1765 lines
50 KiB
Go
1765 lines
50 KiB
Go
// Copyright 2014 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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"fmt"
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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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// Verify that ErrNaN implements the error interface.
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var _ error = ErrNaN{}
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func (x *Float) uint64() uint64 {
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u, acc := x.Uint64()
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if acc != Exact {
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panic(fmt.Sprintf("%s is not a uint64", x.Text('g', 10)))
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}
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return u
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}
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func (x *Float) int64() int64 {
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i, acc := x.Int64()
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if acc != Exact {
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panic(fmt.Sprintf("%s is not an int64", x.Text('g', 10)))
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}
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return i
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}
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func TestFloatZeroValue(t *testing.T) {
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// zero (uninitialized) value is a ready-to-use 0.0
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var x Float
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if s := x.Text('f', 1); s != "0.0" {
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t.Errorf("zero value = %s; want 0.0", s)
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}
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// zero value has precision 0
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if prec := x.Prec(); prec != 0 {
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t.Errorf("prec = %d; want 0", prec)
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}
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// zero value can be used in any and all positions of binary operations
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make := func(x int) *Float {
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var f Float
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if x != 0 {
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f.SetInt64(int64(x))
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}
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// x == 0 translates into the zero value
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return &f
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}
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for _, test := range []struct {
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z, x, y, want int
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opname rune
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op func(z, x, y *Float) *Float
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}{
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{0, 0, 0, 0, '+', (*Float).Add},
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{0, 1, 2, 3, '+', (*Float).Add},
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{1, 2, 0, 2, '+', (*Float).Add},
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{2, 0, 1, 1, '+', (*Float).Add},
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{0, 0, 0, 0, '-', (*Float).Sub},
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{0, 1, 2, -1, '-', (*Float).Sub},
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{1, 2, 0, 2, '-', (*Float).Sub},
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{2, 0, 1, -1, '-', (*Float).Sub},
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{0, 0, 0, 0, '*', (*Float).Mul},
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{0, 1, 2, 2, '*', (*Float).Mul},
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{1, 2, 0, 0, '*', (*Float).Mul},
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{2, 0, 1, 0, '*', (*Float).Mul},
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// {0, 0, 0, 0, '/', (*Float).Quo}, // panics
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{0, 2, 1, 2, '/', (*Float).Quo},
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{1, 2, 0, 0, '/', (*Float).Quo}, // = +Inf
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{2, 0, 1, 0, '/', (*Float).Quo},
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} {
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z := make(test.z)
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test.op(z, make(test.x), make(test.y))
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got := 0
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if !z.IsInf() {
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got = int(z.int64())
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}
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if got != test.want {
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t.Errorf("%d %c %d = %d; want %d", test.x, test.opname, test.y, got, test.want)
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}
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}
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// TODO(gri) test how precision is set for zero value results
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}
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func makeFloat(s string) *Float {
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x, _, err := ParseFloat(s, 0, 1000, ToNearestEven)
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if err != nil {
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panic(err)
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}
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return x
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}
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func TestFloatSetPrec(t *testing.T) {
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for _, test := range []struct {
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x string
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prec uint
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want string
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acc Accuracy
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}{
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// prec 0
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{"0", 0, "0", Exact},
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{"-0", 0, "-0", Exact},
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{"-Inf", 0, "-Inf", Exact},
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{"+Inf", 0, "+Inf", Exact},
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{"123", 0, "0", Below},
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{"-123", 0, "-0", Above},
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// prec at upper limit
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{"0", MaxPrec, "0", Exact},
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{"-0", MaxPrec, "-0", Exact},
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{"-Inf", MaxPrec, "-Inf", Exact},
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{"+Inf", MaxPrec, "+Inf", Exact},
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// just a few regular cases - general rounding is tested elsewhere
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{"1.5", 1, "2", Above},
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{"-1.5", 1, "-2", Below},
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{"123", 1e6, "123", Exact},
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{"-123", 1e6, "-123", Exact},
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} {
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x := makeFloat(test.x).SetPrec(test.prec)
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prec := test.prec
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if prec > MaxPrec {
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prec = MaxPrec
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}
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if got := x.Prec(); got != prec {
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t.Errorf("%s.SetPrec(%d).Prec() == %d; want %d", test.x, test.prec, got, prec)
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}
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if got, acc := x.String(), x.Acc(); got != test.want || acc != test.acc {
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t.Errorf("%s.SetPrec(%d) = %s (%s); want %s (%s)", test.x, test.prec, got, acc, test.want, test.acc)
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}
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}
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}
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func TestFloatMinPrec(t *testing.T) {
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const max = 100
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for _, test := range []struct {
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x string
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want uint
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}{
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{"0", 0},
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{"-0", 0},
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{"+Inf", 0},
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{"-Inf", 0},
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{"1", 1},
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{"2", 1},
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{"3", 2},
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{"0x8001", 16},
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{"0x8001p-1000", 16},
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{"0x8001p+1000", 16},
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{"0.1", max},
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} {
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x := makeFloat(test.x).SetPrec(max)
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if got := x.MinPrec(); got != test.want {
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t.Errorf("%s.MinPrec() = %d; want %d", test.x, got, test.want)
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}
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}
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}
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func TestFloatSign(t *testing.T) {
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for _, test := range []struct {
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x string
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s int
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}{
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{"-Inf", -1},
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{"-1", -1},
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{"-0", 0},
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{"+0", 0},
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{"+1", +1},
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{"+Inf", +1},
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} {
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x := makeFloat(test.x)
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s := x.Sign()
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if s != test.s {
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t.Errorf("%s.Sign() = %d; want %d", test.x, s, test.s)
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}
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}
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}
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// alike(x, y) is like x.Cmp(y) == 0 but also considers the sign of 0 (0 != -0).
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func alike(x, y *Float) bool {
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return x.Cmp(y) == 0 && x.Signbit() == y.Signbit()
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}
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func alike32(x, y float32) bool {
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// we can ignore NaNs
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return x == y && math.Signbit(float64(x)) == math.Signbit(float64(y))
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}
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func alike64(x, y float64) bool {
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// we can ignore NaNs
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return x == y && math.Signbit(x) == math.Signbit(y)
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}
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func TestFloatMantExp(t *testing.T) {
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for _, test := range []struct {
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x string
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mant string
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exp int
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}{
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{"0", "0", 0},
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{"+0", "0", 0},
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{"-0", "-0", 0},
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{"Inf", "+Inf", 0},
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{"+Inf", "+Inf", 0},
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{"-Inf", "-Inf", 0},
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{"1.5", "0.75", 1},
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{"1.024e3", "0.5", 11},
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{"-0.125", "-0.5", -2},
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} {
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x := makeFloat(test.x)
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mant := makeFloat(test.mant)
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m := new(Float)
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e := x.MantExp(m)
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if !alike(m, mant) || e != test.exp {
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t.Errorf("%s.MantExp() = %s, %d; want %s, %d", test.x, m.Text('g', 10), e, test.mant, test.exp)
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}
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}
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}
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func TestFloatMantExpAliasing(t *testing.T) {
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x := makeFloat("0.5p10")
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if e := x.MantExp(x); e != 10 {
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t.Fatalf("Float.MantExp aliasing error: got %d; want 10", e)
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}
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if want := makeFloat("0.5"); !alike(x, want) {
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t.Fatalf("Float.MantExp aliasing error: got %s; want %s", x.Text('g', 10), want.Text('g', 10))
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}
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}
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func TestFloatSetMantExp(t *testing.T) {
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for _, test := range []struct {
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frac string
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exp int
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z string
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}{
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{"0", 0, "0"},
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{"+0", 0, "0"},
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{"-0", 0, "-0"},
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{"Inf", 1234, "+Inf"},
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{"+Inf", -1234, "+Inf"},
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{"-Inf", -1234, "-Inf"},
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{"0", MinExp, "0"},
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{"0.25", MinExp, "+0"}, // exponent underflow
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{"-0.25", MinExp, "-0"}, // exponent underflow
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{"1", MaxExp, "+Inf"}, // exponent overflow
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{"2", MaxExp - 1, "+Inf"}, // exponent overflow
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{"0.75", 1, "1.5"},
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{"0.5", 11, "1024"},
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{"-0.5", -2, "-0.125"},
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{"32", 5, "1024"},
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{"1024", -10, "1"},
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} {
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frac := makeFloat(test.frac)
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want := makeFloat(test.z)
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var z Float
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z.SetMantExp(frac, test.exp)
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if !alike(&z, want) {
