// 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 ( "fmt" "math" "strconv" "testing" ) func TestFloatSetFloat64String(t *testing.T) { inf := math.Inf(0) nan := math.NaN() for _, test := range []struct { s string x float64 // NaNs represent invalid inputs }{ // basics {"0", 0}, {"-0", -0}, {"+0", 0}, {"1", 1}, {"-1", -1}, {"+1", 1}, {"1.234", 1.234}, {"-1.234", -1.234}, {"+1.234", 1.234}, {".1", 0.1}, {"1.", 1}, {"+1.", 1}, // various zeros {"0e100", 0}, {"-0e+100", 0}, {"+0e-100", 0}, {"0E100", 0}, {"-0E+100", 0}, {"+0E-100", 0}, // various decimal exponent formats {"1.e10", 1e10}, {"1e+10", 1e10}, {"+1e-10", 1e-10}, {"1E10", 1e10}, {"1.E+10", 1e10}, {"+1E-10", 1e-10}, // infinities {"Inf", inf}, {"+Inf", inf}, {"-Inf", -inf}, {"inf", inf}, {"+inf", inf}, {"-inf", -inf}, // invalid numbers {"", nan}, {"-", nan}, {"0x", nan}, {"0e", nan}, {"1.2ef", nan}, {"2..3", nan}, {"123..", nan}, {"infinity", nan}, {"foobar", nan}, // misc decimal values {"3.14159265", 3.14159265}, {"-687436.79457e-245", -687436.79457e-245}, {"-687436.79457E245", -687436.79457e245}, {".0000000000000000000000000000000000000001", 1e-40}, {"+10000000000000000000000000000000000000000e-0", 1e40}, // decimal mantissa, binary exponent {"0p0", 0}, {"-0p0", -0}, {"1p10", 1 << 10}, {"1p+10", 1 << 10}, {"+1p-10", 1.0 / (1 << 10)}, {"1024p-12", 0.25}, {"-1p10", -1024}, {"1.5p1", 3}, // binary mantissa, decimal exponent {"0b0", 0}, {"-0b0", -0}, {"0b0e+10", 0}, {"-0b0e-10", -0}, {"0b1010", 10}, {"0B1010E2", 1000}, {"0b.1", 0.5}, {"0b.001", 0.125}, {"0b.001e3", 125}, // binary mantissa, binary exponent {"0b0p+10", 0}, {"-0b0p-10", -0}, {"0b.1010p4", 10}, {"0b1p-1", 0.5}, {"0b001p-3", 0.125}, {"0b.001p3", 1}, {"0b0.01p2", 1}, // hexadecimal mantissa and exponent {"0x0", 0}, {"-0x0", -0}, {"0x0p+10", 0}, {"-0x0p-10", -0}, {"0xff", 255}, {"0X.8p1", 1}, {"-0X0.00008p16", -0.5}, {"0x0.0000000000001p-1022", math.SmallestNonzeroFloat64}, {"0x1.fffffffffffffp1023", math.MaxFloat64}, } { var x Float x.SetPrec(53) _, ok := x.SetString(test.s) if math.IsNaN(test.x) { // test.s is invalid if ok { t.Errorf("%s: want parse error", test.s) } continue } // test.s is valid if !ok { t.Errorf("%s: got parse error", test.s) continue } f, _ := x.Float64() want := new(Float).SetFloat64(test.x) if x.Cmp(want) != 0 { t.Errorf("%s: got %s (%v); want %v", test.s, &x, f, test.x) } } } func fdiv(a, b float64) float64 { return a / b } const ( below1e23 = 99999999999999974834176 above1e23 = 100000000000000008388608 ) func TestFloat64Text(t *testing.T) { for _, test := range []struct { x float64 format byte prec int want string }{ {0, 'f', 0, "0"}, {math.Copysign(0, -1), 'f', 0, "-0"}, {1, 'f', 0, "1"}, {-1, 'f', 0, "-1"}, {0.001, 'e', 0, "1e-03"}, {0.459, 'e', 0, "5e-01"}, {1.459, 'e', 0, "1e+00"}, {2.459, 'e', 1, "2.5e+00"}, {3.459, 