erf.hpp

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//============================================================================
// MCKL/include/mckl/math/erf.hpp
//----------------------------------------------------------------------------
// MCKL: Monte Carlo Kernel Library
//----------------------------------------------------------------------------
// Copyright (c) 2013-2018, Yan Zhou
// All rights reserved.
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#ifndef MCKL_MATH_ERF_HPP
#define MCKL_MATH_ERF_HPP

#include <mckl/internal/config.h>
#include <mckl/math/constants.hpp>

#include <cmath>

namespace mckl {

template <typename T>
inline T erfcinv(T y)
{
    if (y >= 2) {
        return -const_inf<T>();
    }
    if (y <= 0) {
        return const_inf<T>();
    }

    constexpr T a = static_cast<T>(0.70771);
    constexpr T b = static_cast<T>(2.30753);
    constexpr T c = static_cast<T>(0.27061);
    constexpr T d = static_cast<T>(0.99229);
    constexpr T e = static_cast<T>(0.04481);
    constexpr T f = static_cast<T>(1.12837916709551257);

    T z = y < 1 ? y : 2 - y;
    T t = std::sqrt(-2 * std::log(static_cast<T>(0.5) * z));
    T x = -a * ((b + t * c) / (1 + t * (d + t * e)) - t);
    for (int i = 0; i != 2; ++i) {
        T err = std::erfc(x) - z;
        x += err / (f * std::exp(-(x * x)) - x * err);
    }

    return y < 1 ? x : -x;
}

template <typename T>
inline T erfinv(T y)
{
    return erfcinv<T>(1 - y);
}

} // namespace mckl

#endif // MCKL_MATH_ERF_HPP