math/big: change Float.SetMantExp to always multiply mant by 2**exp

Change-Id: If840e647376a2141f8c17729f7ef251bfff13f5f
Reviewed-on: https://go-review.googlesource.com/5810
Reviewed-by: Rob Pike <r@golang.org>

src/math/big/float.go

@@ -219,22 +219,24 @@ func (x *Float) MantExp() (mant *Float, exp int) {
 	return
 }
 
-// SetMantExp is the inverse of MantExp. It sets z to mant × 2**exp and
-// and returns z. The result z has the same precision and rounding mode
-// as mant.
+// SetMantExp sets z to mant × 2**exp and and returns z.
+// The result z has the same precision and rounding mode
+// as mant. SetMantExp is an inverse of MantExp but does
+// not require 0.5 <= |mant| < 1.0. Specifically:
+//
+//	new(Float).SetMantExp(x.MantExp()).Cmp(x) == 0
 //
 // Special cases are:
 //
 //	z.SetMantExp(  ±0, exp) =   ±0
 //	z.SetMantExp(±Inf, exp) = ±Inf
 //
-// The result is ±Inf if the magnitude of exp is > MaxExp.
 func (z *Float) SetMantExp(mant *Float, exp int) *Float {
 	z.Copy(mant)
 	if len(z.mant) == 0 || z.exp == infExp {
 		return z
 	}
-	z.setExp(int64(exp))
+	z.setExp(int64(z.exp) + int64(exp))
 	return z
 }
 

src/math/big/float_test.go

@@ -167,11 +167,17 @@ func TestFloatSetMantExp(t *testing.T) {
 		{"+Inf", -1234, "+Inf"},
 		{"-Inf", -1234, "-Inf"},
 		{"0", -MaxExp - 1, "0"},
-		{"1", -MaxExp - 1, "+Inf"},  // exponent magnitude too large
-		{"-1", -MaxExp - 1, "-Inf"}, // exponent magnitude too large
+		{"0.5", -MaxExp - 1, "+Inf"},  // exponent overflow
+		{"-0.5", -MaxExp - 1, "-Inf"}, // exponent overflow
+		{"0.5", MaxExp + 1, "+Inf"},   // exponent overflow
+		{"-0.5", MaxExp + 1, "-Inf"},  // exponent overflow
+		{"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)
@@ -180,6 +186,10 @@ func TestFloatSetMantExp(t *testing.T) {
 		if !feq(&z, want) {
 			t.Errorf("SetMantExp(%s, %d) = %s; want %s", test.frac, test.exp, z.Format('g', 10), test.z)
 		}
+		// test inverse property
+		if z.SetMantExp(want.MantExp()).Cmp(want) != 0 {
+			t.Errorf("Inverse property not satisfied: got %s; want %s", z.Format('g', 10), test.z)
+		}
 	}
 }