'e', 2, "3.46e+00"}, {4.459, 'e', 3, "4.459e+00"}, {5.459, 'e', 4, "5.4590e+00"}, {0.001, 'f', 0, "0"}, {0.459, 'f', 0, "0"}, {1.459, 'f', 0, "1"}, {2.459, 'f', 1, "2.5"}, {3.459, 'f', 2, "3.46"}, {4.459, 'f', 3, "4.459"}, {5.459, 'f', 4, "5.4590"}, {0, 'b', 0, "0"}, {math.Copysign(0, -1), 'b', 0, "-0"}, {1.0, 'b', 0, "4503599627370496p-52"}, {-1.0, 'b', 0, "-4503599627370496p-52"}, {4503599627370496, 'b', 0, "4503599627370496p+0"}, {0, 'p', 0, "0"}, {math.Copysign(0, -1), 'p', 0, "-0"}, {1024.0, 'p', 0, "0x.8p+11"}, {-1024.0, 'p', 0, "-0x.8p+11"}, // all test cases below from strconv/ftoa_test.go {1, 'e', 5, "1.00000e+00"}, {1, 'f', 5, "1.00000"}, {1, 'g', 5, "1"}, {1, 'g', -1, "1"}, {20, 'g', -1, "20"}, {1234567.8, 'g', -1, "1.2345678e+06"}, {200000, 'g', -1, "200000"}, {2000000, 'g', -1, "2e+06"}, // g conversion and zero suppression {400, 'g', 2, "4e+02"}, {40, 'g', 2, "40"}, {4, 'g', 2, "4"}, {.4, 'g', 2, "0.4"}, {.04, 'g', 2, "0.04"}, {.004, 'g', 2, "0.004"}, {.0004, 'g', 2, "0.0004"}, {.00004, 'g', 2, "4e-05"}, {.000004, 'g', 2, "4e-06"}, {0, 'e', 5, "0.00000e+00"}, {0, 'f', 5, "0.00000"}, {0, 'g', 5, "0"}, {0, 'g', -1, "0"}, {-1, 'e', 5, "-1.00000e+00"}, {-1, 'f', 5, "-1.00000"}, {-1, 'g', 5, "-1"}, {-1, 'g', -1, "-1"}, {12, 'e', 5, "1.20000e+01"}, {12, 'f', 5, "12.00000"}, {12, 'g', 5, "12"}, {12, 'g', -1, "12"}, {123456700, 'e', 5, "1.23457e+08"}, {123456700, 'f', 5, "123456700.00000"}, {123456700, 'g', 5, "1.2346e+08"}, {123456700, 'g', -1, "1.234567e+08"}, {1.2345e6, 'e', 5, "1.23450e+06"}, {1.2345e6, 'f', 5, "1234500.00000"}, {1.2345e6, 'g', 5, "1.2345e+06"}, {1e23, 'e', 17, "9.99999999999999916e+22"}, {1e23, 'f', 17, "99999999999999991611392.00000000000000000"}, {1e23, 'g', 17, "9.9999999999999992e+22"}, {1e23, 'e', -1, "1e+23"}, {1e23, 'f', -1, "100000000000000000000000"}, {1e23, 'g', -1, "1e+23"}, {below1e23, 'e', 17, "9.99999999999999748e+22"}, {below1e23, 'f', 17, "99999999999999974834176.00000000000000000"}, {below1e23, 'g', 17, "9.9999999999999975e+22"}, {below1e23, 'e', -1, "9.999999999999997e+22"}, {below1e23, 'f', -1, "99999999999999970000000"}, {below1e23, 'g', -1, "9.999999999999997e+22"}, {above1e23, 'e', 17, "1.00000000000000008e+23"}, {above1e23, 'f', 17, "100000000000000008388608.00000000000000000"}, {above1e23, 'g', 17, "1.0000000000000001e+23"}, {above1e23, 'e', -1, "1.0000000000000001e+23"}, {above1e23, 'f', -1, "100000000000000010000000"}, {above1e23, 'g', -1, "1.0000000000000001e+23"}, {5e-304 / 1e20, 'g', -1, "5e-324"}, {-5e-304 / 1e20, 'g', -1, "-5e-324"}, {fdiv(5e-304, 1e20), 'g', -1, "5e-324"}, // avoid constant arithmetic {fdiv(-5e-304, 1e20), 'g', -1, "-5e-324"}, // avoid constant arithmetic {32, 'g', -1, "32"}, {32, 'g', 0, "3e+01"}, {100, 'x', -1, "%x"}, // {math.NaN(), 'g', -1, "NaN"}, // Float doesn't