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-rw-r--r--src/math/big/rat_test.go1160
1 files changed, 1160 insertions, 0 deletions
diff --git a/src/math/big/rat_test.go b/src/math/big/rat_test.go
new file mode 100644
index 000000000..5dbbb3510
--- /dev/null
+++ b/src/math/big/rat_test.go
@@ -0,0 +1,1160 @@
+// 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},
+ {in: "1/0", ok: false},
+}
+
+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",
+}
+
+// isFinite reports whether f represents a finite rational value.
+// It is equivalent to !math.IsNan(f) && !math.IsInf(f, 0).
+func isFinite(f float64) bool {
+ return math.Abs(f) <= math.MaxFloat64
+}
+
+func TestFloat32SpecialCases(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.Float32()
+
+ // 1. Check string -> Rat -> float32 conversions are
+ // consistent with strconv.ParseFloat.
+ // Skip this check if the input uses "a/b" rational syntax.
+ if !strings.Contains(input, "/") {
+ e64, _ := strconv.ParseFloat(input, 32)
+ e := float32(e64)
+
+ // Careful: negative Rats too small for
+ // float64 become -0, but Rat obviously cannot
+ // preserve the sign from SetString("-0").
+ switch {
+ case math.Float32bits(e) == math.Float32bits(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(float64(f)) {
+ continue
+ }
+
+ // 2. Check f is best approximation to r.
+ if !checkIsBestApprox32(t, f, r) {
+ // Append context information.
+ t.Errorf("(input was %q)", input)
+ }
+
+ // 3. Check f->R->f roundtrip is non-lossy.
+ checkNonLossyRoundtrip32(t, f)
+
+ // 4. Check exactness using slow algorithm.
+ if wasExact := new(Rat).SetFloat64(float64(f)).Cmp(r) == 0; wasExact != exact {
+ t.Errorf("Rat.SetString(%q).Float32().exact = %t, want %t", input, exact, wasExact)
+ }
+ }
+}
+
+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 !checkIsBestApprox64(t, f, r) {
+ // Append context information.
+ t.Errorf("(input was %q)", input)
+ }
+
+ // 3. Check f->R->f roundtrip is non-lossy.
+ checkNonLossyRoundtrip64(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 TestFloat32Distribution(t *testing.T) {
+ // Generate a distribution of (sign, mantissa, exp) values
+ // broader than the float32 range, and check Rat.Float32()
+ // always picks the closest float32 approximation.
+ var add = []int64{
+ 0,
+ 1,
+ 3,
+ 5,
+ 7,
+ 9,
+ 11,
+ }
+ var winc, einc = uint64(1), 1 // soak test (~1.5s on x86-64)
+ if testing.Short() {
+ winc, einc = 5, 15 // quick test (~60ms on x86-64)
+ }
+
+ for _, sign := range "+-" {
+ for _, a := range add {
+ for wid := uint64(0); wid < 30; wid += winc {
+ b := 1<<wid + a
+ if sign == '-' {
+ b = -b
+ }
+ for exp := -150; exp < 150; exp += einc {
+ num, den := NewInt(b), NewInt(1)
+ if exp > 0 {
+ num.Lsh(num, uint(exp))
+ } else {
+ den.Lsh(den, uint(-exp))
+ }
+ r := new(Rat).SetFrac(num, den)
+ f, _ := r.Float32()
+
+ if !checkIsBestApprox32(t, f, r) {
+ // Append context information.
+ t.Errorf("(input was mantissa %#x, exp %d; f = %g (%b); f ~ %g; r = %v)",
+ b, exp, f, f, math.Ldexp(float64(b), exp), r)
+ }
+
+ checkNonLossyRoundtrip32(t, f)
+ }
+ }
+ }
+ }
+}
+
+func TestFloat64Distribution(t *testing.T) {
+ // Generate a distribution of (sign, mantissa, exp) values
+ // broader than the float64 range, and check Rat.Float64()
+ // always picks the closest float64 approximation.
