Source file src/math/big/ratconv_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  	"io"
    11  	"math"
    12  	"reflect"
    13  	"strconv"
    14  	"strings"
    15  	"testing"
    16  )
    17  
    18  var exponentTests = []struct {
    19  	s       string // string to be scanned
    20  	base2ok bool   // true if 'p'/'P' exponents are accepted
    21  	sepOk   bool   // true if '_' separators are accepted
    22  	x       int64  // expected exponent
    23  	b       int    // expected exponent base
    24  	err     error  // expected error
    25  	next    rune   // next character (or 0, if at EOF)
    26  }{
    27  	// valid, without separators
    28  	{"", false, false, 0, 10, nil, 0},
    29  	{"1", false, false, 0, 10, nil, '1'},
    30  	{"e0", false, false, 0, 10, nil, 0},
    31  	{"E1", false, false, 1, 10, nil, 0},
    32  	{"e+10", false, false, 10, 10, nil, 0},
    33  	{"e-10", false, false, -10, 10, nil, 0},
    34  	{"e123456789a", false, false, 123456789, 10, nil, 'a'},
    35  	{"p", false, false, 0, 10, nil, 'p'},
    36  	{"P+100", false, false, 0, 10, nil, 'P'},
    37  	{"p0", true, false, 0, 2, nil, 0},
    38  	{"P-123", true, false, -123, 2, nil, 0},
    39  	{"p+0a", true, false, 0, 2, nil, 'a'},
    40  	{"p+123__", true, false, 123, 2, nil, '_'}, // '_' is not part of the number anymore
    41  
    42  	// valid, with separators
    43  	{"e+1_0", false, true, 10, 10, nil, 0},
    44  	{"e-1_0", false, true, -10, 10, nil, 0},
    45  	{"e123_456_789a", false, true, 123456789, 10, nil, 'a'},
    46  	{"P+1_00", false, true, 0, 10, nil, 'P'},
    47  	{"p-1_2_3", true, true, -123, 2, nil, 0},
    48  
    49  	// invalid: no digits
    50  	{"e", false, false, 0, 10, errNoDigits, 0},
    51  	{"ef", false, false, 0, 10, errNoDigits, 'f'},
    52  	{"e+", false, false, 0, 10, errNoDigits, 0},
    53  	{"E-x", false, false, 0, 10, errNoDigits, 'x'},
    54  	{"p", true, false, 0, 2, errNoDigits, 0},
    55  	{"P-", true, false, 0, 2, errNoDigits, 0},
    56  	{"p+e", true, false, 0, 2, errNoDigits, 'e'},
    57  	{"e+_x", false, true, 0, 10, errNoDigits, 'x'},
    58  
    59  	// invalid: incorrect use of separator
    60  	{"e0_", false, true, 0, 10, errInvalSep, 0},
    61  	{"e_0", false, true, 0, 10, errInvalSep, 0},
    62  	{"e-1_2__3", false, true, -123, 10, errInvalSep, 0},
    63  }
    64  
    65  func TestScanExponent(t *testing.T) {
    66  	for _, a := range exponentTests {
    67  		r := strings.NewReader(a.s)
    68  		x, b, err := scanExponent(r, a.base2ok, a.sepOk)
    69  		if err != a.err {
    70  			t.Errorf("scanExponent%+v\n\tgot error = %v; want %v", a, err, a.err)
    71  		}
    72  		if x != a.x {
    73  			t.Errorf("scanExponent%+v\n\tgot z = %v; want %v", a, x, a.x)
    74  		}
    75  		if b != a.b {
    76  			t.Errorf("scanExponent%+v\n\tgot b = %d; want %d", a, b, a.b)
    77  		}
    78  		next, _, err := r.ReadRune()
    79  		if err == io.EOF {
    80  			next = 0
    81  			err = nil
    82  		}
    83  		if err == nil && next != a.next {
    84  			t.Errorf("scanExponent%+v\n\tgot next = %q; want %q", a, next, a.next)
    85  		}
    86  	}
    87  }
    88  
    89  type StringTest struct {
    90  	in, out string
    91  	ok      bool
    92  }
    93  
    94  var setStringTests = []StringTest{
    95  	// invalid