support NaNs // {-math.NaN(), 'g', -1, "NaN"}, // Float doesn't support NaNs {math.Inf(0), 'g', -1, "+Inf"}, {math.Inf(-1), 'g', -1, "-Inf"}, {-math.Inf(0), 'g', -1, "-Inf"}, {-1, 'b', -1, "-4503599627370496p-52"}, // fixed bugs {0.9, 'f', 1, "0.9"}, {0.09, 'f', 1, "0.1"}, {0.0999, 'f', 1, "0.1"}, {0.05, 'f', 1, "0.1"}, {0.05, 'f', 0, "0"}, {0.5, 'f', 1, "0.5"}, {0.5, 'f', 0, "0"}, {1.5, 'f', 0, "2"}, // http://www.exploringbinary.com/java-hangs-when-converting-2-2250738585072012e-308/ {2.2250738585072012e-308, 'g', -1, "2.2250738585072014e-308"}, // http://www.exploringbinary.com/php-hangs-on-numeric-value-2-2250738585072011e-308/ {2.2250738585072011e-308, 'g', -1, "2.225073858507201e-308"}, // Issue 2625. {383260575764816448, 'f', 0, "383260575764816448"}, {383260575764816448, 'g', -1, "3.8326057576481645e+17"}, } { // The test cases are from the strconv package which tests float64 values. // When formatting values with prec = -1 (shortest representation), // the actually available mantissa precision matters. // For denormalized values, that precision is < 53 (SetFloat64 default). // Compute and set the actual precision explicitly. f := new(Float).SetPrec(actualPrec(test.x)).SetFloat64(test.x) got := f.Text(test.format, test.prec) if got != test.want { t.Errorf("%v: got %s; want %s", test, got, test.want) continue } if test.format == 'b' && test.x == 0 { continue // 'b' format in strconv.Float requires knowledge of bias for 0.0 } if test.format == 'p' { continue // 'p' format not supported in strconv.Format } // verify that Float format matches strconv format want := strconv.FormatFloat(test.x, test.format, test.prec, 64) if got != want { t.Errorf("%v: got %s; want %s (strconv)", test, got, want) } } } // actualPrec returns the number of actually used mantissa bits. func actualPrec(x float64) uint { if bits := math.Float64bits(x); x != 0 && bits&(0x7ff<<52) == 0 { // x is denormalized return 64 - nlz64(bits&(1<<52-1)) } return 53 } func TestFloatText(t *testing.T) { for _, test := range []struct { x string prec uint format byte digits int want string }{ {"0", 10, 'f', 0, "0"}, {"-0", 10, 'f', 0, "-0"}, {"1", 10, 'f', 0, "1"}, {"-1", 10, 'f', 0, "-1"}, {"1.459", 100, 'e', 0, "1e+00"}, {"2.459", 100, 'e', 1, "2.5e+00"}, {"3.459", 100, 'e', 2, "3.46e+00"}, {"4.459", 100, 'e', 3, "4.459e+00"}, {"5.459", 100, 'e', 4, "5.4590e+00"}, {"1.459", 100, 'E', 0, "1E+00"}, {"2.459", 100, 'E', 1, "2.5E+00"}, {"3.459", 100, 'E', 2, "3.46E+00"}, {"4.459", 100, 'E', 3, "4.459E+00"}, {"5.459", 100, 'E', 4, "5.4590E+00"}, {"1.459", 100, 'f', 0, "1"}, {"2.459", 100, 'f', 1, "2.5"}, {"3.459", 100, 'f', 2, "3.46"}, {"4.459", 100, 'f', 3, "4.459"}, {"5.459", 100, 'f', 4, "5.4590"}, {"1.459", 100, 'g', 0, "1"}, {"2.459", 100, 'g', 1, "2"}, {"3.459", 100, 'g', 2, "3.5"}, {"4.459", 