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-rw-r--r--src/math/big/float_test.go1858
1 files changed, 1858 insertions, 0 deletions
diff --git a/src/math/big/float_test.go b/src/math/big/float_test.go
new file mode 100644
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--- /dev/null
+++ b/src/math/big/float_test.go
@@ -0,0 +1,1858 @@
+// Copyright 2014 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package big
+
+import (
+ "flag"
+ "fmt"
+ "math"
+ "strconv"
+ "strings"
+ "testing"
+)
+
+// Verify that ErrNaN implements the error interface.
+var _ error = ErrNaN{}
+
+func (x *Float) uint64() uint64 {
+ u, acc := x.Uint64()
+ if acc != Exact {
+ panic(fmt.Sprintf("%s is not a uint64", x.Text('g', 10)))
+ }
+ return u
+}
+
+func (x *Float) int64() int64 {
+ i, acc := x.Int64()
+ if acc != Exact {
+ panic(fmt.Sprintf("%s is not an int64", x.Text('g', 10)))
+ }
+ return i
+}
+
+func TestFloatZeroValue(t *testing.T) {
+ // zero (uninitialized) value is a ready-to-use 0.0
+ var x Float
+ if s := x.Text('f', 1); s != "0.0" {
+ t.Errorf("zero value = %s; want 0.0", s)
+ }
+
+ // zero value has precision 0
+ if prec := x.Prec(); prec != 0 {
+ t.Errorf("prec = %d; want 0", prec)
+ }
+
+ // zero value can be used in any and all positions of binary operations
+ make := func(x int) *Float {
+ var f Float
+ if x != 0 {
+ f.SetInt64(int64(x))
+ }
+ // x == 0 translates into the zero value
+ return &f
+ }
+ for _, test := range []struct {
+ z, x, y, want int
+ opname rune
+ op func(z, x, y *Float) *Float
+ }{
+ {0, 0, 0, 0, '+', (*Float).Add},
+ {0, 1, 2, 3, '+', (*Float).Add},
+ {1, 2, 0, 2, '+', (*Float).Add},
+ {2, 0, 1, 1, '+', (*Float).Add},
+
+ {0, 0, 0, 0, '-', (*Float).Sub},
+ {0, 1, 2, -1, '-', (*Float).Sub},
+ {1, 2, 0, 2, '-', (*Float).Sub},
+ {2, 0, 1, -1, '-', (*Float).Sub},
+
+ {0, 0, 0, 0, '*', (*Float).Mul},
+ {0, 1, 2, 2, '*', (*Float).Mul},
+ {1, 2, 0, 0, '*', (*Float).Mul},
+ {2, 0, 1, 0, '*', (*Float).Mul},
+
+ // {0, 0, 0, 0, '/', (*Float).Quo}, // panics
+ {0, 2, 1, 2, '/', (*Float).Quo},
+ {1, 2, 0, 0, '/', (*Float).Quo}, // = +Inf
+ {2, 0, 1, 0, '/', (*Float).Quo},
+ } {
+ z := make(test.z)
+ test.op(z, make(test.x), make(test.y))
+ got := 0
+ if !z.IsInf() {
+ got = int(z.int64())
+ }
+ if got != test.want {
+ t.Errorf("%d %c %d = %d; want %d", test.x, test.opname, test.y, got, test.want)
+ }
+ }
+
+ // TODO(gri) test how precision is set for zero value results
+}
+
+func makeFloat(s string) *Float {
+ x, _, err := ParseFloat(s, 0, 1000, ToNearestEven)
+ if err != nil {
+ panic(err)
+ }
+ return x
+}
+
+func TestFloatSetPrec(t *testing.T) {
+ for _, test := range []struct {
+ x string
+ prec uint
+ want string
+ acc Accuracy
+ }{
+ // prec 0
+ {"0", 0, "0", Exact},
+ {"-0", 0, "-0", Exact},
+ {"-Inf", 0, "-Inf", Exact},
+ {"+Inf", 0, "+Inf", Exact},
+ {"123", 0, "0", Below},
+ {"-123", 0, "-0", Above},
+
+ // prec at upper limit
+ {"0", MaxPrec, "0", Exact},
+ {"-0", MaxPrec, "-0", Exact},
+ {"-Inf", MaxPrec, "-Inf", Exact},
+ {"+Inf", MaxPrec, "+Inf", Exact},
+
+ // just a few regular cases - general rounding is tested elsewhere
+ {"1.5", 1, "2", Above},
+ {"-1.5", 1, "-2", Below},
+ {"123", 1e6, "123", Exact},
+ {"-123", 1e6, "-123", Exact},
+ } {
+ x := makeFloat(test.x).SetPrec(test.prec)
+ prec := test.prec
+ if prec > MaxPrec {
