Source file src/math/big/floatconv_test.go

Documentation: math/big

     1  // Copyright 2015 The Go Authors. All rights reserved.
     2  // Use of this source code is governed by a BSD-style
     3  // license that can be found in the LICENSE file.
     4  
     5  package big
     6  
     7  import (
     8  	"bytes"
     9  	"fmt"
    10  	"math"
    11  	"math/bits"
    12  	"strconv"
    13  	"testing"
    14  )
    15  
    16  var zero_ float64
    17  
    18  func TestFloatSetFloat64String(t *testing.T) {
    19  	inf := math.Inf(0)
    20  	nan := math.NaN()
    21  
    22  	for _, test := range []struct {
    23  		s string
    24  		x float64 // NaNs represent invalid inputs
    25  	}{
    26  		// basics
    27  		{"0", 0},
    28  		{"-0", -zero_},
    29  		{"+0", 0},
    30  		{"1", 1},
    31  		{"-1", -1},
    32  		{"+1", 1},
    33  		{"1.234", 1.234},
    34  		{"-1.234", -1.234},
    35  		{"+1.234", 1.234},
    36  		{".1", 0.1},
    37  		{"1.", 1},
    38  		{"+1.", 1},
    39  
    40  		// various zeros
    41  		{"0e100", 0},
    42  		{"-0e+100", -zero_},
    43  		{"+0e-100", 0},
    44  		{"0E100", 0},
    45  		{"-0E+100", -zero_},
    46  		{"+0E-100", 0},
    47  
    48  		// various decimal exponent formats
    49  		{"1.e10", 1e10},
    50  		{"1e+10", 1e10},
    51  		{"+1e-10", 1e-10},
    52  		{"1E10", 1e10},
    53  		{"1.E+10", 1e10},
    54  		{"+1E-10", 1e-10},
    55  
    56  		// infinities
    57  		{"Inf", inf},
    58  		{"+Inf", inf},
    59  		{"-Inf", -inf},
    60  		{"inf", inf},
    61  		{"+inf", inf},
    62  		{"-inf", -inf},
    63  
    64  		// invalid numbers
    65  		{"", nan},
    66  		{"-", nan},
    67  		{"0x", nan},
    68  		{"0e", nan},
    69  		{"1.2ef", nan},
    70  		{"2..3", nan},
    71  		{"123..", nan},
    72  		{"infinity", nan},
    73  		{"foobar", nan},
    74  
    75  		// invalid underscores
    76  		{"_", nan},
    77  		{"0_", nan},
    78  		{"1__0", nan},
    79  		{"123_.", nan},
    80  		{"123._", nan},
    81  		{"123._4", nan},
    82  		{"1_2.3_4_", nan},
    83  		{"_.123", nan},
    84  		{"_123.456", nan},
    85  		{"10._0", nan},
    86  		{"10.0e_0", nan},
    87  		{"10.0e0_", nan},
    88  		{"0P-0__0", nan},
    89  
    90  		// misc decimal values
    91  		{"3.14159265", 3.14159265},
    92  		{"-687436.79457e-245", -687436.79457e-245},
    93  		{"-687436.79457E245", -687436.79457e245},
    94  		{".0000000000000000000000000000000000000001", 1e-40},
    95  		{"+10000000000000000000000000000000000000000e-0", 1e40},
    96  
    97  		// decimal mantissa, binary exponent
    98  		{"0p0", 0},
    99  		{"-0p0", -zero_},
   100  		{"1p10", 1 << 10},
   101  		{"1p+10", 1 << 10},
   102  		{"+1p-10", 1.0 / (1 << 10)},
   103  		{"1024p-12", 0.25},
   104  		{"-1p10", -1024},
   105  		{"1.5p1", 3},
   106  
   107  		// binary mantissa, decimal exponent
   108  		{"0b0", 0},
   109  		{"-0b0", -zero_},
   110  		{"0b0e+10", 0},
   111  		{"-0b0e-10", -zero_},
   112  		{"0b1010", 10},
   113  		{"0B1010E2", 1000},
   114  		{"0b.1", 0.5},
   115  		{"0b.001", 0.125},
   116  		{"0b.001e3", 125},
   117  
   118  		// binary mantissa, binary exponent
   119  		{"0b0p+10", 0},
   120  		{"-0b0p-10", -zero_},
   121  		{"0b.1010p4", 10},
   122  		{"0b1p-1", 0.5},
   123  		{"0b001p-3", 0.125},
   124  		{"0b.001p3", 1},
   125  		{"0b0.01p2", 1},
   126  		{"0b0.01P+2", 1},
   127  
   128  		// octal mantissa, decimal exponent
   129  		{"0o0", 0},
   130  		{"-0o0", -zero_},
   131  		{"0o0e+10", 0},
   132  		{"-0o0e-10", -zero_},
   133  		{"0o12", 10},
   134  		{"0O12E2", 1000},
   135  		{"0o.4", 0.5},
   136  		{"0o.01", 0.015625},
   137  		{"0o.01e3", 15.625},
   138  
   139  		// octal mantissa, binary exponent
   140  		{"0o0p+10", 0},