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t.Errorf("SetMantExp(%s, %d) = %s; want %s", test.frac, test.exp, z.Text('g', 10), test.z)
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}
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// test inverse property
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mant := new(Float)
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if z.SetMantExp(mant, want.MantExp(mant)).Cmp(want) != 0 {
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t.Errorf("Inverse property not satisfied: got %s; want %s", z.Text('g', 10), test.z)
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}
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}
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}
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func TestFloatPredicates(t *testing.T) {
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for _, test := range []struct {
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x string
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sign int
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signbit, inf bool
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}{
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{x: "-Inf", sign: -1, signbit: true, inf: true},
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{x: "-1", sign: -1, signbit: true},
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{x: "-0", signbit: true},
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{x: "0"},
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{x: "1", sign: 1},
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{x: "+Inf", sign: 1, inf: true},
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} {
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x := makeFloat(test.x)
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if got := x.Signbit(); got != test.signbit {
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t.Errorf("(%s).Signbit() = %v; want %v", test.x, got, test.signbit)
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}
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if got := x.Sign(); got != test.sign {
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t.Errorf("(%s).Sign() = %d; want %d", test.x, got, test.sign)
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}
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if got := x.IsInf(); got != test.inf {
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t.Errorf("(%s).IsInf() = %v; want %v", test.x, got, test.inf)
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}
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}
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}
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func TestFloatIsInt(t *testing.T) {
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for _, test := range []string{
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"0 int",
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"-0 int",
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"1 int",
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"-1 int",
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"0.5",
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"1.23",
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"1.23e1",
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"1.23e2 int",
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"0.000000001e+8",
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"0.000000001e+9 int",
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"1.2345e200 int",
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"Inf",
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"+Inf",
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"-Inf",
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} {
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s := strings.TrimSuffix(test, " int")
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want := s != test
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if got := makeFloat(s).IsInt(); got != want {
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t.Errorf("%s.IsInt() == %t", s, got)
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}
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}
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}
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func fromBinary(s string) int64 {
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x, err := strconv.ParseInt(s, 2, 64)
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if err != nil {
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panic(err)
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}
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return x
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}
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func toBinary(x int64) string {
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return strconv.FormatInt(x, 2)
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}
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func testFloatRound(t *testing.T, x, r int64, prec uint, mode RoundingMode) {
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// verify test data
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var ok bool
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switch mode {
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case ToNearestEven, ToNearestAway:
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ok = true // nothing to do for now
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case ToZero:
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if x < 0 {
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ok = r >= x
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} else {
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ok = r <= x
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}
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case AwayFromZero:
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if x < 0 {
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ok = r <= x
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} else {
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ok = r >= x
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}
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case ToNegativeInf:
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ok = r <= x
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case ToPositiveInf:
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ok = r >= x
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default:
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panic("unreachable")
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}
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if !ok {
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t.Fatalf("incorrect test data for prec = %d, %s: x = %s, r = %s", prec, mode, toBinary(x), toBinary(r))
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}
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// compute expected accuracy
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a := Exact
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switch {
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case r < x:
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a = Below
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case r > x:
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a = Above
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}
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// round
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f := new(Float).SetMode(mode).SetInt64(x).SetPrec(prec)
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// check result
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r1 := f.int64()
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p1 := f.Prec()
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a1 := f.Acc()
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if r1 != r || p1 != prec || a1 != a {
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t.Errorf("round %s (%d bits, %s) incorrect: got %s (%d bits, %s); want %s (%d bits, %s)",
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toBinary(x), prec, mode,
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toBinary(r1), p1, a1,
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toBinary(r), prec, a)
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return
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}
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// g and f should be the same
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// (rounding by SetPrec after SetInt64 using default precision
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// should be the same as rounding by SetInt64 after setting the
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// precision)
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g := new(Float).SetMode(mode).SetPrec(prec).SetInt64(x)
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if !alike(g, f) {
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t.Errorf("round %s (%d bits, %s) not symmetric: got %s and %s; want %s",
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toBinary(x), prec, mode,
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toBinary(g.int64()),
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toBinary(r1),
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toBinary(r),
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)
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return
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}
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// h and f should be the same
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// (repeated rounding should be idempotent)
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h := new(Float).SetMode(mode).SetPrec(prec).Set(f)
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if !alike(h, f) {
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t.Errorf("round %s (%d bits, %s) not idempotent: got %s and %s; want %s",
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toBinary(x), prec, mode,
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toBinary(h.int64()),
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toBinary(r1),
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toBinary(r),
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)
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return
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}
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}
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// TestFloatRound tests basic rounding.
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func TestFloatRound(t *testing.T) {
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for _, test := range []struct {
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prec uint
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x, zero, neven, naway, away string // input, results rounded to prec bits
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}{
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{5, "1000", "1000", "1000", "1000", "1000"},
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{5, "1001", "1001", "1001", "1001", "1001"},
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{5, "1010", "1010", "1010", "1010", "1010"},
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{5, "1011", "1011", "1011", "1011", "1011"},
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{5, "1100", "1100", "1100", "1100", "1100"},
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{5, "1101", "1101", "1101", "1101", "1101"},
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{5, "1110", "1110", "1110", "1110", "1110"},
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{5, "1111", "1111", "1111", "1111", "1111"},
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{4, "1000", "1000", "1000", "1000", "1000"},
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{4, "1001", "1001", "1001", "1001", "1001"},
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{4, "1010", "1010", "1010", "1010", "1010"},
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{4, "1011", "1011", "1011", "1011", "1011"},
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{4, "1100", "1100", "1100", "1100", "1100"},
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{4, "1101", "1101", "1101", "1101", "1101"},
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{4, "1110", "1110", "1110", "1110", "1110"},
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{4, "1111", "1111", "1111", "1111", "1111"},
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{3, "1000", "1000", "1000", "1000", "1000"},
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{3, "1001", "1000", "1000", "1010", "1010"},
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{3, "1010", "1010", "1010", "1010", "1010"},
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{3, "1011", "1010", "1100", "1100", "1100"},
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{3, "1100", "1100", "1100", "1100", "1100"},
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{3, "1101", "1100", "1100", "1110", "1110"},
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{3, "1110", "1110", "1110", "1110", "1110"},
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{3, "1111", "1110", "10000", "10000", "10000"},
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{3, "1000001", "1000000", "1000000", "1000000", "1010000"},
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{3, "1001001", "1000000", "1010000", "1010000", "1010000"},
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{3, "1010001", "1010000", "1010000", "1010000", "1100000"},
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{3, "1011001", "1010000", "1100000", "1100000", "1100000"},
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{3, "1100001", "1100000", "1100000", "1100000", "1110000"},
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{3, "1101001", "1100000", "1110000", "1110000", "1110000"},
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{3, "1110001", "1110000", "1110000", "1110000", "10000000"},
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{3, "1111001", "1110000", "10000000", "10000000", "10000000"},
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{2, "1000", "1000", "1000", "1000", "1000"},
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{2, "1001", "1000", "1000", "1000", "1100"},
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{2, "1010", "1000", "1000", "1100", "1100"},
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{2, "1011", "1000", "1100", "1100", "1100"},
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{2, "1100", "1100", "1100", "1100", "1100"},
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{2, "1101", "1100", "1100", "1100", "10000"},
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{2, "1110", "1100", "10000", "10000", "10000"},
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{2, "1111", "1100", "10000", "10000", "10000"},
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{2, "1000001", "1000000", "1000000", "1000000", "1100000"},
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{2, "1001001", "1000000", "1000000", "1000000", "1100000"},
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{2, "1010001", "1000000", "1100000", "1100000", "1100000"},
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{2, "1011001", "1000000", "1100000", "1100000", "1100000"},
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{2, "1100001", "1100000", "1100000", "1100000", "10000000"},
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{2, "1101001", "1100000", "1100000", "1100000", "10000000"},
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{2, "1110001", "1100000", "10000000", "10000000", "10000000"},
|
|
{2, "1111001", "1100000", "10000000", "10000000", "10000000"},
|
|
|
|
{1, "1000", "1000", "1000", "1000", "1000"},
|
|
{1, "1001", "1000", "1000", "1000", "10000"},
|
|
{1, "1010", "1000", "1000", "1000", "10000"},
|
|
{1, "1011", "1000", "1000", "1000", "10000"},
|
|
{1, "1100", "1000", "10000", "10000", "10000"},
|
|
{1, "1101", "1000", "10000", "10000", "10000"},
|
|
{1, "1110", "1000", "10000", "10000", "10000"},
|
|
{1, "1111", "1000", "10000", "10000", "10000"},
|
|
|
|
{1, "1000001", "1000000", "1000000", "1000000", "10000000"},
|
|
{1, "1001001", "1000000", "1000000", "1000000", "10000000"},
|
|
{1, "1010001", "1000000", "1000000", "1000000", "10000000"},
|
|
{1, "1011001", "1000000", "1000000", "1000000", "10000000"},
|
|
{1, "1100001", "1000000", "10000000", "10000000", "10000000"},
|
|
{1, "1101001", "1000000", "10000000", "10000000", "10000000"},
|
|
{1, "1110001", "1000000", "10000000", "10000000", "10000000"},
|
|
{1, "1111001", "1000000", "10000000", "10000000", "10000000"},
|
|
} {
|
|
x := fromBinary(test.x)
|
|
z := fromBinary(test.zero)
|
|
e := fromBinary(test.neven)
|
|
n := fromBinary(test.naway)
|
|
a := fromBinary(test.away)
|
|
prec := test.prec
|
|
|
|
testFloatRound(t, x, z, prec, ToZero)
|
|
testFloatRound(t, x, e, prec, ToNearestEven)
|
|
testFloatRound(t, x, n, prec, ToNearestAway)
|
|
testFloatRound(t, x, a, prec, AwayFromZero)
|
|
|
|
testFloatRound(t, x, z, prec, ToNegativeInf)
|
|
testFloatRound(t, x, a, prec, ToPositiveInf)
|
|
|
|
testFloatRound(t, -x, -a, prec, ToNegativeInf)
|
|
testFloatRound(t, -x, -z, prec, ToPositiveInf)
|
|
}
|
|
}
|
|
|
|
// TestFloatRound24 tests that rounding a float64 to 24 bits
|
|
// matches IEEE-754 rounding to nearest when converting a
|
|
// float64 to a float32 (excluding denormal numbers).
