618 lines
16 KiB
Go
618 lines
16 KiB
Go
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// Copyright 2015 The Go Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package big
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import (
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"bytes"
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"fmt"
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"io"
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"math"
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"strconv"
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"strings"
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"testing"
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)
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var exponentTests = []struct {
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s string // string to be scanned
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base2ok bool // true if 'p'/'P' exponents are accepted
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sepOk bool // true if '_' separators are accepted
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x int64 // expected exponent
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b int // expected exponent base
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err error // expected error
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next rune // next character (or 0, if at EOF)
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}{
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// valid, without separators
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{"", false, false, 0, 10, nil, 0},
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{"1", false, false, 0, 10, nil, '1'},
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{"e0", false, false, 0, 10, nil, 0},
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{"E1", false, false, 1, 10, nil, 0},
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{"e+10", false, false, 10, 10, nil, 0},
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{"e-10", false, false, -10, 10, nil, 0},
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{"e123456789a", false, false, 123456789, 10, nil, 'a'},
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{"p", false, false, 0, 10, nil, 'p'},
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{"P+100", false, false, 0, 10, nil, 'P'},
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{"p0", true, false, 0, 2, nil, 0},
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{"P-123", true, false, -123, 2, nil, 0},
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{"p+0a", true, false, 0, 2, nil, 'a'},
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{"p+123__", true, false, 123, 2, nil, '_'}, // '_' is not part of the number anymore
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// valid, with separators
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{"e+1_0", false, true, 10, 10, nil, 0},
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{"e-1_0", false, true, -10, 10, nil, 0},
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{"e123_456_789a", false, true, 123456789, 10, nil, 'a'},
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{"P+1_00", false, true, 0, 10, nil, 'P'},
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{"p-1_2_3", true, true, -123, 2, nil, 0},
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// invalid: no digits
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{"e", false, false, 0, 10, errNoDigits, 0},
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{"ef", false, false, 0, 10, errNoDigits, 'f'},
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{"e+", false, false, 0, 10, errNoDigits, 0},
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{"E-x", false, false, 0, 10, errNoDigits, 'x'},
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{"p", true, false, 0, 2, errNoDigits, 0},
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{"P-", true, false, 0, 2, errNoDigits, 0},
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{"p+e", true, false, 0, 2, errNoDigits, 'e'},
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{"e+_x", false, true, 0, 10, errNoDigits, 'x'},
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// invalid: incorrect use of separator
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{"e0_", false, true, 0, 10, errInvalSep, 0},
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{"e_0", false, true, 0, 10, errInvalSep, 0},
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{"e-1_2__3", false, true, -123, 10, errInvalSep, 0},
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}
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func TestScanExponent(t *testing.T) {
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for _, a := range exponentTests {
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r := strings.NewReader(a.s)
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x, b, err := scanExponent(r, a.base2ok, a.sepOk)
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if err != a.err {
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t.Errorf("scanExponent%+v\n\tgot error = %v; want %v", a, err, a.err)
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}
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if x != a.x {
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t.Errorf("scanExponent%+v\n\tgot z = %v; want %v", a, x, a.x)
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}
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if b != a.b {
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t.Errorf("scanExponent%+v\n\tgot b = %d; want %d", a, b, a.b)
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}
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next, _, err := r.ReadRune()
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if err == io.EOF {
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next = 0
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err = nil
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}
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if err == nil && next != a.next {
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t.Errorf("scanExponent%+v\n\tgot next = %q; want %q", a, next, a.next)
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}
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}
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}
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type StringTest struct {
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in, out string
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ok bool
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}
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var setStringTests = []StringTest{
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// invalid
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{in: "1e"},
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{in: "1.e"},
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{in: "1e+14e-5"},
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{in: "1e4.5"},
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{in: "r"},
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{in: "a/b"},
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{in: "a.b"},
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{in: "1/0"},
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{in: "4/3/2"}, // issue 17001
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{in: "4/3/"},
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{in: "4/3."},
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{in: "4/"},
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{in: "13e-9223372036854775808"}, // CVE-2022-23772
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// valid
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{"0", "0", true},
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{"-0", "0", true},
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{"1", "1", true},
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{"-1", "-1", true},
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{"1.", "1", true},
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{"1e0", "1", true},
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{"1.e1", "10", true},
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{"-0.1", "-1/10", true},
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{"-.1", "-1/10", true},
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{"2/4", "1/2", true},
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{".25", "1/4", true},
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{"-1/5", "-1/5", true},
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{"8129567.7690E14", "812956776900000000000", true},
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{"78189e+4", "781890000", true},
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{"553019.8935e+8", "55301989350000", true},
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{"98765432109876543210987654321e-10", "98765432109876543210987654321/10000000000", true},
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{"9877861857500000E-7", "3951144743/4", true},
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{"2169378.417e-3", "2169378417/1000000", true},
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{"884243222337379604041632732738665534", "884243222337379604041632732738665534", true},
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{"53/70893980658822810696", "53/70893980658822810696", true},
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{"106/141787961317645621392", "53/70893980658822810696", true},
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{"204211327800791583.81095", "4084226556015831676219/20000", true},
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{"0e9999999999", "0", true}, // issue #16176
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}
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// These are not supported by fmt.Fscanf.