   141  		{"-0o0p-10", -zero_},
   142  		{"0o.12p6", 10},
   143  		{"0o4p-3", 0.5},
   144  		{"0o0014p-6", 0.1875},
   145  		{"0o.001p9", 1},
   146  		{"0o0.01p7", 2},
   147  		{"0O0.01P+2", 0.0625},
   148  
   149  		// hexadecimal mantissa and exponent
   150  		{"0x0", 0},
   151  		{"-0x0", -zero_},
   152  		{"0x0p+10", 0},
   153  		{"-0x0p-10", -zero_},
   154  		{"0xff", 255},
   155  		{"0X.8p1", 1},
   156  		{"-0X0.00008p16", -0.5},
   157  		{"-0X0.00008P+16", -0.5},
   158  		{"0x0.0000000000001p-1022", math.SmallestNonzeroFloat64},
   159  		{"0x1.fffffffffffffp1023", math.MaxFloat64},
   160  
   161  		// underscores
   162  		{"0_0", 0},
   163  		{"1_000.", 1000},
   164  		{"1_2_3.4_5_6", 123.456},
   165  		{"1.0e0_0", 1},
   166  		{"1p+1_0", 1024},
   167  		{"0b_1000", 0x8},
   168  		{"0b_1011_1101", 0xbd},
   169  		{"0x_f0_0d_1eP+0_8", 0xf00d1e00},
   170  	} {
   171  		var x Float
   172  		x.SetPrec(53)
   173  		_, ok := x.SetString(test.s)
   174  		if math.IsNaN(test.x) {
   175  			// test.s is invalid
   176  			if ok {
   177  				t.Errorf("%s: want parse error", test.s)
   178  			}
   179  			continue
   180  		}
   181  		// test.s is valid
   182  		if !ok {
   183  			t.Errorf("%s: got parse error", test.s)
   184  			continue
   185  		}
   186  		f, _ := x.Float64()
   187  		want := new(Float).SetFloat64(test.x)
   188  		if x.Cmp(want) != 0 || x.Signbit() != want.Signbit() {
   189  			t.Errorf("%s: got %v (%v); want %v", test.s, &x, f, test.x)
   190  		}
   191  	}
   192  }
   193  
   194  func fdiv(a, b float64) float64 { return a / b }
   195  
   196  const (
   197  	below1e23 = 99999999999999974834176
   198  	above1e23 = 100000000000000008388608
   199  )
   200  
   201  func TestFloat64Text(t *testing.T) {
   202  	for _, test := range []struct {
   203  		x      float64
   204  		format byte
   205  		prec   int
   206  		want   string
   207  	}{
   208  		{0, 'f', 0, "0"},
   209  		{math.Copysign(0, -1), 'f', 0, "-0"},
   210  		{1, 'f', 0, "1"},
   211  		{-1, 'f', 0, "-1"},
   212  
   213  		{0.001, 'e', 0, "1e-03"},
   214  		{0.459, 'e', 0, "5e-01"},
   215  		{1.459, 'e', 0, "1e+00"},
   216  		{2.459, 'e', 1, "2.5e+00"},
   217  		{3.459, 'e', 2, "3.46e+00"},
   218  		{4.459, 'e', 3, "4.459e+00"},
   219  		{5.459, 'e', 4, "5.4590e+00"},
   220  
   221  		{0.001, 'f', 0, "0"},
   222  		{0.459, 'f', 0, "0"},
   223  		{1.459, 'f', 0, "1"},
   224  		{2.459, 'f', 1, "2.5"},
   225  		{3.459, 'f', 2, "3.46"},
   226  		{4.459, 'f', 3, "4.459"},
   227  		{5.459, 'f', 4, "5.4590"},
   228  
   229  		{0, 'b', 0, "0"},
   230  		{math.Copysign(0, -1), 'b', 0, "-0"},
   231  		{1.0, 'b', 0, "4503599627370496p-52"},
   232  		{-1.0, 'b', 0, "-4503599627370496p-52"},
   233  		{4503599627370496, 'b', 0, "4503599627370496p+0"},
   234  
   235  		{0, 'p', 0, "0"},
   236  		{math.Copysign(0, -1), 'p', 0, "-0"},
   237  		{1024.0, 'p', 0, "0x.8p+11"},
   238  		{-1024.0, 'p', 0, "-0x.8p+11"},
   239  
   240  		// all test cases below from strconv/ftoa_test.go
   241  		{1, 'e', 5, "1.00000e+00"},
   242  		{1, 'f', 5, "1.00000"},
   243  		{1, 'g', 5, "1"},
   244  		{1, 'g', -1, "1"},
   245  		{20, 'g', -1, "20"},
   246  		{1234567.8, 'g', -1, "1.2345678e+06"},
   247  		{200000, 'g', -1, "200000"},
   248  		{2000000, 'g', -1, "2e+06"},
   249  
   250  		// g conversion and zero suppression
   251  		{400, 'g', 2, "4e+02"},
   252  		{40, 'g', 2, "40"},
   253  		{4, 'g', 2, "4"},
   254  		{.4, 'g', 2, "0.4"},
   255  		{.04, 'g', 2, "0.04"},
   256  		{.004, 'g', 2, "0.004"},
   257  		{.0004, 'g', 2, "0.0004"},
   258  		{.00004, 'g', 2, "4e-05"},
   259  		{.000004, 'g', 2, "4e-06"},
   260  
   261  		{0, 'e', 5, "0.00000e+00"},
   262  		{0, 'f', 5, "0.00000"},