    96  	{in: "1e"},
    97  	{in: "1.e"},
    98  	{in: "1e+14e-5"},
    99  	{in: "1e4.5"},
   100  	{in: "r"},
   101  	{in: "a/b"},
   102  	{in: "a.b"},
   103  	{in: "1/0"},
   104  	{in: "4/3/2"}, // issue 17001
   105  	{in: "4/3/"},
   106  	{in: "4/3."},
   107  	{in: "4/"},
   108  	{in: "13e-9223372036854775808"}, // CVE-2022-23772
   109  
   110  	// valid
   111  	{"0", "0", true},
   112  	{"-0", "0", true},
   113  	{"1", "1", true},
   114  	{"-1", "-1", true},
   115  	{"1.", "1", true},
   116  	{"1e0", "1", true},
   117  	{"1.e1", "10", true},
   118  	{"-0.1", "-1/10", true},
   119  	{"-.1", "-1/10", true},
   120  	{"2/4", "1/2", true},
   121  	{".25", "1/4", true},
   122  	{"-1/5", "-1/5", true},
   123  	{"8129567.7690E14", "812956776900000000000", true},
   124  	{"78189e+4", "781890000", true},
   125  	{"553019.8935e+8", "55301989350000", true},
   126  	{"98765432109876543210987654321e-10", "98765432109876543210987654321/10000000000", true},
   127  	{"9877861857500000E-7", "3951144743/4", true},
   128  	{"2169378.417e-3", "2169378417/1000000", true},
   129  	{"884243222337379604041632732738665534", "884243222337379604041632732738665534", true},
   130  	{"53/70893980658822810696", "53/70893980658822810696", true},
   131  	{"106/141787961317645621392", "53/70893980658822810696", true},
   132  	{"204211327800791583.81095", "4084226556015831676219/20000", true},
   133  	{"0e9999999999", "0", true}, // issue #16176
   134  }
   135  
   136  // These are not supported by fmt.Fscanf.
   137  var setStringTests2 = []StringTest{
   138  	// invalid
   139  	{in: "4/3x"},
   140  	{in: "0/-1"},
   141  	{in: "-1/-1"},
   142  
   143  	// invalid with separators
   144  	// (smoke tests only - a comprehensive set of tests is in natconv_test.go)
   145  	{in: "10_/1"},
   146  	{in: "_10/1"},
   147  	{in: "1/1__0"},
   148  
   149  	// valid
   150  	{"0b1000/3", "8/3", true},
   151  	{"0B1000/0x8", "1", true},
   152  	{"-010/1", "-8", true}, // 0-prefix indicates octal in this case
   153  	{"-010.0", "-10", true},
   154  	{"-0o10/1", "-8", true},
   155  	{"0x10/1", "16", true},
   156  	{"0x10/0x20", "1/2", true},
   157  
   158  	{"0010", "10", true}, // 0-prefix is ignored in this case (not a fraction)
   159  	{"0x10.0", "16", true},
   160  	{"0x1.8", "3/2", true},
   161  	{"0X1.8p4", "24", true},
   162  	{"0x1.1E2", "2289/2048", true}, // E is part of hex mantissa, not exponent
   163  	{"0b1.1E2", "150", true},
   164  	{"0B1.1P3", "12", true},
   165  	{"0o10e-2", "2/25", true},
   166  	{"0O10p-3", "1", true},
   167  
   168  	// valid with separators
   169  	// (smoke tests only - a comprehensive set of tests is in natconv_test.go)
   170  	{"0b_1000/3", "8/3", true},
   171  	{"0B_10_00/0x8", "1", true},
   172  	{"0xdead/0B1101_1110_1010_1101", "1", true},
   173  	{"0B1101_1110_1010_1101/0XD_E_A_D", "1", true},
   174  	{"1_000.0", "1000", true},
   175  
   176  	{"0x_10.0", "16", true},
   177  	{"0x1_0.0", "16", true},
   178  	{"0x1.8_0", "3/2", true},
   179  	{"0X1.8p0_4", "24", true},
   180  	{"0b1.1_0E2", "150", true},
   181  	{"0o1_0e-2", "2/25", true},
   182  	{"0O_10p-3", "1", true},
   183  }
   184  
   185  func TestRatSetString(t *testing.T) {
   186  	var tests []StringTest
   187  	tests = append(tests, setStringTests...)