100, 'g', 3, "4.46"}, {"5.459", 100, 'g', 4, "5.459"}, {"1459", 53, 'g', 0, "1e+03"}, {"2459", 53, 'g', 1, "2e+03"}, {"3459", 53, 'g', 2, "3.5e+03"}, {"4459", 53, 'g', 3, "4.46e+03"}, {"5459", 53, 'g', 4, "5459"}, {"1459", 53, 'G', 0, "1E+03"}, {"2459", 53, 'G', 1, "2E+03"}, {"3459", 53, 'G', 2, "3.5E+03"}, {"4459", 53, 'G', 3, "4.46E+03"}, {"5459", 53, 'G', 4, "5459"}, {"3", 10, 'e', 40, "3.0000000000000000000000000000000000000000e+00"}, {"3", 10, 'f', 40, "3.0000000000000000000000000000000000000000"}, {"3", 10, 'g', 40, "3"}, {"3e40", 100, 'e', 40, "3.0000000000000000000000000000000000000000e+40"}, {"3e40", 100, 'f', 4, "30000000000000000000000000000000000000000.0000"}, {"3e40", 100, 'g', 40, "3e+40"}, // make sure "stupid" exponents don't stall the machine {"1e1000000", 64, 'p', 0, "0x.88b3a28a05eade3ap+3321929"}, {"1e646456992", 64, 'p', 0, "0x.e883a0c5c8c7c42ap+2147483644"}, {"1e646456993", 64, 'p', 0, "+Inf"}, {"1e1000000000", 64, 'p', 0, "+Inf"}, {"1e-1000000", 64, 'p', 0, "0x.efb4542cc8ca418ap-3321928"}, {"1e-646456993", 64, 'p', 0, "0x.e17c8956983d9d59p-2147483647"}, {"1e-646456994", 64, 'p', 0, "0"}, {"1e-1000000000", 64, 'p', 0, "0"}, // minimum and maximum values {"1p2147483646", 64, 'p', 0, "0x.8p+2147483647"}, {"0x.8p2147483647", 64, 'p', 0, "0x.8p+2147483647"}, {"0x.8p-2147483647", 64, 'p', 0, "0x.8p-2147483647"}, {"1p-2147483649", 64, 'p', 0, "0x.8p-2147483648"}, // TODO(gri) need tests for actual large Floats {"0", 53, 'b', 0, "0"}, {"-0", 53, 'b', 0, "-0"}, {"1.0", 53, 'b', 0, "4503599627370496p-52"}, {"-1.0", 53, 'b', 0, "-4503599627370496p-52"}, {"4503599627370496", 53, 'b', 0, "4503599627370496p+0"}, // issue 9939 {"3", 350, 'b', 0, "1720123961992553633708115671476565205597423741876210842803191629540192157066363606052513914832594264915968p-348"}, {"03", 350, 'b', 0, "1720123961992553633708115671476565205597423741876210842803191629540192157066363606052513914832594264915968p-348"}, {"3.", 350, 'b', 0, "1720123961992553633708115671476565205597423741876210842803191629540192157066363606052513914832594264915968p-348"}, {"3.0", 350, 'b', 0, "1720123961992553633708115671476565205597423741876210842803191629540192157066363606052513914832594264915968p-348"}, {"3.00", 350, 'b', 0, "1720123961992553633708115671476565205597423741876210842803191629540192157066363606052513914832594264915968p-348"}, {"3.000", 350, 'b', 0, "1720123961992553633708115671476565205597423741876210842803191629540192157066363606052513914832594264915968p-348"}, {"3", 350, 'p', 0, "0x.cp+2"}, {"03", 350, 'p', 0, "0x.cp+2"}, {"3.", 350, 'p', 0, "0x.cp+2"}, {"3.0", 350, 'p', 0, "0x.cp+2"}, {"3.00", 350, 'p', 0, "0x.cp+2"}, {"3.000", 350, 'p', 0, "0x.cp+2"}, {"0", 64, 'p', 0, "0"}, {"-0", 64, 'p', 0, "-0"}, {"1024.0", 64, 'p', 0, "0x.8p+11"}, {"-1024.0", 64, 'p', 0, "-0x.8p+11"}, // unsupported