math/rand: Float32/64 must only return values in [0,1)

Float32 and Float64 are now both created by taking the ratio
of two integers which are chosen to fit entirely into the
precision of the desired float type. The previous code
could cast a Float64 with more than 23 bits of ".99999"
into a Float32 of 1.0, which is not in [0,1).

Float32 went from 15 to 21 ns/op (but is now correct).

Fixes #6721.

R=golang-dev, iant, rsc
CC=golang-dev
https://golang.org/cl/22730043

src/pkg/math/rand/example_test.go

@@ -83,8 +83,8 @@ func Example_rand() {
 	// Perm generates a random permutation of the numbers [0, n).
 	show("Perm", r.Perm(5), r.Perm(5), r.Perm(5))
 	// Output:
-	// Float32     0.2635776           0.6358173           0.6718283
-	// Float64     0.628605430454327   0.4504798828572669  0.9562755949377957
+	// Float32     0.73793465          0.38461488          0.9940225
+	// Float64     0.6919607852308565  0.29140004584133117 0.2262092163027547
 	// ExpFloat64  0.3362240648200941  1.4256072328483647  0.24354758816173044
 	// NormFloat64 0.17233959114940064 1.577014951434847   0.04259129641113857
 	// Int31       1501292890          1486668269          182840835

src/pkg/math/rand/rand.go

@@ -95,10 +95,10 @@ func (r *Rand) Intn(n int) int {
 }
 
 // Float64 returns, as a float64, a pseudo-random number in [0.0,1.0).
-func (r *Rand) Float64() float64 { return float64(r.Int63()) / (1 << 63) }
+func (r *Rand) Float64() float64 { return float64(r.Int63n(1<<53)) / (1 << 53) }
 
 // Float32 returns, as a float32, a pseudo-random number in [0.0,1.0).
-func (r *Rand) Float32() float32 { return float32(r.Float64()) }
+func (r *Rand) Float32() float32 { return float32(r.Int31n(1<<24)) / (1 << 24) }
 
 // Perm returns, as a slice of n ints, a pseudo-random permutation of the integers [0,n).
 func (r *Rand) Perm(n int) []int {

src/pkg/math/rand/rand_test.go

@@ -322,6 +322,17 @@ func TestExpTables(t *testing.T) {
 	}
 }
 
+// For issue 6721, the problem came after 7533753 calls, so check 10e6.
+func TestFloat32(t *testing.T) {
+	r := New(NewSource(1))
+	for ct := 0; ct < 10e6; ct++ {
+		f := r.Float32()
+		if f >= 1 {
+			t.Fatal("Float32() should be in range [0,1). ct:", ct, "f:", f)
+		}
+	}
+}
+
 // Benchmarks
 
 func BenchmarkInt63Threadsafe(b *testing.B) {
@@ -358,6 +369,13 @@ func BenchmarkInt31n1000(b *testing.B) {
 	}
 }
 
+func BenchmarkFloat32(b *testing.B) {
+	r := New(NewSource(1))
+	for n := b.N; n > 0; n-- {
+		r.Float32()
+	}
+}
+
 func BenchmarkPerm3(b *testing.B) {
 	r := New(NewSource(1))
 	for n := b.N; n > 0; n-- {