diff --git a/src/cmd/gc/go.h b/src/cmd/gc/go.h
index 151032eb90..36d5167594 100644
--- a/src/cmd/gc/go.h
+++ b/src/cmd/gc/go.h
@@ -1255,6 +1255,7 @@ void	mpmovecflt(Mpflt *a, double c);
 void	mpmulfltflt(Mpflt *a, Mpflt *b);
 void	mpnegflt(Mpflt *a);
 void	mpnorm(Mpflt *a);
+void	mpsetexp(Mpflt *a, int exp);
 int	mptestflt(Mpflt *a);
 int	sigfig(Mpflt *a);
 
diff --git a/src/cmd/gc/mparith1.c b/src/cmd/gc/mparith1.c
index 41412c416d..19310a7c8c 100644
--- a/src/cmd/gc/mparith1.c
+++ b/src/cmd/gc/mparith1.c
@@ -416,7 +416,7 @@ mpatoflt(Mpflt *a, char *as)
 	if(eb) {
 		if(dp)
 			goto bad;
-		a->exp += ex;
+		mpsetexp(a, a->exp+ex);
 		goto out;
 	}
 
@@ -427,8 +427,13 @@ mpatoflt(Mpflt *a, char *as)
 			mppow10flt(&b, ex-dp);
 			mpmulfltflt(a, &b);
 		} else {
-			mppow10flt(&b, dp-ex);
-			mpdivfltflt(a, &b);
+			if((short)(dp-ex) != dp-ex) {
+				mpmovecflt(a, 0.0);
+			}
+			else {
+				mppow10flt(&b, dp-ex);
+				mpdivfltflt(a, &b);
+			}
 		}
 	}
 
diff --git a/src/cmd/gc/mparith3.c b/src/cmd/gc/mparith3.c
index f8344c9b4e..da5372cd83 100644
--- a/src/cmd/gc/mparith3.c
+++ b/src/cmd/gc/mparith3.c
@@ -22,6 +22,27 @@ sigfig(Mpflt *a)
 	return i+1;
 }
 
+/*
+ * sets the exponent.
+ * a too large exponent is an error.
+ * a too small exponent rounds the number to zero.
+ */
+void
+mpsetexp(Mpflt *a, int exp) {
+	if((short)exp != exp) {
+		if(exp > 0) {
+			yyerror("float constant is too large");
+			a->exp = 0x7fff;
+		}
+		else {
+			mpmovecflt(a, 0);
+		}
+	}
+	else {
+		a->exp = exp;
+	}
+}
+
 /*
  * shifts the leading non-zero
  * word of the number to Mpnorm
@@ -60,7 +81,7 @@ mpnorm(Mpflt *a)
 	}
 
 	mpshiftfix(&a->val, s);
-	a->exp -= s;
+	mpsetexp(a, a->exp-s);
 }
 
 /// implements float arihmetic
@@ -95,7 +116,7 @@ mpaddfltflt(Mpflt *a, Mpflt *b)
 	if(s < 0) {
 		// b is larger, shift a right
 		mpshiftfix(&a->val, s);
-		a->exp -= s;
+		mpsetexp(a, a->exp-s);
 		mpaddfixfix(&a->val, &b->val, 0);
 		goto out;
 	}
@@ -131,7 +152,7 @@ mpmulfltflt(Mpflt *a, Mpflt *b)
 	}
 
 	mpmulfract(&a->val, &b->val);
-	a->exp = (a->exp + b->exp) + Mpscale*Mpprec - Mpscale - 1;
+	mpsetexp(a, (a->exp + b->exp) + Mpscale*Mpprec - Mpscale - 1);
 
 	mpnorm(a);
 	if(Mpdebug)
@@ -171,7 +192,7 @@ mpdivfltflt(Mpflt *a, Mpflt *b)
 
 	// divide
 	mpdivfract(&a->val, &c.val);
-	a->exp = (a->exp-c.exp) - Mpscale*(Mpprec-1) + 1;
+	mpsetexp(a, (a->exp-c.exp) - Mpscale*(Mpprec-1) + 1);
 
 	mpnorm(a);
 	if(Mpdebug)
@@ -199,7 +220,10 @@ mpgetflt(Mpflt *a)
 
 	while((a->val.a[Mpnorm-1] & Mpsign) == 0) {
 		mpshiftfix(&a->val, 1);
-		a->exp -= 1;
+		mpsetexp(a, a->exp-1);	// can set 'a' to zero
+		s = sigfig(a);
+		if(s == 0)
+			return 0;
 	}
 
 	// the magic numbers (64, 63, 53, 10, -1074) are
diff --git a/test/fixedbugs/issue7419.go b/test/fixedbugs/issue7419.go
new file mode 100644
index 0000000000..39b454c059
--- /dev/null
+++ b/test/fixedbugs/issue7419.go
@@ -0,0 +1,25 @@
+// run
+
+// Copyright 2014 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.
+
+// Issue 7419: odd behavior for float constants underflowing to 0
+
+package main
+
+import (
+	"os"
+)
+
+var x = 1e-779137
+var y = 1e-779138
+
+func main() {
+	if x != 0 {
+		os.Exit(1)
+	}
+	if y != 0 {
+		os.Exit(2)
+	}
+}