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Diffstat (limited to 'src/pkg/math/big/rat_test.go')
-rw-r--r--src/pkg/math/big/rat_test.go994
1 files changed, 0 insertions, 994 deletions
diff --git a/src/pkg/math/big/rat_test.go b/src/pkg/math/big/rat_test.go
deleted file mode 100644
index 414a67d41..000000000
--- a/src/pkg/math/big/rat_test.go
+++ /dev/null
@@ -1,994 +0,0 @@
-// Copyright 2010 The Go Authors. All rights reserved.
-// Use of this source code is governed by a BSD-style
-// license that can be found in the LICENSE file.
-
-package big
-
-import (
- "bytes"
- "encoding/gob"
- "encoding/json"
- "encoding/xml"
- "fmt"
- "math"
- "strconv"
- "strings"
- "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)
-}
-
-var setStringTests = []struct {
- in, out string
- ok bool
-}{
- {"0", "0", true},
- {"-0", "0", true},
- {"1", "1", true},
- {"-1", "-1", true},
- {"1.", "1", true},
- {"1e0", "1", true},
- {"1.e1", "10", true},
- {in: "1e", ok: false},
- {in: "1.e", ok: false},
- {in: "1e+14e-5", ok: false},
- {in: "1e4.5", ok: false},
- {in: "r", ok: false},
- {in: "a/b", ok: false},
- {in: "a.b", ok: false},
- {"-0.1", "-1/10", true},
- {"-.1", "-1/10", true},
- {"2/4", "1/2", true},
- {".25", "1/4", true},
- {"-1/5", "-1/5", true},
- {"8129567.7690E14", "812956776900000000000", true},
- {"78189e+4", "781890000", true},
- {"553019.8935e+8", "55301989350000", true},
- {"98765432109876543210987654321e-10", "98765432109876543210987654321/10000000000", true},
- {"9877861857500000E-7", "3951144743/4", true},
- {"2169378.417e-3", "2169378417/1000000", true},
- {"884243222337379604041632732738665534", "884243222337379604041632732738665534", true},
- {"53/70893980658822810696", "53/70893980658822810696", true},
- {"106/141787961317645621392", "53/70893980658822810696", true},
- {"204211327800791583.81095", "4084226556015831676219/20000", true},
-}
-
-func TestRatSetString(t *testing.T) {
- for i, test := range setStringTests {
- x, ok := new(Rat).SetString(test.in)
-
- if ok {
- if !test.ok {
- t.Errorf("#%d SetString(%q) expected failure", i, test.in)
- } else if x.RatString() != test.out {
- t.Errorf("#%d SetString(%q) got %s want %s", i, test.in, x.RatString(), test.out)
- }
- } else if x != nil {
- t.Errorf("#%d SetString(%q) got %p want nil", i, test.in, x)
- }
- }
-}
-
-func TestRatScan(t *testing.T) {
- var buf bytes.Buffer
- for i, test := range setStringTests {
- x := new(Rat)
- buf.Reset()
- buf.WriteString(test.in)
-
- _, err := fmt.Fscanf(&buf, "%v", x)
- if err == nil != test.ok {
- if test.ok {
- t.Errorf("#%d error: %s", i, err)
- } else {
- t.Errorf("#%d expected error", i)
- }
- continue
- }
- if err == nil && x.RatString() != test.out {
- t.Errorf("#%d got %s want %s", i, x.RatString(), test.out)
- }
- }
-}
-
-var floatStringTests = []struct {
- in string
- prec int
- out string
-}{
- {"0", 0, "0"},
- {"0", 4, "0.0000"},
- {"1", 0, "1"},
- {"1", 2, "1.00"},
- {"-1", 0, "-1"},
- {".25", 2, "0.25"},
- {".25", 1, "0.3"},
- {".25", 3, "0.250"},