   263  		{0, 'g', 5, "0"},
   264  		{0, 'g', -1, "0"},
   265  
   266  		{-1, 'e', 5, "-1.00000e+00"},
   267  		{-1, 'f', 5, "-1.00000"},
   268  		{-1, 'g', 5, "-1"},
   269  		{-1, 'g', -1, "-1"},
   270  
   271  		{12, 'e', 5, "1.20000e+01"},
   272  		{12, 'f', 5, "12.00000"},
   273  		{12, 'g', 5, "12"},
   274  		{12, 'g', -1, "12"},
   275  
   276  		{123456700, 'e', 5, "1.23457e+08"},
   277  		{123456700, 'f', 5, "123456700.00000"},
   278  		{123456700, 'g', 5, "1.2346e+08"},
   279  		{123456700, 'g', -1, "1.234567e+08"},
   280  
   281  		{1.2345e6, 'e', 5, "1.23450e+06"},
   282  		{1.2345e6, 'f', 5, "1234500.00000"},
   283  		{1.2345e6, 'g', 5, "1.2345e+06"},
   284  
   285  		{1e23, 'e', 17, "9.99999999999999916e+22"},
   286  		{1e23, 'f', 17, "99999999999999991611392.00000000000000000"},
   287  		{1e23, 'g', 17, "9.9999999999999992e+22"},
   288  
   289  		{1e23, 'e', -1, "1e+23"},
   290  		{1e23, 'f', -1, "100000000000000000000000"},
   291  		{1e23, 'g', -1, "1e+23"},
   292  
   293  		{below1e23, 'e', 17, "9.99999999999999748e+22"},
   294  		{below1e23, 'f', 17, "99999999999999974834176.00000000000000000"},
   295  		{below1e23, 'g', 17, "9.9999999999999975e+22"},
   296  
   297  		{below1e23, 'e', -1, "9.999999999999997e+22"},
   298  		{below1e23, 'f', -1, "99999999999999970000000"},
   299  		{below1e23, 'g', -1, "9.999999999999997e+22"},
   300  
   301  		{above1e23, 'e', 17, "1.00000000000000008e+23"},
   302  		{above1e23, 'f', 17, "100000000000000008388608.00000000000000000"},
   303  		{above1e23, 'g', 17, "1.0000000000000001e+23"},
   304  
   305  		{above1e23, 'e', -1, "1.0000000000000001e+23"},
   306  		{above1e23, 'f', -1, "100000000000000010000000"},
   307  		{above1e23, 'g', -1, "1.0000000000000001e+23"},
   308  
   309  		{5e-304 / 1e20, 'g', -1, "5e-324"},
   310  		{-5e-304 / 1e20, 'g', -1, "-5e-324"},
   311  		{fdiv(5e-304, 1e20), 'g', -1, "5e-324"},   // avoid constant arithmetic
   312  		{fdiv(-5e-304, 1e20), 'g', -1, "-5e-324"}, // avoid constant arithmetic
   313  
   314  		{32, 'g', -1, "32"},
   315  		{32, 'g', 0, "3e+01"},
   316  
   317  		{100, 'x', -1, "0x1.9p+06"},
   318  
   319  		// {math.NaN(), 'g', -1, "NaN"},  // Float doesn't support NaNs
   320  		// {-math.NaN(), 'g', -1, "NaN"}, // Float doesn't support NaNs
   321  		{math.Inf(0), 'g', -1, "+Inf"},
   322  		{math.Inf(-1), 'g', -1, "-Inf"},
   323  		{-math.Inf(0), 'g', -1, "-Inf"},
   324  
   325  		{-1, 'b', -1, "-4503599627370496p-52"},
   326  
   327  		// fixed bugs
   328  		{0.9, 'f', 1, "0.9"},
   329  		{0.09, 'f', 1, "0.1"},
   330  		{0.0999, 'f', 1, "0.1"},
   331  		{0.05, 'f', 1, "0.1"},
   332  		{0.05, 'f', 0, "0"},
   333  		{0.5, 'f', 1, "0.5"},
   334  		{0.5, 'f', 0, "0"},
   335  		{1.5, 'f', 0, "2"},
   336  
   337  		// https://www.exploringbinary.com/java-hangs-when-converting-2-2250738585072012e-308/
   338  		{2.2250738585072012e-308, 'g', -1, "2.2250738585072014e-308"},
   339  		// https://www.exploringbinary.com/php-hangs-on-numeric-value-2-2250738585072011e-308/
   340  		{2.2250738585072011e-308, 'g', -1, "2.225073858507201e-308"},
   341  
   342  		// Issue 2625.
   343  		{383260575764816448, 'f', 0, "383260575764816448"},
   344  		{383260575764816448, 'g', -1, "3.8326057576481645e+17"},
   345  
   346  		// Issue 15918.
   347  		{1, 'f', -10, "1"},
   348  		{1, 'f', -11, "1"},
   349  		{1, 'f', -12, "1"},
   350  	} {
   351  		// The test cases are from the strconv package which tests float64 values.
   352  		// When formatting values with prec = -1 (shortest representation),
   353  		// the actually available mantissa precision matters.
   354  		// For denormalized values, that precision is < 53 (SetFloat64 default).
   355  		// Compute and set the actual precision explicitly.
