diff --git a/src/internal/strconv/atof.go b/src/internal/strconv/atof.go
index 443c222279fcea..d1470f05c09eb2 100644
--- a/src/internal/strconv/atof.go
+++ b/src/internal/strconv/atof.go
@@ -97,6 +97,7 @@ func (b *decimal) set(s string) (ok bool) {
 	// digits
 	sawdot := false
 	sawdigits := false
+	nd := 0 // number of significant digits
 	for ; i < len(s); i++ {
 		switch {
 		case s[i] == '_':
@@ -107,15 +108,16 @@ func (b *decimal) set(s string) (ok bool) {
 				return
 			}
 			sawdot = true
-			b.dp = b.nd
+			b.dp = nd
 			continue
 
 		case '0' <= s[i] && s[i] <= '9':
 			sawdigits = true
-			if s[i] == '0' && b.nd == 0 { // ignore leading zeros
+			if s[i] == '0' && nd == 0 { // ignore leading zeros
 				b.dp--
 				continue
 			}
+			nd++
 			if b.nd < len(b.d) {
 				b.d[b.nd] = s[i]
 				b.nd++
@@ -130,7 +132,7 @@ func (b *decimal) set(s string) (ok bool) {
 		return
 	}
 	if !sawdot {
-		b.dp = b.nd
+		b.dp = nd
 	}
 
 	// optional exponent moves decimal point.
diff --git a/src/internal/strconv/atof_test.go b/src/internal/strconv/atof_test.go
index 3c5135a5db67dd..80d86e5f5da7d2 100644
--- a/src/internal/strconv/atof_test.go
+++ b/src/internal/strconv/atof_test.go
@@ -300,6 +300,15 @@ var atoftests = []atofTest{
 	{"1.00000000000000011102230246251565404236316680908203125" + strings.Repeat("0", 10000) + "1", "1.0000000000000002", nil},
 	{"0x1.00000000000008" + strings.Repeat("0", 10000) + "1p0", "1.0000000000000002", nil},
 
+	// Integer part longer than the slow path's 800-digit decimal buffer.
+	{"1" + strings.Repeat("0", 799) + "e-673", "1e+126", nil},
+	{"1" + strings.Repeat("0", 800) + "e-674", "1e+126", nil},
+	{"1" + strings.Repeat("0", 826) + "e-700", "1e+126", nil},
+	{"1" + strings.Repeat("0", 826) + ".5e-700", "1e+126", nil},
+	// The nonzero tail sets trunc, and d and d+1 round differently near 1e126,
+	// so the optimized path falls back to the slow path too.
+	{"1" + strings.Repeat("0", 824) + "1e-699", "1e+126", nil},
+
 	// Halfway between x := math.Nextafter(1, 2) and math.Nextafter(x, 2)
 	// Round to even (up).
 	{"1.00000000000000033306690738754696212708950042724609375", "1.0000000000000004", nil},
@@ -371,6 +380,9 @@ var atof32tests = []atofTest{
 	{"1.000000059604644775390625" + strings.Repeat("0", 10000) + "1", "1.0000001", nil},
 	{"0x1.000001" + strings.Repeat("0", 10000) + "1p0", "1.0000001", nil},
 
+	// Integer part longer than the slow path's 800-digit decimal buffer.
+	{"1" + strings.Repeat("0", 824) + "1e-795", "1e+30", nil},
+
 	// largest float32: (1<<128) * (1 - 2^-24)
 	{"340282346638528859811704183484516925440", "3.4028235e+38", nil},
 	{"-340282346638528859811704183484516925440", "-3.4028235e+38", nil},