|
|
func TestFloatRound24(t *testing.T) {
|
|
const x0 = 1<<26 - 0x10 // 11...110000 (26 bits)
|
|
for d := 0; d <= 0x10; d++ {
|
|
x := float64(x0 + d)
|
|
f := new(Float).SetPrec(24).SetFloat64(x)
|
|
got, _ := f.Float32()
|
|
want := float32(x)
|
|
if got != want {
|
|
t.Errorf("Round(%g, 24) = %g; want %g", x, got, want)
|
|
}
|
|
}
|
|
}
|
|
|
|
func TestFloatSetUint64(t *testing.T) {
|
|
for _, want := range []uint64{
|
|
0,
|
|
1,
|
|
2,
|
|
10,
|
|
100,
|
|
1<<32 - 1,
|
|
1 << 32,
|
|
1<<64 - 1,
|
|
} {
|
|
var f Float
|
|
f.SetUint64(want)
|
|
if got := f.uint64(); got != want {
|
|
t.Errorf("got %#x (%s); want %#x", got, f.Text('p', 0), want)
|
|
}
|
|
}
|
|
|
|
// test basic rounding behavior (exhaustive rounding testing is done elsewhere)
|
|
const x uint64 = 0x8765432187654321 // 64 bits needed
|
|
for prec := uint(1); prec <= 64; prec++ {
|
|
f := new(Float).SetPrec(prec).SetMode(ToZero).SetUint64(x)
|
|
got := f.uint64()
|
|
want := x &^ (1<<(64-prec) - 1) // cut off (round to zero) low 64-prec bits
|
|
if got != want {
|
|
t.Errorf("got %#x (%s); want %#x", got, f.Text('p', 0), want)
|
|
}
|
|
}
|
|
}
|
|
|
|
func TestFloatSetInt64(t *testing.T) {
|
|
for _, want := range []int64{
|
|
0,
|
|
1,
|
|
2,
|
|
10,
|
|
100,
|
|
1<<32 - 1,
|
|
1 << 32,
|
|
1<<63 - 1,
|
|
} {
|
|
for i := range [2]int{} {
|
|
if i&1 != 0 {
|
|
want = -want
|
|
}
|
|
var f Float
|
|
f.SetInt64(want)
|
|
if got := f.int64(); got != want {
|
|
t.Errorf("got %#x (%s); want %#x", got, f.Text('p', 0), want)
|
|
}
|
|
}
|
|
}
|
|
|
|
// test basic rounding behavior (exhaustive rounding testing is done elsewhere)
|
|
const x int64 = 0x7654321076543210 // 63 bits needed
|
|
for prec := uint(1); prec <= 63; prec++ {
|
|
f := new(Float).SetPrec(prec).SetMode(ToZero).SetInt64(x)
|
|
got := f.int64()
|
|
want := x &^ (1<<(63-prec) - 1) // cut off (round to zero) low 63-prec bits
|
|
if got != want {
|
|
t.Errorf("got %#x (%s); want %#x", got, f.Text('p', 0), want)
|
|
}
|
|
}
|
|
}
|
|
|
|
func TestFloatSetFloat64(t *testing.T) {
|
|
for _, want := range []float64{
|
|
0,
|
|
1,
|
|
2,
|
|
12345,
|
|
1e10,
|
|
1e100,
|
|
3.14159265e10,
|
|
2.718281828e-123,
|
|
1.0 / 3,
|
|
math.MaxFloat32,
|
|
math.MaxFloat64,
|
|
math.SmallestNonzeroFloat32,
|
|
math.SmallestNonzeroFloat64,
|
|
math.Inf(-1),
|
|
math.Inf(0),
|
|
-math.Inf(1),
|
|
} {
|
|
for i := range [2]int{} {
|
|
if i&1 != 0 {
|
|
want = -want
|
|
}
|
|
var f Float
|
|
f.SetFloat64(want)
|
|
if got, acc := f.Float64(); got != want || acc != Exact {
|
|
t.Errorf("got %g (%s, %s); want %g (Exact)", got, f.Text('p', 0), acc, want)
|
|
}
|
|
}
|
|
}
|
|
|
|
// test basic rounding behavior (exhaustive rounding testing is done elsewhere)
|
|
const x uint64 = 0x8765432143218 // 53 bits needed
|
|
for prec := uint(1); prec <= 52; prec++ {
|
|
f := new(Float).SetPrec(prec).SetMode(ToZero).SetFloat64(float64(x))
|
|
got, _ := f.Float64()
|
|
want := float64(x &^ (1<<(52-prec) - 1)) // cut off (round to zero) low 53-prec bits
|
|
if got != want {
|
|
t.Errorf("got %g (%s); want %g", got, f.Text('p', 0), want)
|
|
}
|
|
}
|
|
|
|
// test NaN
|
|
defer func() {
|
|
if p, ok := recover().(ErrNaN); !ok {
|
|
t.Errorf("got %v; want ErrNaN panic", p)
|
|
}
|
|
}()
|
|
var f Float
|
|
f.SetFloat64(math.NaN())
|
|
// should not reach here
|
|
t.Errorf("got %s; want ErrNaN panic", f.Text('p', 0))
|
|
}
|
|
|
|
func TestFloatSetInt(t *testing.T) {
|
|
for _, want := range []string{
|
|
"0",
|
|
"1",
|
|
"-1",
|
|
"1234567890",
|
|
"123456789012345678901234567890",
|
|
"123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890",
|
|
} {
|
|
var x Int
|
|
_, ok := x.SetString(want, 0)
|
|
if !ok {
|
|
t.Errorf("invalid integer %s", want)
|
|
continue
|
|
}
|
|
n := x.BitLen()
|
|
|
|
var f Float
|
|
f.SetInt(&x)
|
|
|
|
// check precision
|
|
if n < 64 {
|
|
n = 64
|
|
}
|
|
if prec := f.Prec(); prec != uint(n) {
|
|
t.Errorf("got prec = %d; want %d", prec, n)
|
|
}
|
|
|
|
// check value
|
|
got := f.Text('g', 100)
|
|
if got != want {
|
|
t.Errorf("got %s (%s); want %s", got, f.Text('p', 0), want)
|
|
}
|
|
}
|
|
|
|
// TODO(gri) test basic rounding behavior
|
|
}
|
|
|
|
func TestFloatSetRat(t *testing.T) {
|
|
for _, want := range []string{
|
|
"0",
|
|
"1",
|
|
"-1",
|
|
"1234567890",
|
|
"123456789012345678901234567890",
|
|
"123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890",
|
|
"1.2",
|
|
"3.14159265",
|
|
// TODO(gri) expand
|
|
} {
|
|
var x Rat
|
|
_, ok := x.SetString(want)
|
|
if !ok {
|
|
t.Errorf("invalid fraction %s", want)
|
|
continue
|
|
}
|
|
n := max(x.Num().BitLen(), x.Denom().BitLen())
|
|
|
|
var f1, f2 Float
|
|
f2.SetPrec(1000)
|
|
f1.SetRat(&x)
|
|
f2.SetRat(&x)
|
|
|
|
// check precision when set automatically
|
|
if n < 64 {
|
|
n = 64
|
|
}
|
|
if prec := f1.Prec(); prec != uint(n) {
|
|
t.Errorf("got prec = %d; want %d", prec, n)
|
|
}
|
|
|
|
got := f2.Text('g', 100)
|
|
if got != want {
|
|
t.Errorf("got %s (%s); want %s", got, f2.Text('p', 0), want)
|
|
}
|
|
}
|
|
}
|
|
|
|
func TestFloatSetInf(t *testing.T) {
|
|
var f Float
|
|
for _, test := range []struct {
|
|
signbit bool
|
|
prec uint
|
|
want string
|
|
}{
|
|
{false, 0, "+Inf"},
|
|
{true, 0, "-Inf"},
|
|
{false, 10, "+Inf"},
|
|
{true, 30, "-Inf"},
|
|
} {
|
|
x := f.SetPrec(test.prec).SetInf(test.signbit)
|
|
if got := x.String(); got != test.want || x.Prec() != test.prec {
|
|
t.Errorf("SetInf(%v) = %s (prec = %d); want %s (prec = %d)", test.signbit, got, x.Prec(), test.want, test.prec)
|
|
}
|
|
}
|
|
}
|
|
|
|
func TestFloatUint64(t *testing.T) {
|
|
for _, test := range []struct {
|
|
x string
|
|
out uint64
|
|
acc Accuracy
|
|
}{
|
|
{"-Inf", 0, Above},
|
|
{"-1", 0, Above},
|
|
{"-1e-1000", 0, Above},
|
|
{"-0", 0, Exact},
|
|
{"0", 0, Exact},
|
|
{"1e-1000", 0, Below},
|
|
{"1", 1, Exact},
|
|
{"1.000000000000000000001", 1, Below},
|
|
{"12345.0", 12345, Exact},
|
|
{"12345.000000000000000000001", 12345, Below},
|
|
{"18446744073709551615", 18446744073709551615, Exact},
|
|
{"18446744073709551615.000000000000000000001", math.MaxUint64, Below},
|
|
{"18446744073709551616", math.MaxUint64, Below},
|
|
{"1e10000", math.MaxUint64, Below},
|
|
{"+Inf", math.MaxUint64, Below},
|
|
} {
|
|
x := makeFloat(test.x)
|
|
out, acc := x.Uint64()
|
|
if out != test.out || acc != test.acc {
|
|
t.Errorf("%s: got %d (%s); want %d (%s)", test.x, out, acc, test.out, test.acc)
|
|
}
|
|
}
|
|
}
|
|
|
|
func TestFloatInt64(t *testing.T) {
|
|
for _, test := range []struct {
|
|
x string
|
|
out int64
|
|
acc Accuracy