- {"-1/3", 3, "-0.333"},
- {"-2/3", 4, "-0.6667"},
- {"0.96", 1, "1.0"},
- {"0.999", 2, "1.00"},
- {"0.9", 0, "1"},
- {".25", -1, "0"},
- {".55", -1, "1"},
-}
-
-func TestFloatString(t *testing.T) {
- for i, test := range floatStringTests {
- x, _ := new(Rat).SetString(test.in)
-
- if x.FloatString(test.prec) != test.out {
- t.Errorf("#%d got %s want %s", i, x.FloatString(test.prec), test.out)
- }
- }
-}
-
-func TestRatSign(t *testing.T) {
- zero := NewRat(0, 1)
- for _, a := range setStringTests {
- x, ok := new(Rat).SetString(a.in)
- if !ok {
- continue
- }
- s := x.Sign()
- e := x.Cmp(zero)
- if s != e {
- t.Errorf("got %d; want %d for z = %v", s, e, &x)
- }
- }
-}
-
-var ratCmpTests = []struct {
- rat1, rat2 string
- out int
-}{
- {"0", "0/1", 0},
- {"1/1", "1", 0},
- {"-1", "-2/2", 0},
- {"1", "0", 1},
- {"0/1", "1/1", -1},
- {"-5/1434770811533343057144", "-5/1434770811533343057145", -1},
- {"49832350382626108453/8964749413", "49832350382626108454/8964749413", -1},
- {"-37414950961700930/7204075375675961", "37414950961700930/7204075375675961", -1},
- {"37414950961700930/7204075375675961", "74829901923401860/14408150751351922", 0},
-}
-
-func TestRatCmp(t *testing.T) {
- for i, test := range ratCmpTests {
- x, _ := new(Rat).SetString(test.rat1)
- y, _ := new(Rat).SetString(test.rat2)
-
- out := x.Cmp(y)
- if out != test.out {
- t.Errorf("#%d got out = %v; want %v", i, out, test.out)
- }
- }
-}
-
-func TestIsInt(t *testing.T) {
- one := NewInt(1)
- for _, a := range setStringTests {
- x, ok := new(Rat).SetString(a.in)
- if !ok {
- continue
- }
- i := x.IsInt()
- e := x.Denom().Cmp(one) == 0
- if i != e {
- t.Errorf("got IsInt(%v) == %v; want %v", x, i, e)
- }
- }
-}
-
-func TestRatAbs(t *testing.T) {
- zero := new(Rat)
- for _, a := range setStringTests {
- x, ok := new(Rat).SetString(a.in)
- if !ok {
- continue
- }
- e := new(Rat).Set(x)
- if e.Cmp(zero) < 0 {
- e.Sub(zero, e)
- }
- z := new(Rat).Abs(x)
- if z.Cmp(e) != 0 {
- t.Errorf("got Abs(%v) = %v; want %v", x, z, e)
- }
- }
-}
-
-func TestRatNeg(t *testing.T) {
- zero := new(Rat)
- for _, a := range setStringTests {
- x, ok := new(Rat).SetString(a.in)
- if !ok {
- continue
- }
- e := new(Rat).Sub(zero, x)
- z := new(Rat).Neg(x)
- if z.Cmp(e) != 0 {
- t.Errorf("got Neg(%v) = %v; want %v", x, z, e)
- }
- }
-}
-
-func TestRatInv(t *testing.T) {
- zero := new(Rat)
- for _, a := range setStringTests {
- x, ok := new(Rat).SetString(a.in)
- if !ok {
- continue
- }
- if x.Cmp(zero) == 0 {
- continue // avoid division by zero
- }
- e := new(Rat).SetFrac(x.Denom(), x.Num())
- z := new(Rat).Inv(x)
- if z.Cmp(e) != 0 {
- t.Errorf("got Inv(%v) = %v; want %v", x, z, e)
- }
- }
-}
-
-type ratBinFun func(z, x, y *Rat) *Rat
-type ratBinArg struct {
- x, y, z string
-}
-
-func testRatBin(t *testing.T, i int, name string, f ratBinFun, a ratBinArg) {
- x, _ := new(Rat).SetString(a.x)
- y, _ := new(Rat).SetString(a.y)
- z, _ := new(Rat).SetString(a.z)
- out := f(new(Rat), x, y)
-
- if out.Cmp(z) != 0 {
- t.Errorf("%s #%d got %s want %s", name, i, out, z)