+ var add = []int64{
+ 0,
+ 1,
+ 3,
+ 5,
+ 7,
+ 9,
+ 11,
+ }
+ var winc, einc = uint64(1), 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 := 1<<wid + a
+ if sign == '-' {
+ b = -b
+ }
+ for exp := -1100; exp < 1100; exp += einc {
+ num, den := NewInt(b), NewInt(1)
+ if exp > 0 {
+ num.Lsh(num, uint(exp))
+ } else {
+ den.Lsh(den, uint(-exp))
+ }
+ r := new(Rat).SetFrac(num, den)
+ f, _ := r.Float64()
+
+ if !checkIsBestApprox64(t, f, r) {
+ // Append context information.
+ t.Errorf("(input was mantissa %#x, exp %d; f = %g (%b); f ~ %g; r = %v)",
+ b, exp, f, f, math.Ldexp(float64(b), exp), r)
+ }
+
+ checkNonLossyRoundtrip64(t, f)
+ }
+ }
+ }
+ }
+}
+
+// TestSetFloat64NonFinite checks that SetFloat64 of a non-finite value
+// returns nil.
+func TestSetFloat64NonFinite(t *testing.T) {
+ for _, f := range []float64{math.NaN(), math.Inf(+1), math.Inf(-1)} {
+ var r Rat
+ if r2 := r.SetFloat64(f); r2 != nil {
+ t.Errorf("SetFloat64(%g) was %v, want nil", f, r2)
+ }
+ }
+}
+
+// checkNonLossyRoundtrip32 checks that a float->Rat->float roundtrip is
+// non-lossy for finite f.
+func checkNonLossyRoundtrip32(t *testing.T, f float32) {
+ if !isFinite(float64(f)) {
+ return
+ }
+ r := new(Rat).SetFloat64(float64(f))
+ if r == nil {
+ t.Errorf("Rat.SetFloat64(float64(%g) (%b)) == nil", f, f)
+ return
+ }
+ f2, exact := r.Float32()
+ if f != f2 || !exact {
+ t.Errorf("Rat.SetFloat64(float64(%g)).Float32() = %g (%b), %v, want %g (%b), %v; delta = %b",
+ f, f2, f2, exact, f, f, true, f2-f)
+ }
+}
+
+// checkNonLossyRoundtrip64 checks that a float->Rat->float roundtrip is
+// non-lossy for finite f.
+func checkNonLossyRoundtrip64(t *testing.T, f float64) {
+ if !isFinite(f) {
+ return
+ }
+ r := new(Rat).SetFloat64(f)
+ if r == nil {
+ t.Errorf("Rat.SetFloat64(%g (%b)) == nil", f, f)
+ return
+ }
+ f2, exact := r.Float64()
+ if f != f2 || !exact {
+ t.Errorf("Rat.SetFloat64(%g).Float64() = %g (%b), %v, want %g (%b), %v; delta = %b",
+ f, f2, f2, exact, f, f, true, f2-f)
+ }
+}
+
+// delta returns the absolute difference between r and f.
+func delta(r *Rat, f float64) *Rat {
+ d := new(Rat).Sub(r, new(Rat).SetFloat64(f))
+ return d.Abs(d)
+}
+
+// checkIsBestApprox32 checks that f is the best possible float32
+// approximation of r.
+// Returns true on success.
+func checkIsBestApprox32(t *testing.T, f float32, r *Rat) bool {
+ if math.Abs(float64(f)) >= math.MaxFloat32 {
+ // Cannot check +Inf, -Inf, nor the float next to them (MaxFloat32).
+ // But we have tests for these special cases.
+ return true
+ }
+
+ // r must be strictly between f0 and f1, the floats bracketing f.
+ f0 := math.Nextafter32(f, float32(math.Inf(-1)))
+ f1 := math.Nextafter32(f, float32(math.Inf(+1)))
+
+ // For f to be correct, r must be closer to f than to f0 or f1.
