Add pow for qm31 as needed for the fri verifier

stwo_cairo_verifier/src/utils.cairo

@@ -6,6 +6,7 @@ use core::dict::Felt252DictEntryTrait;
 use core::dict::Felt252DictTrait;
 use core::iter::Iterator;
 use core::num::traits::BitSize;
+use stwo_cairo_verifier::fields::qm31::{QM31, qm31};
 use stwo_cairo_verifier::BaseField;
 use core::traits::DivRem;
 
@@ -126,9 +127,35 @@ pub fn find(n: u32, a: Span<u32>) -> bool {
     res
 }
 
+pub fn pow_qm31(base: QM31, mut exponent: u32) -> QM31 {
+    let mut result = qm31(1, 0, 0, 0);
+    let mut base_power = base;
+    loop {
+        if exponent & 1 == 1 {
+            result = result * base_power;
+        }
+        exponent = exponent / 2;
+        if exponent == 0 {
+            break;
+        }
+        base_power = base_power * base_power;
+    };
+    result
+}
+
+pub fn qm31_zero_array(n: u32) -> Array<QM31> {
+    let mut result = array![];
+    let mut i = 0;
+    while i < n {
+        result.append(qm31(0, 0, 0, 0));
+        i += 1;
+    };
+    result
+}
+
 #[cfg(test)]
 mod tests {
-    use super::{pow, bit_reverse_index};
+    use super::{pow, pow_qm31, qm31, bit_reverse_index};
 
     #[test]
     fn test_pow() {
@@ -163,5 +190,27 @@ mod tests {
         // 31 bits
         assert_eq!(16448250, bit_reverse_index(800042880, 31));
     }
+
+
+    #[test]
+    fn test_pow_qm31_1() {
+        let result = pow_qm31(qm31(1, 2, 3, 4), 0);
+        let expected_result = qm31(1, 0, 0, 0);
+        assert_eq!(expected_result, result)
+    }
+
+    #[test]
+    fn test_pow_qm31_2() {
+        let result = pow_qm31(qm31(1, 2, 3, 4), 1);
+        let expected_result = qm31(1, 2, 3, 4);
+        assert_eq!(expected_result, result)
+    }
+
+    #[test]
+    fn test_pow_qm31_3() {
+        let result = pow_qm31(qm31(1, 2, 3, 4), 37);
+        let expected_result = qm31(1394542587, 260510989, 997191897, 2127074080);
+        assert_eq!(expected_result, result)
+    }
 }