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) the denominator of an (uninitialized) zero value is not shared with the value
   333  	s := &zero.b
   334  	d := zero.Denom()
   335  	if d == s {
   336  		t.Errorf("1a) got %s (%p) == %s (%p) want different *Int values", d, d, s, s)
   337  	}
   338  
   339  	// 1b) the denominator of an (uninitialized) value is a new 1 each time
   340  	d1 := zero.Denom()
   341  	d2 := zero.Denom()
   342  	if d1 == d2 {
   343  		t.Errorf("1b) got %s (%p) == %s (%p) want different *Int values", d1, d1, d2, d2)
   344  	}
   345  
   346  	// 1c) the denominator of an initialized zero value is shared with the value
   347  	x := new(Rat)
   348  	x.Set(x) // initialize x (any operation that sets x explicitly will do)
   349  	s = &x.b
   350  	d = x.Denom()
   351  	if d != s {
   352  		t.Errorf("1c) got %s (%p) != %s (%p) want identical *Int values", d, d, s, s)
   353  	}
   354  
   355  	// 1d) a zero value remains zero independent of denominator
   356  	x.Denom().Set(new(Int).Neg(b))
   357  	if x.Cmp(zero) != 0 {
   358  		t.Errorf("1d) got %s want %s", x, zero)
   359  	}
   360  
   361  	// 1e) a zero value may have a denominator != 0 and != 1
   362  	x.Num().Set(a)
   363  	qab := new(Rat).SetFrac(a, b)
   364  	if x.Cmp(qab) != 0 {
   365  		t.Errorf("1e) got %s want %s", x, qab)
   366  	}
   367  
   368  	// 2a) an integral value becomes a fraction depending on denominator
   369  	x.SetFrac64(10, 2)
   370  	x.Denom().SetInt64(3)
   371  	q53 := NewRat(5, 3)
   372  	if x.Cmp(q53) != 0 {
   373  		t.Errorf("2a) got %s want %s", x, q53)
   374  	}
   375  
   376  	// 2b) an integral value becomes a fraction depending on denominator
   377  	x = NewRat(10, 2)
   378  	x.Denom().SetInt64(3)
   379  	if x.Cmp(q53) != 0 {
   380  		t.Errorf("2b) got %s want %s", x, q53)
   381  	}
   382  
   383  	// 3) changing the numerator/denominator of a Rat changes the Rat
   384  	x.SetFrac(a, b)
   385  	a = x.Num()
   386  	b = x.Denom()
   387  	a.SetInt64(5)
   388  	b.SetInt64(3)
   389  	if x.Cmp(q53) != 0 {
   390  		t.Errorf("3) got %s want %s", x, q53)
   391  	}
   392  }
   393  
   394  func TestFloat32Distribution(t *testing.T) {
   395  	// Generate a distribution of (sign, mantissa, exp) values
   396  	// broader than the float32 range, and check Rat.Float32()
   397  	// always picks the closest float32 approximation.
   398  	var add = []int64{
   399  		0,
   400  		1,
   401  		3,
   402  		5,
   403  		7,
   404  		9,
   405  		11,
   406  	}
   407  	var winc, einc = uint64(5), 15 // quick test (~60ms on x86-64)
   408  	if *long {
   409  		winc, einc = uint64(1), 1 // soak test (~1.5s on x86-64)
   410  	}
   411  
   412  	for _, sign := range "+-" {
   413  		for _, a := range add {
   414  			for wid := uint64(0); wid < 30; wid += winc {
   415  				b := 1<<wid + a
   416  				if sign == '-' {
   417  					b = -b
   418  				}
   419  				for exp := -150; exp < 150; exp += einc {
   420  					num, den := NewInt(b), NewInt(1)
   421  					if exp > 0 {
   422  						num.Lsh(num, uint(exp))
   423  					} else {
   424  						den.Lsh(den, uint(-exp))
   425  					}
   426  					r := new(Rat).SetFrac(num, den)
   427  					f, _ := r.Float32()
   428  
   429  					if !checkIsBestApprox32(t, f, r) {
   430  						// Append context information.
   431  						t.Errorf("(input was mantissa %#x, exp %d; f = %g (%b); f ~ %g; r = %v)",
   432  							b, exp, f, f, math.Ldexp(float64(b), exp), r)
   433  					}
   434  
   435  					checkNonLossyRoundtrip32(t, f)
   436  				}
   437  			}
   438  		}
   439  	}
   440  }
   441  
   442  func TestFloat64Distribution(t *testing.T) {
   443  	// Generate a distribution of (sign, mantissa, exp) values
   444  	// broader than the float64 range, and check Rat.Float64()
   445  	// always picks the closest float64 approximation.