- }
-}
-
-var ratBinTests = []struct {
- x, y string
- sum, prod string
-}{
- {"0", "0", "0", "0"},
- {"0", "1", "1", "0"},
- {"-1", "0", "-1", "0"},
- {"-1", "1", "0", "-1"},
- {"1", "1", "2", "1"},
- {"1/2", "1/2", "1", "1/4"},
- {"1/4", "1/3", "7/12", "1/12"},
- {"2/5", "-14/3", "-64/15", "-28/15"},
- {"4707/49292519774798173060", "-3367/70976135186689855734", "84058377121001851123459/1749296273614329067191168098769082663020", "-1760941/388732505247628681598037355282018369560"},
- {"-61204110018146728334/3", "-31052192278051565633/2", "-215564796870448153567/6", "950260896245257153059642991192710872711/3"},
- {"-854857841473707320655/4237645934602118692642972629634714039", "-18/31750379913563777419", "-27/133467566250814981", "15387441146526731771790/134546868362786310073779084329032722548987800600710485341"},
- {"618575745270541348005638912139/19198433543745179392300736", "-19948846211000086/637313996471", "27674141753240653/30123979153216", "-6169936206128396568797607742807090270137721977/6117715203873571641674006593837351328"},
- {"-3/26206484091896184128", "5/2848423294177090248", "15310893822118706237/9330894968229805033368778458685147968", "-5/24882386581946146755650075889827061248"},
- {"26946729/330400702820", "41563965/225583428284", "1238218672302860271/4658307703098666660055", "224002580204097/14906584649915733312176"},
- {"-8259900599013409474/7", "-84829337473700364773/56707961321161574960", "-468402123685491748914621885145127724451/396955729248131024720", "350340947706464153265156004876107029701/198477864624065512360"},
- {"575775209696864/1320203974639986246357", "29/712593081308", "410331716733912717985762465/940768218243776489278275419794956", "808/45524274987585732633"},
- {"1786597389946320496771/2066653520653241", "6269770/1992362624741777", "3559549865190272133656109052308126637/4117523232840525481453983149257", "8967230/3296219033"},
- {"-36459180403360509753/32150500941194292113930", "9381566963714/9633539", "301622077145533298008420642898530153/309723104686531919656937098270", "-3784609207827/3426986245"},
-}
-
-func TestRatBin(t *testing.T) {
- for i, test := range ratBinTests {
- arg := ratBinArg{test.x, test.y, test.sum}
- testRatBin(t, i, "Add", (*Rat).Add, arg)
-
- arg = ratBinArg{test.y, test.x, test.sum}
- testRatBin(t, i, "Add symmetric", (*Rat).Add, arg)
-
- arg = ratBinArg{test.sum, test.x, test.y}
- testRatBin(t, i, "Sub", (*Rat).Sub, arg)
-
- arg = ratBinArg{test.sum, test.y, test.x}
- testRatBin(t, i, "Sub symmetric", (*Rat).Sub, arg)
-
- arg = ratBinArg{test.x, test.y, test.prod}
- testRatBin(t, i, "Mul", (*Rat).Mul, arg)
-
- arg = ratBinArg{test.y, test.x, test.prod}
- testRatBin(t, i, "Mul symmetric", (*Rat).Mul, arg)
-
- if test.x != "0" {
- arg = ratBinArg{test.prod, test.x, test.y}
- testRatBin(t, i, "Quo", (*Rat).Quo, arg)
- }
-
- if test.y != "0" {
- arg = ratBinArg{test.prod, test.y, test.x}
- testRatBin(t, i, "Quo symmetric", (*Rat).Quo, arg)
- }
- }
-}
-
-func TestIssue820(t *testing.T) {
