log1p.h

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/*
 * Copyright 2021 MusicScience37 (Kenta Kabashima)
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *     http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */
#pragma once
 
#include <limits>
#include <type_traits>
 
#include "num_collect/constants/expm1.h"
#include "num_collect/constants/impl/log1m_maclaurin.h"
#include "num_collect/constants/log.h"
#include "num_collect/constants/one.h"  // IWYU pragma: keep
 
namespace num_collect::constants {
 
template <typename T, typename = std::enable_if_t<std::is_floating_point_v<T>>>
constexpr auto log1p(T x) -> T {
    if (x < -one<T>) {
        return std::numeric_limits<T>::quiet_NaN();
    }
    if (x == -one<T>) {
        return -std::numeric_limits<T>::infinity();
    }
 
    if (x > one<T>) {
        return log(x + one<T>);
    }
    if (x > zero<T>) {
        return -log1p(-x / (x + one<T>));
    }
 
    T value = x;
    if (x > zero<T>) {
        value = -log1p(-x / (x + one<T>));
    } else {
        value = impl::log1m_maclaurin(-x);
    }
    constexpr int max_loops = 1000;
    for (int i = 0; i < max_loops; ++i) {
        T expm1_val = expm1(value);
        T next_value = value - (expm1_val - x) / (expm1_val + one<T>);
        if (value == next_value) {
            break;
        }
        value = next_value;
    }
 
    return value;
}
 
}  // namespace num_collect::constants