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math/big: fix known bug in Float.Float64
- handle exponent over- and underflow - handle denormalized numbers - added test cases Change-Id: I1bbb9904b0c104f54696944e1f57559881f6eeeb Reviewed-on: https://go-review.googlesource.com/7982 Reviewed-by: Alan Donovan <adonovan@google.com>
This commit is contained in:
Robert Griesemer
parent
0e55f201d6
commit
2c4cf2f6f2
@ -872,9 +872,14 @@ func (x *Float) Int64() (int64, Accuracy) {
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panic("unreachable")
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}
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// Float64 returns the closest float64 value of x
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// by rounding to nearest with 53 bits precision.
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// BUG(gri) Float.Float64 doesn't handle exponent overflow.
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// Float64 returns the float64 value nearest to x by rounding ToNearestEven
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// with 53 bits of precision.
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// If x is too small to be represented by a float64
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// (|x| < math.SmallestNonzeroFloat64), the result is (0, Below) or
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// (-0, Above), respectively, depending on the sign of x.
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// If x is too large to be represented by a float64 (|x| > math.MaxFloat64),
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// the result is (+Inf, Above) or (-Inf, Below), depending on the sign of x.
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// The result is (NaN, Undef) for NaNs.
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func (x *Float) Float64() (float64, Accuracy) {
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if debugFloat {
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x.validate()
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@ -886,27 +891,67 @@ func (x *Float) Float64() (float64, Accuracy) {
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var r Float
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r.prec = 53
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r.Set(x)
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var s uint64
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// Rounding via Set may have caused r to overflow
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// to ±Inf (rounding never causes underflows to 0).
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if r.form == inf {
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r.exp = 10000 // cause overflow below
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}
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// see also implementation of math.Ldexp
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e := int64(r.exp) + 1022
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if e <= -52 {
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// underflow
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if x.neg {
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z := 0.0
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return -z, Above
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}
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return 0.0, Below
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}
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// e > -52
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if e >= 2047 {
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// overflow
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if x.neg {
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return math.Inf(-1), Below
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}
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return math.Inf(+1), Above
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}
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// -52 < e < 2047
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denormal := false
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if e < 0 {
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denormal = true
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e += 52
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}
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// 0 < e < 2047
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s := uint64(0)
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if r.neg {
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s = 1 << 63
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}
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e := uint64(1022+r.exp) & 0x7ff // TODO(gri) check for overflow
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m := high64(r.mant) >> 11 & (1<<52 - 1)
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return math.Float64frombits(s | e<<52 | m), r.acc
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m := high64(r.mant) >> 11 & (1<<52 - 1) // cut off msb (implicit 1 bit)
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z := math.Float64frombits(s | uint64(e)<<52 | m)
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if denormal {
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// adjust for denormal
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// TODO(gri) does this change accuracy?
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z /= 1 << 52
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}
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return z, r.acc
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case zero:
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z := 0.0
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if x.neg {
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z = -z
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z := 0.0
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return -z, Exact
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}
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return z, Exact
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return 0.0, Exact
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case inf:
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sign := +1
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if x.neg {
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sign = -1
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return math.Inf(-1), Exact
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}
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return math.Inf(sign), Exact
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return math.Inf(+1), Exact
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case nan:
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return math.NaN(), Undef
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@ -627,6 +627,10 @@ func TestFloatSetFloat64(t *testing.T) {
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3.14159265e10,
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2.718281828e-123,
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1.0 / 3,
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math.MaxFloat32,
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math.MaxFloat64,
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math.SmallestNonzeroFloat32,
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math.SmallestNonzeroFloat64,
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math.Inf(-1),
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math.Inf(0),
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-math.Inf(1),
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@ -637,8 +641,8 @@ func TestFloatSetFloat64(t *testing.T) {
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}
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var f Float
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f.SetFloat64(want)
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if got, _ := f.Float64(); got != want {