|
|
}{
|
|
{"-Inf", math.MinInt64, Above},
|
|
{"-1e10000", math.MinInt64, Above},
|
|
{"-9223372036854775809", math.MinInt64, Above},
|
|
{"-9223372036854775808.000000000000000000001", math.MinInt64, Above},
|
|
{"-9223372036854775808", -9223372036854775808, Exact},
|
|
{"-9223372036854775807.000000000000000000001", -9223372036854775807, Above},
|
|
{"-9223372036854775807", -9223372036854775807, Exact},
|
|
{"-12345.000000000000000000001", -12345, Above},
|
|
{"-12345.0", -12345, Exact},
|
|
{"-1.000000000000000000001", -1, Above},
|
|
{"-1.5", -1, Above},
|
|
{"-1", -1, Exact},
|
|
{"-1e-1000", 0, Above},
|
|
{"0", 0, Exact},
|
|
{"1e-1000", 0, Below},
|
|
{"1", 1, Exact},
|
|
{"1.000000000000000000001", 1, Below},
|
|
{"1.5", 1, Below},
|
|
{"12345.0", 12345, Exact},
|
|
{"12345.000000000000000000001", 12345, Below},
|
|
{"9223372036854775807", 9223372036854775807, Exact},
|
|
{"9223372036854775807.000000000000000000001", math.MaxInt64, Below},
|
|
{"9223372036854775808", math.MaxInt64, Below},
|
|
{"1e10000", math.MaxInt64, Below},
|
|
{"+Inf", math.MaxInt64, Below},
|
|
} {
|
|
x := makeFloat(test.x)
|
|
out, acc := x.Int64()
|
|
if out != test.out || acc != test.acc {
|
|
t.Errorf("%s: got %d (%s); want %d (%s)", test.x, out, acc, test.out, test.acc)
|
|
}
|
|
}
|
|
}
|
|
|
|
func TestFloatFloat32(t *testing.T) {
|
|
for _, test := range []struct {
|
|
x string
|
|
out float32
|
|
acc Accuracy
|
|
}{
|
|
{"0", 0, Exact},
|
|
|
|
// underflow to zero
|
|
{"1e-1000", 0, Below},
|
|
{"0x0.000002p-127", 0, Below},
|
|
{"0x.0000010p-126", 0, Below},
|
|
|
|
// denormals
|
|
{"1.401298464e-45", math.SmallestNonzeroFloat32, Above}, // rounded up to smallest denormal
|
|
{"0x.ffffff8p-149", math.SmallestNonzeroFloat32, Above}, // rounded up to smallest denormal
|
|
{"0x.0000018p-126", math.SmallestNonzeroFloat32, Above}, // rounded up to smallest denormal
|
|
{"0x.0000020p-126", math.SmallestNonzeroFloat32, Exact},
|
|
{"0x.8p-148", math.SmallestNonzeroFloat32, Exact},
|
|
{"1p-149", math.SmallestNonzeroFloat32, Exact},
|
|
{"0x.fffffep-126", math.Float32frombits(0x7fffff), Exact}, // largest denormal
|
|
|
|
// special denormal cases (see issues 14553, 14651)
|
|
{"0x0.0000001p-126", math.Float32frombits(0x00000000), Below}, // underflow to zero
|
|
{"0x0.0000008p-126", math.Float32frombits(0x00000000), Below}, // underflow to zero
|
|
{"0x0.0000010p-126", math.Float32frombits(0x00000000), Below}, // rounded down to even
|
|
{"0x0.0000011p-126", math.Float32frombits(0x00000001), Above}, // rounded up to smallest denormal
|
|
{"0x0.0000018p-126", math.Float32frombits(0x00000001), Above}, // rounded up to smallest denormal
|
|
|
|
{"0x1.0000000p-149", math.Float32frombits(0x00000001), Exact}, // smallest denormal
|
|
{"0x0.0000020p-126", math.Float32frombits(0x00000001), Exact}, // smallest denormal
|
|
{"0x0.fffffe0p-126", math.Float32frombits(0x007fffff), Exact}, // largest denormal
|
|
{"0x1.0000000p-126", math.Float32frombits(0x00800000), Exact}, // smallest normal
|
|
|
|
{"0x0.8p-149", math.Float32frombits(0x000000000), Below}, // rounded down to even
|
|
{"0x0.9p-149", math.Float32frombits(0x000000001), Above}, // rounded up to smallest denormal
|
|
{"0x0.ap-149", math.Float32frombits(0x000000001), Above}, // rounded up to smallest denormal
|
|
{"0x0.bp-149", math.Float32frombits(0x000000001), Above}, // rounded up to smallest denormal
|
|
{"0x0.cp-149", math.Float32frombits(0x000000001), Above}, // rounded up to smallest denormal
|
|
|
|
{"0x1.0p-149", math.Float32frombits(0x000000001), Exact}, // smallest denormal
|
|
{"0x1.7p-149", math.Float32frombits(0x000000001), Below},
|
|
{"0x1.8p-149", math.Float32frombits(0x000000002), Above},
|
|
{"0x1.9p-149", math.Float32frombits(0x000000002), Above},
|
|
|
|
{"0x2.0p-149", math.Float32frombits(0x000000002), Exact},
|
|
{"0x2.8p-149", math.Float32frombits(0x000000002), Below}, // rounded down to even
|
|
{"0x2.9p-149", math.Float32frombits(0x000000003), Above},
|
|
|
|
{"0x3.0p-149", math.Float32frombits(0x000000003), Exact},
|
|
{"0x3.7p-149", math.Float32frombits(0x000000003), Below},
|
|
{"0x3.8p-149", math.Float32frombits(0x000000004), Above}, // rounded up to even
|
|
|
|
{"0x4.0p-149", math.Float32frombits(0x000000004), Exact},
|
|
{"0x4.8p-149", math.Float32frombits(0x000000004), Below}, // rounded down to even
|
|
{"0x4.9p-149", math.Float32frombits(0x000000005), Above},
|
|
|
|
// specific case from issue 14553
|
|
{"0x7.7p-149", math.Float32frombits(0x000000007), Below},
|
|
{"0x7.8p-149", math.Float32frombits(0x000000008), Above},
|
|
{"0x7.9p-149", math.Float32frombits(0x000000008), Above},
|
|
|
|
// normals
|
|
{"0x.ffffffp-126", math.Float32frombits(0x00800000), Above}, // rounded up to smallest normal
|
|
{"1p-126", math.Float32frombits(0x00800000), Exact}, // smallest normal
|
|
{"0x1.fffffep-126", math.Float32frombits(0x00ffffff), Exact},
|
|
{"0x1.ffffffp-126", math.Float32frombits(0x01000000), Above}, // rounded up
|
|
{"1", 1, Exact},
|
|
{"1.000000000000000000001", 1, Below},
|
|
{"12345.0", 12345, Exact},
|
|
{"12345.000000000000000000001", 12345, Below},
|
|
{"0x1.fffffe0p127", math.MaxFloat32, Exact},
|
|
{"0x1.fffffe8p127", math.MaxFloat32, Below},
|
|
|
|
// overflow
|
|
{"0x1.ffffff0p127", float32(math.Inf(+1)), Above},
|
|
{"0x1p128", float32(math.Inf(+1)), Above},
|
|
{"1e10000", float32(math.Inf(+1)), Above},
|
|
{"0x1.ffffff0p2147483646", float32(math.Inf(+1)), Above}, // overflow in rounding
|
|
|
|
// inf
|
|
{"Inf", float32(math.Inf(+1)), Exact},
|
|
} {
|
|
for i := 0; i < 2; i++ {
|
|
// test both signs
|
|
tx, tout, tacc := test.x, test.out, test.acc
|
|
if i != 0 {
|
|
tx = "-" + tx
|
|
tout = -tout
|
|
tacc = -tacc
|
|
}
|
|
|
|
// conversion should match strconv where syntax is agreeable
|
|
if f, err := strconv.ParseFloat(tx, 32); err == nil && !alike32(float32(f), tout) {
|
|
t.Errorf("%s: got %g; want %g (incorrect test data)", tx, f, tout)
|
|
}
|
|
|
|
x := makeFloat(tx)
|
|
out, acc := x.Float32()
|
|
if !alike32(out, tout) || acc != tacc {
|
|
t.Errorf("%s: got %g (%#08x, %s); want %g (%#08x, %s)", tx, out, math.Float32bits(out), acc, test.out, math.Float32bits(test.out), tacc)
|
|
}
|
|
|
|
// test that x.SetFloat64(float64(f)).Float32() == f
|
|
var x2 Float
|
|
out2, acc2 := x2.SetFloat64(float64(out)).Float32()
|
|
if !alike32(out2, out) || acc2 != Exact {
|
|
t.Errorf("idempotency test: got %g (%s); want %g (Exact)", out2, acc2, out)
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
func TestFloatFloat64(t *testing.T) {