   188  	tests = append(tests, setStringTests2...)
   189  
   190  	for i, test := range tests {
   191  		x, ok := new(Rat).SetString(test.in)
   192  
   193  		if ok {
   194  			if !test.ok {
   195  				t.Errorf("#%d SetString(%q) expected failure", i, test.in)
   196  			} else if x.RatString() != test.out {
   197  				t.Errorf("#%d SetString(%q) got %s want %s", i, test.in, x.RatString(), test.out)
   198  			}
   199  		} else {
   200  			if test.ok {
   201  				t.Errorf("#%d SetString(%q) expected success", i, test.in)
   202  			} else if x != nil {
   203  				t.Errorf("#%d SetString(%q) got %p want nil", i, test.in, x)
   204  			}
   205  		}
   206  	}
   207  }
   208  
   209  func TestRatSetStringZero(t *testing.T) {
   210  	got, _ := new(Rat).SetString("0")
   211  	want := new(Rat).SetInt64(0)
   212  	if !reflect.DeepEqual(got, want) {
   213  		t.Errorf("got %#+v, want %#+v", got, want)
   214  	}
   215  }
   216  
   217  func TestRatScan(t *testing.T) {
   218  	var buf bytes.Buffer
   219  	for i, test := range setStringTests {
   220  		x := new(Rat)
   221  		buf.Reset()
   222  		buf.WriteString(test.in)
   223  
   224  		_, err := fmt.Fscanf(&buf, "%v", x)
   225  		if err == nil != test.ok {
   226  			if test.ok {
   227  				t.Errorf("#%d (%s) error: %s", i, test.in, err)
   228  			} else {
   229  				t.Errorf("#%d (%s) expected error", i, test.in)
   230  			}
   231  			continue
   232  		}
   233  		if err == nil && x.RatString() != test.out {
   234  			t.Errorf("#%d got %s want %s", i, x.RatString(), test.out)
   235  		}
   236  	}
   237  }
   238  
   239  var floatStringTests = []struct {
   240  	in   string
   241  	prec int
   242  	out  string
   243  }{
   244  	{"0", 0, "0"},
   245  	{"0", 4, "0.0000"},
   246  	{"1", 0, "1"},
   247  	{"1", 2, "1.00"},
   248  	{"-1", 0, "-1"},
   249  	{"0.05", 1, "0.1"},
   250  	{"-0.05", 1, "-0.1"},
   251  	{".25", 2, "0.25"},
   252  	{".25", 1, "0.3"},
   253  	{".25", 3, "0.250"},
   254  	{"-1/3", 3, "-0.333"},
   255  	{"-2/3", 4, "-0.6667"},
   256  	{"0.96", 1, "1.0"},
   257  	{"0.999", 2, "1.00"},
   258  	{"0.9", 0, "1"},
   259  	{".25", -1, "0"},
   260  	{".55", -1, "1"},
   261  }
   262  
   263  func TestFloatString(t *testing.T) {
   264  	for i, test := range floatStringTests {
   265  		x, _ := new(Rat).SetString(test.in)
   266  
   267  		if x.FloatString(test.prec) != test.out {
   268  			t.Errorf("#%d got %s want %s", i, x.FloatString(test.prec), test.out)
   269  		}
   270  	}
   271  }
   272  
   273  // Test inputs to Rat.SetString. The prefix "long:" causes the test
   274  // to be skipped except in -long mode.  (The threshold is about 500us.)