+ df := delta(r, float64(f))
+ df0 := delta(r, float64(f0))
+ df1 := delta(r, float64(f1))
+ if df.Cmp(df0) > 0 {
+ t.Errorf("Rat(%v).Float32() = %g (%b), but previous float32 %g (%b) is closer", r, f, f, f0, f0)
+ return false
+ }
+ if df.Cmp(df1) > 0 {
+ t.Errorf("Rat(%v).Float32() = %g (%b), but next float32 %g (%b) is closer", r, f, f, f1, f1)
+ return false
+ }
+ if df.Cmp(df0) == 0 && !isEven32(f) {
+ t.Errorf("Rat(%v).Float32() = %g (%b); halfway should have rounded to %g (%b) instead", r, f, f, f0, f0)
+ return false
+ }
+ if df.Cmp(df1) == 0 && !isEven32(f) {
+ t.Errorf("Rat(%v).Float32() = %g (%b); halfway should have rounded to %g (%b) instead", r, f, f, f1, f1)
+ return false
+ }
+ return true
+}
+
+// checkIsBestApprox64 checks that f is the best possible float64
+// approximation of r.
+// Returns true on success.
+func checkIsBestApprox64(t *testing.T, f float64, r *Rat) bool {
+ if math.Abs(f) >= math.MaxFloat64 {
+ // Cannot check +Inf, -Inf, nor the float next to them (MaxFloat64).
+ // But we have tests for these special cases.
+ return true
+ }
+
+ // r must be strictly between f0 and f1, the floats bracketing f.
+ f0 := math.Nextafter(f, math.Inf(-1))
+ f1 := math.Nextafter(f, math.Inf(+1))
+
+ // For f to be correct, r must be closer to f than to f0 or f1.
+ df := delta(r, f)
+ df0 := delta(r, f0)
+ df1 := delta(r, f1)
+ if df.Cmp(df0) > 0 {
+ t.Errorf("Rat(%v).Float64() = %g (%b), but previous float64 %g (%b) is closer", r, f, f, f0, f0)
+ return false
+ }
+ if df.Cmp(df1) > 0 {
+ t.Errorf("Rat(%v).Float64() = %g (%b), but next float64 %g (%b) is closer", r, f, f, f1, f1)
+ return false
+ }
+ if df.Cmp(df0) == 0 && !isEven64(f) {
+ t.Errorf("Rat(%v).Float64() = %g (%b); halfway should have rounded to %g (%b) instead", r, f, f, f0, f0)
+ return false
+ }
+ if df.Cmp(df1) == 0 && !isEven64(f) {
+ t.Errorf("Rat(%v).Float64() = %g (%b); halfway should have rounded to %g (%b) instead", r, f, f, f1, f1)
+ return false
+ }
+ return true
+}
+
+func isEven32(f float32) bool { return math.Float32bits(f)&1 == 0 }
+func isEven64(f float64) bool { return math.Float64bits(f)&1 == 0 }
+
+func TestIsFinite(t *testing.T) {
+ finites := []float64{
+ 1.0 / 3,
+ 4891559871276714924261e+222,
+ math.MaxFloat64,
+ math.SmallestNonzeroFloat64,
+ -math.MaxFloat64,
+ -math.SmallestNonzeroFloat64,
+ }
+ for _, f := range finites {
+ if !isFinite(f) {
+ t.Errorf("!IsFinite(%g (%b))", f, f)
+ }
+ }
+ nonfinites := []float64{
+ math.NaN(),
+ math.Inf(-1),
+ math.Inf(+1),
+ }
+ for _, f := range nonfinites {
+ if isFinite(f) {
+ t.Errorf("IsFinite(%g, (%b))", f, f)
+ }
+ }
+}
generated by cgit v1.2.3 (git 2.39.1) at 2024-06-13 16:54:07 +0000