feat: Avoid heap allocs when going to/from field (#7547)

This PR plus [integer operations using
u128](#7518) makes
[this
test](https://github.com/zac-williamson/noir_bigcurve/blob/main/src/bigcurve_test.nr#L129)
go from 110 seconds of ACVM execution to around 22 seconds (34 seconds
with only the change of the integer ops)

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---------

Co-authored-by: Maxim Vezenov <mvezenov@gmail.com>

noir/noir-repo/acvm-repo/acir_field/src/field_element.rs

@@ -139,17 +139,25 @@ impl<'de, T: ark_ff::PrimeField> Deserialize<'de> for FieldElement<T> {
 
 impl<F: PrimeField> From<u128> for FieldElement<F> {
     fn from(a: u128) -> FieldElement<F> {
-        let result = match F::from_str(&a.to_string()) {
-            Ok(result) => result,
-            Err(_) => panic!("Cannot convert u128 as a string to a field element"),
-        };
-        FieldElement(result)
+        FieldElement(F::from(a))
     }
 }
 
 impl<F: PrimeField> From<usize> for FieldElement<F> {
     fn from(a: usize) -> FieldElement<F> {
-        FieldElement::from(a as u128)
+        FieldElement::from(a as u64)
+    }
+}
+
+impl<F: PrimeField> From<u64> for FieldElement<F> {
+    fn from(a: u64) -> FieldElement<F> {
+        FieldElement(F::from(a))
+    }
+}
+
+impl<F: PrimeField> From<u32> for FieldElement<F> {
+    fn from(a: u32) -> FieldElement<F> {
+        FieldElement(F::from(a))
     }
 }
 
@@ -265,8 +273,16 @@ impl<F: PrimeField> AcirField for FieldElement<F> {
     }
 
     fn to_u128(self) -> u128 {
-        let bytes = self.to_be_bytes();
-        u128::from_be_bytes(bytes[16..32].try_into().unwrap())
+        let as_bigint = self.0.into_bigint();
+        let limbs = as_bigint.as_ref();
+
+        let mut result = limbs[0] as u128;
+        if limbs.len() > 1 {
+            let high_limb = limbs[1] as u128;
+            result += high_limb << 64;
+        }
+
+        result
     }
 
     fn try_into_u128(self) -> Option<u128> {