   446  	var add = []int64{
   447  		0,
   448  		1,
   449  		3,
   450  		5,
   451  		7,
   452  		9,
   453  		11,
   454  	}
   455  	var winc, einc = uint64(10), 500 // quick test (~12ms on x86-64)
   456  	if *long {
   457  		winc, einc = uint64(1), 1 // soak test (~75s on x86-64)
   458  	}
   459  
   460  	for _, sign := range "+-" {
   461  		for _, a := range add {
   462  			for wid := uint64(0); wid < 60; wid += winc {
   463  				b := 1<<wid + a
   464  				if sign == '-' {
   465  					b = -b
   466  				}
   467  				for exp := -1100; exp < 1100; exp += einc {
   468  					num, den := NewInt(b), NewInt(1)
   469  					if exp > 0 {
   470  						num.Lsh(num, uint(exp))
   471  					} else {
   472  						den.Lsh(den, uint(-exp))
   473  					}
   474  					r := new(Rat).SetFrac(num, den)
   475  					f, _ := r.Float64()
   476  
   477  					if !checkIsBestApprox64(t, f, r) {
   478  						// Append context information.
   479  						t.Errorf("(input was mantissa %#x, exp %d; f = %g (%b); f ~ %g; r = %v)",
   480  							b, exp, f, f, math.Ldexp(float64(b), exp), r)
   481  					}
   482  
   483  					checkNonLossyRoundtrip64(t, f)
   484  				}
   485  			}
   486  		}
   487  	}
   488  }
   489  
   490  // TestSetFloat64NonFinite checks that SetFloat64 of a non-finite value
   491  // returns nil.
   492  func TestSetFloat64NonFinite(t *testing.T) {
   493  	for _, f := range []float64{math.NaN(), math.Inf(+1), math.Inf(-1)} {
   494  		var r Rat
   495  		if r2 := r.SetFloat64(f); r2 != nil {
   496  			t.Errorf("SetFloat64(%g) was %v, want nil", f, r2)
   497  		}
   498  	}
   499  }
   500  
   501  // checkNonLossyRoundtrip32 checks that a float->Rat->float roundtrip is
   502  // non-lossy for finite f.
   503  func checkNonLossyRoundtrip32(t *testing.T, f float32) {
   504  	if !isFinite(float64(f)) {
   505  		return
   506  	}
   507  	r := new(Rat).SetFloat64(float64(f))
   508  	if r == nil {
   509  		t.Errorf("Rat.SetFloat64(float64(%g) (%b)) == nil", f, f)
   510  		return
   511  	}
   512  	f2, exact := r.Float32()
   513  	if f != f2 || !exact {
   514  		t.Errorf("Rat.SetFloat64(float64(%g)).Float32() = %g (%b), %v, want %g (%b), %v; delta = %b",
   515  			f, f2, f2, exact, f, f, true, f2-f)
   516  	}
   517  }
   518  
   519  // checkNonLossyRoundtrip64 checks that a float->Rat->float roundtrip is
   520  // non-lossy for finite f.
   521  func checkNonLossyRoundtrip64(t *testing.T, f float64) {
   522  	if !isFinite(f) {
   523  		return
   524  	}
   525  	r := new(Rat).SetFloat64(f)
   526  	if r == nil {
   527  		t.Errorf("Rat.SetFloat64(%g (%b)) == nil", f, f)
   528  		return
   529  	}
   530  	f2, exact := r.Float64()
   531  	if f != f2 || !exact {
   532  		t.Errorf("Rat.SetFloat64(%g).Float64() = %g (%b), %v, want %g (%b), %v; delta = %b",
   533  			f, f2, f2, exact, f, f, true, f2-f)
   534  	}
   535  }
   536  
   537  // delta returns the absolute difference between r and f.
   538  func delta(r *Rat, f float64) *Rat {
   539  	d := new(Rat).Sub(r, new(Rat).SetFloat64(f))
   540  	return d.Abs(d)
   541  }
   542  
   543  // checkIsBestApprox32 checks that f is the best possible float32
   544  // approximation of r.
   545  // Returns true on success.
