// 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)
}
}
}
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