src/math/big/ratconv_test.go - go - Git at Google

 // Copyright 2015 The Go Authors. All rights reserved.
 // Use of this source code is governed by a BSD-style
 // license that can be found in the LICENSE file.

 package big

 import (
 	"bytes"
 	"fmt"
 	"io"
 	"math"
 	"strconv"
 	"strings"
 	"testing"
 )

 var exponentTests = []struct {
 	s       string // string to be scanned
 	base2ok bool   // true if 'p'/'P' exponents are accepted
 	sepOk   bool   // true if '_' separators are accepted
 	x       int64  // expected exponent
 	b       int    // expected exponent base
 	err     error  // expected error
 	next    rune   // next character (or 0, if at EOF)
 }{
 	// valid, without separators
 	{"", false, false, 0, 10, nil, 0},
 	{"1", false, false, 0, 10, nil, '1'},
 	{"e0", false, false, 0, 10, nil, 0},
 	{"E1", false, false, 1, 10, nil, 0},
 	{"e+10", false, false, 10, 10, nil, 0},
 	{"e-10", false, false, -10, 10, nil, 0},
 	{"e123456789a", false, false, 123456789, 10, nil, 'a'},
 	{"p", false, false, 0, 10, nil, 'p'},
 	{"P+100", false, false, 0, 10, nil, 'P'},
 	{"p0", true, false, 0, 2, nil, 0},
 	{"P-123", true, false, -123, 2, nil, 0},
 	{"p+0a", true, false, 0, 2, nil, 'a'},
 	{"p+123__", true, false, 123, 2, nil, '_'}, // '_' is not part of the number anymore

 	// valid, with separators
 	{"e+1_0", false, true, 10, 10, nil, 0},
 	{"e-1_0", false, true, -10, 10, nil, 0},
 	{"e123_456_789a", false, true, 123456789, 10, nil, 'a'},
 	{"P+1_00", false, true, 0, 10, nil, 'P'},
 	{"p-1_2_3", true, true, -123, 2, nil, 0},

 	// invalid: no digits
 	{"e", false, false, 0, 10, errNoDigits, 0},
 	{"ef", false, false, 0, 10, errNoDigits, 'f'},
 	{"e+", false, false, 0, 10, errNoDigits, 0},
 	{"E-x", false, false, 0, 10, errNoDigits, 'x'},
 	{"p", true, false, 0, 2, errNoDigits, 0},
 	{"P-", true, false, 0, 2, errNoDigits, 0},
 	{"p+e", true, false, 0, 2, errNoDigits, 'e'},
 	{"e+_x", false, true, 0, 10, errNoDigits, 'x'},

 	// invalid: incorrect use of separator
 	{"e0_", false, true, 0, 10, errInvalSep, 0},
 	{"e_0", false, true, 0, 10, errInvalSep, 0},
 	{"e-1_2__3", false, true, -123, 10, errInvalSep, 0},
 }

 func TestScanExponent(t *testing.T) {
 	for _, a := range exponentTests {
 		r := strings.NewReader(a.s)
 		x, b, err := scanExponent(r, a.base2ok, a.sepOk)
 		if err != a.err {
 			t.Errorf("scanExponent%+v\n\tgot error = %v; want %v", a, err, a.err)
 		}
 		if x != a.x {
 			t.Errorf("scanExponent%+v\n\tgot z = %v; want %v", a, x, a.x)
 		}
 		if b != a.b {
 			t.Errorf("scanExponent%+v\n\tgot b = %d; want %d", a, b, a.b)
 		}
 		next, _, err := r.ReadRune()
 		if err == io.EOF {
 			next = 0
 			err = nil
 		}
 		if err == nil && next != a.next {
 			t.Errorf("scanExponent%+v\n\tgot next = %q; want %q", a, next, a.next)
 		}
 	}
 }

 type StringTest struct {
 	in, out string
 	ok      bool
 }

 var setStringTests = []StringTest{
 	// invalid
 	{in: "1e"},
 	{in: "1.e"},
 	{in: "1e+14e-5"},
 	{in: "1e4.5"},
 	{in: "r"},
 	{in: "a/b"},
 	{in: "a.b"},
 	{in: "1/0"},
 	{in: "4/3/2"}, // issue 17001
 	{in: "4/3/"},
 	{in: "4/3."},
 	{in: "4/"},

 	// valid
 	{"0", "0", true},
 	{"-0", "0", true},
 	{"1", "1", true},
 	{"-1", "-1", true},
 	{"1.", "1", true},
 	{"1e0", "1", true},
 	{"1.e1", "10", true},
 	{"-0.1", "-1/10", true},
 	{"-.1", "-1/10", true},
 	{"2/4", "1/2", true},
 	{".25", "1/4", true},
 	{"-1/5", "-1/5", true},
 	{"8129567.7690E14", "812956776900000000000", true},
 	{"78189e+4", "781890000", true},
 	{"553019.8935e+8", "55301989350000", true},
 	{"98765432109876543210987654321e-10", "98765432109876543210987654321/10000000000", true},
 	{"9877861857500000E-7", "3951144743/4", true},
 	{"2169378.417e-3", "2169378417/1000000", true},
 	{"884243222337379604041632732738665534", "884243222337379604041632732738665534", true},
 	{"53/70893980658822810696", "53/70893980658822810696", true},
 	{"106/141787961317645621392", "53/70893980658822810696", true},
 	{"204211327800791583.81095", "4084226556015831676219/20000", true},
 	{"0e9999999999", "0", true}, // issue #16176
 }

