diff --git a/api/except.txt b/api/except.txt
index f5a7aa854e6..14fe7785fa5 100644
--- a/api/except.txt
+++ b/api/except.txt
@@ -1,5 +1,6 @@
 pkg encoding/json, method (*RawMessage) MarshalJSON() ([]uint8, error)
 pkg math, const MaxFloat64 = 1.79769e+308  // 179769313486231570814527423731704356798100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
+pkg math, const SmallestNonzeroFloat32 = 1.4013e-45  // 17516230804060213386546619791123951641/12500000000000000000000000000000000000000000000000000000000000000000000000000000000
 pkg math, const SmallestNonzeroFloat64 = 4.94066e-324  // 4940656458412465441765687928682213723651/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
 pkg math/big, const MaxBase = 36
 pkg math/big, type Word uintptr
diff --git a/src/math/const.go b/src/math/const.go
index 441b295ed4f..31954b0caea 100644
--- a/src/math/const.go
+++ b/src/math/const.go
@@ -28,11 +28,11 @@ const (
 // Max is the largest finite value representable by the type.
 // SmallestNonzero is the smallest positive, non-zero value representable by the type.
 const (
-	MaxFloat32             = 3.40282346638528859811704183484516925440e+38  // 2**127 * (2**24 - 1) / 2**23
-	SmallestNonzeroFloat32 = 1.401298464324817070923729583289916131280e-45 // 1 / 2**(127 - 1 + 23)
+	MaxFloat32             = 0x1p127 * (1 + (1 - 0x1p-23)) // 3.40282346638528859811704183484516925440e+38
+	SmallestNonzeroFloat32 = 0x1p-126 * 0x1p-23            // 1.401298464324817070923729583289916131280e-45
 
-	MaxFloat64             = 1.79769313486231570814527423731704356798070e+308   // 2**1023 * (2**53 - 1) / 2**52
-	SmallestNonzeroFloat64 = 4.9406564584124654417656879286822137236505980e-324 // 1 / 2**(1023 - 1 + 52)
+	MaxFloat64             = 0x1p1023 * (1 + (1 - 0x1p-52)) // 1.79769313486231570814527423731704356798070e+308
+	SmallestNonzeroFloat64 = 0x1p-1022 * 0x1p-52            // 4.9406564584124654417656879286822137236505980e-324
 )
 
 // Integer limit values.