github.com/xushiwei/go@v0.0.0-20130601165731-2b9d83f45bc9/src/pkg/math/big/rat_test.go (about)

     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  	"bytes"
     9  	"encoding/gob"
    10  	"fmt"
    11  	"math"
    12  	"strconv"
    13  	"strings"
    14  	"testing"
    15  )
    16  
    17  func TestZeroRat(t *testing.T) {
    18  	var x, y, z Rat
    19  	y.SetFrac64(0, 42)
    20  
    21  	if x.Cmp(&y) != 0 {
    22  		t.Errorf("x and y should be both equal and zero")
    23  	}
    24  
    25  	if s := x.String(); s != "0/1" {
    26  		t.Errorf("got x = %s, want 0/1", s)
    27  	}
    28  
    29  	if s := x.RatString(); s != "0" {
    30  		t.Errorf("got x = %s, want 0", s)
    31  	}
    32  
    33  	z.Add(&x, &y)
    34  	if s := z.RatString(); s != "0" {
    35  		t.Errorf("got x+y = %s, want 0", s)
    36  	}
    37  
    38  	z.Sub(&x, &y)
    39  	if s := z.RatString(); s != "0" {
    40  		t.Errorf("got x-y = %s, want 0", s)
    41  	}
    42  
    43  	z.Mul(&x, &y)
    44  	if s := z.RatString(); s != "0" {
    45  		t.Errorf("got x*y = %s, want 0", s)
    46  	}
    47  
    48  	// check for division by zero
    49  	defer func() {
    50  		if s := recover(); s == nil || s.(string) != "division by zero" {
    51  			panic(s)
    52  		}
    53  	}()
    54  	z.Quo(&x, &y)
    55  }
    56  
    57  var setStringTests = []struct {
    58  	in, out string
    59  	ok      bool
    60  }{
    61  	{"0", "0", true},
    62  	{"-0", "0", true},
    63  	{"1", "1", true},
    64  	{"-1", "-1", true},
    65  	{"1.", "1", true},
    66  	{"1e0", "1", true},
    67  	{"1.e1", "10", true},
    68  	{in: "1e", ok: false},
    69  	{in: "1.e", ok: false},
    70  	{in: "1e+14e-5", ok: false},
    71  	{in: "1e4.5", ok: false},
    72  	{in: "r", ok: false},
    73  	{in: "a/b", ok: false},
    74  	{in: "a.b", ok: false},
    75  	{"-0.1", "-1/10", true},
    76  	{"-.1", "-1/10", true},
    77  	{"2/4", "1/2", true},
    78  	{".25", "1/4", true},
    79  	{"-1/5", "-1/5", true},
    80  	{"8129567.7690E14", "812956776900000000000", true},
    81  	{"78189e+4", "781890000", true},
    82  	{"553019.8935e+8", "55301989350000", true},
    83  	{"98765432109876543210987654321e-10", "98765432109876543210987654321/10000000000", true},
    84  	{"9877861857500000E-7", "3951144743/4", true},
    85  	{"2169378.417e-3", "2169378417/1000000", true},
    86  	{"884243222337379604041632732738665534", "884243222337379604041632732738665534", true},
    87  	{"53/70893980658822810696", "53/70893980658822810696", true},
    88  	{"106/141787961317645621392", "53/70893980658822810696", true},
    89  	{"204211327800791583.81095", "4084226556015831676219/20000", true},
    90  }
    91  
    92  func TestRatSetString(t *testing.T) {
    93  	for i, test := range setStringTests {
    94  		x, ok := new(Rat).SetString(test.in)
    95  
    96  		if ok {
    97  			if !test.ok {
    98  				t.Errorf("#%d SetString(%q) expected failure", i, test.in)
    99  			} else if x.RatString() != test.out {
   100  				t.Errorf("#%d SetString(%q) got %s want %s", i, test.in, x.RatString(), test.out)
   101  			}
   102  		} else if x != nil {
   103  			t.Errorf("#%d SetString(%q) got %p want nil", i, test.in, x)
   104  		}
   105  	}
   106  }
   107  
   108  func TestRatScan(t *testing.T) {
   109  	var buf bytes.Buffer
   110  	for i, test := range setStringTests {
   111  		x := new(Rat)
   112  		buf.Reset()
   113  		buf.WriteString(test.in)
   114  
   115  		_, err := fmt.Fscanf(&buf, "%v", x)
   116  		if err == nil != test.ok {
   117  			if test.ok {
   118  				t.Errorf("#%d error: %s", i, err)
   119  			} else {
   120  				t.Errorf("#%d expected error", i)
   121  			}
   122  			continue
   123  		}
   124  		if err == nil && x.RatString() != test.out {