 // These are not supported by fmt.Fscanf.
 var setStringTests2 = []StringTest{
 	// invalid
 	{in: "4/3x"},
 	{in: "0/-1"},
 	{in: "-1/-1"},

 	// invalid with separators
 	// (smoke tests only - a comprehensive set of tests is in natconv_test.go)
 	{in: "10_/1"},
 	{in: "_10/1"},
 	{in: "1/1__0"},

 	// valid
 	{"0b1000/3", "8/3", true},
 	{"0B1000/0x8", "1", true},
 	{"-010/1", "-8", true}, // 0-prefix indicates octal in this case
 	{"-010.0", "-10", true},
 	{"-0o10/1", "-8", true},
 	{"0x10/1", "16", true},
 	{"0x10/0x20", "1/2", true},

 	{"0010", "10", true}, // 0-prefix is ignored in this case (not a fraction)
 	{"0x10.0", "16", true},
 	{"0x1.8", "3/2", true},
 	{"0X1.8p4", "24", true},
 	{"0x1.1E2", "2289/2048", true}, // E is part of hex mantissa, not exponent
 	{"0b1.1E2", "150", true},
 	{"0B1.1P3", "12", true},
 	{"0o10e-2", "2/25", true},
 	{"0O10p-3", "1", true},

 	// valid with separators
 	// (smoke tests only - a comprehensive set of tests is in natconv_test.go)
 	{"0b_1000/3", "8/3", true},
 	{"0B_10_00/0x8", "1", true},
 	{"0xdead/0B1101_1110_1010_1101", "1", true},
 	{"0B1101_1110_1010_1101/0XD_E_A_D", "1", true},
 	{"1_000.0", "1000", true},

 	{"0x_10.0", "16", true},
 	{"0x1_0.0", "16", true},
 	{"0x1.8_0", "3/2", true},
 	{"0X1.8p0_4", "24", true},
 	{"0b1.1_0E2", "150", true},
 	{"0o1_0e-2", "2/25", true},
 	{"0O_10p-3", "1", true},
 }

 func TestRatSetString(t *testing.T) {
 	var tests []StringTest
 	tests = append(tests, setStringTests...)
 	tests = append(tests, setStringTests2...)

 	for i, test := range tests {
 		x, ok := new(Rat).SetString(test.in)

 		if ok {
 			if !test.ok {
 				t.Errorf("#%d SetString(%q) expected failure", i, test.in)
 			} else if x.RatString() != test.out {
 				t.Errorf("#%d SetString(%q) got %s want %s", i, test.in, x.RatString(), test.out)
 			}
 		} else {
 			if test.ok {
 				t.Errorf("#%d SetString(%q) expected success", i, test.in)
 			} else if x != nil {
 				t.Errorf("#%d SetString(%q) got %p want nil", i, test.in, x)
 			}
 		}
 	}
 }

 func TestRatScan(t *testing.T) {
 	var buf bytes.Buffer
 	for i, test := range setStringTests {
 		x := new(Rat)
 		buf.Reset()
 		buf.WriteString(test.in)

 		_, err := fmt.Fscanf(&buf, "%v", x)
 		if err == nil != test.ok {
 			if test.ok {
 				t.Errorf("#%d (%s) error: %s", i, test.in, err)
 			} else {
 				t.Errorf("#%d (%s) expected error", i, test.in)
 			}
 			continue
 		}
 		if err == nil && x.RatString() != test.out {
 			t.Errorf("#%d got %s want %s", i, x.RatString(), test.out)
 		}
 	}
 }

 var floatStringTests = []struct {
 	in   string
 	prec int
 	out  string
 }{
 	{"0", 0, "0"},
 	{"0", 4, "0.0000"},
 	{"1", 0, "1"},
 	{"1", 2, "1.00"},
 	{"-1", 0, "-1"},
 	{"0.05", 1, "0.1"},
 	{"-0.05", 1, "-0.1"},
 	{".25", 2, "0.25"},
 	{".25", 1, "0.3"},
 	{".25", 3, "0.250"},
 	{"-1/3", 3, "-0.333"},
 	{"-2/3", 4, "-0.6667"},
 	{"0.96", 1, "1.0"},
 	{"0.999", 2, "1.00"},
 	{"0.9", 0, "1"},
 	{".25", -1, "0"},
 	{".55", -1, "1"},
 }

 func TestFloatString(t *testing.T) {
 	for i, test := range floatStringTests {
 		x, _ := new(Rat).SetString(test.in)

 		if x.FloatString(test.prec) != test.out {
 			t.Errorf("#%d got %s want %s", i, x.FloatString(test.prec), test.out)
 		}
 	}
 }

 // Test inputs to Rat.SetString. The prefix "long:" causes the test
 // to be skipped except in -long mode.  (The threshold is about 500us.)
 var float64inputs = []string{
 	// Constants plundered from strconv/testfp.txt.