   275  var float64inputs = []string{
   276  	// Constants plundered from strconv/testfp.txt.
   277  
   278  	// Table 1: Stress Inputs for Conversion to 53-bit Binary, < 1/2 ULP
   279  	"5e+125",
   280  	"69e+267",
   281  	"999e-026",
   282  	"7861e-034",
   283  	"75569e-254",
   284  	"928609e-261",
   285  	"9210917e+080",
   286  	"84863171e+114",
   287  	"653777767e+273",
   288  	"5232604057e-298",
   289  	"27235667517e-109",
   290  	"653532977297e-123",
   291  	"3142213164987e-294",
   292  	"46202199371337e-072",
   293  	"231010996856685e-073",
   294  	"9324754620109615e+212",
   295  	"78459735791271921e+049",
   296  	"272104041512242479e+200",
   297  	"6802601037806061975e+198",
   298  	"20505426358836677347e-221",
   299  	"836168422905420598437e-234",
   300  	"4891559871276714924261e+222",
   301  
   302  	// Table 2: Stress Inputs for Conversion to 53-bit Binary, > 1/2 ULP
   303  	"9e-265",
   304  	"85e-037",
   305  	"623e+100",
   306  	"3571e+263",
   307  	"81661e+153",
   308  	"920657e-023",
   309  	"4603285e-024",
   310  	"87575437e-309",
   311  	"245540327e+122",
   312  	"6138508175e+120",
   313  	"83356057653e+193",
   314  	"619534293513e+124",
   315  	"2335141086879e+218",
   316  	"36167929443327e-159",
   317  	"609610927149051e-255",
   318  	"3743626360493413e-165",
   319  	"94080055902682397e-242",
   320  	"899810892172646163e+283",
   321  	"7120190517612959703e+120",
   322  	"25188282901709339043e-252",
   323  	"308984926168550152811e-052",
   324  	"6372891218502368041059e+064",
   325  
   326  	// Table 14: Stress Inputs for Conversion to 24-bit Binary, <1/2 ULP
   327  	"5e-20",
   328  	"67e+14",
   329  	"985e+15",
   330  	"7693e-42",
   331  	"55895e-16",
   332  	"996622e-44",
   333  	"7038531e-32",
   334  	"60419369e-46",
   335  	"702990899e-20",
   336  	"6930161142e-48",
   337  	"25933168707e+13",
   338  	"596428896559e+20",
   339  
   340  	// Table 15: Stress Inputs for Conversion to 24-bit Binary, >1/2 ULP
   341  	"3e-23",
   342  	"57e+18",
   343  	"789e-35",
   344  	"2539e-18",
   345  	"76173e+28",
   346  	"887745e-11",
   347  	"5382571e-37",
   348  	"82381273e-35",
   349  	"750486563e-38",
   350  	"3752432815e-39",
   351  	"75224575729e-45",
   352  	"459926601011e+15",
   353  
   354  	// Constants plundered from strconv/atof_test.go.