   125  			t.Errorf("#%d got %s want %s", i, x.RatString(), test.out)
   126  		}
   127  	}
   128  }
   129  
   130  var floatStringTests = []struct {
   131  	in   string
   132  	prec int
   133  	out  string
   134  }{
   135  	{"0", 0, "0"},
   136  	{"0", 4, "0.0000"},
   137  	{"1", 0, "1"},
   138  	{"1", 2, "1.00"},
   139  	{"-1", 0, "-1"},
   140  	{".25", 2, "0.25"},
   141  	{".25", 1, "0.3"},
   142  	{".25", 3, "0.250"},
   143  	{"-1/3", 3, "-0.333"},
   144  	{"-2/3", 4, "-0.6667"},
   145  	{"0.96", 1, "1.0"},
   146  	{"0.999", 2, "1.00"},
   147  	{"0.9", 0, "1"},
   148  	{".25", -1, "0"},
   149  	{".55", -1, "1"},
   150  }
   151  
   152  func TestFloatString(t *testing.T) {
   153  	for i, test := range floatStringTests {
   154  		x, _ := new(Rat).SetString(test.in)
   155  
   156  		if x.FloatString(test.prec) != test.out {
   157  			t.Errorf("#%d got %s want %s", i, x.FloatString(test.prec), test.out)
   158  		}
   159  	}
   160  }
   161  
   162  func TestRatSign(t *testing.T) {
   163  	zero := NewRat(0, 1)
   164  	for _, a := range setStringTests {
   165  		x, ok := new(Rat).SetString(a.in)
   166  		if !ok {
   167  			continue
   168  		}
   169  		s := x.Sign()
   170  		e := x.Cmp(zero)
   171  		if s != e {
   172  			t.Errorf("got %d; want %d for z = %v", s, e, &x)
   173  		}
   174  	}
   175  }
   176  
   177  var ratCmpTests = []struct {
   178  	rat1, rat2 string
   179  	out        int
   180  }{
   181  	{"0", "0/1", 0},
   182  	{"1/1", "1", 0},
   183  	{"-1", "-2/2", 0},
   184  	{"1", "0", 1},
   185  	{"0/1", "1/1", -1},
   186  	{"-5/1434770811533343057144", "-5/1434770811533343057145", -1},
   187  	{"49832350382626108453/8964749413", "49832350382626108454/8964749413", -1},
   188  	{"-37414950961700930/7204075375675961", "37414950961700930/7204075375675961", -1},
   189  	{"37414950961700930/7204075375675961", "74829901923401860/14408150751351922", 0},
   190  }
   191  
   192  func TestRatCmp(t *testing.T) {
   193  	for i, test := range ratCmpTests {
   194  		x, _ := new(Rat).SetString(test.rat1)
   195  		y, _ := new(Rat).SetString(test.rat2)
   196  
   197  		out := x.Cmp(y)
   198  		if out != test.out {
   199  			t.Errorf("#%d got out = %v; want %v", i, out, test.out)
   200  		}
   201  	}
   202  }
   203  
   204  func TestIsInt(t *testing.T) {
   205  	one := NewInt(1)
   206  	for _, a := range setStringTests {
   207  		x, ok := new(Rat).SetString(a.in)
   208  		if !ok {
   209  			continue
   210  		}
   211  		i := x.IsInt()
   212  		e := x.Denom().Cmp(one) == 0
   213  		if i != e {
   214  			t.Errorf("got IsInt(%v) == %v; want %v", x, i, e)
   215  		}
   216  	}
   217  }
   218  
   219  func TestRatAbs(t *testing.T) {
   220  	zero := new(Rat)
   221  	for _, a := range setStringTests {
   222  		x, ok := new(Rat).SetString(a.in)
   223  		if !ok {
   224  			continue
   225  		}
   226  		e := new(Rat).Set(x)
   227  		if e.Cmp(zero) < 0 {
   228  			e.Sub(zero, e)
   229  		}
   230  		z := new(Rat).Abs(x)
   231  		if z.Cmp(e) != 0 {
   232  			t.Errorf("got Abs(%v) = %v; want %v", x, z, e)
   233  		}
   234  	}
   235  }
   236  
   237  func TestRatNeg(t *testing.T) {
   238  	zero := new(Rat)
   239  	for _, a := range setStringTests {
   240  		x, ok := new(Rat).SetString(a.in)
   241  		if !ok {
   242  			continue
   243  		}
   244  		e := new(Rat).Sub(zero, x)
   245  		z := new(Rat).Neg(x)
   246  		if z.Cmp(e) != 0 {
   247  			t.Errorf("got Neg(%v) = %v; want %v", x, z, e)
   248  		}
   249  	}
   250  }
   251  
   252  func TestRatInv(t *testing.T) {
   253  	zero := new(Rat)
   254  	for _, a := range setStringTests {
   255  		x, ok := new(Rat).SetString(a.in)
   256  		if !ok {
   257  			continue
   258  		}
   259  		if x.Cmp(zero) == 0 {