+ prec = MaxPrec
+ }
+ if got := x.Prec(); got != prec {
+ t.Errorf("%s.SetPrec(%d).Prec() == %d; want %d", test.x, test.prec, got, prec)
+ }
+ if got, acc := x.String(), x.Acc(); got != test.want || acc != test.acc {
+ t.Errorf("%s.SetPrec(%d) = %s (%s); want %s (%s)", test.x, test.prec, got, acc, test.want, test.acc)
+ }
+ }
+}
+
+func TestFloatMinPrec(t *testing.T) {
+ const max = 100
+ for _, test := range []struct {
+ x string
+ want uint
+ }{
+ {"0", 0},
+ {"-0", 0},
+ {"+Inf", 0},
+ {"-Inf", 0},
+ {"1", 1},
+ {"2", 1},
+ {"3", 2},
+ {"0x8001", 16},
+ {"0x8001p-1000", 16},
+ {"0x8001p+1000", 16},
+ {"0.1", max},
+ } {
+ x := makeFloat(test.x).SetPrec(max)
+ if got := x.MinPrec(); got != test.want {
+ t.Errorf("%s.MinPrec() = %d; want %d", test.x, got, test.want)
+ }
+ }
+}
+
+func TestFloatSign(t *testing.T) {
+ for _, test := range []struct {
+ x string
+ s int
+ }{
+ {"-Inf", -1},
+ {"-1", -1},
+ {"-0", 0},
+ {"+0", 0},
+ {"+1", +1},
+ {"+Inf", +1},
+ } {
+ x := makeFloat(test.x)
+ s := x.Sign()
+ if s != test.s {
+ t.Errorf("%s.Sign() = %d; want %d", test.x, s, test.s)
+ }
+ }
+}
+
+// alike(x, y) is like x.Cmp(y) == 0 but also considers the sign of 0 (0 != -0).
+func alike(x, y *Float) bool {
+ return x.Cmp(y) == 0 && x.Signbit() == y.Signbit()
+}
+
+func alike32(x, y float32) bool {
+ // we can ignore NaNs
+ return x == y && math.Signbit(float64(x)) == math.Signbit(float64(y))
+
+}
+
+func alike64(x, y float64) bool {
+ // we can ignore NaNs
+ return x == y && math.Signbit(x) == math.Signbit(y)
+
+}
+
+func TestFloatMantExp(t *testing.T) {
+ for _, test := range []struct {
+ x string
+ mant string
+ exp int
+ }{
+ {"0", "0", 0},
+ {"+0", "0", 0},
+ {"-0", "-0", 0},
+ {"Inf", "+Inf", 0},
+ {"+Inf", "+Inf", 0},
+ {"-Inf", "-Inf", 0},
+ {"1.5", "0.75", 1},
+ {"1.024e3", "0.5", 11},
+ {"-0.125", "-0.5", -2},
+ } {
+ x := makeFloat(test.x)
+ mant := makeFloat(test.mant)
+ m := new(Float)
+ e := x.MantExp(m)
+ if !alike(m, mant) || e != test.exp {
+ t.Errorf("%s.MantExp() = %s, %d; want %s, %d", test.x, m.Text('g', 10), e, test.mant, test.exp)
+ }
+ }
+}
+
+func TestFloatMantExpAliasing(t *testing.T) {
+ x := makeFloat("0.5p10")
+ if e := x.MantExp(x); e != 10 {
+ t.Fatalf("Float.MantExp aliasing error: got %d; want 10", e)
+ }
+ if want := makeFloat("0.5"); !alike(x, want) {
+ t.Fatalf("Float.MantExp aliasing error: got %s; want %s", x.Text('g', 10), want.Text('g', 10))
+ }
+}
+
+func TestFloatSetMantExp(t *testing.T) {
+ for _, test := range []struct {
+ frac string
+ exp int
+ z string
+ }{
+ {"0", 0, "0"},
+ {"+0", 0, "0"},
+ {"-0", 0, "-0"},
+ {"Inf", 1234, "+Inf"},
+ {"+Inf", -1234, "+Inf"},
+ {"-Inf", -1234, "-Inf"},
+ {"0", MinExp, "0"},
+ {"0.25", MinExp, "+0"}, // exponent underflow
+ {"-0.25", MinExp, "-0"}, // exponent underflow
+ {"1", MaxExp, "+Inf"}, // exponent overflow
+ {"2", MaxExp - 1, "+Inf"}, // exponent overflow
+ {"0.75", 1, "1.5"},
+ {"0.5", 11, "1024"},
+ {"-0.5", -2, "-0.125"},
+ {"32", 5, "1024"},
+ {"1024", -10, "1"},
+ } {
+ frac := makeFloat(test.frac)
+ want := makeFloat(test.z)
+ var z Float
+ z.SetMantExp(frac, test.exp)
+ if !alike(&z, want) {
+ t.Errorf("SetMantExp(%s, %d) = %s; want %s", test.frac, test.exp, z.Text('g', 10), test.z)
+ }
+ // test inverse property
+ mant := new(Float)