   355  
   356  	"0",
   357  	"1",
   358  	"+1",
   359  	"1e23",
   360  	"1E23",
   361  	"100000000000000000000000",
   362  	"1e-100",
   363  	"123456700",
   364  	"99999999999999974834176",
   365  	"100000000000000000000001",
   366  	"100000000000000008388608",
   367  	"100000000000000016777215",
   368  	"100000000000000016777216",
   369  	"-1",
   370  	"-0.1",
   371  	"-0", // NB: exception made for this input
   372  	"1e-20",
   373  	"625e-3",
   374  
   375  	// largest float64
   376  	"1.7976931348623157e308",
   377  	"-1.7976931348623157e308",
   378  	// next float64 - too large
   379  	"1.7976931348623159e308",
   380  	"-1.7976931348623159e308",
   381  	// the border is ...158079
   382  	// borderline - okay
   383  	"1.7976931348623158e308",
   384  	"-1.7976931348623158e308",
   385  	// borderline - too large
   386  	"1.797693134862315808e308",
   387  	"-1.797693134862315808e308",
   388  
   389  	// a little too large
   390  	"1e308",
   391  	"2e308",
   392  	"1e309",
   393  
   394  	// way too large
   395  	"1e310",
   396  	"-1e310",
   397  	"1e400",
   398  	"-1e400",
   399  	"long:1e400000",
   400  	"long:-1e400000",
   401  
   402  	// denormalized
   403  	"1e-305",
   404  	"1e-306",
   405  	"1e-307",
   406  	"1e-308",
   407  	"1e-309",
   408  	"1e-310",
   409  	"1e-322",
   410  	// smallest denormal
   411  	"5e-324",
   412  	"4e-324",
   413  	"3e-324",
   414  	// too small
   415  	"2e-324",
   416  	// way too small
   417  	"1e-350",
   418  	"long:1e-400000",
   419  	// way too small, negative
   420  	"-1e-350",
   421  	"long:-1e-400000",
   422  
   423  	// try to overflow exponent
   424  	// [Disabled: too slow and memory-hungry with rationals.]
   425  	// "1e-4294967296",
   426  	// "1e+4294967296",
   427  	// "1e-18446744073709551616",
   428  	// "1e+18446744073709551616",
   429  
   430  	// https://www.exploringbinary.com/java-hangs-when-converting-2-2250738585072012e-308/
   431  	"2.2250738585072012e-308",
   432  	// https://www.exploringbinary.com/php-hangs-on-numeric-value-2-2250738585072011e-308/
   433  	"2.2250738585072011e-308",
   434  
   435  	// A very large number (initially wrongly parsed by the fast algorithm).
   436  	"4.630813248087435e+307",
   437  
   438  	// A different kind of very large number.
   439  	"22.222222222222222",
   440  	"long:2." + strings.Repeat("2", 4000) + "e+1",
   441  
   442  	// Exactly halfway between 1 and math.Nextafter(1, 2).
   443  	// Round to even (down).
   444  	"1.00000000000000011102230246251565404236316680908203125",
   445  	// Slightly lower; still round down.
   446  	"1.00000000000000011102230246251565404236316680908203124",
   447  	// Slightly higher; round up.
   448  	"1.00000000000000011102230246251565404236316680908203126",
   449  	// Slightly higher, but you have to read all the way to the end.
   450  	"long:1.00000000000000011102230246251565404236316680908203125" + strings.Repeat("0", 10000) + "1",
   451  
   452  	// Smallest denormal, 2^(-1022-52)
   453  	"4.940656458412465441765687928682213723651e-324",
   454  	// Half of smallest denormal, 2^(-1022-53)
   455  	"2.470328229206232720882843964341106861825e-324",
   456  	// A little more than the exact half of smallest denormal
   457  	// 2^-1075 + 2^-1100.  (Rounds to 1p-1074.)
   458  	"2.470328302827751011111470718709768633275e-324",
   459  	// The exact halfway between smallest normal and largest denormal:
   460  	// 2^-1022 - 2^-1075.  (Rounds to 2^-1022.)
   461  	"2.225073858507201136057409796709131975935e-308",
   462  
   463  	"1152921504606846975",  //   1<<60 - 1
   464  	"-1152921504606846975", // -(1<<60 - 1)
   465  	"1152921504606846977",  //   1<<60 + 1
   466  	"-1152921504606846977", // -(1<<60 + 1)
   467  
   468  	"1/3",
   469  }
   470  
   471  // isFinite reports whether f represents a finite rational value.
   472  // It is equivalent to !math.IsNan(f) && !math.IsInf(f, 0).
