p521: Use unsaturated limbs

p521/src/arithmetic/field.rs

@@ -101,14 +101,54 @@ impl FieldElement {
         Self::from_uint_unchecked(U576::from_u64(w))
     }
 
+    /// Converts the words into a byte array to be consumed by [`fiat_p521_from_bytes`]
+    const fn words_to_le_bytes_unchecked(words: [u64; 9]) -> [u8; 66] {
+        let mut result: [u8; 66] = [0u8; 66];
+        let mut i = 0;
+        while i < words.len() - 1 {
+            let word = words[i].to_le_bytes();
+            let start = i * 8;
+            result[start] = word[0];
+            result[start + 1] = word[1];
+            result[start + 2] = word[2];
+            result[start + 3] = word[3];
+            result[start + 4] = word[4];
+            result[start + 5] = word[5];
+            result[start + 6] = word[6];
+            result[start + 7] = word[7];
+            i += 1;
+        }
+        let last_word = words[8].to_le_bytes();
+        debug_assert!(
+            last_word[1] <= 0x1,
+            "Input bound for the result[65] is [0x0 ~> 0x1]"
+        );
+        debug_assert!(
+            last_word[2] == 0
+                && last_word[3] == 0
+                && last_word[4] == 0
+                && last_word[5] == 0
+                && last_word[6] == 0
+                && last_word[7] == 0,
+            "Expected last word to have leading zeroes"
+        );
+
+        result[i * 8] = last_word[0];
+        result[(i * 8) + 1] = last_word[1];
+
+        result
+    }
+
     /// Decode [`FieldElement`] from [`U576`].
     ///
     /// Does *not* perform a check that the field element does not overflow the order.
     ///
     /// Used incorrectly this can lead to invalid results!
     #[cfg(target_pointer_width = "32")]
     pub(crate) const fn from_uint_unchecked(w: U576) -> Self {
-        Self(u32x18_to_u64x9(w.as_words()))
+        Self(fiat_p521_from_bytes(&Self::words_to_le_bytes_unchecked(
+            u32x18_to_u64x9(w.as_words()),
+        )))
     }
 
     /// Decode [`FieldElement`] from [`U576`].
@@ -118,7 +158,9 @@ impl FieldElement {
     /// Used incorrectly this can lead to invalid results!
     #[cfg(target_pointer_width = "64")]
     pub(crate) const fn from_uint_unchecked(w: U576) -> Self {
-        Self(w.to_words())
+        Self(fiat_p521_from_bytes(&Self::words_to_le_bytes_unchecked(
+            w.to_words(),
+        )))
     }
 
     /// Returns the big-endian encoding of this [`FieldElement`].