- x := NewRat(3, 1)
- y := NewRat(2, 1)
- z := y.Quo(x, y)
- q := NewRat(3, 2)
- if z.Cmp(q) != 0 {
- t.Errorf("got %s want %s", z, q)
- }
-
- y = NewRat(3, 1)
- x = NewRat(2, 1)
- z = y.Quo(x, y)
- q = NewRat(2, 3)
- if z.Cmp(q) != 0 {
- t.Errorf("got %s want %s", z, q)
- }
-
- x = NewRat(3, 1)
- z = x.Quo(x, x)
- q = NewRat(3, 3)
- if z.Cmp(q) != 0 {
- t.Errorf("got %s want %s", z, q)
- }
-}
-
-var setFrac64Tests = []struct {
- a, b int64
- out string
-}{
- {0, 1, "0"},
- {0, -1, "0"},
- {1, 1, "1"},
- {-1, 1, "-1"},
- {1, -1, "-1"},
- {-1, -1, "1"},
- {-9223372036854775808, -9223372036854775808, "1"},
-}
-
-func TestRatSetFrac64Rat(t *testing.T) {
- for i, test := range setFrac64Tests {
- x := new(Rat).SetFrac64(test.a, test.b)
- if x.RatString() != test.out {
- t.Errorf("#%d got %s want %s", i, x.RatString(), test.out)
- }
- }
-}
-
-func TestRatGobEncoding(t *testing.T) {
- var medium bytes.Buffer
- enc := gob.NewEncoder(&medium)
- dec := gob.NewDecoder(&medium)
- for _, test := range encodingTests {
- medium.Reset() // empty buffer for each test case (in case of failures)
- var tx Rat
- tx.SetString(test + ".14159265")
- if err := enc.Encode(&tx); err != nil {
- t.Errorf("encoding of %s failed: %s", &tx, err)
- }
- var rx Rat
- if err := dec.Decode(&rx); err != nil {
- t.Errorf("decoding of %s failed: %s", &tx, err)
- }
- if rx.Cmp(&tx) != 0 {
- t.Errorf("transmission of %s failed: got %s want %s", &tx, &rx, &tx)
- }
- }
-}
-
-// Sending a nil Rat pointer (inside a slice) on a round trip through gob should yield a zero.
-// TODO: top-level nils.
-func TestGobEncodingNilRatInSlice(t *testing.T) {
- buf := new(bytes.Buffer)
- enc := gob.NewEncoder(buf)
- dec := gob.NewDecoder(buf)
-
- var in = make([]*Rat, 1)
- err := enc.Encode(&in)
- if err != nil {
- t.Errorf("gob encode failed: %q", err)
- }
- var out []*Rat
- err = dec.Decode(&out)
- if err != nil {
- t.Fatalf("gob decode failed: %q", err)
- }
- if len(out) != 1 {
- t.Fatalf("wrong len; want 1 got %d", len(out))
- }
- var zero Rat
- if out[0].Cmp(&zero) != 0 {
- t.Errorf("transmission of (*Int)(nill) failed: got %s want 0", out)
- }
-}
-
-var ratNums = []string{
- "-141592653589793238462643383279502884197169399375105820974944592307816406286",
- "-1415926535897932384626433832795028841971",
- "-141592653589793",
- "-1",
- "0",
- "1",
- "141592653589793",
- "1415926535897932384626433832795028841971",
- "141592653589793238462643383279502884197169399375105820974944592307816406286",
-}
-
-var ratDenoms = []string{
- "1",
- "718281828459045",
- "7182818284590452353602874713526624977572",
- "718281828459045235360287471352662497757247093699959574966967627724076630353",
-}
-
-func TestRatJSONEncoding(t *testing.T) {
- for _, num := range ratNums {
- for _, denom := range ratDenoms {
- var tx Rat
- tx.SetString(num + "/" + denom)
- b, err := json.Marshal(&tx)
- if err != nil {
- t.Errorf("marshaling of %s failed: %s", &tx, err)
- continue
- }
- var rx Rat
- if err := json.Unmarshal(b, &rx); err != nil {