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var setStringTests2 = []StringTest{
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// invalid
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{in: "4/3x"},
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{in: "0/-1"},
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{in: "-1/-1"},
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// invalid with separators
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// (smoke tests only - a comprehensive set of tests is in natconv_test.go)
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{in: "10_/1"},
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{in: "_10/1"},
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{in: "1/1__0"},
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// valid
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{"0b1000/3", "8/3", true},
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{"0B1000/0x8", "1", true},
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{"-010/1", "-8", true}, // 0-prefix indicates octal in this case
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{"-010.0", "-10", true},
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{"-0o10/1", "-8", true},
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{"0x10/1", "16", true},
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{"0x10/0x20", "1/2", true},
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{"0010", "10", true}, // 0-prefix is ignored in this case (not a fraction)
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{"0x10.0", "16", true},
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{"0x1.8", "3/2", true},
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{"0X1.8p4", "24", true},
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{"0x1.1E2", "2289/2048", true}, // E is part of hex mantissa, not exponent
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{"0b1.1E2", "150", true},
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{"0B1.1P3", "12", true},
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{"0o10e-2", "2/25", true},
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{"0O10p-3", "1", true},
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// valid with separators
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// (smoke tests only - a comprehensive set of tests is in natconv_test.go)
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{"0b_1000/3", "8/3", true},
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{"0B_10_00/0x8", "1", true},
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{"0xdead/0B1101_1110_1010_1101", "1", true},
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{"0B1101_1110_1010_1101/0XD_E_A_D", "1", true},
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{"1_000.0", "1000", true},
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{"0x_10.0", "16", true},
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{"0x1_0.0", "16", true},
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{"0x1.8_0", "3/2", true},
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{"0X1.8p0_4", "24", true},
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{"0b1.1_0E2", "150", true},
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{"0o1_0e-2", "2/25", true},
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{"0O_10p-3", "1", true},
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}
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func TestRatSetString(t *testing.T) {
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var tests []StringTest
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tests = append(tests, setStringTests...)
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tests = append(tests, setStringTests2...)
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for i, test := range tests {
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x, ok := new(Rat).SetString(test.in)
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if ok {
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if !test.ok {
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t.Errorf("#%d SetString(%q) expected failure", i, test.in)
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} else if x.RatString() != test.out {
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t.Errorf("#%d SetString(%q) got %s want %s", i, test.in, x.RatString(), test.out)
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}
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} else {
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if test.ok {
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t.Errorf("#%d SetString(%q) expected success", i, test.in)
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} else if x != nil {
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t.Errorf("#%d SetString(%q) got %p want nil", i, test.in, x)
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}
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}
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}
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}
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func TestRatScan(t *testing.T) {
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var buf bytes.Buffer
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for i, test := range setStringTests {
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x := new(Rat)
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buf.Reset()
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buf.WriteString(test.in)
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_, err := fmt.Fscanf(&buf, "%v", x)
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if err == nil != test.ok {
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if test.ok {
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t.Errorf("#%d (%s) error: %s", i, test.in, err)
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} else {
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t.Errorf("#%d (%s) expected error", i, test.in)
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}
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continue
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}
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if err == nil && x.RatString() != test.out {
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t.Errorf("#%d got %s want %s", i, x.RatString(), test.out)
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}
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}
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}
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var floatStringTests = []struct {
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in string
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prec int
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out string
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}{
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{"0", 0, "0"},
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{"0", 4, "0.0000"},
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{"1", 0, "1"},
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{"1", 2, "1.00"},
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{"-1", 0, "-1"},
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{"0.05", 1, "0.1"},
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{"-0.05", 1, "-0.1"},
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{".25", 2, "0.25"},
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{".25", 1, "0.3"},
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{".25", 3, "0.250"},
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{"-1/3", 3, "-0.333"},
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{"-2/3", 4, "-0.6667"},
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{"0.96", 1, "1.0"},
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{"0.999", 2, "1.00"},
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{"0.9", 0, "1"},
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{".25", -1, "0"},
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{".55", -1, "1"},
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}
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func TestFloatString(t *testing.T) {
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for i, test := range floatStringTests {
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x, _ := new(Rat).SetString(test.in)
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if x.FloatString(test.prec) != test.out {
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t.Errorf("#%d got %s want %s", i, x.FloatString(test.prec), test.out)
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}
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}
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}
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// Test inputs to Rat.SetString. The prefix "long:" causes the test
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// to be skipped except in -long mode. (The threshold is about 500us.)