   546  func checkIsBestApprox32(t *testing.T, f float32, r *Rat) bool {
   547  	if math.Abs(float64(f)) >= math.MaxFloat32 {
   548  		// Cannot check +Inf, -Inf, nor the float next to them (MaxFloat32).
   549  		// But we have tests for these special cases.
   550  		return true
   551  	}
   552  
   553  	// r must be strictly between f0 and f1, the floats bracketing f.
   554  	f0 := math.Nextafter32(f, float32(math.Inf(-1)))
   555  	f1 := math.Nextafter32(f, float32(math.Inf(+1)))
   556  
   557  	// For f to be correct, r must be closer to f than to f0 or f1.
   558  	df := delta(r, float64(f))
   559  	df0 := delta(r, float64(f0))
   560  	df1 := delta(r, float64(f1))
   561  	if df.Cmp(df0) > 0 {
   562  		t.Errorf("Rat(%v).Float32() = %g (%b), but previous float32 %g (%b) is closer", r, f, f, f0, f0)
   563  		return false
   564  	}
   565  	if df.Cmp(df1) > 0 {
   566  		t.Errorf("Rat(%v).Float32() = %g (%b), but next float32 %g (%b) is closer", r, f, f, f1, f1)
   567  		return false
   568  	}
   569  	if df.Cmp(df0) == 0 && !isEven32(f) {
   570  		t.Errorf("Rat(%v).Float32() = %g (%b); halfway should have rounded to %g (%b) instead", r, f, f, f0, f0)
   571  		return false
   572  	}
   573  	if df.Cmp(df1) == 0 && !isEven32(f) {
   574  		t.Errorf("Rat(%v).Float32() = %g (%b); halfway should have rounded to %g (%b) instead", r, f, f, f1, f1)
   575  		return false
   576  	}
   577  	return true
   578  }
   579  
   580  // checkIsBestApprox64 checks that f is the best possible float64
   581  // approximation of r.
   582  // Returns true on success.
   583  func checkIsBestApprox64(t *testing.T, f float64, r *Rat) bool {
   584  	if math.Abs(f) >= math.MaxFloat64 {
   585  		// Cannot check +Inf, -Inf, nor the float next to them (MaxFloat64).
   586  		// But we have tests for these special cases.
   587  		return true
   588  	}
   589  
   590  	// r must be strictly between f0 and f1, the floats bracketing f.
   591  	f0 := math.Nextafter(f, math.Inf(-1))
   592  	f1 := math.Nextafter(f, math.Inf(+1))
   593  
   594  	// For f to be correct, r must be closer to f than to f0 or f1.
   595  	df := delta(r, f)
   596  	df0 := delta(r, f0)
   597  	df1 := delta(r, f1)
   598  	if df.Cmp(df0) > 0 {
   599  		t.Errorf("Rat(%v).Float64() = %g (%b), but previous float64 %g (%b) is closer", r, f, f, f0, f0)
   600  		return false
   601  	}
   602  	if df.Cmp(df1) > 0 {
   603  		t.Errorf("Rat(%v).Float64() = %g (%b), but next float64 %g (%b) is closer", r, f, f, f1, f1)
   604  		return false
   605  	}
   606  	if df.Cmp(df0) == 0 && !isEven64(f) {
   607  		t.Errorf("Rat(%v).Float64() = %g (%b); halfway should have rounded to %g (%b) instead", r, f, f, f0, f0)
   608  		return false
   609  	}
   610  	if df.Cmp(df1) == 0 && !isEven64(f) {
   611  		t.Errorf("Rat(%v).Float64() = %g (%b); halfway should have rounded to %g (%b) instead", r, f, f, f1, f1)
   612  		return false
   613  	}
   614  	return true
   615  }
   616  
   617  func isEven32(f float32) bool { return math.Float32bits(f)&1 == 0 }
   618  func isEven64(f float64) bool { return math.Float64bits(f)&1 == 0 }
   619  
   620  func TestIsFinite(t *testing.T) {
   621  	finites := []float64{
   622  		1.0 / 3,
   623  		4891559871276714924261e+222,
   624  		math.MaxFloat64,
   625  		math.SmallestNonzeroFloat64,
   626  		-math.MaxFloat64,
   627  		-math.SmallestNonzeroFloat64,
   628  	}
   629  	for _, f := range finites {
   630  		if !isFinite(f) {
   631  			t.Errorf("!IsFinite(%g (%b))", f, f)
   632  		}
   633  	}
