gc: correct rounding of denormal constants

Fixes #1463.

R=rsc
CC=golang-dev
https://golang.org/cl/4079060

src/cmd/gc/mparith3.c

@@ -179,7 +179,7 @@ mpdivfltflt(Mpflt *a, Mpflt *b)
 double
 mpgetflt(Mpflt *a)
 {
-	int s, i;
+	int s, i, e;
 	uvlong v, vm;
 	double f;
 
@@ -200,12 +200,12 @@ mpgetflt(Mpflt *a)
 		a->exp -= 1;
 	}
 
-	// the magic numbers (64, 63, 53, 10) are
+	// the magic numbers (64, 63, 53, 10, -1074) are
 	// IEEE specific. this should be done machine
 	// independently or in the 6g half of the compiler
 
-	// pick up the mantissa in a uvlong
-	s = 53;
+	// pick up the mantissa and a rounding bit in a uvlong
+	s = 53+1;
 	v = 0;
 	for(i=Mpnorm-1; s>=Mpscale; i--) {
 		v = (v<<Mpscale) | a->val.a[i];
@@ -224,13 +224,26 @@ mpgetflt(Mpflt *a)
 	if(s > 0)
 		v = (v<<s) | (a->val.a[i]>>(Mpscale-s));
 
+	// gradual underflow
+	e = Mpnorm*Mpscale + a->exp - 53;
+	if(e < -1074) {
+		s = -e - 1074;
+		if(s > 54)
+			s = 54;
+		v |= vm & ((1ULL<<s) - 1);
+		vm >>= s;
+		e = -1074;
+	}
+
 //print("vm=%.16llux v=%.16llux\n", vm, v);
 	// round toward even
-	if(v != (1ULL<<63) || (vm&1ULL) != 0)
-		vm += v>>63;
+	if(v != 0 || (vm&2ULL) != 0)
+		vm = (vm>>1) + (vm&1ULL);
+	else
+		vm >>= 1;
 
 	f = (double)(vm);
-	f = ldexp(f, Mpnorm*Mpscale + a->exp - 53);
+	f = ldexp(f, e);
 
 	if(a->val.neg)
 		f = -f;

src/pkg/strconv/ftoa_test.go

@@ -121,9 +121,8 @@ var ftoatests = []ftoaTest{
 
 	// http://www.exploringbinary.com/java-hangs-when-converting-2-2250738585072012e-308/
 	{2.2250738585072012e-308, 'g', -1, "2.2250738585072014e-308"},
-	// TODO: uncomment after fixing issue 1463.
 	// http://www.exploringbinary.com/php-hangs-on-numeric-value-2-2250738585072011e-308/
-	// {2.2250738585072011e-308, 'g', -1, "2.225073858507201e-308"},
+	{2.2250738585072011e-308, 'g', -1, "2.225073858507201e-308"},
 }
 
 func TestFtoa(t *testing.T) {

test/fixedbugs/bug321.go

+// $G $D/$F.go && $L $F.$A && ./$A.out || echo BUG: bug321
+
+// Copyright 2011 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.
+
+// Troublesome floating point constants. Issue 1463.
+
+package main
+
+import "fmt"
+
+func check(test string, got, want float64) bool {
+	if got != want {
+		fmt.Println(test, "got", got, "want", want)
+		return false
+	}
+	return true
+}
+
+func main() {
+	good := true
+	// http://www.exploringbinary.com/java-hangs-when-converting-2-2250738585072012e-308/
+	good = good && check("2.2250738585072012e-308", 2.2250738585072012e-308, 2.2250738585072014e-308)
+	// http://www.exploringbinary.com/php-hangs-on-numeric-value-2-2250738585072011e-308/
+	good = good && check("2.2250738585072011e-308", 2.2250738585072011e-308, 2.225073858507201e-308)
+	if !good {
+		panic("fail")
+	}
+}