|
|
const smallestNormalFloat64 = 2.2250738585072014e-308 // 1p-1022
|
|
for _, test := range []struct {
|
|
x string
|
|
out float64
|
|
acc Accuracy
|
|
}{
|
|
{"0", 0, Exact},
|
|
|
|
// underflow to zero
|
|
{"1e-1000", 0, Below},
|
|
{"0x0.0000000000001p-1023", 0, Below},
|
|
{"0x0.00000000000008p-1022", 0, Below},
|
|
|
|
// denormals
|
|
{"0x0.0000000000000cp-1022", math.SmallestNonzeroFloat64, Above}, // rounded up to smallest denormal
|
|
{"0x0.00000000000010p-1022", math.SmallestNonzeroFloat64, Exact}, // smallest denormal
|
|
{"0x.8p-1073", math.SmallestNonzeroFloat64, Exact},
|
|
{"1p-1074", math.SmallestNonzeroFloat64, Exact},
|
|
{"0x.fffffffffffffp-1022", math.Float64frombits(0x000fffffffffffff), Exact}, // largest denormal
|
|
|
|
// special denormal cases (see issues 14553, 14651)
|
|
{"0x0.00000000000001p-1022", math.Float64frombits(0x00000000000000000), Below}, // underflow to zero
|
|
{"0x0.00000000000004p-1022", math.Float64frombits(0x00000000000000000), Below}, // underflow to zero
|
|
{"0x0.00000000000008p-1022", math.Float64frombits(0x00000000000000000), Below}, // rounded down to even
|
|
{"0x0.00000000000009p-1022", math.Float64frombits(0x00000000000000001), Above}, // rounded up to smallest denormal
|
|
{"0x0.0000000000000ap-1022", math.Float64frombits(0x00000000000000001), Above}, // rounded up to smallest denormal
|
|
|
|
{"0x0.8p-1074", math.Float64frombits(0x00000000000000000), Below}, // rounded down to even
|
|
{"0x0.9p-1074", math.Float64frombits(0x00000000000000001), Above}, // rounded up to smallest denormal
|
|
{"0x0.ap-1074", math.Float64frombits(0x00000000000000001), Above}, // rounded up to smallest denormal
|
|
{"0x0.bp-1074", math.Float64frombits(0x00000000000000001), Above}, // rounded up to smallest denormal
|
|
{"0x0.cp-1074", math.Float64frombits(0x00000000000000001), Above}, // rounded up to smallest denormal
|
|
|
|
{"0x1.0p-1074", math.Float64frombits(0x00000000000000001), Exact},
|
|
{"0x1.7p-1074", math.Float64frombits(0x00000000000000001), Below},
|
|
{"0x1.8p-1074", math.Float64frombits(0x00000000000000002), Above},
|
|
{"0x1.9p-1074", math.Float64frombits(0x00000000000000002), Above},
|
|
|
|
{"0x2.0p-1074", math.Float64frombits(0x00000000000000002), Exact},
|
|
{"0x2.8p-1074", math.Float64frombits(0x00000000000000002), Below}, // rounded down to even
|
|
{"0x2.9p-1074", math.Float64frombits(0x00000000000000003), Above},
|
|
|
|
{"0x3.0p-1074", math.Float64frombits(0x00000000000000003), Exact},
|
|
{"0x3.7p-1074", math.Float64frombits(0x00000000000000003), Below},
|
|
{"0x3.8p-1074", math.Float64frombits(0x00000000000000004), Above}, // rounded up to even
|
|
|
|
{"0x4.0p-1074", math.Float64frombits(0x00000000000000004), Exact},
|
|
{"0x4.8p-1074", math.Float64frombits(0x00000000000000004), Below}, // rounded down to even
|
|
{"0x4.9p-1074", math.Float64frombits(0x00000000000000005), Above},
|
|
|
|
// normals
|
|
{"0x.fffffffffffff8p-1022", math.Float64frombits(0x0010000000000000), Above}, // rounded up to smallest normal
|
|
{"1p-1022", math.Float64frombits(0x0010000000000000), Exact}, // smallest normal
|
|
{"1", 1, Exact},
|
|
{"1.000000000000000000001", 1, Below},
|
|
{"12345.0", 12345, Exact},
|
|
{"12345.000000000000000000001", 12345, Below},
|
|
{"0x1.fffffffffffff0p1023", math.MaxFloat64, Exact},
|
|
{"0x1.fffffffffffff4p1023", math.MaxFloat64, Below},
|
|
|
|
// overflow
|
|
{"0x1.fffffffffffff8p1023", math.Inf(+1), Above},
|
|
{"0x1p1024", math.Inf(+1), Above},
|
|
{"1e10000", math.Inf(+1), Above},
|
|
{"0x1.fffffffffffff8p2147483646", math.Inf(+1), Above}, // overflow in rounding
|
|
{"Inf", math.Inf(+1), Exact},
|
|
|
|
// selected denormalized values that were handled incorrectly in the past
|
|
{"0x.fffffffffffffp-1022", smallestNormalFloat64 - math.SmallestNonzeroFloat64, Exact},
|
|
{"4503599627370495p-1074", smallestNormalFloat64 - math.SmallestNonzeroFloat64, Exact},
|
|
|
|
// http://www.exploringbinary.com/php-hangs-on-numeric-value-2-2250738585072011e-308/
|
|
{"2.2250738585072011e-308", 2.225073858507201e-308, Below},
|
|
// http://www.exploringbinary.com/java-hangs-when-converting-2-2250738585072012e-308/
|
|
{"2.2250738585072012e-308", 2.2250738585072014e-308, Above},
|
|
} {
|
|
for i := 0; i < 2; i++ {
|
|
// test both signs
|
|
tx, tout, tacc := test.x, test.out, test.acc
|
|
if i != 0 {
|
|
tx = "-" + tx
|
|
tout = -tout
|
|
tacc = -tacc
|
|
}
|
|
|
|
// conversion should match strconv where syntax is agreeable
|
|
if f, err := strconv.ParseFloat(tx, 64); err == nil && !alike64(f, tout) {
|
|
t.Errorf("%s: got %g; want %g (incorrect test data)", tx, f, tout)
|
|
}
|
|
|
|
x := makeFloat(tx)
|
|
out, acc := x.Float64()
|
|
if !alike64(out, tout) || acc != tacc {
|
|
t.Errorf("%s: got %g (%#016x, %s); want %g (%#016x, %s)", tx, out, math.Float64bits(out), acc, test.out, math.Float64bits(test.out), tacc)
|
|
}
|
|
|
|
// test that x.SetFloat64(f).Float64() == f
|
|
var x2 Float
|
|
out2, acc2 := x2.SetFloat64(out).Float64()
|
|
if !alike64(out2, out) || acc2 != Exact {
|
|
t.Errorf("idempotency test: got %g (%s); want %g (Exact)", out2, acc2, out)
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
func TestFloatInt(t *testing.T) {
|
|
for _, test := range []struct {
|
|
x string
|
|
want string
|
|
acc Accuracy
|
|
}{
|
|
{"0", "0", Exact},
|
|
{"+0", "0", Exact},
|
|
{"-0", "0", Exact},
|
|
{"Inf", "nil", Below},
|
|
{"+Inf", "nil", Below},
|
|
{"-Inf", "nil", Above},
|
|
{"1", "1", Exact},
|
|
{"-1", "-1", Exact},
|
|
{"1.23", "1", Below},
|
|
{"-1.23", "-1", Above},
|
|
{"123e-2", "1", Below},
|
|
{"123e-3", "0", Below},
|
|
{"123e-4", "0", Below},
|
|
{"1e-1000", "0", Below},
|
|
{"-1e-1000", "0", Above},
|
|
{"1e+10", "10000000000", Exact},
|
|
{"1e+100", "10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", Exact},
|
|
} {
|
|
x := makeFloat(test.x)
|
|
res, acc := x.Int(nil)
|
|
got := "nil"
|
|
if res != nil {
|
|
got = res.String()
|
|
}
|
|
if got != test.want || acc != test.acc {
|
|
t.Errorf("%s: got %s (%s); want %s (%s)", test.x, got, acc, test.want, test.acc)
|
|
}
|
|
}
|
|
|
|
// check that supplied *Int is used
|
|
for _, f := range []string{"0", "1", "-1", "1234"} {
|
|
x := makeFloat(f)
|
|
i := new(Int)
|
|
if res, _ := x.Int(i); res != i {
|
|
t.Errorf("(%s).Int is not using supplied *Int", f)
|
|
}
|
|
}
|
|
}
|
|
|
|
func TestFloatRat(t *testing.T) {
|
|
for _, test := range []struct {
|
|
x, want string
|
|
acc Accuracy
|
|
}{
|
|
{"0", "0/1", Exact},
|
|
{"+0", "0/1", Exact},
|
|
{"-0", "0/1", Exact},
|
