diff --git a/mopro-msm/src/msm/metal_msm/host/shader.rs b/mopro-msm/src/msm/metal_msm/host/shader.rs
index 2ce0e5c..dc9d665 100644
--- a/mopro-msm/src/msm/metal_msm/host/shader.rs
+++ b/mopro-msm/src/msm/metal_msm/host/shader.rs
@@ -111,6 +111,7 @@ pub fn write_constants(
 ) {
     let two_pow_word_size = 2u32.pow(log_limb_size);
     let mask = two_pow_word_size - 1u32;
+    let slack = num_limbs as u32 * log_limb_size - BaseField::MODULUS_BIT_SIZE;
     let num_limbs_wide = num_limbs + 1;
     let basefield_modulus = BaseField::MODULUS.to_limbs(num_limbs, log_limb_size);
     let r = calc_mont_radix(num_limbs, log_limb_size);
@@ -132,6 +133,7 @@ pub fn write_constants(
     data += format!("#define MASK {}\n", mask).as_str();
     data += format!("#define N0 {}\n", n0).as_str();
     data += format!("#define NSAFE {}\n", nsafe).as_str();
+    data += format!("#define SLACK {}\n", slack).as_str();
 
     write_constant_array!(
         data,
@@ -182,7 +184,6 @@ pub fn write_constants(
     );
 
     let p: BigUint = BaseField::MODULUS.try_into().unwrap();
-    let (rinv, n0) = calc_rinv_and_n0(&p, &r, log_limb_size);
     let (bn254_zero_xr_limbs, bn254_zero_yr_limbs, bn254_zero_zr_limbs) = {
         let bn254_zero_x: BigUint = bn254_zero.x.into();
         let bn254_zero_y: BigUint = bn254_zero.y.into();
diff --git a/mopro-msm/src/msm/metal_msm/utils/limbs_conversion.rs b/mopro-msm/src/msm/metal_msm/utils/limbs_conversion.rs
index 3d087c1..e71d4a5 100644
--- a/mopro-msm/src/msm/metal_msm/utils/limbs_conversion.rs
+++ b/mopro-msm/src/msm/metal_msm/utils/limbs_conversion.rs
@@ -1,9 +1,9 @@
-use ark_ff::biginteger::{BigInteger, BigInteger256, BigInteger384};
+use ark_ff::biginteger::{BigInt, BigInteger};
 use std::convert::TryInto;
 
 /// A trait that abstracts "to/from limbs" for *any* BigInteger type
 pub trait GenericLimbConversion {
-    /// The number of 64-bit words in this BigInteger (e.g., 4 for BigInteger256)
+    /// The number of 64-bit words in this BigInteger (e.g., 4 for BigInt<4>)
     const NUM_WORDS: usize;
 
     /// Convert to big-endian `u32` limbs of length `2 * NUM_WORDS`.
@@ -26,12 +26,12 @@ pub trait GenericLimbConversion {
     fn from_limbs(limbs: &[u32], log_limb_size: u32) -> Self;
 }
 
-impl GenericLimbConversion for BigInteger256 {
+impl GenericLimbConversion for BigInt<4> {
     const NUM_WORDS: usize = 4; // 4 x 64-bit words
 
     fn to_u32_limbs(&self) -> Vec<u32> {
         let mut limbs = Vec::new();
-        // BigInteger256::to_bytes_be() gives us 32 bytes in BE
+        // BigInt<4>::to_bytes_be() gives us 32 bytes in BE
         self.to_bytes_be().chunks(8).for_each(|chunk| {
             let high = u32::from_be_bytes(chunk[0..4].try_into().unwrap());
             let low = u32::from_be_bytes(chunk[4..8].try_into().unwrap());
@@ -81,17 +81,17 @@ impl GenericLimbConversion for BigInteger256 {
             let low = u64::from(limb_pair[1]);
             big_int[i] = (high << 32) | low;
         }
-        BigInteger256::new(big_int)
+        BigInt::<4>::new(big_int)
     }
 