   260  			continue // avoid division by zero
   261  		}
   262  		e := new(Rat).SetFrac(x.Denom(), x.Num())
   263  		z := new(Rat).Inv(x)
   264  		if z.Cmp(e) != 0 {
   265  			t.Errorf("got Inv(%v) = %v; want %v", x, z, e)
   266  		}
   267  	}
   268  }
   269  
   270  type ratBinFun func(z, x, y *Rat) *Rat
   271  type ratBinArg struct {
   272  	x, y, z string
   273  }
   274  
   275  func testRatBin(t *testing.T, i int, name string, f ratBinFun, a ratBinArg) {
   276  	x, _ := new(Rat).SetString(a.x)
   277  	y, _ := new(Rat).SetString(a.y)
   278  	z, _ := new(Rat).SetString(a.z)
   279  	out := f(new(Rat), x, y)
   280  
   281  	if out.Cmp(z) != 0 {
   282  		t.Errorf("%s #%d got %s want %s", name, i, out, z)
   283  	}
   284  }
   285  
   286  var ratBinTests = []struct {
   287  	x, y      string
   288  	sum, prod string
   289  }{
   290  	{"0", "0", "0", "0"},
   291  	{"0", "1", "1", "0"},
   292  	{"-1", "0", "-1", "0"},
   293  	{"-1", "1", "0", "-1"},
   294  	{"1", "1", "2", "1"},
   295  	{"1/2", "1/2", "1", "1/4"},
   296  	{"1/4", "1/3", "7/12", "1/12"},
   297  	{"2/5", "-14/3", "-64/15", "-28/15"},
   298  	{"4707/49292519774798173060", "-3367/70976135186689855734", "84058377121001851123459/1749296273614329067191168098769082663020", "-1760941/388732505247628681598037355282018369560"},
   299  	{"-61204110018146728334/3", "-31052192278051565633/2", "-215564796870448153567/6", "950260896245257153059642991192710872711/3"},
   300  	{"-854857841473707320655/4237645934602118692642972629634714039", "-18/31750379913563777419", "-27/133467566250814981", "15387441146526731771790/134546868362786310073779084329032722548987800600710485341"},
   301  	{"618575745270541348005638912139/19198433543745179392300736", "-19948846211000086/637313996471", "27674141753240653/30123979153216", "-6169936206128396568797607742807090270137721977/6117715203873571641674006593837351328"},
   302  	{"-3/26206484091896184128", "5/2848423294177090248", "15310893822118706237/9330894968229805033368778458685147968", "-5/24882386581946146755650075889827061248"},
   303  	{"26946729/330400702820", "41563965/225583428284", "1238218672302860271/4658307703098666660055", "224002580204097/14906584649915733312176"},
   304  	{"-8259900599013409474/7", "-84829337473700364773/56707961321161574960", "-468402123685491748914621885145127724451/396955729248131024720", "350340947706464153265156004876107029701/198477864624065512360"},
   305  	{"575775209696864/1320203974639986246357", "29/712593081308", "410331716733912717985762465/940768218243776489278275419794956", "808/45524274987585732633"},
   306  	{"1786597389946320496771/2066653520653241", "6269770/1992362624741777", "3559549865190272133656109052308126637/4117523232840525481453983149257", "8967230/3296219033"},
   307  	{"-36459180403360509753/32150500941194292113930", "9381566963714/9633539", "301622077145533298008420642898530153/309723104686531919656937098270", "-3784609207827/3426986245"},
   308  }
   309  
   310  func TestRatBin(t *testing.T) {
   311  	for i, test := range ratBinTests {
   312  		arg := ratBinArg{test.x, test.y, test.sum}
   313  		testRatBin(t, i, "Add", (*Rat).Add, arg)
   314  
   315  		arg = ratBinArg{test.y, test.x, test.sum}
   316  		testRatBin(t, i, "Add symmetric", (*Rat).Add, arg)
   317  
   318  		arg = ratBinArg{test.sum, test.x, test.y}
   319  		testRatBin(t, i, "Sub", (*Rat).Sub, arg)
   320  
   321  		arg = ratBinArg{test.sum, test.y, test.x}
   322  		testRatBin(t, i, "Sub symmetric", (*Rat).Sub, arg)
   323  
   324  		arg = ratBinArg{test.x, test.y, test.prod}
   325  		testRatBin(t, i, "Mul", (*Rat).Mul, arg)
   326  
   327  		arg = ratBinArg{test.y, test.x, test.prod}
   328  		testRatBin(t, i, "Mul symmetric", (*Rat).Mul, arg)
   329  
   330  		if test.x != "0" {