   473  func isFinite(f float64) bool {
   474  	return math.Abs(f) <= math.MaxFloat64
   475  }
   476  
   477  func TestFloat32SpecialCases(t *testing.T) {
   478  	for _, input := range float64inputs {
   479  		if strings.HasPrefix(input, "long:") {
   480  			if !*long {
   481  				continue
   482  			}
   483  			input = input[len("long:"):]
   484  		}
   485  
   486  		r, ok := new(Rat).SetString(input)
   487  		if !ok {
   488  			t.Errorf("Rat.SetString(%q) failed", input)
   489  			continue
   490  		}
   491  		f, exact := r.Float32()
   492  
   493  		// 1. Check string -> Rat -> float32 conversions are
   494  		// consistent with strconv.ParseFloat.
   495  		// Skip this check if the input uses "a/b" rational syntax.
   496  		if !strings.Contains(input, "/") {
   497  			e64, _ := strconv.ParseFloat(input, 32)
   498  			e := float32(e64)
   499  
   500  			// Careful: negative Rats too small for
   501  			// float64 become -0, but Rat obviously cannot
   502  			// preserve the sign from SetString("-0").
   503  			switch {
   504  			case math.Float32bits(e) == math.Float32bits(f):
   505  				// Ok: bitwise equal.
   506  			case f == 0 && r.Num().BitLen() == 0:
   507  				// Ok: Rat(0) is equivalent to both +/- float64(0).
   508  			default:
   509  				t.Errorf("strconv.ParseFloat(%q) = %g (%b), want %g (%b); delta = %g", input, e, e, f, f, f-e)
   510  			}
   511  		}
   512  
   513  		if !isFinite(float64(f)) {
   514  			continue
   515  		}
   516  
   517  		// 2. Check f is best approximation to r.
   518  		if !checkIsBestApprox32(t, f, r) {
   519  			// Append context information.
   520  			t.Errorf("(input was %q)", input)
   521  		}
   522  
   523  		// 3. Check f->R->f roundtrip is non-lossy.
   524  		checkNonLossyRoundtrip32(t, f)
   525  
   526  		// 4. Check exactness using slow algorithm.
   527  		if wasExact := new(Rat).SetFloat64(float64(f)).Cmp(r) == 0; wasExact != exact {
   528  			t.Errorf("Rat.SetString(%q).Float32().exact = %t, want %t", input, exact, wasExact)
   529  		}
   530  	}
   531  }
   532  
   533  func TestFloat64SpecialCases(t *testing.T) {
   534  	for _, input := range float64inputs {
   535  		if strings.HasPrefix(input, "long:") {
   536  			if !*long {
   537  				continue
   538  			}
   539  			input = input[len("long:"):]
   540  		}
   541  
   542  		r, ok := new(Rat).SetString(input)
   543  		if !ok {
   544  			t.Errorf("Rat.SetString(%q) failed", input)
   545  			continue
   546  		}
   547  		f, exact := r.Float64()
   548  
   549  		// 1. Check string -> Rat -> float64 conversions are
   550  		// consistent with strconv.ParseFloat.
   551  		// Skip this check if the input uses "a/b" rational syntax.
   552  		if !strings.Contains(input, "/") {
   553  			e, _ := strconv.ParseFloat(input, 64)
   554  
   555  			// Careful: negative Rats too small for
   556  			// float64 become -0, but Rat obviously cannot
   557  			// preserve the sign from SetString("-0").
   558  			switch {
   559  			case math.Float64bits(e) == math.Float64bits(f):
   560  				// Ok: bitwise equal.
   561  			case f == 0 && r.Num().BitLen() == 0:
   562  				// Ok: Rat(0) is equivalent to both +/- float64(0).
   563  			default:
   564  				t.Errorf("strconv.ParseFloat(%q) = %g (%b), want %g (%b); delta = %g", input, e, e, f, f, f-e)
   565  			}
   566  		}
   567  
   568  		if !isFinite(f) {
   569  			continue
   570  		}
   571  
   572  		// 2. Check f is best approximation to r.
   573  		if !checkIsBestApprox64(t, f, r) {
   574  			// Append context information.