   356  		f := new(Float).SetPrec(actualPrec(test.x)).SetFloat64(test.x)
   357  		got := f.Text(test.format, test.prec)
   358  		if got != test.want {
   359  			t.Errorf("%v: got %s; want %s", test, got, test.want)
   360  			continue
   361  		}
   362  
   363  		if test.format == 'b' && test.x == 0 {
   364  			continue // 'b' format in strconv.Float requires knowledge of bias for 0.0
   365  		}
   366  		if test.format == 'p' {
   367  			continue // 'p' format not supported in strconv.Format
   368  		}
   369  
   370  		// verify that Float format matches strconv format
   371  		want := strconv.FormatFloat(test.x, test.format, test.prec, 64)
   372  		if got != want {
   373  			t.Errorf("%v: got %s; want %s (strconv)", test, got, want)
   374  		}
   375  	}
   376  }
   377  
   378  // actualPrec returns the number of actually used mantissa bits.
   379  func actualPrec(x float64) uint {
   380  	if mant := math.Float64bits(x); x != 0 && mant&(0x7ff<<52) == 0 {
   381  		// x is denormalized
   382  		return 64 - uint(bits.LeadingZeros64(mant&(1<<52-1)))
   383  	}
   384  	return 53
   385  }
   386  
   387  func TestFloatText(t *testing.T) {
   388  	const defaultRound = ^RoundingMode(0)
   389  
   390  	for _, test := range []struct {
   391  		x      string
   392  		round  RoundingMode
   393  		prec   uint
   394  		format byte
   395  		digits int
   396  		want   string
   397  	}{
   398  		{"0", defaultRound, 10, 'f', 0, "0"},
   399  		{"-0", defaultRound, 10, 'f', 0, "-0"},
   400  		{"1", defaultRound, 10, 'f', 0, "1"},
   401  		{"-1", defaultRound, 10, 'f', 0, "-1"},
   402  
   403  		{"1.459", defaultRound, 100, 'e', 0, "1e+00"},
   404  		{"2.459", defaultRound, 100, 'e', 1, "2.5e+00"},
   405  		{"3.459", defaultRound, 100, 'e', 2, "3.46e+00"},
   406  		{"4.459", defaultRound, 100, 'e', 3, "4.459e+00"},
   407  		{"5.459", defaultRound, 100, 'e', 4, "5.4590e+00"},
   408  
   409  		{"1.459", defaultRound, 100, 'E', 0, "1E+00"},
   410  		{"2.459", defaultRound, 100, 'E', 1, "2.5E+00"},
   411  		{"3.459", defaultRound, 100, 'E', 2, "3.46E+00"},
   412  		{"4.459", defaultRound, 100, 'E', 3, "4.459E+00"},
   413  		{"5.459", defaultRound, 100, 'E', 4, "5.4590E+00"},
   414  
   415  		{"1.459", defaultRound, 100, 'f', 0, "1"},
   416  		{"2.459", defaultRound, 100, 'f', 1, "2.5"},
   417  		{"3.459", defaultRound, 100, 'f', 2, "3.46"},
   418  		{"4.459", defaultRound, 100, 'f', 3, "4.459"},
   419  		{"5.459", defaultRound, 100, 'f', 4, "5.4590"},
   420  
   421  		{"1.459", defaultRound, 100, 'g', 0, "1"},
   422  		{"2.459", defaultRound, 100, 'g', 1, "2"},
   423  		{"3.459", defaultRound, 100, 'g', 2, "3.5"},
   424  		{"4.459", defaultRound, 100, 'g', 3, "4.46"},
   425  		{"5.459", defaultRound, 100, 'g', 4, "5.459"},
   426  
   427  		{"1459", defaultRound, 53, 'g', 0, "1e+03"},
   428  		{"2459", defaultRound, 53, 'g', 1, "2e+03"},
   429  		{"3459", defaultRound, 53, 'g', 2, "3.5e+03"},
   430  		{"4459", defaultRound, 53, 'g', 3, "4.46e+03"},
   431  		{"5459", defaultRound, 53, 'g', 4, "5459"},
   432  
   433  		{"1459", defaultRound, 53, 'G', 0, "1E+03"},
   434  		{"2459", defaultRound, 53, 'G', 1, "2E+03"},
   435  		{"3459", defaultRound, 53, 'G', 2, "3.5E+03"},
   436  		{"4459", defaultRound, 53, 'G', 3, "4.46E+03"},
   437  		{"5459", defaultRound, 53, 'G', 4, "5459"},
   438  
   439  		{"3", defaultRound, 10, 'e', 40, "3.0000000000000000000000000000000000000000e+00"},
   440  		{"3", defaultRound, 10, 'f', 40, "3.0000000000000000000000000000000000000000"},
   441  		{"3", defaultRound, 10, 'g', 40, "3"},
   442  
   443  		{"3e40", defaultRound, 100, 'e', 40, "3.0000000000000000000000000000000000000000e+40"},
   444  		{"3e40", defaultRound, 100, 'f', 4, "30000000000000000000000000000000000000000.0000"},
   445  		{"3e40", defaultRound, 100, 'g', 40, "3e+40"},
   446  
   447  		// make sure "stupid" exponents don't stall the machine
   448  		{"1e1000000", defaultRound, 64, 'p', 0, "0x.88b3a28a05eade3ap+3321929"},
