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// Copyright ©2013 The Gonum Authors. All rights reserved.
// Use of this code is governed by a BSD-style
// license that can be found in the LICENSE file.
package scalar
import (
"math"
"testing"
)
func TestEqualsRelative(t *testing.T) {
t.Parallel()
equalityTests := []struct {
a, b float64
tol float64
equal bool
}{
{1000000, 1000001, 0, true},
{1000001, 1000000, 0, true},
{10000, 10001, 0, false},
{10001, 10000, 0, false},
{-1000000, -1000001, 0, true},
{-1000001, -1000000, 0, true},
{-10000, -10001, 0, false},
{-10001, -10000, 0, false},
{1.0000001, 1.0000002, 0, true},
{1.0000002, 1.0000001, 0, true},
{1.0002, 1.0001, 0, false},
{1.0001, 1.0002, 0, false},
{-1.000001, -1.000002, 0, true},
{-1.000002, -1.000001, 0, true},
{-1.0001, -1.0002, 0, false},
{-1.0002, -1.0001, 0, false},
{0.000000001000001, 0.000000001000002, 0, true},
{0.000000001000002, 0.000000001000001, 0, true},
{0.000000000001002, 0.000000000001001, 0, false},
{0.000000000001001, 0.000000000001002, 0, false},
{-0.000000001000001, -0.000000001000002, 0, true},
{-0.000000001000002, -0.000000001000001, 0, true},
{-0.000000000001002, -0.000000000001001, 0, false},
{-0.000000000001001, -0.000000000001002, 0, false},
{0, 0, 0, true},
{0, -0, 0, true},
{-0, -0, 0, true},
{0.00000001, 0, 0, false},
{0, 0.00000001, 0, false},
{-0.00000001, 0, 0, false},
{0, -0.00000001, 0, false},
{0, 1e-310, 0.01, true},
{1e-310, 0, 0.01, true},
{1e-310, 0, 0.000001, false},
{0, 1e-310, 0.000001, false},
{0, -1e-310, 0.1, true},
{-1e-310, 0, 0.1, true},
{-1e-310, 0, 0.00000001, false},
{0, -1e-310, 0.00000001, false},
{math.Inf(1), math.Inf(1), 0, true},
{math.Inf(-1), math.Inf(-1), 0, true},
{math.Inf(-1), math.Inf(1), 0, false},
{math.Inf(1), math.MaxFloat64, 0, false},
{math.Inf(-1), -math.MaxFloat64, 0, false},
{math.NaN(), math.NaN(), 0, false},
{math.NaN(), 0, 0, false},
{-0, math.NaN(), 0, false},
{math.NaN(), -0, 0, false},
{0, math.NaN(), 0, false},
{math.NaN(), math.Inf(1), 0, false},
{math.Inf(1), math.NaN(), 0, false},
{math.NaN(), math.Inf(-1), 0, false},
{math.Inf(-1), math.NaN(), 0, false},
{math.NaN(), math.MaxFloat64, 0, false},
{math.MaxFloat64, math.NaN(), 0, false},
{math.NaN(), -math.MaxFloat64, 0, false},
{-math.MaxFloat64, math.NaN(), 0, false},
{math.NaN(), math.SmallestNonzeroFloat64, 0, false},
{math.SmallestNonzeroFloat64, math.NaN(), 0, false},
{math.NaN(), -math.SmallestNonzeroFloat64, 0, false},
{-math.SmallestNonzeroFloat64, math.NaN(), 0, false},
{1.000000001, -1.0, 0, false},
{-1.0, 1.000000001, 0, false},
{-1.000000001, 1.0, 0, false},
{1.0, -1.000000001, 0, false},
{10 * math.SmallestNonzeroFloat64, 10 * -math.SmallestNonzeroFloat64, 0, true},
{1e11 * math.SmallestNonzeroFloat64, 1e11 * -math.SmallestNonzeroFloat64, 0, false},
{math.SmallestNonzeroFloat64, -math.SmallestNonzeroFloat64, 0, true},