     fn from_u128(num: u128) -> Self {
         let high = (num >> 64) as u64;
         let low = num as u64;
-        BigInteger256::new([low, high, 0, 0])
+        BigInt::<4>::new([low, high, 0, 0])
     }
 
     fn from_u32(num: u32) -> Self {
-        BigInteger256::new([num as u64, 0, 0, 0])
+        BigInt::<4>::new([num as u64, 0, 0, 0])
     }
 
     fn from_limbs(limbs: &[u32], log_limb_size: u32) -> Self {
@@ -116,11 +116,11 @@ impl GenericLimbConversion for BigInteger256 {
         if accumulated_bits > 0 && result_idx < 4 {
             result[result_idx] = current_u64;
         }
-        BigInteger256::new(result)
+        BigInt::<4>::new(result)
     }
 }
 
-impl GenericLimbConversion for BigInteger384 {
+impl GenericLimbConversion for BigInt<6> {
     const NUM_WORDS: usize = 6; // 6 x 64-bit words
 
     fn to_u32_limbs(&self) -> Vec<u32> {
@@ -172,17 +172,17 @@ impl GenericLimbConversion for BigInteger384 {
             let low = u64::from(limb_pair[1]);
             big_int[i] = (high << 32) | low;
         }
-        BigInteger384::new(big_int)
+        BigInt::<6>::new(big_int)
     }
 
     fn from_u128(num: u128) -> Self {
         let high = (num >> 64) as u64;
         let low = num as u64;
-        BigInteger384::new([low, high, 0, 0, 0, 0])
+        BigInt::<6>::new([low, high, 0, 0, 0, 0])
     }
 
     fn from_u32(num: u32) -> Self {
-        BigInteger384::new([num as u64, 0, 0, 0, 0, 0])
+        BigInt::<6>::new([num as u64, 0, 0, 0, 0, 0])
     }
 
     fn from_limbs(limbs: &[u32], log_limb_size: u32) -> Self {
@@ -206,7 +206,96 @@ impl GenericLimbConversion for BigInteger384 {
         if accumulated_bits > 0 && result_idx < 6 {
             result[result_idx] = current_u64;
         }
-        BigInteger384::new(result)
+        BigInt::<6>::new(result)
+    }
+}
+
+impl GenericLimbConversion for BigInt<8> {
+    const NUM_WORDS: usize = 8; // 8 x 64-bit words
+
+    fn to_u32_limbs(&self) -> Vec<u32> {
+        let mut limbs = Vec::new();
+        self.to_bytes_be().chunks(8).for_each(|chunk| {
+            let high = u32::from_be_bytes(chunk[0..4].try_into().unwrap());
+            let low = u32::from_be_bytes(chunk[4..8].try_into().unwrap());
+            limbs.push(high);
+            limbs.push(low);
+        });
+        limbs
+    }
+
+    fn to_limbs(&self, num_limbs: usize, log_limb_size: u32) -> Vec<u32> {
+        let mut result = vec![0u32; num_limbs];
+        let limb_size = 1u32 << log_limb_size;
+        let mask = limb_size - 1;
+
+        let bytes = self.to_bytes_le();
+        let mut val = 0u32;
+        let mut bits = 0u32;
+        let mut limb_idx = 0;
+
+        for &byte in bytes.iter() {
+            if limb_idx >= num_limbs {
+                break;
+            }
+            val |= (byte as u32) << bits;
+            bits += 8;
+
+            while bits >= log_limb_size && limb_idx < num_limbs {
+                result[limb_idx] = val & mask;
+                val >>= log_limb_size;
+                bits -= log_limb_size;
+                limb_idx += 1;
+            }
+        }
+        if bits > 0 && limb_idx < num_limbs {
+            result[limb_idx] = val;
+        }
+        result
+    }
+
+    fn from_u32_limbs(limbs: &[u32]) -> Self {
+        let mut big_int = [0u64; 8];
+        for (i, limb_pair) in limbs.chunks(2).rev().enumerate() {
+            let high = u64::from(limb_pair[0]);
+            let low = u64::from(limb_pair[1]);
+            big_int[i] = (high << 32) | low;
+        }
+        BigInt::<8>::new(big_int)
+    }
+
+    fn from_u128(num: u128) -> Self {
+        let high = (num >> 64) as u64;
+        let low = num as u64;
+        BigInt::<8>::new([low, high, 0, 0, 0, 0, 0, 0])
+    }
+
+    fn from_u32(num: u32) -> Self {
+        BigInt::<8>::new([num as u64, 0, 0, 0, 0, 0, 0, 0])
+    }
+
+    fn from_limbs(limbs: &[u32], log_limb_size: u32) -> Self {
+        let mut result = [0u64; 8];
+        let limb_bits = log_limb_size as usize;
+        let mut accumulated_bits = 0;
+        let mut current_u64 = 0u64;
+        let mut result_idx = 0;
+
+        for &limb in limbs {
+            current_u64 |= (limb as u64) << accumulated_bits;
+            accumulated_bits += limb_bits;
+
+            while accumulated_bits >= 64 && result_idx < 8 {
+                result[result_idx] = current_u64;
+                current_u64 = (limb as u64) >> (limb_bits - (accumulated_bits - 64));
+                accumulated_bits -= 64;
+                result_idx += 1;
+            }
+        }
+        if accumulated_bits > 0 && result_idx < 8 {
+            result[result_idx] = current_u64;
+        }
+        BigInt::<8>::new(result)
     }
 }
 