+ if z.SetMantExp(mant, want.MantExp(mant)).Cmp(want) != 0 {
+ t.Errorf("Inverse property not satisfied: got %s; want %s", z.Text('g', 10), test.z)
+ }
+ }
+}
+
+func TestFloatPredicates(t *testing.T) {
+ for _, test := range []struct {
+ x string
+ sign int
+ signbit, inf bool
+ }{
+ {x: "-Inf", sign: -1, signbit: true, inf: true},
+ {x: "-1", sign: -1, signbit: true},
+ {x: "-0", signbit: true},
+ {x: "0"},
+ {x: "1", sign: 1},
+ {x: "+Inf", sign: 1, inf: true},
+ } {
+ x := makeFloat(test.x)
+ if got := x.Signbit(); got != test.signbit {
+ t.Errorf("(%s).Signbit() = %v; want %v", test.x, got, test.signbit)
+ }
+ if got := x.Sign(); got != test.sign {
+ t.Errorf("(%s).Sign() = %d; want %d", test.x, got, test.sign)
+ }
+ if got := x.IsInf(); got != test.inf {
+ t.Errorf("(%s).IsInf() = %v; want %v", test.x, got, test.inf)
+ }
+ }
+}
+
+func TestFloatIsInt(t *testing.T) {
+ for _, test := range []string{
+ "0 int",
+ "-0 int",
+ "1 int",
+ "-1 int",
+ "0.5",
+ "1.23",
+ "1.23e1",
+ "1.23e2 int",
+ "0.000000001e+8",
+ "0.000000001e+9 int",
+ "1.2345e200 int",
+ "Inf",
+ "+Inf",
+ "-Inf",
+ } {
+ s := strings.TrimSuffix(test, " int")
+ want := s != test
+ if got := makeFloat(s).IsInt(); got != want {
+ t.Errorf("%s.IsInt() == %t", s, got)
+ }
+ }
+}
+
+func fromBinary(s string) int64 {
+ x, err := strconv.ParseInt(s, 2, 64)
+ if err != nil {
+ panic(err)
+ }
+ return x
+}
+
+func toBinary(x int64) string {
+ return strconv.FormatInt(x, 2)
+}
+
+func testFloatRound(t *testing.T, x, r int64, prec uint, mode RoundingMode) {
+ // verify test data
+ var ok bool
+ switch mode {
+ case ToNearestEven, ToNearestAway:
+ ok = true // nothing to do for now
+ case ToZero:
+ if x < 0 {
+ ok = r >= x
+ } else {
+ ok = r <= x
+ }
+ case AwayFromZero:
+ if x < 0 {
+ ok = r <= x
+ } else {
+ ok = r >= x
+ }
+ case ToNegativeInf:
+ ok = r <= x
+ case ToPositiveInf:
+ ok = r >= x
+ default:
+ panic("unreachable")
+ }
+ if !ok {
+ t.Fatalf("incorrect test data for prec = %d, %s: x = %s, r = %s", prec, mode, toBinary(x), toBinary(r))
+ }
+
+ // compute expected accuracy
+ a := Exact
+ switch {
+ case r < x:
+ a = Below
+ case r > x:
+ a = Above
+ }
+
+ // round
+ f := new(Float).SetMode(mode).SetInt64(x).SetPrec(prec)
+
+ // check result
+ r1 := f.int64()
+ p1 := f.Prec()
+ a1 := f.Acc()
+ if r1 != r || p1 != prec || a1 != a {
+ t.Errorf("round %s (%d bits, %s) incorrect: got %s (%d bits, %s); want %s (%d bits, %s)",
+ toBinary(x), prec, mode,
+ toBinary(r1), p1, a1,
+ toBinary(r), prec, a)
+ return
+ }
+
+ // g and f should be the same
+ // (rounding by SetPrec after SetInt64 using default precision
+ // should be the same as rounding by SetInt64 after setting the
+ // precision)
+ g := new(Float).SetMode(mode).SetPrec(prec).SetInt64(x)
+ if !alike(g, f) {
+ t.Errorf("round %s (%d bits, %s) not symmetric: got %s and %s; want %s",
+ toBinary(x), prec, mode,
+ toBinary(g.int64()),
+ toBinary(r1),
+ toBinary(r),
+ )
+ return
+ }
+
+ // h and f should be the same
+ // (repeated rounding should be idempotent)
+ h := new(Float).SetMode(mode).SetPrec(prec).Set(f)
+ if !alike(h, f) {
+ t.Errorf("round %s (%d bits, %s) not idempotent: got %s and %s; want %s",
+ toBinary(x), prec, mode,
+ toBinary(h.int64()),
+ toBinary(r1),
+ toBinary(r),
+ )
+ return
+ }
+}
+
+// TestFloatRound tests basic rounding.
