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