|
{"Inf", "nil", Below},
|
|
{"+Inf", "nil", Below},
|
|
{"-Inf", "nil", Above},
|
|
{"1", "1/1", Exact},
|
|
{"-1", "-1/1", Exact},
|
|
{"1.25", "5/4", Exact},
|
|
{"-1.25", "-5/4", Exact},
|
|
{"1e10", "10000000000/1", Exact},
|
|
{"1p10", "1024/1", Exact},
|
|
{"-1p-10", "-1/1024", Exact},
|
|
{"3.14159265", "7244019449799623199/2305843009213693952", Exact},
|
|
} {
|
|
x := makeFloat(test.x).SetPrec(64)
|
|
res, acc := x.Rat(nil)
|
|
got := "nil"
|
|
if res != nil {
|
|
got = res.String()
|
|
}
|
|
if got != test.want {
|
|
t.Errorf("%s: got %s; want %s", test.x, got, test.want)
|
|
continue
|
|
}
|
|
if acc != test.acc {
|
|
t.Errorf("%s: got %s; want %s", test.x, acc, test.acc)
|
|
continue
|
|
}
|
|
|
|
// inverse conversion
|
|
if res != nil {
|
|
got := new(Float).SetPrec(64).SetRat(res)
|
|
if got.Cmp(x) != 0 {
|
|
t.Errorf("%s: got %s; want %s", test.x, got, x)
|
|
}
|
|
}
|
|
}
|
|
|
|
// check that supplied *Rat is used
|
|
for _, f := range []string{"0", "1", "-1", "1234"} {
|
|
x := makeFloat(f)
|
|
r := new(Rat)
|
|
if res, _ := x.Rat(r); res != r {
|
|
t.Errorf("(%s).Rat is not using supplied *Rat", f)
|
|
}
|
|
}
|
|
}
|
|
|
|
func TestFloatAbs(t *testing.T) {
|
|
for _, test := range []string{
|
|
"0",
|
|
"1",
|
|
"1234",
|
|
"1.23e-2",
|
|
"1e-1000",
|
|
"1e1000",
|
|
"Inf",
|
|
} {
|
|
p := makeFloat(test)
|
|
a := new(Float).Abs(p)
|
|
if !alike(a, p) {
|
|
t.Errorf("%s: got %s; want %s", test, a.Text('g', 10), test)
|
|
}
|
|
|
|
n := makeFloat("-" + test)
|
|
a.Abs(n)
|
|
if !alike(a, p) {
|
|
t.Errorf("-%s: got %s; want %s", test, a.Text('g', 10), test)
|
|
}
|
|
}
|
|
}
|
|
|
|
func TestFloatNeg(t *testing.T) {
|
|
for _, test := range []string{
|
|
"0",
|
|
"1",
|
|
"1234",
|
|
"1.23e-2",
|
|
"1e-1000",
|
|
"1e1000",
|
|
"Inf",
|
|
} {
|
|
p1 := makeFloat(test)
|
|
n1 := makeFloat("-" + test)
|
|
n2 := new(Float).Neg(p1)
|
|
p2 := new(Float).Neg(n2)
|
|
if !alike(n2, n1) {
|
|
t.Errorf("%s: got %s; want %s", test, n2.Text('g', 10), n1.Text('g', 10))
|
|
}
|
|
if !alike(p2, p1) {
|
|
t.Errorf("%s: got %s; want %s", test, p2.Text('g', 10), p1.Text('g', 10))
|
|
}
|
|
}
|
|
}
|
|
|
|
func TestFloatInc(t *testing.T) {
|
|
const n = 10
|
|
for _, prec := range precList {
|
|
if 1<<prec < n {
|
|
continue // prec must be large enough to hold all numbers from 0 to n
|
|
}
|
|
var x, one Float
|
|
x.SetPrec(prec)
|
|
one.SetInt64(1)
|
|
for i := 0; i < n; i++ {
|
|
x.Add(&x, &one)
|
|
}
|
|
if x.Cmp(new(Float).SetInt64(n)) != 0 {
|
|
t.Errorf("prec = %d: got %s; want %d", prec, &x, n)
|
|
}
|
|
}
|
|
}
|
|
|
|
// Selected precisions with which to run various tests.
|
|
var precList = [...]uint{1, 2, 5, 8, 10, 16, 23, 24, 32, 50, 53, 64, 100, 128, 500, 511, 512, 513, 1000, 10000}
|
|
|
|
// Selected bits with which to run various tests.
|
|
// Each entry is a list of bits representing a floating-point number (see fromBits).
|
|
var bitsList = [...]Bits{
|
|
{}, // = 0
|
|
{0}, // = 1
|
|
{1}, // = 2
|
|
{-1}, // = 1/2
|
|
{10}, // = 2**10 == 1024
|
|
{-10}, // = 2**-10 == 1/1024
|
|
{100, 10, 1}, // = 2**100 + 2**10 + 2**1
|
|
{0, -1, -2, -10},
|
|
// TODO(gri) add more test cases
|
|
}
|
|
|
|
// TestFloatAdd tests Float.Add/Sub by comparing the result of a "manual"
|
|
// addition/subtraction of arguments represented by Bits values with the
|
|
// respective Float addition/subtraction for a variety of precisions
|
|
// and rounding modes.
|
|
func TestFloatAdd(t *testing.T) {
|
|
for _, xbits := range bitsList {
|
|
for _, ybits := range bitsList {
|
|
// exact values
|
|
x := xbits.Float()
|
|
y := ybits.Float()
|
|
zbits := xbits.add(ybits)
|
|
z := zbits.Float()
|
|
|
|
for i, mode := range [...]RoundingMode{ToZero, ToNearestEven, AwayFromZero} {
|
|
for _, prec := range precList {
|
|
got := new(Float).SetPrec(prec).SetMode(mode)
|
|
got.Add(x, y)
|
|
want := zbits.round(prec, mode)
|
|
if got.Cmp(want) != 0 {
|
|
t.Errorf("i = %d, prec = %d, %s:\n\t %s %v\n\t+ %s %v\n\t= %s\n\twant %s",
|
|
i, prec, mode, x, xbits, y, ybits, got, want)
|
|
}
|
|
|
|
got.Sub(z, x)
|
|
want = ybits.round(prec, mode)
|
|
if got.Cmp(want) != 0 {
|
|
t.Errorf("i = %d, prec = %d, %s:\n\t %s %v\n\t- %s %v\n\t= %s\n\twant %s",
|
|
i, prec, mode, z, zbits, x, xbits, got, want)
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
// TestFloatAdd32 tests that Float.Add/Sub of numbers with
|
|
// 24bit mantissa behaves like float32 addition/subtraction
|
|
// (excluding denormal numbers).
|
|
func TestFloatAdd32(t *testing.T) {
|
|
// chose base such that we cross the mantissa precision limit
|
|
const base = 1<<26 - 0x10 // 11...110000 (26 bits)
|
|
for d := 0; d <= 0x10; d++ {
|
|
for i := range [2]int{} {
|
|
x0, y0 := float64(base), float64(d)
|
|
if i&1 != 0 {
|
|
x0, y0 = y0, x0
|
|
}
|
|
|
|
x := NewFloat(x0)
|
|
y := NewFloat(y0)
|
|
z := new(Float).SetPrec(24)
|
|
|
|
z.Add(x, y)
|
|
got, acc := z.Float32()
|
|
want := float32(y0) + float32(x0)
|
|
if got != want || acc != Exact {
|
|
t.Errorf("d = %d: %g + %g = %g (%s); want %g (Exact)", d, x0, y0, got, acc, want)
|
|
}
|
|
|
|
z.Sub(z, y)
|
|
got, acc = z.Float32()
|
|
want = float32(want) - float32(y0)
|
|
if got != want || acc != Exact {
|
|
t.Errorf("d = %d: %g - %g = %g (%s); want %g (Exact)", d, x0+y0, y0, got, acc, want)
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
// TestFloatAdd64 tests that Float.Add/Sub of numbers with
|
|
// 53bit mantissa behaves like float64 addition/subtraction.
|
|
func TestFloatAdd64(t *testing.T) {
|
|
// chose base such that we cross the mantissa precision limit
|
|
const base = 1<<55 - 0x10 // 11...110000 (55 bits)
|
|
for d := 0; d <= 0x10; d++ {
|
|
for i := range [2]int{} {
|
|
x0, y0 := float64(base), float64(d)
|
|
if i&1 != 0 {
|
|
x0, y0 = y0, x0
|
|
}
|
|
|
|
x := NewFloat(x0)
|
|
y := NewFloat(y0)
|
|
z := new(Float).SetPrec(53)
|
|
|
|
z.Add(x, y)
|
|
got, acc := z.Float64()
|
|
want := x0 + y0
|
|
if got != want || acc != Exact {
|
|
t.Errorf("d = %d: %g + %g = %g (%s); want %g (Exact)", d, x0, y0, got, acc, want)
|
|
}
|
|
|
|
z.Sub(z, y)
|
|
got, acc = z.Float64()
|
|
want -= y0
|
|
if got != want || acc != Exact {
|
|
t.Errorf("d = %d: %g - %g = %g (%s); want %g (Exact)", d, x0+y0, y0, got, acc, want)
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
// TestFloatMul tests Float.Mul/Quo by comparing the result of a "manual"
|
|
// multiplication/division of arguments represented by Bits values with the
|
|
// respective Float multiplication/division for a variety of precisions
|
|
// and rounding modes.