{-math.SmallestNonzeroFloat64, math.SmallestNonzeroFloat64, 0, true},
{math.SmallestNonzeroFloat64, 0, 0, true},
{0, math.SmallestNonzeroFloat64, 0, true},
{-math.SmallestNonzeroFloat64, 0, 0, true},
{0, -math.SmallestNonzeroFloat64, 0, true},
{0.000000001, -math.SmallestNonzeroFloat64, 0, false},
{0.000000001, math.SmallestNonzeroFloat64, 0, false},
{math.SmallestNonzeroFloat64, 0.000000001, 0, false},
{-math.SmallestNonzeroFloat64, 0.000000001, 0, false},
}
for _, ts := range equalityTests {
if ts.tol == 0 {
ts.tol = 1e-5
}
if equal := EqualWithinRel(ts.a, ts.b, ts.tol); equal != ts.equal {
t.Errorf("Relative equality of %g and %g with tolerance %g returned: %v. Expected: %v",
ts.a, ts.b, ts.tol, equal, ts.equal)
}
}
}
func TestEqualsULP(t *testing.T) {
t.Parallel()
if f := 67329.242; !EqualWithinULP(f, nextAfterN(f, math.Inf(1), 10), 10) {
t.Errorf("Equal values returned as unequal")
}
if f := 67329.242; EqualWithinULP(f, nextAfterN(f, math.Inf(1), 5), 1) {
t.Errorf("Unequal values returned as equal")
}
if f := 67329.242; EqualWithinULP(nextAfterN(f, math.Inf(1), 5), f, 1) {
t.Errorf("Unequal values returned as equal")
}
if f := nextAfterN(0, math.Inf(1), 2); !EqualWithinULP(f, nextAfterN(f, math.Inf(-1), 5), 10) {
t.Errorf("Equal values returned as unequal")
}
if !EqualWithinULP(67329.242, 67329.242, 10) {
t.Errorf("Equal float64s not returned as equal")
}
if EqualWithinULP(1, math.NaN(), 10) {
t.Errorf("NaN returned as equal")
}
}
func nextAfterN(x, y float64, n int) float64 {
for i := 0; i < n; i++ {
x = math.Nextafter(x, y)
}
return x
}
func TestNaNWith(t *testing.T) {
t.Parallel()
tests := []struct {
payload uint64
bits uint64
}{
{0, math.Float64bits(0 / func() float64 { return 0 }())}, // Hide the division by zero from the compiler.
{1, math.Float64bits(math.NaN())},
{1954, 0x7ff80000000007a2}, // R NA.
}
for _, test := range tests {
nan := NaNWith(test.payload)
if !math.IsNaN(nan) {
t.Errorf("expected NaN value, got:%f", nan)
}
bits := math.Float64bits(nan)
// Strip sign bit.
const sign = 1 << 63
bits &^= sign
test.bits &^= sign
if bits != test.bits {
t.Errorf("expected NaN bit representation: got:%x want:%x", bits, test.bits)
}
}
}
func TestNaNPayload(t *testing.T) {
t.Parallel()
tests := []struct {
f float64
payload uint64
ok bool
}{
{0 / func() float64 { return 0 }(), 0, true}, // Hide the division by zero from the compiler.
// The following two line are written explicitly to defend against potential changes to math.Copysign.
{math.Float64frombits(math.Float64bits(math.NaN()) | (1 << 63)), 1, true}, // math.Copysign(math.NaN(), -1)
{math.Float64frombits(math.Float64bits(math.NaN()) &^ (1 << 63)), 1, true}, // math.Copysign(math.NaN(), 1)
{NaNWith(1954), 1954, true}, // R NA.
{math.Copysign(0, -1), 0, false},
{0, 0, false},
{math.Inf(-1), 0, false},
{math.Inf(1), 0, false},
{math.Float64frombits(0x7ff0000000000001), 0, false}, // Signalling NaN.
