diff --git a/crates/wast/src/lexer.rs b/crates/wast/src/lexer.rs
index 0888646c8f..041ac5da8b 100644
--- a/crates/wast/src/lexer.rs
+++ b/crates/wast/src/lexer.rs
@@ -225,7 +225,7 @@ pub enum Float<'a> {
     /// A float `NaN` representation
     Nan {
         /// The specific bits to encode for this float, optionally
-        val: Option<u64>,
+        val: Option<Cow<'a, str>>,
         /// Whether or not this is a negative `NaN` or not.
         negative: bool,
     },
@@ -955,13 +955,10 @@ impl Token {
             } => {
                 let src = self.src(s);
                 let src = if src.starts_with("n") { src } else { &src[1..] };
-                let mut src = src.strip_prefix("nan:0x").unwrap();
-                let owned;
+                let mut val = Cow::Borrowed(src.strip_prefix("nan:0x").unwrap());
                 if has_underscores {
-                    owned = src.replace("_", "");
-                    src = &owned;
+                    *val.to_mut() = val.replace("_", "");
                 }
-                let val = u64::from_str_radix(src, 16).unwrap();
                 Float::Nan {
                     val: Some(val),
                     negative,
@@ -1344,14 +1341,14 @@ mod tests {
         assert_eq!(
             get_float("+nan:0x1"),
             Float::Nan {
-                val: Some(1),
+                val: Some("1".into()),
                 negative: false,
             },
         );
         assert_eq!(
             get_float("nan:0x7f_ffff"),
             Float::Nan {
-                val: Some(0x7fffff),
+                val: Some("7fffff".into()),
                 negative: false,
             },
         );
diff --git a/crates/wast/src/token.rs b/crates/wast/src/token.rs
index 575d62e7e6..9a93bccd3f 100644
--- a/crates/wast/src/token.rs
+++ b/crates/wast/src/token.rs
@@ -441,7 +441,10 @@ macro_rules! float {
                 Float::Nan { negative, val } => {
                     let exp_bits = (1 << $exp_bits) - 1;
                     let neg_bit = *negative as $int;
-                    let signif = val.unwrap_or(1 << (signif_bits - 1)) as $int;
+                    let signif = match val {
+                        Some(val) => $int::from_str_radix(val,16).ok()?,
+                        None => 1 << (signif_bits - 1),
+                    };
                     // If the significand is zero then this is actually infinity
                     // so we fail to parse it.
                     if signif & signif_mask == 0 {
diff --git a/tests/local/bad-nan.wast b/tests/local/bad-nan.wast
new file mode 100644
index 0000000000..dc532723c6
--- /dev/null
+++ b/tests/local/bad-nan.wast
@@ -0,0 +1,11 @@
+(assert_malformed
+  (module quote "(func (result f64) (f64.const nan:0x11111111800800080))")
+  "constant out of range")
+
+(assert_malformed
+  (module quote "(func (result f64) (f64.const nan:0xffffffffffffffff0))")
+  "constant out of range")
+
+(assert_malformed
+  (module quote "(func (result f32) (f32.const nan:0xffffffff0))")
+  "constant out of range")