   634  	nonfinites := []float64{
   635  		math.NaN(),
   636  		math.Inf(-1),
   637  		math.Inf(+1),
   638  	}
   639  	for _, f := range nonfinites {
   640  		if isFinite(f) {
   641  			t.Errorf("IsFinite(%g, (%b))", f, f)
   642  		}
   643  	}
   644  }
   645  
   646  func TestRatSetInt64(t *testing.T) {
   647  	var testCases = []int64{
   648  		0,
   649  		1,
   650  		-1,
   651  		12345,
   652  		-98765,
   653  		math.MaxInt64,
   654  		math.MinInt64,
   655  	}
   656  	var r = new(Rat)
   657  	for i, want := range testCases {
   658  		r.SetInt64(want)
   659  		if !r.IsInt() {
   660  			t.Errorf("#%d: Rat.SetInt64(%d) is not an integer", i, want)
   661  		}
   662  		num := r.Num()
   663  		if !num.IsInt64() {
   664  			t.Errorf("#%d: Rat.SetInt64(%d) numerator is not an int64", i, want)
   665  		}
   666  		got := num.Int64()
   667  		if got != want {
   668  			t.Errorf("#%d: Rat.SetInt64(%d) = %d, but expected %d", i, want, got, want)
   669  		}
   670  	}
   671  }
   672  
   673  func TestRatSetUint64(t *testing.T) {
   674  	var testCases = []uint64{
   675  		0,
   676  		1,
   677  		12345,
   678  		^uint64(0),
   679  	}
   680  	var r = new(Rat)
   681  	for i, want := range testCases {
   682  		r.SetUint64(want)
   683  		if !r.IsInt() {
   684  			t.Errorf("#%d: Rat.SetUint64(%d) is not an integer", i, want)
   685  		}
   686  		num := r.Num()
   687  		if !num.IsUint64() {
   688  			t.Errorf("#%d: Rat.SetUint64(%d) numerator is not a uint64", i, want)
   689  		}
   690  		got := num.Uint64()
   691  		if got != want {
   692  			t.Errorf("#%d: Rat.SetUint64(%d) = %d, but expected %d", i, want, got, want)
   693  		}
   694  	}
   695  }
   696  
   697  func BenchmarkRatCmp(b *testing.B) {
   698  	x, y := NewRat(4, 1), NewRat(7, 2)
   699  	for i := 0; i < b.N; i++ {
   700  		x.Cmp(y)
   701  	}
   702  }
   703  
   704  // TestIssue34919 verifies that a Rat's denominator is not modified
   705  // when simply accessing the Rat value.
   706  func TestIssue34919(t *testing.T) {
   707  	for _, acc := range []struct {
   708  		name string
   709  		f    func(*Rat)
   710  	}{
   711  		{"Float32", func(x *Rat) { x.Float32() }},
   712  		{"Float64", func(x *Rat) { x.Float64() }},
   713  		{"Inv", func(x *Rat) { new(Rat).Inv(x) }},
   714  		{"Sign", func(x *Rat) { x.Sign() }},
   715  		{"IsInt", func(x *Rat) { x.IsInt() }},
   716  		{"Num", func(x *Rat) { x.Num() }},
   717  		// {"Denom", func(x *Rat) { x.Denom() }}, TODO(gri) should we change the API? See issue #33792.
   718  	} {
   719  		// A denominator of length 0 is interpreted as 1. Make sure that
   720  		// "materialization" of the denominator doesn't lead to setting
   721  		// the underlying array element 0 to 1.
   722  		r := &Rat{Int{abs: nat{991}}, Int{abs: make(nat, 0, 1)}}
   723  		acc.f(r)
   724  		if d := r.b.abs[:1][0]; d != 0 {
   725  			t.Errorf("%s modified denominator: got %d, want 0", acc.name, d)
   726  		}
   727  	}
   728  }
   729  
   730  func TestDenomRace(t *testing.T) {
   731  	x := NewRat(1, 2)
   732  	const N = 3
   733  	c := make(chan bool, N)
   734  	for i := 0; i < N; i++ {
   735  		go func() {
   736  			// Denom (also used by Float.SetRat) used to mutate x unnecessarily,
   737  			// provoking race reports when run in the race detector.
   738  			x.Denom()
   739  			new(Float).SetRat(x)
   740  			c <- true
   741  		}()
   742  	}
   743  	for i := 0; i < N; i++ {
   744  		<-c
   745  	}
   746  }
   747  

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