math: Fix off-by-one error in Ilogb and Logb.

Fixes #1141.

R=rsc
CC=adg, golang-dev
https://golang.org/cl/2194047

src/pkg/math/all_test.go

@@ -383,16 +383,16 @@ var log = []float64{
 	2.161703872847352815363655e+00,
 }
 var logb = []float64{
-	3.0000000000000000e+00,
-	3.0000000000000000e+00,
-	-1.0000000000000000e+00,
-	3.0000000000000000e+00,
-	4.0000000000000000e+00,
+	2.0000000000000000e+00,
+	2.0000000000000000e+00,
+	-2.0000000000000000e+00,
 	2.0000000000000000e+00,
 	3.0000000000000000e+00,
+	1.0000000000000000e+00,
 	2.0000000000000000e+00,
 	1.0000000000000000e+00,
-	4.0000000000000000e+00,
+	0.0000000000000000e+00,
+	3.0000000000000000e+00,
 }
 var log10 = []float64{
 	6.9714316642508290997617083e-01,
@@ -1806,8 +1806,9 @@ func TestHypot(t *testing.T) {
 
 func TestIlogb(t *testing.T) {
 	for i := 0; i < len(vf); i++ {
-		if e := Ilogb(vf[i]); frexp[i].i != e {
-			t.Errorf("Ilogb(%g) = %d, want %d", vf[i], e, frexp[i].i)
+		a := frexp[i].i - 1 // adjust because fr in the interval [½, 1)
+		if e := Ilogb(vf[i]); a != e {
+			t.Errorf("Ilogb(%g) = %d, want %d", vf[i], e, a)
 		}
 	}
 	for i := 0; i < len(vflogbSC); i++ {

src/pkg/math/logb.go

@@ -4,7 +4,7 @@
 
 package math
 
-// Logb(x) returns the binary logarithm of non-zero x.
+// Logb(x) returns the binary exponent of non-zero x.
 //
 // Special cases are:
 //	Logb(±Inf) = +Inf
@@ -22,10 +22,10 @@ func Logb(x float64) float64 {
 	case x != x: // IsNaN(x):
 		return x
 	}
-	return float64(int((Float64bits(x)>>shift)&mask) - bias)
+	return float64(int((Float64bits(x)>>shift)&mask) - (bias + 1))
 }
 
-// Ilogb(x) returns the binary logarithm of non-zero x as an integer.
+// Ilogb(x) returns the binary exponent of non-zero x as an integer.
 //
 // Special cases are:
 //	Ilogb(±Inf) = MaxInt32
@@ -43,5 +43,5 @@ func Ilogb(x float64) int {
 	case x < -MaxFloat64 || x > MaxFloat64: // IsInf(x, 0):
 		return MaxInt32
 	}
-	return int((Float64bits(x)>>shift)&mask) - bias
+	return int((Float64bits(x)>>shift)&mask) - (bias + 1)
 }