- t.Errorf("unmarshaling of %s failed: %s", &tx, err)
- continue
- }
- if rx.Cmp(&tx) != 0 {
- t.Errorf("JSON encoding of %s failed: got %s want %s", &tx, &rx, &tx)
- }
- }
- }
-}
-
-func TestRatXMLEncoding(t *testing.T) {
- for _, num := range ratNums {
- for _, denom := range ratDenoms {
- var tx Rat
- tx.SetString(num + "/" + denom)
- b, err := xml.Marshal(&tx)
- if err != nil {
- t.Errorf("marshaling of %s failed: %s", &tx, err)
- continue
- }
- var rx Rat
- if err := xml.Unmarshal(b, &rx); err != nil {
- t.Errorf("unmarshaling of %s failed: %s", &tx, err)
- continue
- }
- if rx.Cmp(&tx) != 0 {
- t.Errorf("XML encoding of %s failed: got %s want %s", &tx, &rx, &tx)
- }
- }
- }
-}
-
-func TestIssue2379(t *testing.T) {
- // 1) no aliasing
- q := NewRat(3, 2)
- x := new(Rat)
- x.SetFrac(NewInt(3), NewInt(2))
- if x.Cmp(q) != 0 {
- t.Errorf("1) got %s want %s", x, q)
- }
-
- // 2) aliasing of numerator
- x = NewRat(2, 3)
- x.SetFrac(NewInt(3), x.Num())
- if x.Cmp(q) != 0 {
- t.Errorf("2) got %s want %s", x, q)
- }
-
- // 3) aliasing of denominator
- x = NewRat(2, 3)
- x.SetFrac(x.Denom(), NewInt(2))
- if x.Cmp(q) != 0 {
- t.Errorf("3) got %s want %s", x, q)
- }
-
- // 4) aliasing of numerator and denominator
- x = NewRat(2, 3)
- x.SetFrac(x.Denom(), x.Num())
- if x.Cmp(q) != 0 {
- t.Errorf("4) got %s want %s", x, q)
- }
-
- // 5) numerator and denominator are the same
- q = NewRat(1, 1)
- x = new(Rat)
- n := NewInt(7)
- x.SetFrac(n, n)
- if x.Cmp(q) != 0 {
- t.Errorf("5) got %s want %s", x, q)
- }
-}
-
-func TestIssue3521(t *testing.T) {
- a := new(Int)
- b := new(Int)
- a.SetString("64375784358435883458348587", 0)
- b.SetString("4789759874531", 0)
-
- // 0) a raw zero value has 1 as denominator
- zero := new(Rat)
- one := NewInt(1)
- if zero.Denom().Cmp(one) != 0 {
- t.Errorf("0) got %s want %s", zero.Denom(), one)
- }
-
- // 1a) a zero value remains zero independent of denominator
- x := new(Rat)
- x.Denom().Set(new(Int).Neg(b))
- if x.Cmp(zero) != 0 {
- t.Errorf("1a) got %s want %s", x, zero)
- }
-
- // 1b) a zero value may have a denominator != 0 and != 1
- x.Num().Set(a)
- qab := new(Rat).SetFrac(a, b)
- if x.Cmp(qab) != 0 {
- t.Errorf("1b) got %s want %s", x, qab)
- }
-
- // 2a) an integral value becomes a fraction depending on denominator
- x.SetFrac64(10, 2)
- x.Denom().SetInt64(3)
- q53 := NewRat(5, 3)
- if x.Cmp(q53) != 0 {
- t.Errorf("2a) got %s want %s", x, q53)
- }
-
- // 2b) an integral value becomes a fraction depending on denominator
- x = NewRat(10, 2)
- x.Denom().SetInt64(3)
- if x.Cmp(q53) != 0 {
- t.Errorf("2b) got %s want %s", x, q53)
- }
-
- // 3) changing the numerator/denominator of a Rat changes the Rat
- x.SetFrac(a, b)
- a = x.Num()
- b = x.Denom()
- a.SetInt64(5)
- b.SetInt64(3)
- if x.Cmp(q53) != 0 {
- t.Errorf("3) got %s want %s", x, q53)
- }
-}
-
-// Test inputs to Rat.SetString. The prefix "long:" causes the test
-// to be skipped in --test.short mode. (The threshold is about 500us.)
-var float64inputs = []string{
- // Constants plundered from strconv/testfp.txt.