   575  			t.Errorf("(input was %q)", input)
   576  		}
   577  
   578  		// 3. Check f->R->f roundtrip is non-lossy.
   579  		checkNonLossyRoundtrip64(t, f)
   580  
   581  		// 4. Check exactness using slow algorithm.
   582  		if wasExact := new(Rat).SetFloat64(f).Cmp(r) == 0; wasExact != exact {
   583  			t.Errorf("Rat.SetString(%q).Float64().exact = %t, want %t", input, exact, wasExact)
   584  		}
   585  	}
   586  }
   587  
   588  func TestIssue31184(t *testing.T) {
   589  	var x Rat
   590  	for _, want := range []string{
   591  		"-213.090",
   592  		"8.192",
   593  		"16.000",
   594  	} {
   595  		x.SetString(want)
   596  		got := x.FloatString(3)
   597  		if got != want {
   598  			t.Errorf("got %s, want %s", got, want)
   599  		}
   600  	}
   601  }
   602  
   603  func TestIssue45910(t *testing.T) {
   604  	var x Rat
   605  	for _, test := range []struct {
   606  		input string
   607  		want  bool
   608  	}{
   609  		{"1e-1000001", false},
   610  		{"1e-1000000", true},
   611  		{"1e+1000000", true},
   612  		{"1e+1000001", false},
   613  
   614  		{"0p1000000000000", true},
   615  		{"1p-10000001", false},
   616  		{"1p-10000000", true},
   617  		{"1p+10000000", true},
   618  		{"1p+10000001", false},
   619  		{"1.770p02041010010011001001", false}, // test case from issue
   620  	} {
   621  		_, got := x.SetString(test.input)
   622  		if got != test.want {
   623  			t.Errorf("SetString(%s) got ok = %v; want %v", test.input, got, test.want)
   624  		}
   625  	}
   626  }
   627  func TestFloatPrec(t *testing.T) {
   628  	var tests = []struct {
   629  		f    string
   630  		prec int
   631  		ok   bool
   632  		fdec string
   633  	}{
   634  		// examples from the issue #50489
   635  		{"10/100", 1, true, "0.1"},
   636  		{"3/100", 2, true, "0.03"},
   637  		{"10", 0, true, "10"},
   638  
   639  		// more examples
   640  		{"zero", 0, true, "0"},      // test uninitialized zero value for Rat
   641  		{"0", 0, true, "0"},         // 0
   642  		{"1", 0, true, "1"},         // 1
   643  		{"1/2", 1, true, "0.5"},     // 0.5
   644  		{"1/3", 0, false, "0"},      // 0.(3)
   645  		{"1/4", 2, true, "0.25"},    // 0.25
   646  		{"1/5", 1, true, "0.2"},     // 0.2
   647  		{"1/6", 1, false, "0.2"},    // 0.1(6)
   648  		{"1/7", 0, false, "0"},      // 0.(142857)
   649  		{"1/8", 3, true, "0.125"},   // 0.125
   650  		{"1/9", 0, false, "0"},      // 0.(1)
   651  		{"1/10", 1, true, "0.1"},    // 0.1
   652  		{"1/11", 0, false, "0"},     // 0.(09)
   653  		{"1/12", 2, false, "0.08"},  // 0.08(3)
   654  		{"1/13", 0, false, "0"},     // 0.(076923)
   655  		{"1/14", 1, false, "0.1"},   // 0.0(714285)
   656  		{"1/15", 1, false, "0.1"},   // 0.0(6)
   657  		{"1/16", 4, true, "0.0625"}, // 0.0625
   658  
   659  		{"10/2", 0, true, "5"},                    // 5
   660  		{"10/3", 0, false, "3"},                   // 3.(3)
   661  		{"10/6", 0, false, "2"},                   // 1.(6)
   662  		{"1/10000000", 7, true, "0.0000001"},      // 0.0000001
   663  		{"1/3125", 5, true, "0.00032"},            // "0.00032"
   664  		{"1/1024", 10, true, "0.0009765625"},      // 0.0009765625