 	// Table 1: Stress Inputs for Conversion to 53-bit Binary, < 1/2 ULP
 	"5e+125",
 	"69e+267",
 	"999e-026",
 	"7861e-034",
 	"75569e-254",
 	"928609e-261",
 	"9210917e+080",
 	"84863171e+114",
 	"653777767e+273",
 	"5232604057e-298",
 	"27235667517e-109",
 	"653532977297e-123",
 	"3142213164987e-294",
 	"46202199371337e-072",
 	"231010996856685e-073",
 	"9324754620109615e+212",
 	"78459735791271921e+049",
 	"272104041512242479e+200",
 	"6802601037806061975e+198",
 	"20505426358836677347e-221",
 	"836168422905420598437e-234",
 	"4891559871276714924261e+222",

 	// Table 2: Stress Inputs for Conversion to 53-bit Binary, > 1/2 ULP
 	"9e-265",
 	"85e-037",
 	"623e+100",
 	"3571e+263",
 	"81661e+153",
 	"920657e-023",
 	"4603285e-024",
 	"87575437e-309",
 	"245540327e+122",
 	"6138508175e+120",
 	"83356057653e+193",
 	"619534293513e+124",
 	"2335141086879e+218",
 	"36167929443327e-159",
 	"609610927149051e-255",
 	"3743626360493413e-165",
 	"94080055902682397e-242",
 	"899810892172646163e+283",
 	"7120190517612959703e+120",
 	"25188282901709339043e-252",
 	"308984926168550152811e-052",
 	"6372891218502368041059e+064",

 	// Table 14: Stress Inputs for Conversion to 24-bit Binary, <1/2 ULP
 	"5e-20",
 	"67e+14",
 	"985e+15",
 	"7693e-42",
 	"55895e-16",
 	"996622e-44",
 	"7038531e-32",
 	"60419369e-46",
 	"702990899e-20",
 	"6930161142e-48",
 	"25933168707e+13",
 	"596428896559e+20",

 	// Table 15: Stress Inputs for Conversion to 24-bit Binary, >1/2 ULP
 	"3e-23",
 	"57e+18",
 	"789e-35",
 	"2539e-18",
 	"76173e+28",
 	"887745e-11",
 	"5382571e-37",
 	"82381273e-35",
 	"750486563e-38",
 	"3752432815e-39",
 	"75224575729e-45",
 	"459926601011e+15",

 	// Constants plundered from strconv/atof_test.go.

 	"0",
 	"1",
 	"+1",
 	"1e23",
 	"1E23",
 	"100000000000000000000000",
 	"1e-100",
 	"123456700",
 	"99999999999999974834176",
 	"100000000000000000000001",
 	"100000000000000008388608",
 	"100000000000000016777215",
 	"100000000000000016777216",
 	"-1",
 	"-0.1",
 	"-0", // NB: exception made for this input
 	"1e-20",
 	"625e-3",

 	// largest float64
 	"1.7976931348623157e308",
 	"-1.7976931348623157e308",
 	// next float64 - too large
 	"1.7976931348623159e308",
 	"-1.7976931348623159e308",
 	// the border is ...158079
 	// borderline - okay
 	"1.7976931348623158e308",
 	"-1.7976931348623158e308",
 	// borderline - too large
 	"1.797693134862315808e308",
 	"-1.797693134862315808e308",

 	// a little too large
 	"1e308",
 	"2e308",
 	"1e309",

 	// way too large
 	"1e310",
 	"-1e310",
 	"1e400",
 	"-1e400",
 	"long:1e400000",
 	"long:-1e400000",

 	// denormalized
 	"1e-305",
 	"1e-306",
 	"1e-307",
 	"1e-308",
 	"1e-309",
 	"1e-310",
 	"1e-322",
 	// smallest denormal
 	"5e-324",
 	"4e-324",
 	"3e-324",
 	// too small
 	"2e-324",
 	// way too small
 	"1e-350",
 	"long:1e-400000",
 	// way too small, negative
 	"-1e-350",
 	"long:-1e-400000",

 	// try to overflow exponent
 	// [Disabled: too slow and memory-hungry with rationals.]
 	// "1e-4294967296",
 	// "1e+4294967296",
 	// "1e-18446744073709551616",
 	// "1e+18446744073709551616",

 	// https://www.exploringbinary.com/java-hangs-when-converting-2-2250738585072012e-308/
 	"2.2250738585072012e-308",
 	// https://www.exploringbinary.com/php-hangs-on-numeric-value-2-2250738585072011e-308/
 	"2.2250738585072011e-308",

 	// A very large number (initially wrongly parsed by the fast algorithm).
 	"4.630813248087435e+307",

 	// A different kind of very large number.
 	"22.222222222222222",
 	"long:2." + strings.Repeat("2", 4000) + "e+1",