+func TestFloatRound(t *testing.T) {
+ for _, test := range []struct {
+ prec uint
+ x, zero, neven, naway, away string // input, results rounded to prec bits
+ }{
+ {5, "1000", "1000", "1000", "1000", "1000"},
+ {5, "1001", "1001", "1001", "1001", "1001"},
+ {5, "1010", "1010", "1010", "1010", "1010"},
+ {5, "1011", "1011", "1011", "1011", "1011"},
+ {5, "1100", "1100", "1100", "1100", "1100"},
+ {5, "1101", "1101", "1101", "1101", "1101"},
+ {5, "1110", "1110", "1110", "1110", "1110"},
+ {5, "1111", "1111", "1111", "1111", "1111"},
+
+ {4, "1000", "1000", "1000", "1000", "1000"},
+ {4, "1001", "1001", "1001", "1001", "1001"},
+ {4, "1010", "1010", "1010", "1010", "1010"},
+ {4, "1011", "1011", "1011", "1011", "1011"},
+ {4, "1100", "1100", "1100", "1100", "1100"},
+ {4, "1101", "1101", "1101", "1101", "1101"},
+ {4, "1110", "1110", "1110", "1110", "1110"},
+ {4, "1111", "1111", "1111", "1111", "1111"},
+
+ {3, "1000", "1000", "1000", "1000", "1000"},
+ {3, "1001", "1000", "1000", "1010", "1010"},
+ {3, "1010", "1010", "1010", "1010", "1010"},
+ {3, "1011", "1010", "1100", "1100", "1100"},
+ {3, "1100", "1100", "1100", "1100", "1100"},
+ {3, "1101", "1100", "1100", "1110", "1110"},
+ {3, "1110", "1110", "1110", "1110", "1110"},
+ {3, "1111", "1110", "10000", "10000", "10000"},
+
+ {3, "1000001", "1000000", "1000000", "1000000", "1010000"},
+ {3, "1001001", "1000000", "1010000", "1010000", "1010000"},
+ {3, "1010001", "1010000", "1010000", "1010000", "1100000"},
+ {3, "1011001", "1010000", "1100000", "1100000", "1100000"},
+ {3, "1100001", "1100000", "1100000", "1100000", "1110000"},
+ {3, "1101001", "1100000", "1110000", "1110000", "1110000"},
+ {3, "1110001", "1110000", "1110000", "1110000", "10000000"},
+ {3, "1111001", "1110000", "10000000", "10000000", "10000000"},
+
+ {2, "1000", "1000", "1000", "1000", "1000"},
+ {2, "1001", "1000", "1000", "1000", "1100"},
+ {2, "1010", "1000", "1000", "1100", "1100"},
+ {2, "1011", "1000", "1100", "1100", "1100"},
+ {2, "1100", "1100", "1100", "1100", "1100"},
+ {2, "1101", "1100", "1100", "1100", "10000"},
+ {2, "1110", "1100", "10000", "10000", "10000"},
+ {2, "1111", "1100", "10000", "10000", "10000"},
+
+ {2, "1000001", "1000000", "1000000", "1000000", "1100000"},
+ {2, "1001001", "1000000", "1000000", "1000000", "1100000"},
+ {2, "1010001", "1000000", "1100000", "1100000", "1100000"},
+ {2, "1011001", "1000000", "1100000", "1100000", "1100000"},
+ {2, "1100001", "1100000", "1100000", "1100000", "10000000"},
+ {2, "1101001", "1100000", "1100000", "1100000", "10000000"},
+ {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},
+
+ // https://www.exploringbinary.com/php-hangs-on-numeric-value-2-2250738585072011e-308/
+ {"2.2250738585072011e-308", 2.225073858507201e-308, Below},
+ // https://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)
+ }
+ }
+ }
+ }
+ }
+}
+
+// TestFloatAddRoundZero tests Float.Add/Sub rounding when the result is exactly zero.
