numeric.hpp

// Copyright (c) 2014-2022 Thomas Fussell
// Copyright (c) 2024-2025 xlnt-community
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
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// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in
// all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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// @license: http://www.opensource.org/licenses/mit-license.php
// @author: see AUTHORS file

#pragma once

#include <cmath>
#include <limits>
#include <type_traits>

#undef min
#undef max

namespace xlnt {
namespace detail {

template <typename Number>
constexpr Number abs(Number val)
{
    return (val < Number{0}) ? -val : val;
}

template <typename NumberL, typename NumberR>
constexpr typename std::common_type<NumberL, NumberR>::type (max)(NumberL lval, NumberR rval)
{
    return (lval < rval) ? rval : lval;
}

template <typename NumberL, typename NumberR>
constexpr typename std::common_type<NumberL, NumberR>::type (min)(NumberL lval, NumberR rval)
{
    return (lval < rval) ? lval : rval;
}

template <typename EpsilonType = float, // the type to extract epsilon from
    typename LNumber, typename RNumber> // parameter types (deduced)
bool float_equals(const LNumber &lhs, const RNumber &rhs,
    int epsilon_scale = 20) // scale the "fuzzy" equality. Higher value gives a more tolerant comparison
{
    // a type that lhs and rhs can agree on
    using common_t = typename std::common_type<LNumber, RNumber>::type;
    // asserts for sane usage
    static_assert(std::is_floating_point<LNumber>::value || std::is_floating_point<RNumber>::value,
        "Using this function with two integers is just wasting time. Use ==");
    static_assert(std::numeric_limits<EpsilonType>::epsilon() < EpsilonType{1},
        "epsilon >= 1.0 will cause all comparisons to return true");

    // NANs always compare false with themselves
    if (std::isnan(lhs) || std::isnan(rhs))
    {
        return false;
    }
    // epsilon type defaults to float because even if both args are a higher precision type
    // either or both could have been promoted by prior operations
    // if a higher precision is required, the template type can be changed
    constexpr common_t epsilon = static_cast<common_t>(std::numeric_limits<EpsilonType>::epsilon());
    // the "epsilon" then needs to be scaled into the comparison range
    // epsilon for numeric_limits is valid when abs(x) <1.0, scaling only needs to be upwards
    // in particular, this prevents a lhs of 0 from requiring an exact comparison
    // additionally, a scale factor is applied.
    common_t scaled_fuzz = epsilon_scale * epsilon * max(max(xlnt::detail::abs<common_t>(lhs),
                                                             xlnt::detail::abs<common_t>(rhs)), // |max| of parameters.
                               common_t{1}); // clamp
    return ((lhs + scaled_fuzz) >= rhs) && ((rhs + scaled_fuzz) >= lhs);
}

} // namespace detail
} // namespace xlnt