|
|
func TestFloatMul(t *testing.T) {
|
|
for _, xbits := range bitsList {
|
|
for _, ybits := range bitsList {
|
|
// exact values
|
|
x := xbits.Float()
|
|
y := ybits.Float()
|
|
zbits := xbits.mul(ybits)
|
|
z := zbits.Float()
|
|
|
|
for i, mode := range [...]RoundingMode{ToZero, ToNearestEven, AwayFromZero} {
|
|
for _, prec := range precList {
|
|
got := new(Float).SetPrec(prec).SetMode(mode)
|
|
got.Mul(x, y)
|
|
want := zbits.round(prec, mode)
|
|
if got.Cmp(want) != 0 {
|
|
t.Errorf("i = %d, prec = %d, %s:\n\t %s %v\n\t* %s %v\n\t= %s\n\twant %s",
|
|
i, prec, mode, x, xbits, y, ybits, got, want)
|
|
}
|
|
|
|
if x.Sign() == 0 {
|
|
continue // ignore div-0 case (not invertable)
|
|
}
|
|
got.Quo(z, x)
|
|
want = ybits.round(prec, mode)
|
|
if got.Cmp(want) != 0 {
|
|
t.Errorf("i = %d, prec = %d, %s:\n\t %s %v\n\t/ %s %v\n\t= %s\n\twant %s",
|
|
i, prec, mode, z, zbits, x, xbits, got, want)
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
// TestFloatMul64 tests that Float.Mul/Quo of numbers with
|
|
// 53bit mantissa behaves like float64 multiplication/division.
|
|
func TestFloatMul64(t *testing.T) {
|
|
for _, test := range []struct {
|
|
x, y float64
|
|
}{
|
|
{0, 0},
|
|
{0, 1},
|
|
{1, 1},
|
|
{1, 1.5},
|
|
{1.234, 0.5678},
|
|
{2.718281828, 3.14159265358979},
|
|
{2.718281828e10, 3.14159265358979e-32},
|
|
{1.0 / 3, 1e200},
|
|
} {
|
|
for i := range [8]int{} {
|
|
x0, y0 := test.x, test.y
|
|
if i&1 != 0 {
|
|
x0 = -x0
|
|
}
|
|
if i&2 != 0 {
|
|
y0 = -y0
|
|
}
|
|
if i&4 != 0 {
|
|
x0, y0 = y0, x0
|
|
}
|
|
|
|
x := NewFloat(x0)
|
|
y := NewFloat(y0)
|
|
z := new(Float).SetPrec(53)
|
|
|
|
z.Mul(x, y)
|
|
got, _ := z.Float64()
|
|
want := x0 * y0
|
|
if got != want {
|
|
t.Errorf("%g * %g = %g; want %g", x0, y0, got, want)
|
|
}
|
|
|
|
if y0 == 0 {
|
|
continue // avoid division-by-zero
|
|
}
|
|
z.Quo(z, y)
|
|
got, _ = z.Float64()
|
|
want /= y0
|
|
if got != want {
|
|
t.Errorf("%g / %g = %g; want %g", x0*y0, y0, got, want)
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
func TestIssue6866(t *testing.T) {
|
|
for _, prec := range precList {
|
|
two := new(Float).SetPrec(prec).SetInt64(2)
|
|
one := new(Float).SetPrec(prec).SetInt64(1)
|
|
three := new(Float).SetPrec(prec).SetInt64(3)
|
|
msix := new(Float).SetPrec(prec).SetInt64(-6)
|
|
psix := new(Float).SetPrec(prec).SetInt64(+6)
|
|
|
|
p := new(Float).SetPrec(prec)
|
|
z1 := new(Float).SetPrec(prec)
|
|
z2 := new(Float).SetPrec(prec)
|
|
|
|
// z1 = 2 + 1.0/3*-6
|
|
p.Quo(one, three)
|
|
p.Mul(p, msix)
|
|
z1.Add(two, p)
|
|
|
|
// z2 = 2 - 1.0/3*+6
|
|
p.Quo(one, three)
|
|
p.Mul(p, psix)
|
|
z2.Sub(two, p)
|
|
|
|
if z1.Cmp(z2) != 0 {
|
|
t.Fatalf("prec %d: got z1 = %s != z2 = %s; want z1 == z2\n", prec, z1, z2)
|
|
}
|
|
if z1.Sign() != 0 {
|
|
t.Errorf("prec %d: got z1 = %s; want 0", prec, z1)
|
|
}
|
|
if z2.Sign() != 0 {
|
|
t.Errorf("prec %d: got z2 = %s; want 0", prec, z2)
|
|
}
|
|
}
|
|
}
|
|
|
|
func TestFloatQuo(t *testing.T) {
|
|
// TODO(gri) make the test vary these precisions
|
|
preci := 200 // precision of integer part
|
|
precf := 20 // precision of fractional part
|
|
|
|
for i := 0; i < 8; i++ {
|
|
// compute accurate (not rounded) result z
|
|
bits := Bits{preci - 1}
|
|
if i&3 != 0 {
|
|
bits = append(bits, 0)
|
|
}
|
|
if i&2 != 0 {
|
|
bits = append(bits, -1)
|
|
}
|
|
if i&1 != 0 {
|
|
bits = append(bits, -precf)
|
|
}
|
|
z := bits.Float()
|
|
|
|
// compute accurate x as z*y
|
|
y := NewFloat(3.14159265358979323e123)
|
|
|
|
x := new(Float).SetPrec(z.Prec() + y.Prec()).SetMode(ToZero)
|
|
x.Mul(z, y)
|
|
|
|
// leave for debugging
|
|
// fmt.Printf("x = %s\ny = %s\nz = %s\n", x, y, z)
|
|
|
|
if got := x.Acc(); got != Exact {
|
|
t.Errorf("got acc = %s; want exact", got)
|
|
}
|
|
|
|
// round accurate z for a variety of precisions and
|
|
// modes and compare against result of x / y.
|
|
for _, mode := range [...]RoundingMode{ToZero, ToNearestEven, AwayFromZero} {
|
|
for d := -5; d < 5; d++ {
|
|
prec := uint(preci + d)
|
|
got := new(Float).SetPrec(prec).SetMode(mode).Quo(x, y)
|
|
want := bits.round(prec, mode)
|
|
if got.Cmp(want) != 0 {
|
|
t.Errorf("i = %d, prec = %d, %s:\n\t %s\n\t/ %s\n\t= %s\n\twant %s",
|
|
i, prec, mode, x, y, got, want)
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
// TestFloatQuoSmoke tests all divisions x/y for values x, y in the range [-n, +n];
|
|
// it serves as a smoke test for basic correctness of division.
|
|
func TestFloatQuoSmoke(t *testing.T) {
|
|
n := 1000
|
|
if testing.Short() {
|
|
n = 10
|
|
}
|
|
|
|
const dprec = 3 // max. precision variation
|
|
const prec = 10 + dprec // enough bits to hold n precisely
|
|
for x := -n; x <= n; x++ {
|
|
for y := -n; y < n; y++ {
|
|
if y == 0 {
|
|
continue
|
|
}
|
|
|
|
a := float64(x)
|
|
b := float64(y)
|
|
c := a / b
|
|
|
|
// vary operand precision (only ok as long as a, b can be represented correctly)
|
|
for ad := -dprec; ad <= dprec; ad++ {
|
|
for bd := -dprec; bd <= dprec; bd++ {
|
|
A := new(Float).SetPrec(uint(prec + ad)).SetFloat64(a)
|
|
B := new(Float).SetPrec(uint(prec + bd)).SetFloat64(b)
|
|
C := new(Float).SetPrec(53).Quo(A, B) // C has float64 mantissa width
|
|
|
|
cc, acc := C.Float64()
|
|
if cc != c {
|
|
t.Errorf("%g/%g = %s; want %.5g\n", a, b, C.Text('g', 5), c)
|
|
continue
|
|
}
|
|
if acc != Exact {
|
|
t.Errorf("%g/%g got %s result; want exact result", a, b, acc)
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
// TestFloatArithmeticSpecialValues tests that Float operations produce the
|
|
// correct results for combinations of zero (±0), finite (±1 and ±2.71828),
|
|
// and infinite (±Inf) operands.