 	// Exactly halfway between 1 and math.Nextafter(1, 2).
 	// Round to even (down).
 	"1.00000000000000011102230246251565404236316680908203125",
 	// Slightly lower; still round down.
 	"1.00000000000000011102230246251565404236316680908203124",
 	// Slightly higher; round up.
 	"1.00000000000000011102230246251565404236316680908203126",
 	// Slightly higher, but you have to read all the way to the end.
 	"long:1.00000000000000011102230246251565404236316680908203125" + strings.Repeat("0", 10000) + "1",

 	// Smallest denormal, 2^(-1022-52)
 	"4.940656458412465441765687928682213723651e-324",
 	// Half of smallest denormal, 2^(-1022-53)
 	"2.470328229206232720882843964341106861825e-324",
 	// A little more than the exact half of smallest denormal
 	// 2^-1075 + 2^-1100.  (Rounds to 1p-1074.)
 	"2.470328302827751011111470718709768633275e-324",
 	// The exact halfway between smallest normal and largest denormal:
 	// 2^-1022 - 2^-1075.  (Rounds to 2^-1022.)
 	"2.225073858507201136057409796709131975935e-308",

 	"1152921504606846975",  //   1<<60 - 1
 	"-1152921504606846975", // -(1<<60 - 1)
 	"1152921504606846977",  //   1<<60 + 1
 	"-1152921504606846977", // -(1<<60 + 1)

 	"1/3",
 }

 // isFinite reports whether f represents a finite rational value.
 // It is equivalent to !math.IsNan(f) && !math.IsInf(f, 0).
 func isFinite(f float64) bool {
 	return math.Abs(f) <= math.MaxFloat64
 }

 func TestFloat32SpecialCases(t *testing.T) {
 	for _, input := range float64inputs {
 		if strings.HasPrefix(input, "long:") {
 			if !*long {
 				continue
 			}
 			input = input[len("long:"):]
 		}

 		r, ok := new(Rat).SetString(input)
 		if !ok {
 			t.Errorf("Rat.SetString(%q) failed", input)
 			continue
 		}
 		f, exact := r.Float32()

 		// 1. Check string -> Rat -> float32 conversions are
 		// consistent with strconv.ParseFloat.
 		// Skip this check if the input uses "a/b" rational syntax.
 		if !strings.Contains(input, "/") {
 			e64, _ := strconv.ParseFloat(input, 32)
 			e := float32(e64)

 			// Careful: negative Rats too small for
 			// float64 become -0, but Rat obviously cannot
 			// preserve the sign from SetString("-0").
 			switch {
 			case math.Float32bits(e) == math.Float32bits(f):
 				// Ok: bitwise equal.
 			case f == 0 && r.Num().BitLen() == 0:
 				// Ok: Rat(0) is equivalent to both +/- float64(0).
 			default:
 				t.Errorf("strconv.ParseFloat(%q) = %g (%b), want %g (%b); delta = %g", input, e, e, f, f, f-e)
 			}
 		}

 		if !isFinite(float64(f)) {
 			continue
 		}

 		// 2. Check f is best approximation to r.
 		if !checkIsBestApprox32(t, f, r) {
 			// Append context information.
 			t.Errorf("(input was %q)", input)
 		}

 		// 3. Check f->R->f roundtrip is non-lossy.
 		checkNonLossyRoundtrip32(t, f)

 		// 4. Check exactness using slow algorithm.
 		if wasExact := new(Rat).SetFloat64(float64(f)).Cmp(r) == 0; wasExact != exact {
 			t.Errorf("Rat.SetString(%q).Float32().exact = %t, want %t", input, exact, wasExact)
 		}
 	}
 }

 func TestFloat64SpecialCases(t *testing.T) {
 	for _, input := range float64inputs {
 		if strings.HasPrefix(input, "long:") {
 			if !*long {
 				continue
 			}
 			input = input[len("long:"):]
 		}

 		r, ok := new(Rat).SetString(input)
 		if !ok {
 			t.Errorf("Rat.SetString(%q) failed", input)
 			continue
 		}
 		f, exact := r.Float64()

 		// 1. Check string -> Rat -> float64 conversions are
 		// consistent with strconv.ParseFloat.
 		// Skip this check if the input uses "a/b" rational syntax.
 		if !strings.Contains(input, "/") {
 			e, _ := strconv.ParseFloat(input, 64)

 			// Careful: negative Rats too small for
 			// float64 become -0, but Rat obviously cannot
 			// preserve the sign from SetString("-0").
 			switch {
 			case math.Float64bits(e) == math.Float64bits(f):
 				// Ok: bitwise equal.
 			case f == 0 && r.Num().BitLen() == 0:
 				// Ok: Rat(0) is equivalent to both +/- float64(0).
 			default:
 				t.Errorf("strconv.ParseFloat(%q) = %g (%b), want %g (%b); delta = %g", input, e, e, f, f, f-e)
 			}
 		}

 		if !isFinite(f) {
 			continue
 		}

 		// 2. Check f is best approximation to r.
 		if !checkIsBestApprox64(t, f, r) {
 			// Append context information.
 			t.Errorf("(input was %q)", input)
 		}

 		// 3. Check f->R->f roundtrip is non-lossy.
 		checkNonLossyRoundtrip64(t, f)