   449  		{"1e646456992", defaultRound, 64, 'p', 0, "0x.e883a0c5c8c7c42ap+2147483644"},
   450  		{"1e646456993", defaultRound, 64, 'p', 0, "+Inf"},
   451  		{"1e1000000000", defaultRound, 64, 'p', 0, "+Inf"},
   452  		{"1e-1000000", defaultRound, 64, 'p', 0, "0x.efb4542cc8ca418ap-3321928"},
   453  		{"1e-646456993", defaultRound, 64, 'p', 0, "0x.e17c8956983d9d59p-2147483647"},
   454  		{"1e-646456994", defaultRound, 64, 'p', 0, "0"},
   455  		{"1e-1000000000", defaultRound, 64, 'p', 0, "0"},
   456  
   457  		// minimum and maximum values
   458  		{"1p2147483646", defaultRound, 64, 'p', 0, "0x.8p+2147483647"},
   459  		{"0x.8p2147483647", defaultRound, 64, 'p', 0, "0x.8p+2147483647"},
   460  		{"0x.8p-2147483647", defaultRound, 64, 'p', 0, "0x.8p-2147483647"},
   461  		{"1p-2147483649", defaultRound, 64, 'p', 0, "0x.8p-2147483648"},
   462  
   463  		// TODO(gri) need tests for actual large Floats
   464  
   465  		{"0", defaultRound, 53, 'b', 0, "0"},
   466  		{"-0", defaultRound, 53, 'b', 0, "-0"},
   467  		{"1.0", defaultRound, 53, 'b', 0, "4503599627370496p-52"},
   468  		{"-1.0", defaultRound, 53, 'b', 0, "-4503599627370496p-52"},
   469  		{"4503599627370496", defaultRound, 53, 'b', 0, "4503599627370496p+0"},
   470  
   471  		// issue 9939
   472  		{"3", defaultRound, 350, 'b', 0, "1720123961992553633708115671476565205597423741876210842803191629540192157066363606052513914832594264915968p-348"},
   473  		{"03", defaultRound, 350, 'b', 0, "1720123961992553633708115671476565205597423741876210842803191629540192157066363606052513914832594264915968p-348"},
   474  		{"3.", defaultRound, 350, 'b', 0, "1720123961992553633708115671476565205597423741876210842803191629540192157066363606052513914832594264915968p-348"},
   475  		{"3.0", defaultRound, 350, 'b', 0, "1720123961992553633708115671476565205597423741876210842803191629540192157066363606052513914832594264915968p-348"},
   476  		{"3.00", defaultRound, 350, 'b', 0, "1720123961992553633708115671476565205597423741876210842803191629540192157066363606052513914832594264915968p-348"},
   477  		{"3.000", defaultRound, 350, 'b', 0, "1720123961992553633708115671476565205597423741876210842803191629540192157066363606052513914832594264915968p-348"},
   478  
   479  		{"3", defaultRound, 350, 'p', 0, "0x.cp+2"},
   480  		{"03", defaultRound, 350, 'p', 0, "0x.cp+2"},
   481  		{"3.", defaultRound, 350, 'p', 0, "0x.cp+2"},
   482  		{"3.0", defaultRound, 350, 'p', 0, "0x.cp+2"},
   483  		{"3.00", defaultRound, 350, 'p', 0, "0x.cp+2"},
   484  		{"3.000", defaultRound, 350, 'p', 0, "0x.cp+2"},
   485  
   486  		{"0", defaultRound, 64, 'p', 0, "0"},
   487  		{"-0", defaultRound, 64, 'p', 0, "-0"},
   488  		{"1024.0", defaultRound, 64, 'p', 0, "0x.8p+11"},
   489  		{"-1024.0", defaultRound, 64, 'p', 0, "-0x.8p+11"},
   490  
   491  		{"0", defaultRound, 64, 'x', -1, "0x0p+00"},
   492  		{"0", defaultRound, 64, 'x', 0, "0x0p+00"},
   493  		{"0", defaultRound, 64, 'x', 1, "0x0.0p+00"},
   494  		{"0", defaultRound, 64, 'x', 5, "0x0.00000p+00"},
   495  		{"3.25", defaultRound, 64, 'x', 0, "0x1p+02"},
   496  		{"-3.25", defaultRound, 64, 'x', 0, "-0x1p+02"},
   497  		{"3.25", defaultRound, 64, 'x', 1, "0x1.ap+01"},
   498  		{"-3.25", defaultRound, 64, 'x', 1, "-0x1.ap+01"},
   499  		{"3.25", defaultRound, 64, 'x', -1, "0x1.ap+01"},
   500  		{"-3.25", defaultRound, 64, 'x', -1, "-0x1.ap+01"},
   501  		{"1024.0", defaultRound, 64, 'x', 0, "0x1p+10"},
   502  		{"-1024.0", defaultRound, 64, 'x', 0, "-0x1p+10"},
   503  		{"1024.0", defaultRound, 64, 'x', 5, "0x1.00000p+10"},
   504  		{"8191.0", defaultRound, 53, 'x', -1, "0x1.fffp+12"},
   505  		{"8191.5", defaultRound, 53, 'x', -1, "0x1.fff8p+12"},
   506  		{"8191.53125", defaultRound, 53, 'x', -1, "0x1.fff88p+12"},
   507  		{"8191.53125", defaultRound, 53, 'x', 4, "0x1.fff8p+12"},
   508  		{"8191.53125", defaultRound, 53, 'x', 3, "0x1.000p+13"},
   509  		{"8191.53125", defaultRound, 53, 'x', 0, "0x1p+13"},
