numeric.h

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#pragma once
 
#include <cmath>
 
#include "../config.h"
 
namespace alfi::util::numeric {
    template <typename Number = DefaultNumber>
    bool are_equal(const Number& a, const Number& b, const Number& epsilon = std::numeric_limits<Number>::epsilon()) {
        return std::abs(a - b) <= epsilon || std::abs(a - b) <= std::max(std::abs(a), std::abs(b)) * epsilon;
    }

    template <typename Number, typename ExponentType>
    Number binpow(Number x, ExponentType n) {
        if constexpr (std::is_signed_v<ExponentType>) {
            if (n < 0) {
                return 1 / binpow(x, -n);
            }
        }
        Number result = 1;
        while (n > 0) {
            if ((n & 1) == 1) {
                result *= x;
            }
            x *= x;
            n >>= 1;
        }
        return result;
    }
}