 		// 4. Check exactness using slow algorithm.
 		if wasExact := new(Rat).SetFloat64(f).Cmp(r) == 0; wasExact != exact {
 			t.Errorf("Rat.SetString(%q).Float64().exact = %t, want %t", input, exact, wasExact)
 		}
 	}
 }

 func TestIssue31184(t *testing.T) {
 	var x Rat
 	for _, want := range []string{
 		"-213.090",
 		"8.192",
 		"16.000",
 	} {
 		x.SetString(want)
 		got := x.FloatString(3)
 		if got != want {
 			t.Errorf("got %s, want %s", got, want)
 		}
 	}
 }
	// Copyright 2015 The Go Authors. All rights reserved.
	// Use of this source code is governed by a BSD-style
	// license that can be found in the LICENSE file.

	package big

	import (
	"bytes"
	"fmt"
	"io"
	"math"
	"strconv"
	"strings"
	"testing"
	)

	var exponentTests = []struct {
	s string // string to be scanned
	base2ok bool // true if 'p'/'P' exponents are accepted
	sepOk bool // true if '_' separators are accepted
	x int64 // expected exponent
	b int // expected exponent base
	err error // expected error
	next rune // next character (or 0, if at EOF)
	}{
	// valid, without separators
	{"", false, false, 0, 10, nil, 0},
	{"1", false, false, 0, 10, nil, '1'},
	{"e0", false, false, 0, 10, nil, 0},
	{"E1", false, false, 1, 10, nil, 0},
	{"e+10", false, false, 10, 10, nil, 0},
	{"e-10", false, false, -10, 10, nil, 0},
	{"e123456789a", false, false, 123456789, 10, nil, 'a'},
	{"p", false, false, 0, 10, nil, 'p'},
	{"P+100", false, false, 0, 10, nil, 'P'},
	{"p0", true, false, 0, 2, nil, 0},
	{"P-123", true, false, -123, 2, nil, 0},
	{"p+0a", true, false, 0, 2, nil, 'a'},
	{"p+123__", true, false, 123, 2, nil, '_'}, // '_' is not part of the number anymore

	// valid, with separators
	{"e+1_0", false, true, 10, 10, nil, 0},
	{"e-1_0", false, true, -10, 10, nil, 0},
	{"e123_456_789a", false, true, 123456789, 10, nil, 'a'},
	{"P+1_00", false, true, 0, 10, nil, 'P'},
	{"p-1_2_3", true, true, -123, 2, nil, 0},

	// invalid: no digits
	{"e", false, false, 0, 10, errNoDigits, 0},
	{"ef", false, false, 0, 10, errNoDigits, 'f'},
	{"e+", false, false, 0, 10, errNoDigits, 0},
	{"E-x", false, false, 0, 10, errNoDigits, 'x'},
	{"p", true, false, 0, 2, errNoDigits, 0},
	{"P-", true, false, 0, 2, errNoDigits, 0},
	{"p+e", true, false, 0, 2, errNoDigits, 'e'},
	{"e+_x", false, true, 0, 10, errNoDigits, 'x'},

	// invalid: incorrect use of separator
	{"e0_", false, true, 0, 10, errInvalSep, 0},
	{"e_0", false, true, 0, 10, errInvalSep, 0},
	{"e-1_2__3", false, true, -123, 10, errInvalSep, 0},
	}

	func TestScanExponent(t *testing.T) {
	for _, a := range exponentTests {
	r := strings.NewReader(a.s)
	x, b, err := scanExponent(r, a.base2ok, a.sepOk)
	if err != a.err {
	t.Errorf("scanExponent%+v\n\tgot error = %v; want %v", a, err, a.err)
	}
	if x != a.x {
	t.Errorf("scanExponent%+v\n\tgot z = %v; want %v", a, x, a.x)
	}
	if b != a.b {
	t.Errorf("scanExponent%+v\n\tgot b = %d; want %d", a, b, a.b)
	}
	next, _, err := r.ReadRune()
	if err == io.EOF {
	next = 0
	err = nil
	}
	if err == nil && next != a.next {
	t.Errorf("scanExponent%+v\n\tgot next = %q; want %q", a, next, a.next)
	}
	}
	}

	type StringTest struct {
	in, out string
	ok bool
	}

	var setStringTests = []StringTest{
	// invalid
	{in: "1e"},
	{in: "1.e"},
	{in: "1e+14e-5"},
	{in: "1e4.5"},
	{in: "r"},
	{in: "a/b"},
	{in: "a.b"},
	{in: "1/0"},
	{in: "4/3/2"}, // issue 17001
	{in: "4/3/"},
	{in: "4/3."},
	{in: "4/"},