|
|
func TestFloatArithmeticSpecialValues(t *testing.T) {
|
|
zero := 0.0
|
|
args := []float64{math.Inf(-1), -2.71828, -1, -zero, zero, 1, 2.71828, math.Inf(1)}
|
|
xx := new(Float)
|
|
yy := new(Float)
|
|
got := new(Float)
|
|
want := new(Float)
|
|
for i := 0; i < 4; i++ {
|
|
for _, x := range args {
|
|
xx.SetFloat64(x)
|
|
// check conversion is correct
|
|
// (no need to do this for y, since we see exactly the
|
|
// same values there)
|
|
if got, acc := xx.Float64(); got != x || acc != Exact {
|
|
t.Errorf("Float(%g) == %g (%s)", x, got, acc)
|
|
}
|
|
for _, y := range args {
|
|
yy.SetFloat64(y)
|
|
var (
|
|
op string
|
|
z float64
|
|
f func(z, x, y *Float) *Float
|
|
)
|
|
switch i {
|
|
case 0:
|
|
op = "+"
|
|
z = x + y
|
|
f = (*Float).Add
|
|
case 1:
|
|
op = "-"
|
|
z = x - y
|
|
f = (*Float).Sub
|
|
case 2:
|
|
op = "*"
|
|
z = x * y
|
|
f = (*Float).Mul
|
|
case 3:
|
|
op = "/"
|
|
z = x / y
|
|
f = (*Float).Quo
|
|
default:
|
|
panic("unreachable")
|
|
}
|
|
var errnan bool // set if execution of f panicked with ErrNaN
|
|
// protect execution of f
|
|
func() {
|
|
defer func() {
|
|
if p := recover(); p != nil {
|
|
_ = p.(ErrNaN) // re-panic if not ErrNaN
|
|
errnan = true
|
|
}
|
|
}()
|
|
f(got, xx, yy)
|
|
}()
|
|
if math.IsNaN(z) {
|
|
if !errnan {
|
|
t.Errorf("%5g %s %5g = %5s; want ErrNaN panic", x, op, y, got)
|
|
}
|
|
continue
|
|
}
|
|
if errnan {
|
|
t.Errorf("%5g %s %5g panicked with ErrNan; want %5s", x, op, y, want)
|
|
continue
|
|
}
|
|
want.SetFloat64(z)
|
|
if !alike(got, want) {
|
|
t.Errorf("%5g %s %5g = %5s; want %5s", x, op, y, got, want)
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
func TestFloatArithmeticOverflow(t *testing.T) {
|
|
for _, test := range []struct {
|
|
prec uint
|
|
mode RoundingMode
|
|
op byte
|
|
x, y, want string
|
|
acc Accuracy
|
|
}{
|
|
{4, ToNearestEven, '+', "0", "0", "0", Exact}, // smoke test
|
|
{4, ToNearestEven, '+', "0x.8p+0", "0x.8p+0", "0x.8p+1", Exact}, // smoke test
|
|
|
|
{4, ToNearestEven, '+', "0", "0x.8p2147483647", "0x.8p+2147483647", Exact},
|
|
{4, ToNearestEven, '+', "0x.8p2147483500", "0x.8p2147483647", "0x.8p+2147483647", Below}, // rounded to zero
|
|
{4, ToNearestEven, '+', "0x.8p2147483647", "0x.8p2147483647", "+Inf", Above}, // exponent overflow in +
|
|
{4, ToNearestEven, '+', "-0x.8p2147483647", "-0x.8p2147483647", "-Inf", Below}, // exponent overflow in +
|
|
{4, ToNearestEven, '-', "-0x.8p2147483647", "0x.8p2147483647", "-Inf", Below}, // exponent overflow in -
|
|
|
|
{4, ToZero, '+', "0x.fp2147483647", "0x.8p2147483643", "0x.fp+2147483647", Below}, // rounded to zero
|
|
{4, ToNearestEven, '+', "0x.fp2147483647", "0x.8p2147483643", "+Inf", Above}, // exponent overflow in rounding
|
|
{4, AwayFromZero, '+', "0x.fp2147483647", "0x.8p2147483643", "+Inf", Above}, // exponent overflow in rounding
|
|
|
|
{4, AwayFromZero, '-', "-0x.fp2147483647", "0x.8p2147483644", "-Inf", Below}, // exponent overflow in rounding
|
|
{4, ToNearestEven, '-', "-0x.fp2147483647", "0x.8p2147483643", "-Inf", Below}, // exponent overflow in rounding
|
|
{4, ToZero, '-', "-0x.fp2147483647", "0x.8p2147483643", "-0x.fp+2147483647", Above}, // rounded to zero
|
|
|
|
{4, ToNearestEven, '+', "0", "0x.8p-2147483648", "0x.8p-2147483648", Exact},
|
|
{4, ToNearestEven, '+', "0x.8p-2147483648", "0x.8p-2147483648", "0x.8p-2147483647", Exact},
|
|
|
|
{4, ToNearestEven, '*', "1", "0x.8p2147483647", "0x.8p+2147483647", Exact},
|
|
{4, ToNearestEven, '*', "2", "0x.8p2147483647", "+Inf", Above}, // exponent overflow in *
|
|
{4, ToNearestEven, '*', "-2", "0x.8p2147483647", "-Inf", Below}, // exponent overflow in *
|
|
|
|
{4, ToNearestEven, '/', "0.5", "0x.8p2147483647", "0x.8p-2147483646", Exact},
|
|
{4, ToNearestEven, '/', "0x.8p+0", "0x.8p2147483647", "0x.8p-2147483646", Exact},
|
|
{4, ToNearestEven, '/', "0x.8p-1", "0x.8p2147483647", "0x.8p-2147483647", Exact},
|
|
{4, ToNearestEven, '/', "0x.8p-2", "0x.8p2147483647", "0x.8p-2147483648", Exact},
|
|
{4, ToNearestEven, '/', "0x.8p-3", "0x.8p2147483647", "0", Below}, // exponent underflow in /
|
|
} {
|
|
x := makeFloat(test.x)
|
|
y := makeFloat(test.y)
|
|
z := new(Float).SetPrec(test.prec).SetMode(test.mode)
|
|
switch test.op {
|
|
case '+':
|
|
z.Add(x, y)
|
|
case '-':
|
|
z.Sub(x, y)
|
|
case '*':
|
|
z.Mul(x, y)
|
|
case '/':
|
|
z.Quo(x, y)
|
|
default:
|
|
panic("unreachable")
|
|
}
|
|
if got := z.Text('p', 0); got != test.want || z.Acc() != test.acc {
|
|
t.Errorf(
|
|
"prec = %d (%s): %s %c %s = %s (%s); want %s (%s)",
|
|
test.prec, test.mode, x.Text('p', 0), test.op, y.Text('p', 0), got, z.Acc(), test.want, test.acc,
|
|
)
|
|
}
|
|
}
|
|
}
|
|
|
|
// TODO(gri) Add tests that check correctness in the presence of aliasing.
|
|
|
|
// For rounding modes ToNegativeInf and ToPositiveInf, rounding is affected
|
|
// by the sign of the value to be rounded. Test that rounding happens after
|
|
// the sign of a result has been set.
|
|
// This test uses specific values that are known to fail if rounding is
|
|
// "factored" out before setting the result sign.
|
|
func TestFloatArithmeticRounding(t *testing.T) {
|
|
for _, test := range []struct {
|
|
mode RoundingMode
|
|
prec uint
|
|
x, y, want int64
|
|
op byte
|
|
}{
|
|
{ToZero, 3, -0x8, -0x1, -0x8, '+'},
|
|
{AwayFromZero, 3, -0x8, -0x1, -0xa, '+'},
|
|
{ToNegativeInf, 3, -0x8, -0x1, -0xa, '+'},
|
|
|
|
{ToZero, 3, -0x8, 0x1, -0x8, '-'},
|
|
{AwayFromZero, 3, -0x8, 0x1, -0xa, '-'},
|
|
{ToNegativeInf, 3, -0x8, 0x1, -0xa, '-'},
|
|
|
|
{ToZero, 3, -0x9, 0x1, -0x8, '*'},
|
|
{AwayFromZero, 3, -0x9, 0x1, -0xa, '*'},
|
|
{ToNegativeInf, 3, -0x9, 0x1, -0xa, '*'},
|
|
|
|
{ToZero, 3, -0x9, 0x1, -0x8, '/'},
|
|
{AwayFromZero, 3, -0x9, 0x1, -0xa, '/'},
|
|
{ToNegativeInf, 3, -0x9, 0x1, -0xa, '/'},
|
|
} {
|
|
var x, y, z Float
|
|
x.SetInt64(test.x)
|
|
y.SetInt64(test.y)
|
|
z.SetPrec(test.prec).SetMode(test.mode)
|
|
switch test.op {
|
|
case '+':
|
|
z.Add(&x, &y)
|
|
case '-':
|
|
z.Sub(&x, &y)
|
|
case '*':
|
|
z.Mul(&x, &y)
|
|
case '/':
|
|
z.Quo(&x, &y)
|
|
default:
|
|
panic("unreachable")
|
|
}
|
|
if got, acc := z.Int64(); got != test.want || acc != Exact {
|
|
t.Errorf("%s, %d bits: %d %c %d = %d (%s); want %d (Exact)",
|
|
test.mode, test.prec, test.x, test.op, test.y, got, acc, test.want,
|
|
)
|
|
}
|
|
}
|
|
}
|
|
|
|
// TestFloatCmpSpecialValues tests that Cmp produces the correct results for
|
|
// combinations of zero (±0), finite (±1 and ±2.71828), and infinite (±Inf)
|
|
// operands.
|
|
func TestFloatCmpSpecialValues(t *testing.T) {
|
|
zero := 0.0
|
|
args := []float64{math.Inf(-1), -2.71828, -1, -zero, zero, 1, 2.71828, math.Inf(1)}
|
|
xx := new(Float)
|
|
yy := new(Float)
|
|
for i := 0; i < 4; i++ {
|
|
for _, x := range args {
|
|
xx.SetFloat64(x)
|
|
// check conversion is correct
|
|
// (no need to do this for y, since we see exactly the
|
|
// same values there)
|
|
if got, acc := xx.Float64(); got != x || acc != Exact {
|
|
t.Errorf("Float(%g) == %g (%s)", x, got, acc)
|
|
}
|
|
for _, y := range args {
|
|
yy.SetFloat64(y)
|
|
got := xx.Cmp(yy)
|
|
want := 0
|
|
switch {
|
|
case x < y:
|
|
want = -1
|
|
case x > y:
|
|
want = +1
|
|
}
|
|
if got != want {
|
|
t.Errorf("(%g).Cmp(%g) = %v; want %v", x, y, got, want)
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|