+// x + (-x) or x - x for non-zero x should be +0 in all cases except when
+// the rounding mode is ToNegativeInf in which case it should be -0.
+func TestFloatAddRoundZero(t *testing.T) {
+ for _, mode := range [...]RoundingMode{ToNearestEven, ToNearestAway, ToZero, AwayFromZero, ToPositiveInf, ToNegativeInf} {
+ x := NewFloat(5.0)
+ y := new(Float).Neg(x)
+ want := NewFloat(0.0)
+ if mode == ToNegativeInf {
+ want.Neg(want)
+ }
+ got := new(Float).SetMode(mode)
+ got.Add(x, y)
+ if got.Cmp(want) != 0 || got.neg != (mode == ToNegativeInf) {
+ t.Errorf("%s:\n\t %v\n\t+ %v\n\t= %v\n\twant %v",
+ mode, x, y, got, want)
+ }
+ got.Sub(x, x)
+ if got.Cmp(want) != 0 || got.neg != (mode == ToNegativeInf) {
+ t.Errorf("%v:\n\t %v\n\t- %v\n\t= %v\n\twant %v",
+ mode, x, x, 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)
+ }
+ }
+ }
+}
+
+func TestIssue20490(t *testing.T) {
+ var tests = []struct {
+ a, b float64
+ }{
+ {4, 1},
+ {-4, 1},
+ {4, -1},
+ {-4, -1},
+ }
+
+ for _, test := range tests {
+ a, b := NewFloat(test.a), NewFloat(test.b)
+ diff := new(Float).Sub(a, b)
+ b.Sub(a, b)
+ if b.Cmp(diff) != 0 {
+ t.Errorf("got %g - %g = %g; want %g\n", a, NewFloat(test.b), b, diff)
+ }
+
+ b = NewFloat(test.b)
+ sum := new(Float).Add(a, b)
+ b.Add(a, b)
+ if b.Cmp(sum) != 0 {
+ t.Errorf("got %g + %g = %g; want %g\n", a, NewFloat(test.b), b, sum)
+ }
+
+ }
+}
+
+// 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 %v %v\n\t* %v %v\n\t= %v\n\twant %v",
+ 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 %v %v\n\t/ %v %v\n\t= %v\n\twant %v",
+ 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 = %v != z2 = %v; want z1 == z2\n", prec, z1, z2)
+ }
+ if z1.Sign() != 0 {
+ t.Errorf("prec %d: got z1 = %v; want 0", prec, z1)
+ }
+ if z2.Sign() != 0 {
+ t.Errorf("prec %d: got z2 = %v; 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)
+ }
+ }
+ }
+ }
+}
+
+var long = flag.Bool("long", false, "run very long tests")
+
+// 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 := 10
+ if *long {
+ n = 1000
+ }
+
+ 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)
+ }
+ }
+ }
+ }
+}
+
+func BenchmarkFloatAdd(b *testing.B) {
+ x := new(Float)
+ y := new(Float)
+ z := new(Float)
+
+ for _, prec := range []uint{10, 1e2, 1e3, 1e4, 1e5} {
+ x.SetPrec(prec).SetRat(NewRat(1, 3))
+ y.SetPrec(prec).SetRat(NewRat(1, 6))
+ z.SetPrec(prec)
+
+ b.Run(fmt.Sprintf("%v", prec), func(b *testing.B) {
+ b.ReportAllocs()
+ for i := 0; i < b.N; i++ {
+ z.Add(x, y)
+ }
+ })
+ }
+}
+
+func BenchmarkFloatSub(b *testing.B) {
+ x := new(Float)
+ y := new(Float)
+ z := new(Float)
+
+ for _, prec := range []uint{10, 1e2, 1e3, 1e4, 1e5} {
+ x.SetPrec(prec).SetRat(NewRat(1, 3))
+ y.SetPrec(prec).SetRat(NewRat(1, 6))
+ z.SetPrec(prec)
+
+ b.Run(fmt.Sprintf("%v", prec), func(b *testing.B) {
+ b.ReportAllocs()
+ for i := 0; i < b.N; i++ {
+ z.Sub(x, y)
+ }
+ })
+ }
+}
generated by cgit v1.2.3 (git 2.39.1) at 2024-12-22 21:13:26 +0000