	// valid
	{"0", "0", true},
	{"-0", "0", true},
	{"1", "1", true},
	{"-1", "-1", true},
	{"1.", "1", true},
	{"1e0", "1", true},
	{"1.e1", "10", true},
	{"-0.1", "-1/10", true},
	{"-.1", "-1/10", true},
	{"2/4", "1/2", true},
	{".25", "1/4", true},
	{"-1/5", "-1/5", true},
	{"8129567.7690E14", "812956776900000000000", true},
	{"78189e+4", "781890000", true},
	{"553019.8935e+8", "55301989350000", true},
	{"98765432109876543210987654321e-10", "98765432109876543210987654321/10000000000", true},
	{"9877861857500000E-7", "3951144743/4", true},
	{"2169378.417e-3", "2169378417/1000000", true},
	{"884243222337379604041632732738665534", "884243222337379604041632732738665534", true},
	{"53/70893980658822810696", "53/70893980658822810696", true},
	{"106/141787961317645621392", "53/70893980658822810696", true},
	{"204211327800791583.81095", "4084226556015831676219/20000", true},
	{"0e9999999999", "0", true}, // issue #16176
	}

	// These are not supported by fmt.Fscanf.
	var setStringTests2 = []StringTest{
	// invalid
	{in: "4/3x"},
	{in: "0/-1"},
	{in: "-1/-1"},

	// invalid with separators
	// (smoke tests only - a comprehensive set of tests is in natconv_test.go)
	{in: "10_/1"},
	{in: "_10/1"},
	{in: "1/1__0"},

	// valid
	{"0b1000/3", "8/3", true},
	{"0B1000/0x8", "1", true},
	{"-010/1", "-8", true}, // 0-prefix indicates octal in this case
	{"-010.0", "-10", true},
	{"-0o10/1", "-8", true},
	{"0x10/1", "16", true},
	{"0x10/0x20", "1/2", true},

	{"0010", "10", true}, // 0-prefix is ignored in this case (not a fraction)
	{"0x10.0", "16", true},
	{"0x1.8", "3/2", true},
	{"0X1.8p4", "24", true},
	{"0x1.1E2", "2289/2048", true}, // E is part of hex mantissa, not exponent
	{"0b1.1E2", "150", true},
	{"0B1.1P3", "12", true},
	{"0o10e-2", "2/25", true},
	{"0O10p-3", "1", true},

	// valid with separators
	// (smoke tests only - a comprehensive set of tests is in natconv_test.go)
	{"0b_1000/3", "8/3", true},
	{"0B_10_00/0x8", "1", true},
	{"0xdead/0B1101_1110_1010_1101", "1", true},
	{"0B1101_1110_1010_1101/0XD_E_A_D", "1", true},
	{"1_000.0", "1000", true},

	{"0x_10.0", "16", true},
	{"0x1_0.0", "16", true},
	{"0x1.8_0", "3/2", true},
	{"0X1.8p0_4", "24", true},
	{"0b1.1_0E2", "150", true},
	{"0o1_0e-2", "2/25", true},
	{"0O_10p-3", "1", true},
	}

	func TestRatSetString(t *testing.T) {
	var tests []StringTest
	tests = append(tests, setStringTests...)
	tests = append(tests, setStringTests2...)

	for i, test := range tests {
	x, ok := new(Rat).SetString(test.in)

	if ok {
	if !test.ok {
	t.Errorf("#%d SetString(%q) expected failure", i, test.in)
	} else if x.RatString() != test.out {
	t.Errorf("#%d SetString(%q) got %s want %s", i, test.in, x.RatString(), test.out)
	}
	} else {
	if test.ok {
	t.Errorf("#%d SetString(%q) expected success", i, test.in)
	} else if x != nil {
	t.Errorf("#%d SetString(%q) got %p want nil", i, test.in, x)
	}
	}
	}
	}

	func TestRatScan(t *testing.T) {
	var buf bytes.Buffer
	for i, test := range setStringTests {
	x := new(Rat)
	buf.Reset()
	buf.WriteString(test.in)

	_, err := fmt.Fscanf(&buf, "%v", x)
	if err == nil != test.ok {
	if test.ok {
	t.Errorf("#%d (%s) error: %s", i, test.in, err)
	} else {
	t.Errorf("#%d (%s) expected error", i, test.in)
	}
	continue
	}
	if err == nil && x.RatString() != test.out {
	t.Errorf("#%d got %s want %s", i, x.RatString(), test.out)
	}
	}
	}

	var floatStringTests = []struct {
	in string
	prec int
	out string
	}{
	{"0", 0, "0"},
	{"0", 4, "0.0000"},
	{"1", 0, "1"},
	{"1", 2, "1.00"},
	{"-1", 0, "-1"},
	{"0.05", 1, "0.1"},
	{"-0.05", 1, "-0.1"},
	{".25", 2, "0.25"},
	{".25", 1, "0.3"},
	{".25", 3, "0.250"},
	{"-1/3", 3, "-0.333"},
	{"-2/3", 4, "-0.6667"},
	{"0.96", 1, "1.0"},
	{"0.999", 2, "1.00"},
	{"0.9", 0, "1"},
	{".25", -1, "0"},
	{".55", -1, "1"},
	}

	func TestFloatString(t *testing.T) {
	for i, test := range floatStringTests {
	x, _ := new(Rat).SetString(test.in)

	if x.FloatString(test.prec) != test.out {
	t.Errorf("#%d got %s want %s", i, x.FloatString(test.prec), test.out)
	}
	}
	}

	// Test inputs to Rat.SetString. The prefix "long:" causes the test
	// to be skipped except in -long mode. (The threshold is about 500us.)
	var float64inputs = []string{
	// Constants plundered from strconv/testfp.txt.

