fix fpow overflow

[neotheprogramist]

Problem Description

In the implementation of bitshifts in lib.cairo, the existing fpow function exhibits an overflow error when computing 2^n for n ≥ 64 using the generic function for u128.

Details

When we want to compute 2^n for n ≥ 64 using the generic function for u128, we encounter an overflow error. The error occurs in the last steps where we need to compute x * x, and x is greater than or equal to 2^64. Thus, x * x is greater than or equal to 2^128, leading to an overflow error.

Proposed Solution

The proposed solution is to modify the fpow function with a specific condition for n == 1. Below are the old and new code snippets:

Old function code:

fn fpow(x: u128, n: u128) -> u128 {
    if n == 0 {
        1
    } else if (n & 1) == 1 {
        x * fpow(x * x, n / 2)
    } else {
        fpow(x * x, n / 2)
    }
}

New function code:

fn fpow(x: u128, n: u128) -> u128 {
    if n == 0 {
        1
    } else if n == 1 {
        x
    } else if (n & 1) == 1 {
        x * fpow(x * x, n / 2)
    } else {
        fpow(x * x, n / 2)
    }
}

This change fixes the issue by handling the specific case where n is 1, preventing the overflow error.