   510  		{"8191.533203125", defaultRound, 53, 'x', -1, "0x1.fff888p+12"},
   511  		{"8191.533203125", defaultRound, 53, 'x', 5, "0x1.fff88p+12"},
   512  		{"8191.533203125", defaultRound, 53, 'x', 4, "0x1.fff9p+12"},
   513  
   514  		{"8191.53125", defaultRound, 53, 'x', -1, "0x1.fff88p+12"},
   515  		{"8191.53125", ToNearestEven, 53, 'x', 5, "0x1.fff88p+12"},
   516  		{"8191.53125", ToNearestAway, 53, 'x', 5, "0x1.fff88p+12"},
   517  		{"8191.53125", ToZero, 53, 'x', 5, "0x1.fff88p+12"},
   518  		{"8191.53125", AwayFromZero, 53, 'x', 5, "0x1.fff88p+12"},
   519  		{"8191.53125", ToNegativeInf, 53, 'x', 5, "0x1.fff88p+12"},
   520  		{"8191.53125", ToPositiveInf, 53, 'x', 5, "0x1.fff88p+12"},
   521  
   522  		{"8191.53125", defaultRound, 53, 'x', 4, "0x1.fff8p+12"},
   523  		{"8191.53125", defaultRound, 53, 'x', 3, "0x1.000p+13"},
   524  		{"8191.53125", defaultRound, 53, 'x', 0, "0x1p+13"},
   525  		{"8191.533203125", defaultRound, 53, 'x', -1, "0x1.fff888p+12"},
   526  		{"8191.533203125", defaultRound, 53, 'x', 6, "0x1.fff888p+12"},
   527  		{"8191.533203125", defaultRound, 53, 'x', 5, "0x1.fff88p+12"},
   528  		{"8191.533203125", defaultRound, 53, 'x', 4, "0x1.fff9p+12"},
   529  
   530  		{"8191.53125", ToNearestEven, 53, 'x', 4, "0x1.fff8p+12"},
   531  		{"8191.53125", ToNearestAway, 53, 'x', 4, "0x1.fff9p+12"},
   532  		{"8191.53125", ToZero, 53, 'x', 4, "0x1.fff8p+12"},
   533  		{"8191.53125", ToZero, 53, 'x', 2, "0x1.ffp+12"},
   534  		{"8191.53125", AwayFromZero, 53, 'x', 4, "0x1.fff9p+12"},
   535  		{"8191.53125", ToNegativeInf, 53, 'x', 4, "0x1.fff8p+12"},
   536  		{"-8191.53125", ToNegativeInf, 53, 'x', 4, "-0x1.fff9p+12"},
   537  		{"8191.53125", ToPositiveInf, 53, 'x', 4, "0x1.fff9p+12"},
   538  		{"-8191.53125", ToPositiveInf, 53, 'x', 4, "-0x1.fff8p+12"},
   539  
   540  		// issue 34343
   541  		{"0x.8p-2147483648", ToNearestEven, 4, 'p', -1, "0x.8p-2147483648"},
   542  		{"0x.8p-2147483648", ToNearestEven, 4, 'x', -1, "0x1p-2147483649"},
   543  	} {
   544  		f, _, err := ParseFloat(test.x, 0, test.prec, ToNearestEven)
   545  		if err != nil {
   546  			t.Errorf("%v: %s", test, err)
   547  			continue
   548  		}
   549  		if test.round != defaultRound {
   550  			f.SetMode(test.round)
   551  		}
   552  
   553  		got := f.Text(test.format, test.digits)
   554  		if got != test.want {
   555  			t.Errorf("%v: got %s; want %s", test, got, test.want)
   556  		}
   557  
   558  		// compare with strconv.FormatFloat output if possible
   559  		// ('p' format is not supported by strconv.FormatFloat,
   560  		// and its output for 0.0 prints a biased exponent value
   561  		// as in 0p-1074 which makes no sense to emulate here)
   562  		if test.prec == 53 && test.format != 'p' && f.Sign() != 0 && (test.round == ToNearestEven || test.round == defaultRound) {
   563  			f64, acc := f.Float64()
   564  			if acc != Exact {
   565  				t.Errorf("%v: expected exact conversion to float64", test)
   566  				continue
   567  			}
   568  			got := strconv.FormatFloat(f64, test.format, test.digits, 64)
   569  			if got != test.want {
   570  				t.Errorf("%v: got %s; want %s", test, got, test.want)
   571  			}
   572  		}
   573  	}
   574  }
   575  
   576  func TestFloatFormat(t *testing.T) {
   577  	for _, test := range []struct {
   578  		format string
   579  		value  any // float32, float64, or string (== 512bit *Float)
   580  		want   string
   581  	}{
   582  		// from fmt/fmt_test.go
   583  		{"%+.3e", 0.0, "+0.000e+00"},
   584  		{"%+.3e", 1.0, "+1.000e+00"},
   585  		{"%+.3f", -1.0, "-1.000"},
   586  		{"%+.3F", -1.0, "-1.000"},
   587  		{"%+.3F", float32(-1.0), "-1.000"},
   588  		{"%+07.2f", 1.0, "+001.00"},
   589  		{"%+07.2f", -1.0, "-001.00"},
   590  		{"%+10.2f", +1.0, "     +1.00"},
   591  		{"%+10.2f", -1.0, "     -1.00"},
   592  		{"% .3E", -1.0, "-1.000E+00"},
   593  		{"% .3e", 1.0, " 1.000e+00"},
   594  		{"%+.3g", 0.0, "+0"},
   595  		{"%+.3g", 1.0, "+1"},