	// Table 1: Stress Inputs for Conversion to 53-bit Binary, < 1/2 ULP
	"5e+125",
	"69e+267",
	"999e-026",
	"7861e-034",
	"75569e-254",
	"928609e-261",
	"9210917e+080",
	"84863171e+114",
	"653777767e+273",
	"5232604057e-298",
	"27235667517e-109",
	"653532977297e-123",
	"3142213164987e-294",
	"46202199371337e-072",
	"231010996856685e-073",
	"9324754620109615e+212",
	"78459735791271921e+049",
	"272104041512242479e+200",
	"6802601037806061975e+198",
	"20505426358836677347e-221",
	"836168422905420598437e-234",
	"4891559871276714924261e+222",

	// Table 2: Stress Inputs for Conversion to 53-bit Binary, > 1/2 ULP
	"9e-265",
	"85e-037",
	"623e+100",
	"3571e+263",
	"81661e+153",
	"920657e-023",
	"4603285e-024",
	"87575437e-309",
	"245540327e+122",
	"6138508175e+120",
	"83356057653e+193",
	"619534293513e+124",
	"2335141086879e+218",
	"36167929443327e-159",
	"609610927149051e-255",
	"3743626360493413e-165",
	"94080055902682397e-242",
	"899810892172646163e+283",
	"7120190517612959703e+120",
	"25188282901709339043e-252",
	"308984926168550152811e-052",
	"6372891218502368041059e+064",

	// Table 14: Stress Inputs for Conversion to 24-bit Binary, <1/2 ULP
	"5e-20",
	"67e+14",
	"985e+15",
	"7693e-42",
	"55895e-16",
	"996622e-44",
	"7038531e-32",
	"60419369e-46",
	"702990899e-20",
	"6930161142e-48",
	"25933168707e+13",
	"596428896559e+20",

	// Table 15: Stress Inputs for Conversion to 24-bit Binary, >1/2 ULP
	"3e-23",
	"57e+18",
	"789e-35",
	"2539e-18",
	"76173e+28",
	"887745e-11",
	"5382571e-37",
	"82381273e-35",
	"750486563e-38",
	"3752432815e-39",
	"75224575729e-45",
	"459926601011e+15",

	// Constants plundered from strconv/atof_test.go.

	"0",
	"1",
	"+1",
	"1e23",
	"1E23",
	"100000000000000000000000",
	"1e-100",
	"123456700",
	"99999999999999974834176",
	"100000000000000000000001",
	"100000000000000008388608",
	"100000000000000016777215",
	"100000000000000016777216",
	"-1",
	"-0.1",
	"-0", // NB: exception made for this input
	"1e-20",
	"625e-3",

	// largest float64
	"1.7976931348623157e308",
	"-1.7976931348623157e308",
	// next float64 - too large
	"1.7976931348623159e308",
	"-1.7976931348623159e308",
	// the border is ...158079
	// borderline - okay
	"1.7976931348623158e308",
	"-1.7976931348623158e308",
	// borderline - too large
	"1.797693134862315808e308",
	"-1.797693134862315808e308",

	// a little too large
	"1e308",
	"2e308",
	"1e309",

	// way too large
	"1e310",
	"-1e310",
	"1e400",
	"-1e400",
	"long:1e400000",
	"long:-1e400000",

	// denormalized
	"1e-305",
	"1e-306",
	"1e-307",
	"1e-308",
	"1e-309",
	"1e-310",
	"1e-322",
	// smallest denormal
	"5e-324",
	"4e-324",
	"3e-324",
	// too small
	"2e-324",
	// way too small
	"1e-350",
	"long:1e-400000",
	// way too small, negative
	"-1e-350",
	"long:-1e-400000",

	// try to overflow exponent
	// [Disabled: too slow and memory-hungry with rationals.]
	// "1e-4294967296",
	// "1e+4294967296",
	// "1e-18446744073709551616",
	// "1e+18446744073709551616",

	// https://www.exploringbinary.com/java-hangs-when-converting-2-2250738585072012e-308/
	"2.2250738585072012e-308",
	// https://www.exploringbinary.com/php-hangs-on-numeric-value-2-2250738585072011e-308/
	"2.2250738585072011e-308",

	// A very large number (initially wrongly parsed by the fast algorithm).
	"4.630813248087435e+307",

	// A different kind of very large number.
	"22.222222222222222",
	"long:2." + strings.Repeat("2", 4000) + "e+1",

	// Exactly halfway between 1 and math.Nextafter(1, 2).
	// Round to even (down).
	"1.00000000000000011102230246251565404236316680908203125",
	// Slightly lower; still round down.
	"1.00000000000000011102230246251565404236316680908203124",
	// Slightly higher; round up.
	"1.00000000000000011102230246251565404236316680908203126",
	// Slightly higher, but you have to read all the way to the end.
	"long:1.00000000000000011102230246251565404236316680908203125" + strings.Repeat("0", 10000) + "1",