format {"3.14", 64, 'x', 0, "%x"}, {"-3.14", 64, 'x', 0, "%x"}, } { f, _, err := ParseFloat(test.x, 0, test.prec, ToNearestEven) if err != nil { t.Errorf("%v: %s", test, err) continue } got := f.Text(test.format, test.digits) if got != test.want { t.Errorf("%v: got %s; want %s", test, got, test.want) } // compare with strconv.FormatFloat output if possible // ('p' format is not supported by strconv.FormatFloat, // and its output for 0.0 prints a biased exponent value // as in 0p-1074 which makes no sense to emulate here) if test.prec == 53 && test.format != 'p' && f.Sign() != 0 { f64, acc := f.Float64() if acc != Exact { t.Errorf("%v: expected exact conversion to float64", test) continue } got := strconv.FormatFloat(f64, test.format, test.digits, 64) if got != test.want { t.Errorf("%v: got %s; want %s", test, got, test.want) } } } } func TestFloatFormat(t *testing.T) { for _, test := range []struct { format string value interface{} // float32, float64, or string (== 512bit *Float) want string }{ // from fmt/fmt_test.go {"%+.3e", 0.0, "+0.000e+00"}, {"%+.3e", 1.0, "+1.000e+00"}, {"%+.3f", -1.0, "-1.000"}, {"%+.3F", -1.0, "-1.000"}, {"%+.3F", float32(-1.0), "-1.000"}, {"%+07.2f", 1.0, "+001.00"}, {"%+07.2f", -1.0, "-001.00"}, {"%+10.2f", +1.0, " +1.00"}, {"%+10.2f", -1.0, " -1.00"}, {"% .3E", -1.0, "-1.000E+00"}, {"% .3e", 1.0, " 1.000e+00"}, {"%+.3g", 0.0, "+0"}, {"%+.3g", 1.0, "+1"}, {"%+.3g", -1.0, "-1"}, {"% .3g", -1.0, "-1"}, {"% .3g", 1.0, " 1"}, {"%b", float32(1.0), "8388608p-23"}, {"%b", 1.0, "4503599627370496p-52"}, // from fmt/fmt_test.go: old test/fmt_test.go {"%e", 1.0, "1.000000e+00"}, {"%e", 1234.5678e3, "1.234568e+06"}, {"%e", 1234.5678e-8, "1.234568e-05"}, {"%e", -7.0, "-7.000000e+00"}, {"%e", -1e-9, "-1.000000e-09"}, {"%f", 1234.5678e3, "1234567.800000"}, {"%f", 1234.5678e-8, "0.000012"}, {"%f", -7.0, "-7.000000"}, {"%f", -1e-9, "-0.000000"}, {"%g", 1234.5678e3, "1.2345678e+06"}, {"%g", float32(1234.5678e3), "1.2345678e+06"}, {"%g", 1234.5678e-8, "1.2345678e-05"}, {"%g", -7.0, "-7"}, {"%g", -1e-9, "-1e-09"}, {"%g", float32(-1e-9), "-1e-09"}, {"%E", 1.0, "1.000000E+00"}, {"%E", 1234.5678e3, "1.234568E+06"}, {"%E", 1234.5678e-8, "1.234568E-05"}, {"%E", -7.0, "-7.000000E+00"}, {"%E", -1e-9, "-1.000000E-09"}, {"%G", 1234.5678e3, "1.2345678E+06"}, {"%G", float32(1234.5678e3), "1.2345678E+06"}, {"%G", 1234.5678e-8, "1.2345678E-05"}, {"%G", -7.0, "-7"}, {"%G", -1e-9, "-1E-09"}, {"%G", float32(-1e-9), "-1E-09"}, {"%20.6e", 1.2345e3, " 1.234500e+03"}, {"%20.6e", 1.2345e-3, " 1.234500e-03"}, {"%20e", 1.2345e3, " 1.234500e+03"}, {"%20e", 1.2345e-3, " 1.234500e-03"}, {"%20.8e", 1.2345e3, " 1.23450000e+03"}, {"%20f", 1.23456789e3, " 1234.567890"}, {"%20f", 1.23456789e-3, " 0.001235"}, {"%20f", 12345678901.23456789, " 12345678901.234568"}, {"%-20f", 