erf.h

#pragma once

#include <funcy/concepts.h>
#include <funcy/util/chainer.h>

#include <cmath>

namespace funcy
{
    struct Erf : Chainer< Erf >
    {
        explicit Erf( double x = 0. ) noexcept
        {
            update( x );
        }

        void update( double x ) noexcept
        {
            x_ = x;
            value = std::erf( x_ );
            firstDerivative = scale * std::exp( -x_ * x_ );
        }

        [[nodiscard]] double d0() const noexcept
        {
            return value;
        }

        [[nodiscard]] double d1( double dx = 1. ) const noexcept
        {
            return firstDerivative * dx;
        }

        [[nodiscard]] double d2( double dx = 1., double dy = 1. ) const noexcept
        {
            return -2 * x_ * d1( dx ) * dy;
        }

        [[nodiscard]] double d3( double dx = 1., double dy = 1., double dz = 1. ) const noexcept
        {
            return ( 4 * x_ * x_ - 2 ) * d1( dx ) * dy * dz;
        }

    private:
        double scale = 2 / std::sqrt( M_PI );
        double value = 0.;
        double firstDerivative = 1.;
        double x_ = 0;
    };

    template < Function F >
    [[nodiscard]] auto erf( const F& f )
    {
        return Erf( f() )( f );
    }
} // namespace funcy