/*
 * This file is part of the GROMACS molecular simulation package.
 *
 * Copyright (c) 2015,2016,2018,2019, by the GROMACS development team, led by
 * Mark Abraham, David van der Spoel, Berk Hess, and Erik Lindahl,
 * and including many others, as listed in the AUTHORS file in the
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/*! \file
 * \brief
 * Declares simple math functions
 *
 * \author Erik Lindahl <erik.lindahl@gmail.com>
 * \inpublicapi
 * \ingroup module_math
 */
#ifndef GMX_MATH_FUNCTIONS_H
#define GMX_MATH_FUNCTIONS_H

#include <cmath>
#include <cstdint>

#include "gromacs/utility/gmxassert.h"
#include "gromacs/utility/real.h"

namespace gmx
{

/*! \brief Evaluate log2(n) for integer n statically at compile time.
 *
 * Use as staticLog2<n>::value, where n must be a positive integer.
 * Negative n will be reinterpreted as the corresponding unsigned integer,
 * and you will get a compile-time error if n==0.
 * The calculation is done by recursively dividing n by 2 (until it is 1),
 * and incrementing the result by 1 in each step.
 *
 * \tparam n Value to recursively calculate log2(n) for
 */
template<std::uint64_t n>
struct StaticLog2
{
    static const int value = StaticLog2<n / 2>::value
                             + 1; //!< Variable value used for recursive static calculation of Log2(int)
};

/*! \brief Specialization of StaticLog2<n> for n==1.
 *
 *  This specialization provides the final value in the recursion; never
 *  call it directly, but use StaticLog2<n>::value.
 */
template<>
struct StaticLog2<1>
{
    static const int value = 0; //!< Base value for recursive static calculation of Log2(int)
};

/*! \brief Specialization of StaticLog2<n> for n==0.
 *
 *  This specialization should never actually be used since log2(0) is
 *  negative infinity. However, since Log2() is often used to calculate the number
 *  of bits needed for a number, we might be using the value 0 with a conditional
 *  statement around the logarithm. Depending on the compiler the expansion of
 *  the template can occur before the conditional statement, so to avoid infinite
 *  recursion we need a specialization for the case n==0.
 */
template<>
struct StaticLog2<0>
{
    static const int value = -1; //!< Base value for recursive static calculation of Log2(int)
};


/*! \brief Compute floor of logarithm to base 2, 32 bit signed argument
 *
 *  \param x 32-bit signed argument
 *
 *  \return log2(x)
 *
 *  \note This version of the overloaded function will assert that x is
 *        not negative.
 */
unsigned int log2I(std::int32_t x);

/*! \brief Compute floor of logarithm to base 2, 64 bit signed argument
 *
 *  \param x 64-bit signed argument
 *
 *  \return log2(x)
 *
 *  \note This version of the overloaded function will assert that x is
 *        not negative.
 */
unsigned int log2I(std::int64_t x);

/*! \brief Compute floor of logarithm to base 2, 32 bit unsigned argument
 *
 *  \param x 32-bit unsigned argument
 *
 *  \return log2(x)
 *
 *  \note This version of the overloaded function uses unsigned arguments to
 *        be able to handle arguments using all 32 bits.
 */
unsigned int log2I(std::uint32_t x);

/*! \brief Compute floor of logarithm to base 2, 64 bit unsigned argument
 *
 *  \param x 64-bit unsigned argument
 *
 *  \return log2(x)
 *
 *  \note This version of the overloaded function uses unsigned arguments to
 *        be able to handle arguments using all 64 bits.
 */
unsigned int log2I(std::uint64_t x);

/*! \brief Find greatest common divisor of two numbers
 *
 *  \param p First number, positive
 *  \param q Second number, positive
 *
 * \return Greatest common divisor of p and q
 */
std::int64_t greatestCommonDivisor(std::int64_t p, std::int64_t q);


/*! \brief Calculate 1.0/sqrt(x) in single precision
 *
 * \param  x  Positive value to calculate inverse square root for
 *
 * For now this is implemented with std::sqrt(x) since gcc seems to do a
 * decent job optimizing it. However, we might decide to use instrinsics
 * or compiler-specific functions in the future.
 *
 * \return 1.0/sqrt(x)
 */
static inline float invsqrt(float x)
{
    return 1.0F / std::sqrt(x);
}

