = %b",
   493  			f, f2, f2, exact, f, f, true, f2-f)
   494  	}
   495  }
   496  
   497  // checkNonLossyRoundtrip64 checks that a float->Rat->float roundtrip is
   498  // non-lossy for finite f.
   499  func checkNonLossyRoundtrip64(t *testing.T, f float64) {
   500  	if !isFinite(f) {
   501  		return
   502  	}
   503  	r := new(Rat).SetFloat64(f)
   504  	if r == nil {
   505  		t.Errorf("Rat.SetFloat64(%g (%b)) == nil", f, f)
   506  		return
   507  	}
   508  	f2, exact := r.Float64()
   509  	if f != f2 || !exact {
   510  		t.Errorf("Rat.SetFloat64(%g).Float64() = %g (%b), %v, want %g (%b), %v; delta = %b",
   511  			f, f2, f2, exact, f, f, true, f2-f)
   512  	}
   513  }
   514  
   515  // delta returns the absolute difference between r and f.
   516  func delta(r *Rat, f float64) *Rat {
   517  	d := new(Rat).Sub(r, new(Rat).SetFloat64(f))
   518  	return d.Abs(d)
   519  }
   520  
   521  // checkIsBestApprox32 checks that f is the best possible float32
   522  // approximation of r.
   523  // Returns true on success.
   524  func checkIsBestApprox32(t *testing.T, f float32, r *Rat) bool {
   525  	if math.Abs(float64(f)) >= math.MaxFloat32 {
   526  		// Cannot check +Inf, -Inf, nor the float next to them (MaxFloat32).
   527  		// But we have tests for these special cases.
   528  		return true
   529  	}
   530  
   531  	// r must be strictly between f0 and f1, the floats bracketing f.
   532  	f0 := math.Nextafter32(f, float32(math.Inf(-1)))
   533  	f1 := math.Nextafter32(f, float32(math.Inf(+1)))
   534  
   535  	// For f to be correct, r must be closer to f than to f0 or f1.
   536  	df := delta(r, float64(f))
   537  	df0 := delta(r, float64(f0))
   538  	df1 := delta(r, float64(f1))
   539  	if df.Cmp(df0) > 0 {
   540  		t.Errorf("Rat(%v).Float32() = %g (%b), but previous float32 %g (%b) is closer", r, f, f, f0, f0)
   541  		return false
   542  	}
   543  	if df.Cmp(df1) > 0 {
   544  		t.Errorf("Rat(%v).Float32() = %g (%b), but next float32 %g (%b) is closer", r, f, f, f1, f1)
   545  		return false
   546  	}
   547  	if df.Cmp(df0) == 0 && !isEven32(f) {
   548  		t.Errorf("Rat(%v).Float32() = %g (%b); halfway should have rounded to %g (%b) instead", r, f, f, f0, f0)
   549  		return false
   550  	}
   551  	if df.Cmp(df1) == 0 && !isEven32(f) {
   552  		t.Errorf("Rat(%v).Float32() = %g (%b); halfway should have rounded to %g (%b) instead", r, f, f, f1, f1)
   553  		return false
   554  	}
   555  	return true
   556  }
   557  
   558  // checkIsBestApprox64 checks that f is the best possible float64
   559  // approximation of r.
   560  // Returns true on success.
   561  func checkIsBestApprox64(t *testing.T, f float64, r *Rat) bool {
   562  	if math.Abs(f) >= math.MaxFloat64 {
   563  		// Cannot check +Inf, -Inf, nor the float next to them (MaxFloat64).
   564  		// But we have tests for these special cases.
   565  		return true
   566  	}
   567  
   568  	// r must be strictly between f0 and f1, the floats bracketing f.
   569  	f0 := math.Nextafter(f, math.Inf(-1))
   570  	f1 := math.Nextafter(f, math.Inf(+1))
   571  
   572  	// For f to be correct, r must be closer to f than to f0 or f1.
   573  	df := delta(r, f)
   574  	df0 := delta(r, f0)
   575  	df1 := delta(r, f1)
   576  	if df.Cmp(df0) > 0 {
   577  		t.Errorf("Rat(%v).Float64() = %g (%b), but previous float64 %g (%b) is closer", r, f, f, f0, f0)
   578  		return false
   579  	}
   580  	if df.Cmp(df1) > 0 {
   581  		t.Errorf("Rat(%v).Float64() = %g (%b), but next float64 %g (%b) is closer", r, f, f, f1, f1)
   582  		return false
   583  	}
   584  	if df.Cmp(df0) == 0 && !isEven64(f) {
   585  		t.Errorf("Rat(%v).Float64() = %g (%b); halfway should have rounded to %g (%b) instead", r, f, f, f0, f0)
   586  		return false
   587  	}
   588  	if df.Cmp(df1) == 0 && !isEven64(f) {
   589  		t.Errorf("Rat(%v).Float64() = %g (%b); halfway should have rounded to %g (%b) instead", r, f, f, f1, f1)
   590  		return false
   591  	}
   592  	return true
   593  }
   594  
   595  func isEven32(f float32) bool { return math.Float32bits(f)&1 == 0 }
   596  func isEven64(f float64) bool { return math.Float64bits(f)&1 == 0 }
   597  
   598  func TestIsFinite(t *testing.T) {
   599  	finites := []float64{
   600  		1.0 / 3,
   601  		4891559871276714924261e+222,
   602  		math.MaxFloat64,
   603  		math.SmallestNonzeroFloat64,
   604  		-math.MaxFloat64,
   605  		-math.SmallestNonzeroFloat64,
   606  	}
   607  	for _, f := range finites {
   608  		if !isFinite(f) {
   609  			t.Errorf("!IsFinite(%g (%b))", f, f)
   610  		}
   611  	}
   612  	nonfinites := []float64{
   613  		math.NaN(),
   614  		math.Inf(-1),
   615  		math.Inf(+1),
   616  	}
   617  	for _, f := range nonfinites {
   618  		if isFinite(f) {
   619  			t.Errorf("IsFinite(%g, (%b))", f, f)
   620  		}
   621  	}
   622  }
   623  

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