   596  		{"%+.3g", -1.0, "-1"},
   597  		{"% .3g", -1.0, "-1"},
   598  		{"% .3g", 1.0, " 1"},
   599  		{"%b", float32(1.0), "8388608p-23"},
   600  		{"%b", 1.0, "4503599627370496p-52"},
   601  
   602  		// from fmt/fmt_test.go: old test/fmt_test.go
   603  		{"%e", 1.0, "1.000000e+00"},
   604  		{"%e", 1234.5678e3, "1.234568e+06"},
   605  		{"%e", 1234.5678e-8, "1.234568e-05"},
   606  		{"%e", -7.0, "-7.000000e+00"},
   607  		{"%e", -1e-9, "-1.000000e-09"},
   608  		{"%f", 1234.5678e3, "1234567.800000"},
   609  		{"%f", 1234.5678e-8, "0.000012"},
   610  		{"%f", -7.0, "-7.000000"},
   611  		{"%f", -1e-9, "-0.000000"},
   612  		{"%g", 1234.5678e3, "1.2345678e+06"},
   613  		{"%g", float32(1234.5678e3), "1.2345678e+06"},
   614  		{"%g", 1234.5678e-8, "1.2345678e-05"},
   615  		{"%g", -7.0, "-7"},
   616  		{"%g", -1e-9, "-1e-09"},
   617  		{"%g", float32(-1e-9), "-1e-09"},
   618  		{"%E", 1.0, "1.000000E+00"},
   619  		{"%E", 1234.5678e3, "1.234568E+06"},
   620  		{"%E", 1234.5678e-8, "1.234568E-05"},
   621  		{"%E", -7.0, "-7.000000E+00"},
   622  		{"%E", -1e-9, "-1.000000E-09"},
   623  		{"%G", 1234.5678e3, "1.2345678E+06"},
   624  		{"%G", float32(1234.5678e3), "1.2345678E+06"},
   625  		{"%G", 1234.5678e-8, "1.2345678E-05"},
   626  		{"%G", -7.0, "-7"},
   627  		{"%G", -1e-9, "-1E-09"},
   628  		{"%G", float32(-1e-9), "-1E-09"},
   629  
   630  		{"%20.6e", 1.2345e3, "        1.234500e+03"},
   631  		{"%20.6e", 1.2345e-3, "        1.234500e-03"},
   632  		{"%20e", 1.2345e3, "        1.234500e+03"},
   633  		{"%20e", 1.2345e-3, "        1.234500e-03"},
   634  		{"%20.8e", 1.2345e3, "      1.23450000e+03"},
   635  		{"%20f", 1.23456789e3, "         1234.567890"},
   636  		{"%20f", 1.23456789e-3, "            0.001235"},
   637  		{"%20f", 12345678901.23456789, "  12345678901.234568"},
   638  		{"%-20f", 1.23456789e3, "1234.567890         "},
   639  		{"%20.8f", 1.23456789e3, "       1234.56789000"},
   640  		{"%20.8f", 1.23456789e-3, "          0.00123457"},
   641  		{"%g", 1.23456789e3, "1234.56789"},
   642  		{"%g", 1.23456789e-3, "0.00123456789"},
   643  		{"%g", 1.23456789e20, "1.23456789e+20"},
   644  		{"%20e", math.Inf(1), "                +Inf"},
   645  		{"%-20f", math.Inf(-1), "-Inf                "},
   646  
   647  		// from fmt/fmt_test.go: comparison of padding rules with C printf
   648  		{"%.2f", 1.0, "1.00"},
   649  		{"%.2f", -1.0, "-1.00"},
   650  		{"% .2f", 1.0, " 1.00"},
   651  		{"% .2f", -1.0, "-1.00"},
   652  		{"%+.2f", 1.0, "+1.00"},
   653  		{"%+.2f", -1.0, "-1.00"},
   654  		{"%7.2f", 1.0, "   1.00"},
   655  		{"%7.2f", -1.0, "  -1.00"},
   656  		{"% 7.2f", 1.0, "   1.00"},
   657  		{"% 7.2f", -1.0, "  -1.00"},
   658  		{"%+7.2f", 1.0, "  +1.00"},
   659  		{"%+7.2f", -1.0, "  -1.00"},
   660  		{"%07.2f", 1.0, "0001.00"},
   661  		{"%07.2f", -1.0, "-001.00"},
   662  		{"% 07.2f", 1.0, " 001.00"},
   663  		{"% 07.2f", -1.0, "-001.00"},
   664  		{"%+07.2f", 1.0, "+001.00"},
   665  		{"%+07.2f", -1.0, "-001.00"},
   666  
   667  		// from fmt/fmt_test.go: zero padding does not apply to infinities
   668  		{"%020f", math.Inf(-1), "                -Inf"},
   669  		{"%020f", math.Inf(+1), "                +Inf"},
   670  		{"% 020f", math.Inf(-1), "                -Inf"},
   671  		{"% 020f", math.Inf(+1), "                 Inf"},
   672  		{"%+020f", math.Inf(-1), "                -Inf"},
   673  		{"%+020f", math.Inf(+1), "                +Inf"},
   674  		{"%20f", -1.0, "           -1.000000"},
   675  
   676  		// handle %v like %g
   677  		{"%v", 0.0, "0"},
   678  		{"%v", -7.0, "-7"},
   679  		{"%v", -1e-9, "-1e-09"},
   680  		{"%v", float32(-1e-9), "-1e-09"},
   681  		{"%010v", 0.0, "0000000000"},
   682  
   683  		// *Float cases
   684  		{"%.20f", "1e-20", "0.00000000000000000001"},
   685  		{"%.20f", "-1e-20", "-0.00000000000000000001"},
   686  		{"%30.20f", "-1e-20", "       -0.00000000000000000001"},