   331  			arg = ratBinArg{test.prod, test.x, test.y}
   332  			testRatBin(t, i, "Quo", (*Rat).Quo, arg)
   333  		}
   334  
   335  		if test.y != "0" {
   336  			arg = ratBinArg{test.prod, test.y, test.x}
   337  			testRatBin(t, i, "Quo symmetric", (*Rat).Quo, arg)
   338  		}
   339  	}
   340  }
   341  
   342  func TestIssue820(t *testing.T) {
   343  	x := NewRat(3, 1)
   344  	y := NewRat(2, 1)
   345  	z := y.Quo(x, y)
   346  	q := NewRat(3, 2)
   347  	if z.Cmp(q) != 0 {
   348  		t.Errorf("got %s want %s", z, q)
   349  	}
   350  
   351  	y = NewRat(3, 1)
   352  	x = NewRat(2, 1)
   353  	z = y.Quo(x, y)
   354  	q = NewRat(2, 3)
   355  	if z.Cmp(q) != 0 {
   356  		t.Errorf("got %s want %s", z, q)
   357  	}
   358  
   359  	x = NewRat(3, 1)
   360  	z = x.Quo(x, x)
   361  	q = NewRat(3, 3)
   362  	if z.Cmp(q) != 0 {
   363  		t.Errorf("got %s want %s", z, q)
   364  	}
   365  }
   366  
   367  var setFrac64Tests = []struct {
   368  	a, b int64
   369  	out  string
   370  }{
   371  	{0, 1, "0"},
   372  	{0, -1, "0"},
   373  	{1, 1, "1"},
   374  	{-1, 1, "-1"},
   375  	{1, -1, "-1"},
   376  	{-1, -1, "1"},
   377  	{-9223372036854775808, -9223372036854775808, "1"},
   378  }
   379  
   380  func TestRatSetFrac64Rat(t *testing.T) {
   381  	for i, test := range setFrac64Tests {
   382  		x := new(Rat).SetFrac64(test.a, test.b)
   383  		if x.RatString() != test.out {
   384  			t.Errorf("#%d got %s want %s", i, x.RatString(), test.out)
   385  		}
   386  	}
   387  }
   388  
   389  func TestRatGobEncoding(t *testing.T) {
   390  	var medium bytes.Buffer
   391  	enc := gob.NewEncoder(&medium)
   392  	dec := gob.NewDecoder(&medium)
   393  	for _, test := range encodingTests {
   394  		medium.Reset() // empty buffer for each test case (in case of failures)
   395  		var tx Rat
   396  		tx.SetString(test + ".14159265")
   397  		if err := enc.Encode(&tx); err != nil {
   398  			t.Errorf("encoding of %s failed: %s", &tx, err)
   399  		}
   400  		var rx Rat
   401  		if err := dec.Decode(&rx); err != nil {
   402  			t.Errorf("decoding of %s failed: %s", &tx, err)
   403  		}
   404  		if rx.Cmp(&tx) != 0 {
   405  			t.Errorf("transmission of %s failed: got %s want %s", &tx, &rx, &tx)
   406  		}
   407  	}
   408  }
   409  
   410  func TestIssue2379(t *testing.T) {
   411  	// 1) no aliasing
   412  	q := NewRat(3, 2)
   413  	x := new(Rat)
   414  	x.SetFrac(NewInt(3), NewInt(2))
   415  	if x.Cmp(q) != 0 {
   416  		t.Errorf("1) got %s want %s", x, q)
   417  	}
   418  
   419  	// 2) aliasing of numerator
   420  	x = NewRat(2, 3)
   421  	x.SetFrac(NewInt(3), x.Num())
   422  	if x.Cmp(q) != 0 {
   423  		t.Errorf("2) got %s want %s", x, q)
   424  	}
   425  
   426  	// 3) aliasing of denominator
   427  	x = NewRat(2, 3)
   428  	x.SetFrac(x.Denom(), NewInt(2))
   429  	if x.Cmp(q) != 0 {
   430  		t.Errorf("3) got %s want %s", x, q)
   431  	}
   432  
   433  	// 4) aliasing of numerator and denominator
   434  	x = NewRat(2, 3)
   435  	x.SetFrac(x.Denom(), x.Num())
   436  	if x.Cmp(q) != 0 {
   437  		t.Errorf("4) got %s want %s", x, q)
   438  	}
   439  
   440  	// 5) numerator and denominator are the same
   441  	q = NewRat(1, 1)
   442  	x = new(Rat)
   443  	n := NewInt(7)
   444  	x.SetFrac(n, n)
   445  	if x.Cmp(q) != 0 {
   446  		t.Errorf("5) got %s want %s", x, q)
   447  	}
   448  }
   449  
   450  func TestIssue3521(t *testing.T) {
   451  	a := new(Int)
   452  	b := new(Int)
   453  	a.SetString("64375784358435883458348587", 0)
   454  	b.SetString("4789759874531", 0)
   455  
   456  	// 0) a raw zero value has 1 as denominator
   457  	zero := new(Rat)
   458  	one := NewInt(1)
   459  	if zero.Denom().Cmp(one) != 0 {
   460  		t.Errorf("0) got %s want %s", zero.Denom(), one)