/*! \brief Calculate 1.0/sqrt(x) in double precision, but single range
 *
 * \param  x  Positive value to calculate inverse square root for, must be
 *            in the input domain valid for single precision.
 *
 * For now this is implemented with std::sqrt(x). However, we might
 * decide to use instrinsics or compiler-specific functions in the future, and
 * then we want to have the freedom to do the first step in single precision.
 *
 * \return 1.0/sqrt(x)
 */
static inline double invsqrt(double x)
{
    return 1.0 / std::sqrt(x);
}

/*! \brief Calculate 1.0/sqrt(x) for integer x in double precision.
 *
 * \param  x  Positive value to calculate inverse square root for.
 *
 * \return 1.0/sqrt(x)
 */
static inline double invsqrt(int x)
{
    return invsqrt(static_cast<double>(x));
}

/*! \brief Calculate inverse cube root of x in single precision
 *
 *  \param  x  Argument
 *
 *  \return x^(-1/3)
 *
 *  This routine is typically faster than using std::pow().
 */
static inline float invcbrt(float x)
{
    return 1.0F / std::cbrt(x);
}

/*! \brief Calculate inverse sixth root of x in double precision
 *
 *  \param  x  Argument
 *
 *  \return x^(-1/3)
 *
 *  This routine is typically faster than using std::pow().
 */
static inline double invcbrt(double x)
{
    return 1.0 / std::cbrt(x);
}

/*! \brief Calculate inverse sixth root of integer x in double precision
 *
 *  \param  x  Argument
 *
 *  \return x^(-1/3)
 *
 *  This routine is typically faster than using std::pow().
 */
static inline double invcbrt(int x)
{
    return 1.0 / std::cbrt(x);
}

/*! \brief Calculate sixth root of x in single precision.
 *
 *  \param  x  Argument, must be greater than or equal to zero.
 *
 *  \return x^(1/6)
 *
 *  This routine is typically faster than using std::pow().
 */
static inline float sixthroot(float x)
{
    return std::sqrt(std::cbrt(x));
}

/*! \brief Calculate sixth root of x in double precision.
 *
 *  \param  x  Argument, must be greater than or equal to zero.
 *
 *  \return x^(1/6)
 *
 *  This routine is typically faster than using std::pow().
 */
static inline double sixthroot(double x)
{
    return std::sqrt(std::cbrt(x));
}

/*! \brief Calculate sixth root of integer x, return double.
 *
 *  \param  x  Argument, must be greater than or equal to zero.
 *
 *  \return x^(1/6)
 *
 *  This routine is typically faster than using std::pow().
 */
static inline double sixthroot(int x)
{
    return std::sqrt(std::cbrt(x));
}

/*! \brief Calculate inverse sixth root of x in single precision
 *
 *  \param  x  Argument, must be greater than zero.
 *
 *  \return x^(-1/6)
 *
 *  This routine is typically faster than using std::pow().
 */
static inline float invsixthroot(float x)
{
    return invsqrt(std::cbrt(x));
}

/*! \brief Calculate inverse sixth root of x in double precision
 *
 *  \param  x  Argument, must be greater than zero.
 *
 *  \return x^(-1/6)
 *
 *  This routine is typically faster than using std::pow().
 */
static inline double invsixthroot(double x)
{
    return invsqrt(std::cbrt(x));
}

/*! \brief Calculate inverse sixth root of integer x in double precision
 *
 *  \param  x  Argument, must be greater than zero.
 *
 *  \return x^(-1/6)
 *
 *  This routine is typically faster than using std::pow().
 */
static inline double invsixthroot(int x)
{
    return invsqrt(std::cbrt(x));
}

/*! \brief calculate x^2
 *
 *  \tparam T  Type of argument and return value
 *  \param  x  argument
 *
 *  \return x^2
 */
template<typename T>
T square(T x)
{
    return x * x;
}