}
for _, test := range tests {
payload, ok := NaNPayload(test.f)
if payload != test.payload {
t.Errorf("expected NaN payload: got:%x want:%x", payload, test.payload)
}
if ok != test.ok {
t.Errorf("expected NaN status: got:%t want:%t", ok, test.ok)
}
}
}
func TestRound(t *testing.T) {
t.Parallel()
for _, test := range []struct {
x float64
prec int
want float64
}{
{x: 0, prec: 1, want: 0},
{x: math.Inf(1), prec: 1, want: math.Inf(1)},
{x: math.Inf(-1), prec: 1, want: math.Inf(-1)},
{x: math.NaN(), prec: 1, want: math.NaN()},
{x: func() float64 { var f float64; return -f }(), prec: 1, want: 0},
{x: math.MaxFloat64 / 2, prec: 1, want: math.MaxFloat64 / 2},
{x: 1 << 64, prec: 1, want: 1 << 64},
{x: 454.4445, prec: 3, want: 454.445},
{x: 454.44445, prec: 4, want: 454.4445},
{x: 0.42499, prec: 4, want: 0.425},
{x: 0.42599, prec: 4, want: 0.426},
{x: 0.424999999999993, prec: 2, want: 0.42},
{x: 0.425, prec: 2, want: 0.43},
{x: 0.425000000000001, prec: 2, want: 0.43},
{x: 123.4244999999999, prec: 3, want: 123.424},
{x: 123.4245, prec: 3, want: 123.425},
{x: 123.4245000000001, prec: 3, want: 123.425},
{x: -0.49999999999999994, prec: 0, want: 0},
{x: 0.49999999999999994, prec: 0, want: 0},
{x: 454.45, prec: 0, want: 454},
{x: 454.45, prec: 1, want: 454.5},
{x: 454.45, prec: 2, want: 454.45},
{x: 454.45, prec: 3, want: 454.45},
{x: 454.445, prec: 0, want: 454},
{x: 454.445, prec: 1, want: 454.4},
{x: 454.445, prec: 2, want: 454.45},
{x: 454.445, prec: 3, want: 454.445},
{x: 454.445, prec: 4, want: 454.445},
{x: 454.55, prec: 0, want: 455},
{x: 454.55, prec: 1, want: 454.6},
{x: 454.55, prec: 2, want: 454.55},
{x: 454.55, prec: 3, want: 454.55},
{x: 454.455, prec: 0, want: 454},
{x: 454.455, prec: 1, want: 454.5},
{x: 454.455, prec: 2, want: 454.46},
{x: 454.455, prec: 3, want: 454.455},
{x: 454.455, prec: 4, want: 454.455},
// Negative precision.
{x: math.Inf(1), prec: -1, want: math.Inf(1)},
{x: math.Inf(-1), prec: -1, want: math.Inf(-1)},
{x: math.NaN(), prec: -1, want: math.NaN()},
{x: func() float64 { var f float64; return -f }(), prec: -1, want: 0},
{x: 454.45, prec: -1, want: 450},
{x: 454.45, prec: -2, want: 500},
{x: 500, prec: -3, want: 1000},
{x: 500, prec: -4, want: 0},
{x: 1500, prec: -3, want: 2000},
{x: 1500, prec: -4, want: 0},
} {
for _, sign := range []float64{1, -1} {
got := Round(sign*test.x, test.prec)
want := sign * test.want
if want == 0 {
want = 0
}
if (got != want || math.Signbit(got) != math.Signbit(want)) && !(math.IsNaN(got) && math.IsNaN(want)) {
t.Errorf("unexpected result for Round(%g, %d): got: %g, want: %g", sign*test.x, test.prec, got, want)
}
}
}
}
func TestRoundEven(t *testing.T) {
t.Parallel()
for _, test := range []struct {
x float64
prec int
want float64
}{
{x: 0, prec: 1, want: 0},
{x: math.Inf(1), prec: 1, want: math.Inf(1)},
{x: math.Inf(-1), prec: 1, want: math.Inf(-1)},
{x: math.NaN(), prec: 1, want: math.NaN()},