1.23456789e3, "1234.567890 "}, {"%20.8f", 1.23456789e3, " 1234.56789000"}, {"%20.8f", 1.23456789e-3, " 0.00123457"}, {"%g", 1.23456789e3, "1234.56789"}, {"%g", 1.23456789e-3, "0.00123456789"}, {"%g", 1.23456789e20, "1.23456789e+20"}, {"%20e", math.Inf(1), " +Inf"}, {"%-20f", math.Inf(-1), "-Inf "}, // from fmt/fmt_test.go: comparison of padding rules with C printf {"%.2f", 1.0, "1.00"}, {"%.2f", -1.0, "-1.00"}, {"% .2f", 1.0, " 1.00"}, {"% .2f", -1.0, "-1.00"}, {"%+.2f", 1.0, "+1.00"}, {"%+.2f", -1.0, "-1.00"}, {"%7.2f", 1.0, " 1.00"}, {"%7.2f", -1.0, " -1.00"}, {"% 7.2f", 1.0, " 1.00"}, {"% 7.2f", -1.0, " -1.00"}, {"%+7.2f", 1.0, " +1.00"}, {"%+7.2f", -1.0, " -1.00"}, {"%07.2f", 1.0, "0001.00"}, {"%07.2f", -1.0, "-001.00"}, {"% 07.2f", 1.0, " 001.00"}, {"% 07.2f", -1.0, "-001.00"}, {"%+07.2f", 1.0, "+001.00"}, {"%+07.2f", -1.0, "-001.00"}, // from fmt/fmt_test.go: zero padding does not apply to infinities {"%020f", math.Inf(-1), " -Inf"}, {"%020f", math.Inf(+1), " +Inf"}, {"% 020f", math.Inf(-1), " -Inf"}, {"% 020f", math.Inf(+1), " Inf"}, {"%+020f", math.Inf(-1), " -Inf"}, {"%+020f", math.Inf(+1), " +Inf"}, {"%20f", -1.0, " -1.000000"}, // handle %v like %g {"%v", 0.0, "0"}, {"%v", -7.0, "-7"}, {"%v", -1e-9, "-1e-09"}, {"%v", float32(-1e-9), "-1e-09"}, {"%010v", 0.0, "0000000000"}, // *Float cases {"%.20f", "1e-20", "0.00000000000000000001"}, {"%.20f", "-1e-20", "-0.00000000000000000001"}, {"%30.20f", "-1e-20", " -0.00000000000000000001"}, {"%030.20f", "-1e-20", "-00000000.00000000000000000001"}, {"%030.20f", "+1e-20", "000000000.00000000000000000001"}, {"% 030.20f", "+1e-20", " 00000000.00000000000000000001"}, // erroneous formats {"%s", 1.0, "%!s(*big.Float=1)"}, } { value := new(Float) switch v := test.value.(type) { case float32: value.SetPrec(24).SetFloat64(float64(v)) case float64: value.SetPrec(53).SetFloat64(v) case string: value.SetPrec(512).Parse(v, 0) default: t.Fatalf("unsupported test value: %v (%T)", v, v) } if got := fmt.Sprintf(test.format, value); got != test.want { t.Errorf("%v: got %q; want %q", test, got, test.want) } } } func BenchmarkParseFloatSmallExp(b *testing.B) { for i := 0; i < b.N; i++ { for _, s := range []string{ "1e0", "1e-1", "1e-2", "1e-3", "1e-4", "1e-5", "1e-10", "1e-20", "1e-50", "1e1", "1e2", "1e3", "1e4", "1e5", "1e10", "1e20", "1e50", } { var x Float _, _, err := x.Parse(s, 0) if err != nil { b.Fatalf("%s: %v", s, err) } } } } func BenchmarkParseFloatLargeExp(b *testing.B) { for i := 0; i < b.N; i++ { for _, s := range []string{ "1e0", "1e-10", "1e-20", "1e-30", "1e-40", "1e-50", "1e-100", "1e-500", "1e-1000", "1e-5000", "1e-10000", "1e10", "1e20", "1e30", "1e40", "1e50", "1e100", "1e500", "1e1000", "1e5000", "1e10000", } { var x Float _, _, err := x.Parse(s, 0) if err != nil { b.Fatalf("%s: %v", s, err) } } } }