-
- // Table 1: Stress Inputs for Conversion to 53-bit Binary, < 1/2 ULP
- "5e+125",
- "69e+267",
- "999e-026",
- "7861e-034",
- "75569e-254",
- "928609e-261",
- "9210917e+080",
- "84863171e+114",
- "653777767e+273",
- "5232604057e-298",
- "27235667517e-109",
- "653532977297e-123",
- "3142213164987e-294",
- "46202199371337e-072",
- "231010996856685e-073",
- "9324754620109615e+212",
- "78459735791271921e+049",
- "272104041512242479e+200",
- "6802601037806061975e+198",
- "20505426358836677347e-221",
- "836168422905420598437e-234",
- "4891559871276714924261e+222",
-
- // Table 2: Stress Inputs for Conversion to 53-bit Binary, > 1/2 ULP
- "9e-265",
- "85e-037",
- "623e+100",
- "3571e+263",
- "81661e+153",
- "920657e-023",
- "4603285e-024",
- "87575437e-309",
- "245540327e+122",
- "6138508175e+120",
- "83356057653e+193",
- "619534293513e+124",
- "2335141086879e+218",
- "36167929443327e-159",
- "609610927149051e-255",
- "3743626360493413e-165",
- "94080055902682397e-242",
- "899810892172646163e+283",
- "7120190517612959703e+120",
- "25188282901709339043e-252",
- "308984926168550152811e-052",
- "6372891218502368041059e+064",
-
- // Table 14: Stress Inputs for Conversion to 24-bit Binary, <1/2 ULP
- "5e-20",
- "67e+14",
- "985e+15",
- "7693e-42",
- "55895e-16",
- "996622e-44",
- "7038531e-32",
- "60419369e-46",
- "702990899e-20",
- "6930161142e-48",
- "25933168707e+13",
- "596428896559e+20",
-
- // Table 15: Stress Inputs for Conversion to 24-bit Binary, >1/2 ULP
- "3e-23",
- "57e+18",
- "789e-35",
- "2539e-18",
- "76173e+28",
- "887745e-11",
- "5382571e-37",
- "82381273e-35",
- "750486563e-38",
- "3752432815e-39",
- "75224575729e-45",
- "459926601011e+15",
-
- // Constants plundered from strconv/atof_test.go.
-
- "0",
- "1",
- "+1",
- "1e23",
- "1E23",
- "100000000000000000000000",
- "1e-100",
- "123456700",
- "99999999999999974834176",
- "100000000000000000000001",
- "100000000000000008388608",
- "100000000000000016777215",
- "100000000000000016777216",
- "-1",
- "-0.1",
- "-0", // NB: exception made for this input
- "1e-20",
- "625e-3",
-
- // largest float64
- "1.7976931348623157e308",
- "-1.7976931348623157e308",
- // next float64 - too large
- "1.7976931348623159e308",
- "-1.7976931348623159e308",
- // the border is ...158079
- // borderline - okay
- "1.7976931348623158e308",
- "-1.7976931348623158e308",
- // borderline - too large
- "1.797693134862315808e308",
- "-1.797693134862315808e308",
-
- // a little too large
- "1e308",
- "2e308",
- "1e309",
-
- // way too large
- "1e310",
- "-1e310",
- "1e400",
- "-1e400",
- "long:1e400000",
- "long:-1e400000",
-
- // denormalized
- "1e-305",
- "1e-306",
- "1e-307",
- "1e-308",
- "1e-309",
- "1e-310",
- "1e-322",
- // smallest denormal
- "5e-324",
- "4e-324",
- "3e-324",
- // too small
- "2e-324",
- // way too small
- "1e-350",
- "long:1e-400000",
- // way too small, negative
- "-1e-350",
- "long:-1e-400000",
-
- // try to overflow exponent
- // [Disabled: too slow and memory-hungry with rationals.]
- // "1e-4294967296",
- // "1e+4294967296",
- // "1e-18446744073709551616",
- // "1e+18446744073709551616",
-
- // http://www.exploringbinary.com/java-hangs-when-converting-2-2250738585072012e-308/
- "2.2250738585072012e-308",
- // http://www.exploringbinary.com/php-hangs-on-numeric-value-2-2250738585072011e-308/
-
- "2.2250738585072011e-308",
-
- // A very large number (initially wrongly parsed by the fast algorithm).
- "4.630813248087435e+307",
-
- // A different kind of very large number.
- "22.222222222222222",
- "long:2." + strings.Repeat("2", 4000) + "e+1",
-
- // Exactly halfway between 1 and math.Nextafter(1, 2).
- // Round to even (down).
- "1.00000000000000011102230246251565404236316680908203125",
- // Slightly lower; still round down.
- "1.00000000000000011102230246251565404236316680908203124",
- // Slightly higher; round up.
- "1.00000000000000011102230246251565404236316680908203126",
- // Slightly higher, but you have to read all the way to the end.