{x: func() float64 { var f float64; return -f }(), prec: 1, want: 0},
{x: math.MaxFloat64 / 2, prec: 1, want: math.MaxFloat64 / 2},
{x: 1 << 64, prec: 1, want: 1 << 64},
{x: 454.4445, prec: 3, want: 454.444},
{x: 454.44445, prec: 4, want: 454.4444},
{x: 0.42499, prec: 4, want: 0.425},
{x: 0.42599, prec: 4, want: 0.426},
{x: 0.424999999999993, prec: 2, want: 0.42},
{x: 0.425, prec: 2, want: 0.42},
{x: 0.425000000000001, prec: 2, want: 0.43},
{x: 123.4244999999999, prec: 3, want: 123.424},
{x: 123.4245, prec: 3, want: 123.424},
{x: 123.4245000000001, prec: 3, want: 123.425},
{x: -0.49999999999999994, prec: 0, want: 0},
{x: 0.49999999999999994, prec: 0, want: 0},
{x: 454.45, prec: 0, want: 454},
{x: 454.45, prec: 1, want: 454.4},
{x: 454.45, prec: 2, want: 454.45},
{x: 454.45, prec: 3, want: 454.45},
{x: 454.445, prec: 0, want: 454},
{x: 454.445, prec: 1, want: 454.4},
{x: 454.445, prec: 2, want: 454.44},
{x: 454.445, prec: 3, want: 454.445},
{x: 454.445, prec: 4, want: 454.445},
{x: 454.55, prec: 0, want: 455},
{x: 454.55, prec: 1, want: 454.6},
{x: 454.55, prec: 2, want: 454.55},
{x: 454.55, prec: 3, want: 454.55},
{x: 454.455, prec: 0, want: 454},
{x: 454.455, prec: 1, want: 454.5},
{x: 454.455, prec: 2, want: 454.46},
{x: 454.455, prec: 3, want: 454.455},
{x: 454.455, prec: 4, want: 454.455},
// Negative precision.
{x: math.Inf(1), prec: -1, want: math.Inf(1)},
{x: math.Inf(-1), prec: -1, want: math.Inf(-1)},
{x: math.NaN(), prec: -1, want: math.NaN()},
{x: func() float64 { var f float64; return -f }(), prec: -1, want: 0},
{x: 454.45, prec: -1, want: 450},
{x: 454.45, prec: -2, want: 500},
{x: 500, prec: -3, want: 0},
{x: 500, prec: -4, want: 0},
{x: 1500, prec: -3, want: 2000},
{x: 1500, prec: -4, want: 0},
} {
for _, sign := range []float64{1, -1} {
got := RoundEven(sign*test.x, test.prec)
want := sign * test.want
if want == 0 {
want = 0
}
if (got != want || math.Signbit(got) != math.Signbit(want)) && !(math.IsNaN(got) && math.IsNaN(want)) {
t.Errorf("unexpected result for RoundEven(%g, %d): got: %g, want: %g", sign*test.x, test.prec, got, want)
}
}
}
}
func TestSame(t *testing.T) {
t.Parallel()
for _, test := range []struct {
a, b float64
want bool
}{
{a: 0, b: 0, want: true},
{a: 1, b: 1, want: true},
{a: -1, b: 1, want: false},
{a: 0, b: 1, want: false},
{a: 1, b: 0, want: false},
{a: -1, b: 1, want: false},
{a: math.NaN(), b: math.NaN(), want: true},
{a: 1, b: math.NaN(), want: false},
{a: math.Inf(1), b: math.NaN(), want: false},
{a: math.NaN(), b: math.Inf(1), want: false},
{a: math.NaN(), b: 1, want: false},
{a: math.Inf(1), b: math.Inf(1), want: true},
{a: math.Inf(-1), b: math.Inf(1), want: false},
{a: math.Inf(1), b: math.Inf(-1), want: false},
} {
got := Same(test.a, test.b)
if got != test.want {
t.Errorf("unexpected results for a=%f b=%f: got:%t want:%t", test.a, test.b, got, test.want)
}
}
}
|