   461  	}
   462  
   463  	// 1a) a zero value remains zero independent of denominator
   464  	x := new(Rat)
   465  	x.Denom().Set(new(Int).Neg(b))
   466  	if x.Cmp(zero) != 0 {
   467  		t.Errorf("1a) got %s want %s", x, zero)
   468  	}
   469  
   470  	// 1b) a zero value may have a denominator != 0 and != 1
   471  	x.Num().Set(a)
   472  	qab := new(Rat).SetFrac(a, b)
   473  	if x.Cmp(qab) != 0 {
   474  		t.Errorf("1b) got %s want %s", x, qab)
   475  	}
   476  
   477  	// 2a) an integral value becomes a fraction depending on denominator
   478  	x.SetFrac64(10, 2)
   479  	x.Denom().SetInt64(3)
   480  	q53 := NewRat(5, 3)
   481  	if x.Cmp(q53) != 0 {
   482  		t.Errorf("2a) got %s want %s", x, q53)
   483  	}
   484  
   485  	// 2b) an integral value becomes a fraction depending on denominator
   486  	x = NewRat(10, 2)
   487  	x.Denom().SetInt64(3)
   488  	if x.Cmp(q53) != 0 {
   489  		t.Errorf("2b) got %s want %s", x, q53)
   490  	}
   491  
   492  	// 3) changing the numerator/denominator of a Rat changes the Rat
   493  	x.SetFrac(a, b)
   494  	a = x.Num()
   495  	b = x.Denom()
   496  	a.SetInt64(5)
   497  	b.SetInt64(3)
   498  	if x.Cmp(q53) != 0 {
   499  		t.Errorf("3) got %s want %s", x, q53)
   500  	}
   501  }
   502  
   503  // Test inputs to Rat.SetString.  The prefix "long:" causes the test
   504  // to be skipped in --test.short mode.  (The threshold is about 500us.)
   505  var float64inputs = []string{
   506  	// Constants plundered from strconv/testfp.txt.
   507  
   508  	// Table 1: Stress Inputs for Conversion to 53-bit Binary, < 1/2 ULP
   509  	"5e+125",
   510  	"69e+267",
   511  	"999e-026",
   512  	"7861e-034",
   513  	"75569e-254",
   514  	"928609e-261",
   515  	"9210917e+080",
   516  	"84863171e+114",
   517  	"653777767e+273",
   518  	"5232604057e-298",
   519  	"27235667517e-109",
   520  	"653532977297e-123",
   521  	"3142213164987e-294",
   522  	"46202199371337e-072",
   523  	"231010996856685e-073",
   524  	"9324754620109615e+212",
   525  	"78459735791271921e+049",
   526  	"272104041512242479e+200",
   527  	"6802601037806061975e+198",
   528  	"20505426358836677347e-221",
   529  	"836168422905420598437e-234",
   530  	"4891559871276714924261e+222",
   531  
   532  	// Table 2: Stress Inputs for Conversion to 53-bit Binary, > 1/2 ULP
   533  	"9e-265",
   534  	"85e-037",
   535  	"623e+100",
   536  	"3571e+263",
   537  	"81661e+153",
   538  	"920657e-023",
   539  	"4603285e-024",
   540  	"87575437e-309",
   541  	"245540327e+122",
   542  	"6138508175e+120",
   543  	"83356057653e+193",
   544  	"619534293513e+124",
   545  	"2335141086879e+218",
   546  	"36167929443327e-159",
   547  	"609610927149051e-255",
   548  	"3743626360493413e-165",
   549  	"94080055902682397e-242",
   550  	"899810892172646163e+283",
   551  	"7120190517612959703e+120",
   552  	"25188282901709339043e-252",
   553  	"308984926168550152811e-052",
   554  	"6372891218502368041059e+064",
   555  
   556  	// Table 14: Stress Inputs for Conversion to 24-bit Binary, <1/2 ULP
   557  	"5e-20",
   558  	"67e+14",
   559  	"985e+15",
   560  	"7693e-42",
   561  	"55895e-16",
   562  	"996622e-44",
   563  	"7038531e-32",
   564  	"60419369e-46",
   565  	"702990899e-20",
   566  	"6930161142e-48",
   567  	"25933168707e+13",
   568  	"596428896559e+20",
   569  
   570  	// Table 15: Stress Inputs for Conversion to 24-bit Binary, >1/2 ULP
   571  	"3e-23",
   572  	"57e+18",
   573  	"789e-35",
   574  	"2539e-18",
   575  	"76173e+28",
   576  	"887745e-11",
   577  	"5382571e-37",
   578  	"82381273e-35",
   579  	"750486563e-38",
   580  	"3752432815e-39",
   581  	"75224575729e-45",
   582  	"459926601011e+15",
   583  
   584  	// Constants plundered from strconv/atof_test.go.