- "long:1.00000000000000011102230246251565404236316680908203125" + strings.Repeat("0", 10000) + "1",
-
- // Smallest denormal, 2^(-1022-52)
- "4.940656458412465441765687928682213723651e-324",
- // Half of smallest denormal, 2^(-1022-53)
- "2.470328229206232720882843964341106861825e-324",
- // A little more than the exact half of smallest denormal
- // 2^-1075 + 2^-1100. (Rounds to 1p-1074.)
- "2.470328302827751011111470718709768633275e-324",
- // The exact halfway between smallest normal and largest denormal:
- // 2^-1022 - 2^-1075. (Rounds to 2^-1022.)
- "2.225073858507201136057409796709131975935e-308",
-
- "1152921504606846975", // 1<<60 - 1
- "-1152921504606846975", // -(1<<60 - 1)
- "1152921504606846977", // 1<<60 + 1
- "-1152921504606846977", // -(1<<60 + 1)
-
- "1/3",
-}
-
-func TestFloat64SpecialCases(t *testing.T) {
- for _, input := range float64inputs {
- if strings.HasPrefix(input, "long:") {
- if testing.Short() {
- continue
- }
- input = input[len("long:"):]
- }
-
- r, ok := new(Rat).SetString(input)
- if !ok {
- t.Errorf("Rat.SetString(%q) failed", input)
- continue
- }
- f, exact := r.Float64()
-
- // 1. Check string -> Rat -> float64 conversions are
- // consistent with strconv.ParseFloat.
- // Skip this check if the input uses "a/b" rational syntax.
- if !strings.Contains(input, "/") {
- e, _ := strconv.ParseFloat(input, 64)
-
- // Careful: negative Rats too small for
- // float64 become -0, but Rat obviously cannot
- // preserve the sign from SetString("-0").
- switch {
- case math.Float64bits(e) == math.Float64bits(f):
- // Ok: bitwise equal.
- case f == 0 && r.Num().BitLen() == 0:
- // Ok: Rat(0) is equivalent to both +/- float64(0).
- default:
- t.Errorf("strconv.ParseFloat(%q) = %g (%b), want %g (%b); delta = %g", input, e, e, f, f, f-e)
- }
- }
-
- if !isFinite(f) {
- continue
- }
-
- // 2. Check f is best approximation to r.
- if !checkIsBestApprox(t, f, r) {
- // Append context information.
- t.Errorf("(input was %q)", input)
- }
-
- // 3. Check f->R->f roundtrip is non-lossy.
- checkNonLossyRoundtrip(t, f)
-
- // 4. Check exactness using slow algorithm.
- if wasExact := new(Rat).SetFloat64(f).Cmp(r) == 0; wasExact != exact {
- t.Errorf("Rat.SetString(%q).Float64().exact = %t, want %t", input, exact, wasExact)
- }
- }
-}
-
-func TestFloat64Distribution(t *testing.T) {
- // Generate a distribution of (sign, mantissa, exp) values
- // broader than the float64 range, and check Rat.Float64()
- // always picks the closest float64 approximation.
- var add = []int64{
- 0,
- 1,
- 3,
- 5,
- 7,
- 9,
- 11,
- }
- var winc, einc = uint64(1), int(1) // soak test (~75s on x86-64)
- if testing.Short() {
- winc, einc = 10, 500 // quick test (~12ms on x86-64)
- }
-
- for _, sign := range "+-" {
- for _, a := range add {
- for wid := uint64(0); wid < 60; wid += winc {
- b := int64(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 !checkIsBestApprox(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)
- }
-
- checkNonLossyRoundtrip(t, f)
- }
- }
- }
- }
-}
-
-// TestFloat64NonFinite 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)
- }
- }
-}
-
-// checkNonLossyRoundtrip checks that a float->Rat->float roundtrip is
-// non-lossy for finite f.
-func checkNonLossyRoundtrip(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)
-}
-
-// checkIsBestApprox checks that f is the best possible float64
-// approximation of r.
-// Returns true on success.
-func checkIsBestApprox(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 && !isEven(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 && !isEven(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 isEven(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)
- }
- }
-}
generated by cgit v1.2.3 (git 2.39.1) at 2025-04-30 04:58:00 +0000