@@ -217,6 +306,7 @@ mod tests {
     use crate::msm::metal_msm::utils::mont_params::calc_mont_radix;
     use ark_bn254::Fq as BaseField;
     use ark_ff::{BigInt, PrimeField};
+    use num_bigint::{BigUint, RandBigInt};
 
     #[test]
     fn test_within_bigint256() {
@@ -224,7 +314,7 @@ mod tests {
         let log_limb_size = 16;
 
         let p_limbs = BaseField::MODULUS.to_limbs(num_limbs, log_limb_size);
-        let p_bigint256 = BigInteger256::from_limbs(&p_limbs, log_limb_size);
+        let p_bigint256 = BigInt::<4>::from_limbs(&p_limbs, log_limb_size);
 
         assert_eq!(BaseField::MODULUS, p_bigint256);
     }
@@ -238,9 +328,30 @@ mod tests {
         let r = calc_mont_radix(num_limbs, log_limb_size); // r has 257 bits
         let r_bigint384: BigInt<6> = r.try_into().unwrap();
         let r_limbs = r_bigint384.to_limbs(num_limbs_wide, log_limb_size);
-        let r_reconstructed = BigInteger384::from_limbs(&r_limbs, log_limb_size);
+        let r_reconstructed = BigInt::<6>::from_limbs(&r_limbs, log_limb_size);
 
         // Check if the original and reconstructed values are equal
         assert_eq!(r_bigint384, r_reconstructed);
     }
+
+    #[test]
+    fn test_within_bigint512() {
+        let num_limbs = 16;
+        let num_limbs_extra_wide = num_limbs * 2;
+        let log_limb_size = 16;
+
+        let mut rng = rand::thread_rng();
+        let p: BigUint = BaseField::MODULUS.try_into().unwrap();
+        let a = rng.gen_biguint_below(&p); // a has at most 254 bits
+        let r = calc_mont_radix(num_limbs, log_limb_size); // r has 257 bits
+
+        let mont_a = &a * &r; // mont_a has at most 511 bits
+
+        let mont_a_bigint512: BigInt<8> = mont_a.try_into().unwrap();
+        let mont_a_limbs = mont_a_bigint512.to_limbs(num_limbs_extra_wide, log_limb_size);
+        let mont_a_reconstructed = BigInt::<8>::from_limbs(&mont_a_limbs, log_limb_size);
+
+        // Check if the original and reconstructed values are equal
+        assert_eq!(mont_a_bigint512, mont_a_reconstructed);
+    }
 }