   585  
   586  	"0",
   587  	"1",
   588  	"+1",
   589  	"1e23",
   590  	"1E23",
   591  	"100000000000000000000000",
   592  	"1e-100",
   593  	"123456700",
   594  	"99999999999999974834176",
   595  	"100000000000000000000001",
   596  	"100000000000000008388608",
   597  	"100000000000000016777215",
   598  	"100000000000000016777216",
   599  	"-1",
   600  	"-0.1",
   601  	"-0", // NB: exception made for this input
   602  	"1e-20",
   603  	"625e-3",
   604  
   605  	// largest float64
   606  	"1.7976931348623157e308",
   607  	"-1.7976931348623157e308",
   608  	// next float64 - too large
   609  	"1.7976931348623159e308",
   610  	"-1.7976931348623159e308",
   611  	// the border is ...158079
   612  	// borderline - okay
   613  	"1.7976931348623158e308",
   614  	"-1.7976931348623158e308",
   615  	// borderline - too large
   616  	"1.797693134862315808e308",
   617  	"-1.797693134862315808e308",
   618  
   619  	// a little too large
   620  	"1e308",
   621  	"2e308",
   622  	"1e309",
   623  
   624  	// way too large
   625  	"1e310",
   626  	"-1e310",
   627  	"1e400",
   628  	"-1e400",
   629  	"long:1e400000",
   630  	"long:-1e400000",
   631  
   632  	// denormalized
   633  	"1e-305",
   634  	"1e-306",
   635  	"1e-307",
   636  	"1e-308",
   637  	"1e-309",
   638  	"1e-310",
   639  	"1e-322",
   640  	// smallest denormal
   641  	"5e-324",
   642  	"4e-324",
   643  	"3e-324",
   644  	// too small
   645  	"2e-324",
   646  	// way too small
   647  	"1e-350",
   648  	"long:1e-400000",
   649  	// way too small, negative
   650  	"-1e-350",
   651  	"long:-1e-400000",
   652  
   653  	// try to overflow exponent
   654  	// [Disabled: too slow and memory-hungry with rationals.]
   655  	// "1e-4294967296",
   656  	// "1e+4294967296",
   657  	// "1e-18446744073709551616",
   658  	// "1e+18446744073709551616",
   659  
   660  	// http://www.exploringbinary.com/java-hangs-when-converting-2-2250738585072012e-308/
   661  	"2.2250738585072012e-308",
   662  	// http://www.exploringbinary.com/php-hangs-on-numeric-value-2-2250738585072011e-308/
   663  
   664  	"2.2250738585072011e-308",
   665  
   666  	// A very large number (initially wrongly parsed by the fast algorithm).
   667  	"4.630813248087435e+307",
   668  
   669  	// A different kind of very large number.
   670  	"22.222222222222222",
   671  	"long:2." + strings.Repeat("2", 4000) + "e+1",
   672  
   673  	// Exactly halfway between 1 and math.Nextafter(1, 2).
   674  	// Round to even (down).
   675  	"1.00000000000000011102230246251565404236316680908203125",
   676  	// Slightly lower; still round down.
   677  	"1.00000000000000011102230246251565404236316680908203124",
   678  	// Slightly higher; round up.
   679  	"1.00000000000000011102230246251565404236316680908203126",
   680  	// Slightly higher, but you have to read all the way to the end.
   681  	"long:1.00000000000000011102230246251565404236316680908203125" + strings.Repeat("0", 10000) + "1",
   682  
   683  	// Smallest denormal, 2^(-1022-52)
   684  	"4.940656458412465441765687928682213723651e-324",
   685  	// Half of smallest denormal, 2^(-1022-53)
   686  	"2.470328229206232720882843964341106861825e-324",
   687  	// A little more than the exact half of smallest denormal
   688  	// 2^-1075 + 2^-1100.  (Rounds to 1p-1074.)
