From: Robert Griesemer Date: Fri, 30 Jan 2015 22:20:04 +0000 (-0800) Subject: math/big: split rat conversion routines and tests into separate files X-Git-Tag: go1.5beta1~2191 X-Git-Url: http://www.git.cypherpunks.su/?a=commitdiff_plain;h=20a96a1f68cfe608b8066f3ee1b0db28d1d3e4e0;p=gostls13.git math/big: split rat conversion routines and tests into separate files No other functional changes. Change-Id: I8be1fc488caa4f3d4c00afcb8c00475bfcd10709 Reviewed-on: https://go-review.googlesource.com/3673 Reviewed-by: Alan Donovan --- diff --git a/src/math/big/rat.go b/src/math/big/rat.go index bc4029a721..b73377ea3f 100644 --- a/src/math/big/rat.go +++ b/src/math/big/rat.go @@ -10,10 +10,7 @@ import ( "encoding/binary" "errors" "fmt" - "io" "math" - "strconv" - "strings" ) // A Rat represents a quotient a/b of arbitrary precision. @@ -514,229 +511,6 @@ func (z *Rat) Quo(x, y *Rat) *Rat { return z.norm() } -func ratTok(ch rune) bool { - return strings.IndexRune("+-/0123456789.eE", ch) >= 0 -} - -// Scan is a support routine for fmt.Scanner. It accepts the formats -// 'e', 'E', 'f', 'F', 'g', 'G', and 'v'. All formats are equivalent. -func (z *Rat) Scan(s fmt.ScanState, ch rune) error { - tok, err := s.Token(true, ratTok) - if err != nil { - return err - } - if strings.IndexRune("efgEFGv", ch) < 0 { - return errors.New("Rat.Scan: invalid verb") - } - if _, ok := z.SetString(string(tok)); !ok { - return errors.New("Rat.Scan: invalid syntax") - } - return nil -} - -// SetString sets z to the value of s and returns z and a boolean indicating -// success. s can be given as a fraction "a/b" or as a floating-point number -// optionally followed by an exponent. If the operation failed, the value of -// z is undefined but the returned value is nil. -func (z *Rat) SetString(s string) (*Rat, bool) { - if len(s) == 0 { - return nil, false - } - // len(s) > 0 - - // parse fraction a/b, if any - if sep := strings.Index(s, "/"); sep >= 0 { - if _, ok := z.a.SetString(s[:sep], 0); !ok { - return nil, false - } - s = s[sep+1:] - var err error - if z.b.abs, _, _, err = z.b.abs.scan(strings.NewReader(s), 0, false); err != nil { - return nil, false - } - if len(z.b.abs) == 0 { - return nil, false - } - return z.norm(), true - } - - // parse floating-point number - r := strings.NewReader(s) - - // sign - neg, err := scanSign(r) - if err != nil { - return nil, false - } - - // mantissa - var ecorr int - z.a.abs, _, ecorr, err = z.a.abs.scan(r, 10, true) - if err != nil { - return nil, false - } - - // exponent - var exp int64 - var ebase int - exp, ebase, err = scanExponent(r) - if ebase == 2 || err != nil { - return nil, false - } - - // there should be no unread characters left - if _, err = r.ReadByte(); err != io.EOF { - return nil, false - } - - // correct exponent - if ecorr < 0 { - exp += int64(ecorr) - } - - // compute exponent power - expabs := exp - if expabs < 0 { - expabs = -expabs - } - powTen := nat(nil).expNN(natTen, nat(nil).setWord(Word(expabs)), nil) - - // complete fraction - if exp < 0 { - z.b.abs = powTen - z.norm() - } else { - z.a.abs = z.a.abs.mul(z.a.abs, powTen) - z.b.abs = z.b.abs[:0] - } - - z.a.neg = neg && len(z.a.abs) > 0 // 0 has no sign - - return z, true -} - -func scanExponent(r io.ByteScanner) (exp int64, base int, err error) { - base = 10 - - var ch byte - if ch, err = r.ReadByte(); err != nil { - if err == io.EOF { - err = nil // no exponent; same as e0 - } - return - } - - switch ch { - case 'e', 'E': - // ok - case 'p': - base = 2 - default: - r.UnreadByte() - return // no exponent; same as e0 - } - - var neg bool - if neg, err = scanSign(r); err != nil { - return - } - - var digits []byte - if neg { - digits = append(digits, '-') - } - - // no need to use nat.scan for exponent digits - // since we only care about int64 values - the - // from-scratch scan is easy enough and faster - for i := 0; ; i++ { - if ch, err = r.ReadByte(); err != nil { - if err != io.EOF || i == 0 { - return - } - err = nil - break // i > 0 - } - if ch < '0' || '9' < ch { - if i == 0 { - r.UnreadByte() - err = fmt.Errorf("invalid exponent (missing digits)") - return - } - break // i > 0 - } - digits = append(digits, byte(ch)) - } - // i > 0 => we have at least one digit - - exp, err = strconv.ParseInt(string(digits), 10, 64) - return -} - -// String returns a string representation of x in the form "a/b" (even if b == 1). -func (x *Rat) String() string { - s := "/1" - if len(x.b.abs) != 0 { - s = "/" + x.b.abs.decimalString() - } - return x.a.String() + s -} - -// RatString returns a string representation of x in the form "a/b" if b != 1, -// and in the form "a" if b == 1. -func (x *Rat) RatString() string { - if x.IsInt() { - return x.a.String() - } - return x.String() -} - -// FloatString returns a string representation of x in decimal form with prec -// digits of precision after the decimal point and the last digit rounded. -func (x *Rat) FloatString(prec int) string { - if x.IsInt() { - s := x.a.String() - if prec > 0 { - s += "." + strings.Repeat("0", prec) - } - return s - } - // x.b.abs != 0 - - q, r := nat(nil).div(nat(nil), x.a.abs, x.b.abs) - - p := natOne - if prec > 0 { - p = nat(nil).expNN(natTen, nat(nil).setUint64(uint64(prec)), nil) - } - - r = r.mul(r, p) - r, r2 := r.div(nat(nil), r, x.b.abs) - - // see if we need to round up - r2 = r2.add(r2, r2) - if x.b.abs.cmp(r2) <= 0 { - r = r.add(r, natOne) - if r.cmp(p) >= 0 { - q = nat(nil).add(q, natOne) - r = nat(nil).sub(r, p) - } - } - - s := q.decimalString() - if x.a.neg { - s = "-" + s - } - - if prec > 0 { - rs := r.decimalString() - leadingZeros := prec - len(rs) - s += "." + strings.Repeat("0", leadingZeros) + rs - } - - return s -} - // Gob codec version. Permits backward-compatible changes to the encoding. const ratGobVersion byte = 1 diff --git a/src/math/big/rat_test.go b/src/math/big/rat_test.go index 37f672ee3d..012d0c47ec 100644 --- a/src/math/big/rat_test.go +++ b/src/math/big/rat_test.go @@ -9,10 +9,7 @@ import ( "encoding/gob" "encoding/json" "encoding/xml" - "fmt" "math" - "strconv" - "strings" "testing" ) @@ -56,128 +53,6 @@ func TestZeroRat(t *testing.T) { z.Quo(&x, &y) } -type StringTest struct { - in, out string - ok bool -} - -var setStringTests = []StringTest{ - {"0", "0", true}, - {"-0", "0", true}, - {"1", "1", true}, - {"-1", "-1", true}, - {"1.", "1", true}, - {"1e0", "1", true}, - {"1.e1", "10", true}, - {in: "1e"}, - {in: "1.e"}, - {in: "1e+14e-5"}, - {in: "1e4.5"}, - {in: "r"}, - {in: "a/b"}, - {in: "a.b"}, - {"-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"}, -} - -// These are not supported by fmt.Fscanf. -var setStringTests2 = []StringTest{ - {"0x10", "16", true}, - {"-010/1", "-8", true}, // TODO(gri) should we even permit octal here? - {"-010.", "-10", true}, - {"0x10/0x20", "1/2", true}, - {"0b1000/3", "8/3", true}, - // TODO(gri) add more tests -} - -func TestRatSetString(t *testing.T) { - var tests []StringTest - tests = append(tests, setStringTests...) - tests = append(tests, setStringTests2...) - - for i, test := range tests { - 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 (%s) error: %s", i, test.in, err) - } else { - t.Errorf("#%d (%s) expected error", i, test.in) - } - 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 { @@ -608,321 +483,6 @@ func TestIssue3521(t *testing.T) { } } -// 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() diff --git a/src/math/big/ratconv.go b/src/math/big/ratconv.go new file mode 100644 index 0000000000..da4915e74d --- /dev/null +++ b/src/math/big/ratconv.go @@ -0,0 +1,238 @@ +// Copyright 2015 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. + +// This file implements rat-to-string conversion functions. + +package big + +import ( + "errors" + "fmt" + "io" + "strconv" + "strings" +) + +func ratTok(ch rune) bool { + return strings.IndexRune("+-/0123456789.eE", ch) >= 0 +} + +// Scan is a support routine for fmt.Scanner. It accepts the formats +// 'e', 'E', 'f', 'F', 'g', 'G', and 'v'. All formats are equivalent. +func (z *Rat) Scan(s fmt.ScanState, ch rune) error { + tok, err := s.Token(true, ratTok) + if err != nil { + return err + } + if strings.IndexRune("efgEFGv", ch) < 0 { + return errors.New("Rat.Scan: invalid verb") + } + if _, ok := z.SetString(string(tok)); !ok { + return errors.New("Rat.Scan: invalid syntax") + } + return nil +} + +// SetString sets z to the value of s and returns z and a boolean indicating +// success. s can be given as a fraction "a/b" or as a floating-point number +// optionally followed by an exponent. If the operation failed, the value of +// z is undefined but the returned value is nil. +func (z *Rat) SetString(s string) (*Rat, bool) { + if len(s) == 0 { + return nil, false + } + // len(s) > 0 + + // parse fraction a/b, if any + if sep := strings.Index(s, "/"); sep >= 0 { + if _, ok := z.a.SetString(s[:sep], 0); !ok { + return nil, false + } + s = s[sep+1:] + var err error + if z.b.abs, _, _, err = z.b.abs.scan(strings.NewReader(s), 0, false); err != nil { + return nil, false + } + if len(z.b.abs) == 0 { + return nil, false + } + return z.norm(), true + } + + // parse floating-point number + r := strings.NewReader(s) + + // sign + neg, err := scanSign(r) + if err != nil { + return nil, false + } + + // mantissa + var ecorr int + z.a.abs, _, ecorr, err = z.a.abs.scan(r, 10, true) + if err != nil { + return nil, false + } + + // exponent + var exp int64 + var ebase int + exp, ebase, err = scanExponent(r) + if ebase == 2 || err != nil { + return nil, false + } + + // there should be no unread characters left + if _, err = r.ReadByte(); err != io.EOF { + return nil, false + } + + // correct exponent + if ecorr < 0 { + exp += int64(ecorr) + } + + // compute exponent power + expabs := exp + if expabs < 0 { + expabs = -expabs + } + powTen := nat(nil).expNN(natTen, nat(nil).setWord(Word(expabs)), nil) + + // complete fraction + if exp < 0 { + z.b.abs = powTen + z.norm() + } else { + z.a.abs = z.a.abs.mul(z.a.abs, powTen) + z.b.abs = z.b.abs[:0] + } + + z.a.neg = neg && len(z.a.abs) > 0 // 0 has no sign + + return z, true +} + +func scanExponent(r io.ByteScanner) (exp int64, base int, err error) { + base = 10 + + var ch byte + if ch, err = r.ReadByte(); err != nil { + if err == io.EOF { + err = nil // no exponent; same as e0 + } + return + } + + switch ch { + case 'e', 'E': + // ok + case 'p': + base = 2 + default: + r.UnreadByte() + return // no exponent; same as e0 + } + + var neg bool + if neg, err = scanSign(r); err != nil { + return + } + + var digits []byte + if neg { + digits = append(digits, '-') + } + + // no need to use nat.scan for exponent digits + // since we only care about int64 values - the + // from-scratch scan is easy enough and faster + for i := 0; ; i++ { + if ch, err = r.ReadByte(); err != nil { + if err != io.EOF || i == 0 { + return + } + err = nil + break // i > 0 + } + if ch < '0' || '9' < ch { + if i == 0 { + r.UnreadByte() + err = fmt.Errorf("invalid exponent (missing digits)") + return + } + break // i > 0 + } + digits = append(digits, byte(ch)) + } + // i > 0 => we have at least one digit + + exp, err = strconv.ParseInt(string(digits), 10, 64) + return +} + +// String returns a string representation of x in the form "a/b" (even if b == 1). +func (x *Rat) String() string { + s := "/1" + if len(x.b.abs) != 0 { + s = "/" + x.b.abs.decimalString() + } + return x.a.String() + s +} + +// RatString returns a string representation of x in the form "a/b" if b != 1, +// and in the form "a" if b == 1. +func (x *Rat) RatString() string { + if x.IsInt() { + return x.a.String() + } + return x.String() +} + +// FloatString returns a string representation of x in decimal form with prec +// digits of precision after the decimal point and the last digit rounded. +func (x *Rat) FloatString(prec int) string { + if x.IsInt() { + s := x.a.String() + if prec > 0 { + s += "." + strings.Repeat("0", prec) + } + return s + } + // x.b.abs != 0 + + q, r := nat(nil).div(nat(nil), x.a.abs, x.b.abs) + + p := natOne + if prec > 0 { + p = nat(nil).expNN(natTen, nat(nil).setUint64(uint64(prec)), nil) + } + + r = r.mul(r, p) + r, r2 := r.div(nat(nil), r, x.b.abs) + + // see if we need to round up + r2 = r2.add(r2, r2) + if x.b.abs.cmp(r2) <= 0 { + r = r.add(r, natOne) + if r.cmp(p) >= 0 { + q = nat(nil).add(q, natOne) + r = nat(nil).sub(r, p) + } + } + + s := q.decimalString() + if x.a.neg { + s = "-" + s + } + + if prec > 0 { + rs := r.decimalString() + leadingZeros := prec - len(rs) + s += "." + strings.Repeat("0", leadingZeros) + rs + } + + return s +} diff --git a/src/math/big/ratconv_test.go b/src/math/big/ratconv_test.go new file mode 100644 index 0000000000..16b3a19418 --- /dev/null +++ b/src/math/big/ratconv_test.go @@ -0,0 +1,451 @@ +// Copyright 2015 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" + "fmt" + "math" + "strconv" + "strings" + "testing" +) + +type StringTest struct { + in, out string + ok bool +} + +var setStringTests = []StringTest{ + {"0", "0", true}, + {"-0", "0", true}, + {"1", "1", true}, + {"-1", "-1", true}, + {"1.", "1", true}, + {"1e0", "1", true}, + {"1.e1", "10", true}, + {in: "1e"}, + {in: "1.e"}, + {in: "1e+14e-5"}, + {in: "1e4.5"}, + {in: "r"}, + {in: "a/b"}, + {in: "a.b"}, + {"-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"}, +} + +// These are not supported by fmt.Fscanf. +var setStringTests2 = []StringTest{ + {"0x10", "16", true}, + {"-010/1", "-8", true}, // TODO(gri) should we even permit octal here? + {"-010.", "-10", true}, + {"0x10/0x20", "1/2", true}, + {"0b1000/3", "8/3", true}, + // TODO(gri) add more tests +} + +func TestRatSetString(t *testing.T) { + var tests []StringTest + tests = append(tests, setStringTests...) + tests = append(tests, setStringTests2...) + + for i, test := range tests { + 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 (%s) error: %s", i, test.in, err) + } else { + t.Errorf("#%d (%s) expected error", i, test.in) + } + 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) + } + } +} + +// 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) + } + } +}