   687  		{"%030.20f", "-1e-20", "-00000000.00000000000000000001"},
   688  		{"%030.20f", "+1e-20", "000000000.00000000000000000001"},
   689  		{"% 030.20f", "+1e-20", " 00000000.00000000000000000001"},
   690  
   691  		// erroneous formats
   692  		{"%s", 1.0, "%!s(*big.Float=1)"},
   693  	} {
   694  		value := new(Float)
   695  		switch v := test.value.(type) {
   696  		case float32:
   697  			value.SetPrec(24).SetFloat64(float64(v))
   698  		case float64:
   699  			value.SetPrec(53).SetFloat64(v)
   700  		case string:
   701  			value.SetPrec(512).Parse(v, 0)
   702  		default:
   703  			t.Fatalf("unsupported test value: %v (%T)", v, v)
   704  		}
   705  
   706  		if got := fmt.Sprintf(test.format, value); got != test.want {
   707  			t.Errorf("%v: got %q; want %q", test, got, test.want)
   708  		}
   709  	}
   710  }
   711  
   712  func BenchmarkParseFloatSmallExp(b *testing.B) {
   713  	for i := 0; i < b.N; i++ {
   714  		for _, s := range []string{
   715  			"1e0",
   716  			"1e-1",
   717  			"1e-2",
   718  			"1e-3",
   719  			"1e-4",
   720  			"1e-5",
   721  			"1e-10",
   722  			"1e-20",
   723  			"1e-50",
   724  			"1e1",
   725  			"1e2",
   726  			"1e3",
   727  			"1e4",
   728  			"1e5",
   729  			"1e10",
   730  			"1e20",
   731  			"1e50",
   732  		} {
   733  			var x Float
   734  			_, _, err := x.Parse(s, 0)
   735  			if err != nil {
   736  				b.Fatalf("%s: %v", s, err)
   737  			}
   738  		}
   739  	}
   740  }
   741  
   742  func BenchmarkParseFloatLargeExp(b *testing.B) {
   743  	for i := 0; i < b.N; i++ {
   744  		for _, s := range []string{
   745  			"1e0",
   746  			"1e-10",
   747  			"1e-20",
   748  			"1e-30",
   749  			"1e-40",
   750  			"1e-50",
   751  			"1e-100",
   752  			"1e-500",
   753  			"1e-1000",
   754  			"1e-5000",
   755  			"1e-10000",
   756  			"1e10",
   757  			"1e20",
   758  			"1e30",
   759  			"1e40",
   760  			"1e50",
   761  			"1e100",
   762  			"1e500",
   763  			"1e1000",
   764  			"1e5000",
   765  			"1e10000",
   766  		} {
   767  			var x Float
   768  			_, _, err := x.Parse(s, 0)
   769  			if err != nil {
   770  				b.Fatalf("%s: %v", s, err)
   771  			}
   772  		}
   773  	}
   774  }
   775  
   776  func TestFloatScan(t *testing.T) {
   777  	var floatScanTests = []struct {
   778  		input     string
   779  		format    string
   780  		output    string
   781  		remaining int
   782  		wantErr   bool
   783  	}{
   784  		0: {"10.0", "%f", "10", 0, false},
   785  		1: {"23.98+2.0", "%v", "23.98", 4, false},
   786  		2: {"-1+1", "%v", "-1", 2, false},
   787  		3: {" 00000", "%v", "0", 0, false},
   788  		4: {"-123456p-78", "%b", "-4.084816388e-19", 0, false},
   789  		5: {"+123", "%b", "123", 0, false},
   790  		6: {"-1.234e+56", "%e", "-1.234e+56", 0, false},
   791  		7: {"-1.234E-56", "%E", "-1.234e-56", 0, false},
   792  		8: {"-1.234e+567", "%g", "-1.234e+567", 0, false},
   793  		9: {"+1234567891011.234", "%G", "1.234567891e+12", 0, false},
   794  
   795  		// Scan doesn't handle ±Inf.
   796  		10: {"Inf", "%v", "", 3, true},
   797  		11: {"-Inf", "%v", "", 3, true},
   798  		12: {"-Inf", "%v", "", 3, true},
   799  	}
   800  
   801  	var buf bytes.Buffer
   802  	for i, test := range floatScanTests {
   803  		x := new(Float)
   804  		buf.Reset()
   805  		buf.WriteString(test.input)
   806  		_, err := fmt.Fscanf(&buf, test.format, x)
   807  		if test.wantErr {
   808  			if err == nil {
   809  				t.Errorf("#%d want non-nil err", i)
   810  			}
   811  			continue
   812  		}
   813  
   814  		if err != nil {
   815  			t.Errorf("#%d error: %s", i, err)
   816  		}
   817  
   818  		if x.String() != test.output {
   819  			t.Errorf("#%d got %s; want %s", i, x.String(), test.output)
   820  		}
   821  		if buf.Len() != test.remaining {
   822  			t.Errorf("#%d got %d bytes remaining; want %d", i, buf.Len(), test.remaining)
   823  		}
   824  	}
   825  }
   826  

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