   689  	"2.470328302827751011111470718709768633275e-324",
   690  	// The exact halfway between smallest normal and largest denormal:
   691  	// 2^-1022 - 2^-1075.  (Rounds to 2^-1022.)
   692  	"2.225073858507201136057409796709131975935e-308",
   693  
   694  	"1152921504606846975",  //   1<<60 - 1
   695  	"-1152921504606846975", // -(1<<60 - 1)
   696  	"1152921504606846977",  //   1<<60 + 1
   697  	"-1152921504606846977", // -(1<<60 + 1)
   698  
   699  	"1/3",
   700  }
   701  
   702  func TestFloat64SpecialCases(t *testing.T) {
   703  	for _, input := range float64inputs {
   704  		if strings.HasPrefix(input, "long:") {
   705  			if testing.Short() {
   706  				continue
   707  			}
   708  			input = input[len("long:"):]
   709  		}
   710  
   711  		r, ok := new(Rat).SetString(input)
   712  		if !ok {
   713  			t.Errorf("Rat.SetString(%q) failed", input)
   714  			continue
   715  		}
   716  		f, exact := r.Float64()
   717  
   718  		// 1. Check string -> Rat -> float64 conversions are
   719  		// consistent with strconv.ParseFloat.
   720  		// Skip this check if the input uses "a/b" rational syntax.
   721  		if !strings.Contains(input, "/") {
   722  			e, _ := strconv.ParseFloat(input, 64)
   723  
   724  			// Careful: negative Rats too small for
   725  			// float64 become -0, but Rat obviously cannot
   726  			// preserve the sign from SetString("-0").
   727  			switch {
   728  			case math.Float64bits(e) == math.Float64bits(f):
   729  				// Ok: bitwise equal.
   730  			case f == 0 && r.Num().BitLen() == 0:
   731  				// Ok: Rat(0) is equivalent to both +/- float64(0).
   732  			default:
   733  				t.Errorf("strconv.ParseFloat(%q) = %g (%b), want %g (%b); delta = %g", input, e, e, f, f, f-e)
   734  			}
   735  		}
   736  
   737  		if !isFinite(f) {
   738  			continue
   739  		}
   740  
   741  		// 2. Check f is best approximation to r.
   742  		if !checkIsBestApprox(t, f, r) {
   743  			// Append context information.
   744  			t.Errorf("(input was %q)", input)
   745  		}
   746  
   747  		// 3. Check f->R->f roundtrip is non-lossy.
   748  		checkNonLossyRoundtrip(t, f)
   749  
   750  		// 4. Check exactness using slow algorithm.
   751  		if wasExact := new(Rat).SetFloat64(f).Cmp(r) == 0; wasExact != exact {
   752  			t.Errorf("Rat.SetString(%q).Float64().exact = %t, want %t", input, exact, wasExact)
   753  		}
   754  	}
   755  }
   756  
   757  func TestFloat64Distribution(t *testing.T) {
   758  	// Generate a distribution of (sign, mantissa, exp) values
   759  	// broader than the float64 range, and check Rat.Float64()
   760  	// always picks the closest float64 approximation.
   761  	var add = []int64{
   762  		0,
   763  		1,
   764  		3,
   765  		5,
   766  		7,
   767  		9,
   768  		11,
   769  	}
   770  	var winc, einc = uint64(1), int(1) // soak test (~75s on x86-64)
   771  	if testing.Short() {
   772  		winc, einc = 10, 500 // quick test (~12ms on x86-64)
   773  	}
   774  
   775  	for _, sign := range "+-" {
   776  		for _, a := range add {
   777  			for wid := uint64(0); wid < 60; wid += winc {
   778  				b := int64(1<<wid + a)
   779  				if sign == '-' {
   780  					b = -b
   781  				}
   782  				for exp := -1100; exp < 1100; exp += einc {
   783  					num, den := NewInt(b), NewInt(1)
   784  					if exp > 0 {
   785  						num.Lsh(num, uint(exp))
   786  					} else {
   787  						den.Lsh(den, uint(-exp))
   788  					}
   789  					r := new(Rat).SetFrac(num, den)
   790  					f, _ := r.Float64()
   791  
   792  					if !checkIsBestApprox(t, f, r) {
   793  						// Append context information.
