math.hpp

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// -----------------------------------------------------------------------------------------------------
// Copyright (c) 2006-2021, Knut Reinert & Freie Universität Berlin
// Copyright (c) 2016-2021, Knut Reinert & MPI für molekulare Genetik
// This file may be used, modified and/or redistributed under the terms of the 3-clause BSD-License
// shipped with this file and also available at: https://github.com/seqan/seqan3/blob/master/LICENSE.md
// -----------------------------------------------------------------------------------------------------
 
#pragma once
 
#include <seqan3/std/bit>
#include <cassert>
#include <cmath>
#include <seqan3/std/concepts>
#include <stdexcept>
 
#include <seqan3/core/platform.hpp>
 
namespace seqan3::detail
{
 
template <std::unsigned_integral unsigned_t>
constexpr unsigned_t floor_log2(unsigned_t const n) noexcept
{
    assert(n > 0u); // n == 0 is undefined behaviour
    return std::bit_width(n) - 1;
}
 
template <std::unsigned_integral unsigned_t>
constexpr unsigned_t ceil_log2(unsigned_t const n) noexcept
{
    assert(n > 0u); // n == 0 is undefined behaviour
    return (n == 1u) ? 0u : seqan3::detail::floor_log2(n - 1u) + 1u;
}
 
} // namespace seqan3::detail
 
namespace seqan3
{
template <typename base_t, std::unsigned_integral exp_t>
    requires (std::same_as<base_t, uint64_t> || std::same_as<base_t, int64_t>)
base_t pow(base_t base, exp_t exp)
{
    base_t result{1};
#ifndef NDEBUG
    if (base == 0)
        return 0;
 
    for (exp_t i = 0; i < exp; ++i)
    {
        if ((base < 0 ? std::numeric_limits<base_t>::min() : std::numeric_limits<base_t>::max()) / base < result)
        {
            std::string error_message{"Calculating " + std::to_string(base) + '^' + std::to_string(exp) +
                                      " will result in an " + (std::same_as<base_t, int64_t> ? "int64_t" : "uint64_t")};
            if (base < 0)
                throw std::underflow_error{error_message + " underflow."};
            else
                throw std::overflow_error{error_message + " overflow."};
        }
        result *= base;
    }
#else
    for (; exp; exp >>= 1, base *= base)
        result *= (exp & 1) ? base : 1;
#endif
    return result;
}
 
// If base and exponent are unsigned integrals, promote the base to `uint64_t`.
template <std::integral base_t, std::unsigned_integral exp_t>
    requires (std::unsigned_integral<base_t> && !std::same_as<base_t, uint64_t>)
uint64_t pow(base_t base, exp_t exp)
{
    return pow(static_cast<uint64_t>(base), exp);
}
 
// If the base is a signed integral and the exponent is an unsigned integral, promote the base to `int64_t`.
template <std::integral base_t, std::unsigned_integral exp_t>
    requires (!std::unsigned_integral<base_t> && !std::same_as<base_t, int64_t>)
int64_t pow(base_t base, exp_t exp)
{
    return pow(static_cast<int64_t>(base), exp);
}
 
// Otherwise delegate to `std::pow`.
template <typename base_t, typename exp_t>
    requires (!(std::integral<base_t> && std::unsigned_integral<exp_t>))
auto pow(base_t base, exp_t exp)
{
    return std::pow(base, exp);
}
 
} // namespace seqan3