/*! \brief calculate x^3
 *
 *  \tparam T  Type of argument and return value
 *  \param  x  argument
 *
 *  \return x^3
 */
template<typename T>
T power3(T x)
{
    return x * square(x);
}

/*! \brief calculate x^4
 *
 *  \tparam T  Type of argument and return value
 *  \param  x  argument
 *
 *  \return x^4
 */
template<typename T>
T power4(T x)
{
    return square(square(x));
}

/*! \brief calculate x^5
 *
 *  \tparam T  Type of argument and return value
 *  \param  x  argument
 *
 *  \return x^5
 */
template<typename T>
T power5(T x)
{
    return x * power4(x);
}

/*! \brief calculate x^6
 *
 *  \tparam T  Type of argument and return value
 *  \param  x  argument
 *
 *  \return x^6
 */
template<typename T>
T power6(T x)
{
    return square(power3(x));
}

/*! \brief calculate x^12
 *
 *  \tparam T  Type of argument and return value
 *  \param  x  argument
 *
 *  \return x^12
 */
template<typename T>
T power12(T x)
{
    return square(power6(x));
}

/*! \brief Maclaurin series for sinh(x)/x.
 *
 * Used for NH chains and MTTK pressure control.
 * Here, we compute it to 10th order, which might be an overkill.
 * 8th is probably enough, but it's not very much more expensive.
 */
static inline real series_sinhx(real x)
{
    real x2 = x * x;
    return (1
            + (x2 / 6.0_real)
                      * (1
                         + (x2 / 20.0_real)
                                   * (1 + (x2 / 42.0_real) * (1 + (x2 / 72.0_real) * (1 + (x2 / 110.0_real))))));
}

/*! \brief Inverse error function, double precision.
 *
 *  \param x Argument, should be in the range -1.0 < x < 1.0
 *
 *  \return The inverse of the error function if the argument is inside the
 *          range, +/- infinity if it is exactly 1.0 or -1.0, and NaN otherwise.
 */
double erfinv(double x);

/*! \brief Inverse error function, single precision.
 *
 *  \param x Argument, should be in the range -1.0 < x < 1.0
 *
 *  \return The inverse of the error function if the argument is inside the
 *          range, +/- infinity if it is exactly 1.0 or -1.0, and NaN otherwise.
 */
float erfinv(float x);

/*! \brief Exact integer division, 32bit.
 *
 * \param a dividend. Function asserts that it is a multiple of divisor
 * \param b divisor
 *
 * \return quotient of division
 */
constexpr int32_t exactDiv(int32_t a, int32_t b)
{
    return GMX_ASSERT(a % b == 0, "exactDiv called with non-divisible arguments"), a / b;
}

//! Exact integer division, 64bit.
constexpr int64_t exactDiv(int64_t a, int64_t b)
{
    return GMX_ASSERT(a % b == 0, "exactDiv called with non-divisible arguments"), a / b;
}

/*! \brief Round float to int
 *
 * Rounding behavior is round to nearest. Rounding of halfway cases is implemention defined
 * (either halway to even or halway away from zero).
 */
/* Implementation details: It is assumed that FE_TONEAREST is default and not changed by anyone.
 * Currently the implementation is using rint(f) because 1) on all known HW that is faster than
 * lround and 2) some compilers (e.g. clang (#22944) and icc) don't optimize (l)lrint(f) well.
 * GCC(>=4.7) optimizes (l)lrint(f) well but with "-fno-math-errno -funsafe-math-optimizations"
 * rint(f) is optimized as well. This avoids using intrinsics.
 * rint(f) followed by float/double to int/int64 conversion produces the same result as directly
 * rounding to int/int64.
 */
static inline int roundToInt(float x)
{
    return static_cast<int>(rintf(x));
}
//! Round double to int
static inline int roundToInt(double x)
{
    return static_cast<int>(rint(x));
}
//! Round float to int64_t
static inline int64_t roundToInt64(float x)
{
    return static_cast<int>(rintf(x));
}
//! Round double to int64_t
static inline int64_t roundToInt64(double x)
{
    return static_cast<int>(rint(x));
}

} // namespace gmx


#endif // GMX_MATH_FUNCTIONS_H