   794  						t.Errorf("(input was mantissa %#x, exp %d; f = %g (%b); f ~ %g; r = %v)",
   795  							b, exp, f, f, math.Ldexp(float64(b), exp), r)
   796  					}
   797  
   798  					checkNonLossyRoundtrip(t, f)
   799  				}
   800  			}
   801  		}
   802  	}
   803  }
   804  
   805  // TestFloat64NonFinite checks that SetFloat64 of a non-finite value
   806  // returns nil.
   807  func TestSetFloat64NonFinite(t *testing.T) {
   808  	for _, f := range []float64{math.NaN(), math.Inf(+1), math.Inf(-1)} {
   809  		var r Rat
   810  		if r2 := r.SetFloat64(f); r2 != nil {
   811  			t.Errorf("SetFloat64(%g) was %v, want nil", f, r2)
   812  		}
   813  	}
   814  }
   815  
   816  // checkNonLossyRoundtrip checks that a float->Rat->float roundtrip is
   817  // non-lossy for finite f.
   818  func checkNonLossyRoundtrip(t *testing.T, f float64) {
   819  	if !isFinite(f) {
   820  		return
   821  	}
   822  	r := new(Rat).SetFloat64(f)
   823  	if r == nil {
   824  		t.Errorf("Rat.SetFloat64(%g (%b)) == nil", f, f)
   825  		return
   826  	}
   827  	f2, exact := r.Float64()
   828  	if f != f2 || !exact {
   829  		t.Errorf("Rat.SetFloat64(%g).Float64() = %g (%b), %v, want %g (%b), %v; delta = %b",
   830  			f, f2, f2, exact, f, f, true, f2-f)
   831  	}
   832  }
   833  
   834  // delta returns the absolute difference between r and f.
   835  func delta(r *Rat, f float64) *Rat {
   836  	d := new(Rat).Sub(r, new(Rat).SetFloat64(f))
   837  	return d.Abs(d)
   838  }
   839  
   840  // checkIsBestApprox checks that f is the best possible float64
   841  // approximation of r.
   842  // Returns true on success.
   843  func checkIsBestApprox(t *testing.T, f float64, r *Rat) bool {
   844  	if math.Abs(f) >= math.MaxFloat64 {
   845  		// Cannot check +Inf, -Inf, nor the float next to them (MaxFloat64).
   846  		// But we have tests for these special cases.
   847  		return true
   848  	}
   849  
   850  	// r must be strictly between f0 and f1, the floats bracketing f.
   851  	f0 := math.Nextafter(f, math.Inf(-1))
   852  	f1 := math.Nextafter(f, math.Inf(+1))
   853  
   854  	// For f to be correct, r must be closer to f than to f0 or f1.
   855  	df := delta(r, f)
   856  	df0 := delta(r, f0)
   857  	df1 := delta(r, f1)
   858  	if df.Cmp(df0) > 0 {
   859  		t.Errorf("Rat(%v).Float64() = %g (%b), but previous float64 %g (%b) is closer", r, f, f, f0, f0)
   860  		return false
   861  	}
   862  	if df.Cmp(df1) > 0 {
   863  		t.Errorf("Rat(%v).Float64() = %g (%b), but next float64 %g (%b) is closer", r, f, f, f1, f1)
   864  		return false
   865  	}
   866  	if df.Cmp(df0) == 0 && !isEven(f) {
   867  		t.Errorf("Rat(%v).Float64() = %g (%b); halfway should have rounded to %g (%b) instead", r, f, f, f0, f0)
   868  		return false
   869  	}
   870  	if df.Cmp(df1) == 0 && !isEven(f) {
   871  		t.Errorf("Rat(%v).Float64() = %g (%b); halfway should have rounded to %g (%b) instead", r, f, f, f1, f1)
   872  		return false
   873  	}
   874  	return true
   875  }
   876  
   877  func isEven(f float64) bool { return math.Float64bits(f)&1 == 0 }
   878  
   879  func TestIsFinite(t *testing.T) {
   880  	finites := []float64{
   881  		1.0 / 3,
   882  		4891559871276714924261e+222,
   883  		math.MaxFloat64,
   884  		math.SmallestNonzeroFloat64,
   885  		-math.MaxFloat64,
   886  		-math.SmallestNonzeroFloat64,
   887  	}
   888  	for _, f := range finites {
   889  		if !isFinite(f) {
   890  			t.Errorf("!IsFinite(%g (%b))", f, f)
   891  		}
   892  	}
   893  	nonfinites := []float64{
   894  		math.NaN(),
   895  		math.Inf(-1),
   896  		math.Inf(+1),
   897  	}
   898  	for _, f := range nonfinites {
   899  		if isFinite(f) {
   900  			t.Errorf("IsFinite(%g, (%b))", f, f)
   901  		}
   902  	}
   903  }