diff --git a/plonky2/src/gates/base_sum.rs b/plonky2/src/gates/base_sum.rs
index a7f4fcb3..37f03414 100644
--- a/plonky2/src/gates/base_sum.rs
+++ b/plonky2/src/gates/base_sum.rs
@@ -32,7 +32,8 @@ impl<const B: usize> BaseSumGate<B> {
     }
 
     pub fn new_from_config<F: Field64>(config: &CircuitConfig) -> Self {
-        let num_limbs = F::BITS.min(config.num_routed_wires - Self::START_LIMBS);
+        let num_limbs =
+            logarithm(F::ORDER as usize, B).min(config.num_routed_wires - Self::START_LIMBS);
         Self::new(num_limbs)
     }
 
@@ -192,6 +193,23 @@ impl<F: RichField, const B: usize> SimpleGenerator<F> for BaseSplitGenerator<B>
     }
 }
 
+/// Returns the largest `i` such that `base**i < n`.
+const fn logarithm(n: usize, base: usize) -> usize {
+    assert!(n > 0);
+    assert!(base > 1);
+    let mut i = 0;
+    let mut cur: usize = 1;
+    loop {
+        let (mul, overflow) = cur.overflowing_mul(base);
+        if overflow || mul >= n {
+            return i;
+        } else {
+            i += 1;
+            cur = mul;
+        }
+    }
+}
+
 #[cfg(test)]
 mod tests {
     use anyhow::Result;