   665  		{"1/304000", 7, false, "0.0000033"},       // 0.0000032(894736842105263157)
   666  		{"1/48828125", 11, true, "0.00000002048"}, // 0.00000002048
   667  	}
   668  
   669  	for _, test := range tests {
   670  		var f Rat
   671  
   672  		// check uninitialized zero value
   673  		if test.f != "zero" {
   674  			_, ok := f.SetString(test.f)
   675  			if !ok {
   676  				t.Fatalf("invalid test case: f = %s", test.f)
   677  			}
   678  		}
   679  
   680  		// results for f and -f must be the same
   681  		fdec := test.fdec
   682  		for i := 0; i < 2; i++ {
   683  			prec, ok := f.FloatPrec()
   684  			if prec != test.prec || ok != test.ok {
   685  				t.Errorf("%s: FloatPrec(%s): got prec, ok = %d, %v; want %d, %v", test.f, &f, prec, ok, test.prec, test.ok)
   686  			}
   687  			s := f.FloatString(test.prec)
   688  			if s != fdec {
   689  				t.Errorf("%s: FloatString(%s, %d): got %s; want %s", test.f, &f, prec, s, fdec)
   690  			}
   691  			// proceed with -f but don't add a "-" before a "0"
   692  			if f.Sign() > 0 {
   693  				f.Neg(&f)
   694  				fdec = "-" + fdec
   695  			}
   696  		}
   697  	}
   698  }
   699  
   700  func BenchmarkFloatPrecExact(b *testing.B) {
   701  	for _, n := range []int{1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6} {
   702  		// d := 5^n
   703  		d := NewInt(5)
   704  		p := NewInt(int64(n))
   705  		d.Exp(d, p, nil)
   706  
   707  		// r := 1/d
   708  		var r Rat
   709  		r.SetFrac(NewInt(1), d)
   710  
   711  		b.Run(fmt.Sprint(n), func(b *testing.B) {
   712  			for i := 0; i < b.N; i++ {
   713  				prec, ok := r.FloatPrec()
   714  				if prec != n || !ok {
   715  					b.Fatalf("got exact, ok = %d, %v; want %d, %v", prec, ok, uint64(n), true)
   716  				}
   717  			}
   718  		})
   719  	}
   720  }
   721  
   722  func BenchmarkFloatPrecMixed(b *testing.B) {
   723  	for _, n := range []int{1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6} {
   724  		// d := (3·5·7·11)^n
   725  		d := NewInt(3 * 5 * 7 * 11)
   726  		p := NewInt(int64(n))
   727  		d.Exp(d, p, nil)
   728  
   729  		// r := 1/d
   730  		var r Rat
   731  		r.SetFrac(NewInt(1), d)
   732  
   733  		b.Run(fmt.Sprint(n), func(b *testing.B) {
   734  			for i := 0; i < b.N; i++ {
   735  				prec, ok := r.FloatPrec()
   736  				if prec != n || ok {
   737  					b.Fatalf("got exact, ok = %d, %v; want %d, %v", prec, ok, uint64(n), false)
   738  				}
   739  			}
   740  		})
   741  	}
   742  }
   743  
   744  func BenchmarkFloatPrecInexact(b *testing.B) {
   745  	for _, n := range []int{1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6} {
   746  		// d := 5^n + 1
   747  		d := NewInt(5)
   748  		p := NewInt(int64(n))
   749  		d.Exp(d, p, nil)
   750  		d.Add(d, NewInt(1))
   751  
   752  		// r := 1/d
   753  		var r Rat
   754  		r.SetFrac(NewInt(1), d)
   755  
   756  		b.Run(fmt.Sprint(n), func(b *testing.B) {
   757  			for i := 0; i < b.N; i++ {
   758  				_, ok := r.FloatPrec()
   759  				if ok {
   760  					b.Fatalf("got unexpected ok")
   761  				}
   762  			}
   763  		})
   764  	}
   765  }
   766  

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