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var float64inputs = []string{
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// Constants plundered from strconv/testfp.txt.
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// Table 1: Stress Inputs for Conversion to 53-bit Binary, < 1/2 ULP
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"5e+125",
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"69e+267",
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"999e-026",
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"7861e-034",
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"75569e-254",
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"928609e-261",
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"9210917e+080",
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"84863171e+114",
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"653777767e+273",
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"5232604057e-298",
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"27235667517e-109",
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"653532977297e-123",
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"3142213164987e-294",
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"46202199371337e-072",
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"231010996856685e-073",
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"9324754620109615e+212",
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"78459735791271921e+049",
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"272104041512242479e+200",
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"6802601037806061975e+198",
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"20505426358836677347e-221",
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"836168422905420598437e-234",
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"4891559871276714924261e+222",
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// Table 2: Stress Inputs for Conversion to 53-bit Binary, > 1/2 ULP
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"9e-265",
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"85e-037",
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"623e+100",
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"3571e+263",
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"81661e+153",
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"920657e-023",
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"4603285e-024",
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"87575437e-309",
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"245540327e+122",
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"6138508175e+120",
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"83356057653e+193",
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"619534293513e+124",
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"2335141086879e+218",
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"36167929443327e-159",
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"609610927149051e-255",
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"3743626360493413e-165",
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"94080055902682397e-242",
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"899810892172646163e+283",
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"7120190517612959703e+120",
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"25188282901709339043e-252",
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"308984926168550152811e-052",
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"6372891218502368041059e+064",
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// Table 14: Stress Inputs for Conversion to 24-bit Binary, <1/2 ULP
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"5e-20",
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"67e+14",
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"985e+15",
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"7693e-42",
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"55895e-16",
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"996622e-44",
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"7038531e-32",
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"60419369e-46",
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"702990899e-20",
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"6930161142e-48",
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"25933168707e+13",
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"596428896559e+20",
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// Table 15: Stress Inputs for Conversion to 24-bit Binary, >1/2 ULP
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"3e-23",
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"57e+18",
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"789e-35",
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"2539e-18",
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"76173e+28",
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"887745e-11",
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"5382571e-37",
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"82381273e-35",
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"750486563e-38",
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"3752432815e-39",
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"75224575729e-45",
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"459926601011e+15",
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// Constants plundered from strconv/atof_test.go.
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"0",
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"1",
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"+1",
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"1e23",
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"1E23",
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"100000000000000000000000",
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"1e-100",
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"123456700",
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"99999999999999974834176",
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"100000000000000000000001",
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"100000000000000008388608",
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"100000000000000016777215",
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"100000000000000016777216",
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"-1",
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"-0.1",
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"-0", // NB: exception made for this input
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"1e-20",
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"625e-3",
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// largest float64
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"1.7976931348623157e308",
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"-1.7976931348623157e308",
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// next float64 - too large
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"1.7976931348623159e308",
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"-1.7976931348623159e308",
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// the border is ...158079
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// borderline - okay
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"1.7976931348623158e308",
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"-1.7976931348623158e308",
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// borderline - too large
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"1.797693134862315808e308",
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"-1.797693134862315808e308",
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// a little too large
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"1e308",
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"2e308",
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"1e309",
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// way too large
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"1e310",
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"-1e310",
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"1e400",
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"-1e400",
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"long:1e400000",
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"long:-1e400000",
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// denormalized
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"1e-305",
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"1e-306",
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"1e-307",
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"1e-308",
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||
|
"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)
|
||
|
}
|
||
|
}
|
||
|
}
|
||
|
|
||
|
func TestIssue45910(t *testing.T) {
|
||
|
var x Rat
|
||
|
for _, test := range []struct {
|
||
|
input string
|
||
|
want bool
|
||
|
}{
|
||
|
{"1e-1000001", false},
|
||
|
{"1e-1000000", true},
|
||
|
{"1e+1000000", true},
|
||
|
{"1e+1000001", false},
|
||
|
|
||
|
{"0p1000000000000", true},
|
||
|
{"1p-10000001", false},
|
||
|
{"1p-10000000", true},
|
||
|
{"1p+10000000", true},
|
||
|
{"1p+10000001", false},
|
||
|
{"1.770p02041010010011001001", false}, // test case from issue
|
||
|
} {
|
||
|
_, got := x.SetString(test.input)
|
||
|
if got != test.want {
|
||
|
t.Errorf("SetString(%s) got ok = %v; want %v", test.input, got, test.want)
|
||
|
}
|
||
|
}
|
||
|
}
|