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t.Errorf("got %g (%s); want %g", got, f.Format('p', 0), want)
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if got, acc := f.Float64(); got != want || acc != Exact {
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t.Errorf("got %g (%s, %s); want %g (Exact)", got, f.Format('p', 0), acc, want)
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}
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}
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}
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@ -833,6 +837,56 @@ func TestFloatInt64(t *testing.T) {
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}
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}
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func TestFloatFloat64(t *testing.T) {
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for _, test := range []struct {
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x string
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out float64
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acc Accuracy
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}{
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{"-Inf", math.Inf(-1), Exact},
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{"-0x1.fffffffffffff8p2147483646", -math.Inf(+1), Below}, // overflow in rounding
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{"-1e10000", math.Inf(-1), Below}, // overflow
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{"-0x1p1024", math.Inf(-1), Below}, // overflow
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{"-0x1.fffffffffffff8p1023", -math.Inf(+1), Below}, // overflow
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{"-0x1.fffffffffffff4p1023", -math.MaxFloat64, Above},
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{"-0x1.fffffffffffffp1023", -math.MaxFloat64, Exact},
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{"-12345.000000000000000000001", -12345, Above},
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{"-12345.0", -12345, Exact},
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{"-1.000000000000000000001", -1, Above},
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{"-1", -1, Exact},
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{"-0x0.0000000000001p-1022", -math.SmallestNonzeroFloat64, Exact},
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{"-0x0.0000000000001p-1023", -0, Above}, // underflow
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{"-1e-1000", -0, Above}, // underflow
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{"0", 0, Exact},
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{"1e-1000", 0, Below}, // underflow
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{"0x0.0000000000001p-1023", 0, Below}, // underflow
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{"0x0.0000000000001p-1022", math.SmallestNonzeroFloat64, Exact},
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{"1", 1, Exact},
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{"1.000000000000000000001", 1, Below},
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{"12345.0", 12345, Exact},
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{"12345.000000000000000000001", 12345, Below},
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{"0x1.fffffffffffffp1023", math.MaxFloat64, Exact},
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{"0x1.fffffffffffff4p1023", math.MaxFloat64, Below},
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{"0x1.fffffffffffff8p1023", math.Inf(+1), Above}, // overflow
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{"0x1p1024", math.Inf(+1), Above}, // overflow
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{"1e10000", math.Inf(+1), Above}, // overflow
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{"0x1.fffffffffffff8p2147483646", math.Inf(+1), Above}, // overflow in rounding
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{"+Inf", math.Inf(+1), Exact},
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} {
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x := makeFloat(test.x)
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out, acc := x.Float64()
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if out != test.out || acc != test.acc {
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t.Errorf("%s: got %g (%s); want %g (%s)", test.x, out, acc, test.out, test.acc)
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}
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}
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// test NaN
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x := makeFloat("NaN")
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if out, acc := x.Float64(); out == out || acc != Undef {
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t.Errorf("NaN: got %g (%s); want NaN (Undef)", out, acc)
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}
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}
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func TestFloatInt(t *testing.T) {
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for _, test := range []struct {
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x string
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@ -1073,14 +1127,14 @@ func TestFloatAdd32(t *testing.T) {
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got, acc := z.Float64()
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want := float64(float32(y0) + float32(x0))
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if got != want || acc != Exact {
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t.Errorf("d = %d: %g + %g = %g (%s); want %g exactly", d, x0, y0, got, acc, want)
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t.Errorf("d = %d: %g + %g = %g (%s); want %g (Exact)", d, x0, y0, got, acc, want)
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}
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z.Sub(z, y)
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got, acc = z.Float64()
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want = float64(float32(want) - float32(y0))
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if got != want || acc != Exact {
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t.Errorf("d = %d: %g - %g = %g (%s); want %g exactly", d, x0+y0, y0, got, acc, want)
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t.Errorf("d = %d: %g - %g = %g (%s); want %g (Exact)", d, x0+y0, y0, got, acc, want)
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}
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}
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}
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@ -1106,14 +1160,14 @@ func TestFloatAdd64(t *testing.T) {
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got, acc := z.Float64()
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want := x0 + y0
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if got != want || acc != Exact {
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t.Errorf("d = %d: %g + %g = %g (%s); want %g exactly", d, x0, y0, got, acc, want)
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t.Errorf("d = %d: %g + %g = %g (%s); want %g (Exact)", d, x0, y0, got, acc, want)
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}
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z.Sub(z, y)
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got, acc = z.Float64()
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want -= y0
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if got != want || acc != Exact {
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t.Errorf("d = %d: %g - %g = %g (%s); want %g exactly", d, x0+y0, y0, got, acc, want)
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t.Errorf("d = %d: %g - %g = %g (%s); want %g (Exact)", d, x0+y0, y0, got, acc, want)
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}
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}
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}
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