	// Smallest denormal, 2^(-1022-52)
	"4.940656458412465441765687928682213723651e-324",
	// Half of smallest denormal, 2^(-1022-53)
	"2.470328229206232720882843964341106861825e-324",
	// A little more than the exact half of smallest denormal
	// 2^-1075 + 2^-1100. (Rounds to 1p-1074.)
	"2.470328302827751011111470718709768633275e-324",
	// The exact halfway between smallest normal and largest denormal:
	// 2^-1022 - 2^-1075. (Rounds to 2^-1022.)
	"2.225073858507201136057409796709131975935e-308",

	"1152921504606846975", // 1<<60 - 1
	"-1152921504606846975", // -(1<<60 - 1)
	"1152921504606846977", // 1<<60 + 1
	"-1152921504606846977", // -(1<<60 + 1)

	"1/3",
	}

	// isFinite reports whether f represents a finite rational value.
	// It is equivalent to !math.IsNan(f) && !math.IsInf(f, 0).
	func isFinite(f float64) bool {
	return math.Abs(f) <= math.MaxFloat64
	}

	func TestFloat32SpecialCases(t *testing.T) {
	for _, input := range float64inputs {
	if strings.HasPrefix(input, "long:") {
	if !*long {
	continue
	}
	input = input[len("long:"):]
	}

	r, ok := new(Rat).SetString(input)
	if !ok {
	t.Errorf("Rat.SetString(%q) failed", input)
	continue
	}
	f, exact := r.Float32()

	// 1. Check string -> Rat -> float32 conversions are
	// consistent with strconv.ParseFloat.
	// Skip this check if the input uses "a/b" rational syntax.
	if !strings.Contains(input, "/") {
	e64, _ := strconv.ParseFloat(input, 32)
	e := float32(e64)

	// Careful: negative Rats too small for
	// float64 become -0, but Rat obviously cannot
	// preserve the sign from SetString("-0").
	switch {
	case math.Float32bits(e) == math.Float32bits(f):
	// Ok: bitwise equal.
	case f == 0 && r.Num().BitLen() == 0:
	// Ok: Rat(0) is equivalent to both +/- float64(0).
	default:
	t.Errorf("strconv.ParseFloat(%q) = %g (%b), want %g (%b); delta = %g", input, e, e, f, f, f-e)
	}
	}

	if !isFinite(float64(f)) {
	continue
	}

	// 2. Check f is best approximation to r.
	if !checkIsBestApprox32(t, f, r) {
	// Append context information.
	t.Errorf("(input was %q)", input)
	}

	// 3. Check f->R->f roundtrip is non-lossy.
	checkNonLossyRoundtrip32(t, f)

	// 4. Check exactness using slow algorithm.
	if wasExact := new(Rat).SetFloat64(float64(f)).Cmp(r) == 0; wasExact != exact {
	t.Errorf("Rat.SetString(%q).Float32().exact = %t, want %t", input, exact, wasExact)
	}
	}
	}

	func TestFloat64SpecialCases(t *testing.T) {
	for _, input := range float64inputs {
	if strings.HasPrefix(input, "long:") {
	if !*long {
	continue
	}
	input = input[len("long:"):]
	}

	r, ok := new(Rat).SetString(input)
	if !ok {
	t.Errorf("Rat.SetString(%q) failed", input)
	continue
	}
	f, exact := r.Float64()

	// 1. Check string -> Rat -> float64 conversions are
	// consistent with strconv.ParseFloat.
	// Skip this check if the input uses "a/b" rational syntax.
	if !strings.Contains(input, "/") {
	e, _ := strconv.ParseFloat(input, 64)

	// Careful: negative Rats too small for
	// float64 become -0, but Rat obviously cannot
	// preserve the sign from SetString("-0").
	switch {
	case math.Float64bits(e) == math.Float64bits(f):
	// Ok: bitwise equal.
	case f == 0 && r.Num().BitLen() == 0:
	// Ok: Rat(0) is equivalent to both +/- float64(0).
	default:
	t.Errorf("strconv.ParseFloat(%q) = %g (%b), want %g (%b); delta = %g", input, e, e, f, f, f-e)
	}
	}

	if !isFinite(f) {
	continue
	}

	// 2. Check f is best approximation to r.
	if !checkIsBestApprox64(t, f, r) {
	// Append context information.
	t.Errorf("(input was %q)", input)
	}

	// 3. Check f->R->f roundtrip is non-lossy.
	checkNonLossyRoundtrip64(t, f)

	// 4. Check exactness using slow algorithm.
	if wasExact := new(Rat).SetFloat64(f).Cmp(r) == 0; wasExact != exact {
	t.Errorf("Rat.SetString(%q).Float64().exact = %t, want %t", input, exact, wasExact)
	}
	}
	}

	func TestIssue31184(t *testing.T) {
	var x Rat
	for _, want := range []string{
	"-213.090",
	"8.192",
	"16.000",
	} {
	x.SetString(want)
	got := x.FloatString(3)
	if got != want {
	t.Errorf("got %s, want %s", got, want)
	}
	}
	}