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#ifndef GEOGRAM_BASIC_NUMERIC
#define GEOGRAM_BASIC_NUMERIC

#include <geogram/basic/common.h>
#include <cmath>
#include <float.h>
#include <limits.h>
#include <algorithm> // for std::min / std::max
#include <stdint.h>
#include <limits>

#ifndef M_PI
/**
 * \brief Value of the constant PI if not defined by the system
 */
#define M_PI 3.14159265358979323846
#endif

/**
 * \file geogram/basic/numeric.h
 * \brief Types and functions for numbers manipulation
 */

namespace GEO {

    /**
     * \brief Integer constants that represent the sign of a value
     */
    enum Sign {
        /** Value is negative */
        NEGATIVE = -1,
        /** Value is zero */
        ZERO = 0,
        /** Value is positive */
        POSITIVE = 1
    };


    /**
     * \brief Compares two values
     * \param[in] a , b the two values to compare
     * \tparam T the type of the value
     * \retval POSITIVE if \p a is greater than \p b
     * \retval ZERO if \p a is equal to \p b
     * \retval NEGATIVE if \p a is smaller than \p b
     * \see Sign
     */
    template <class T>
    inline Sign geo_cmp(const T& a, const T& b) {
        return Sign((a > b) - (a < b));
    }


    /**
     * \brief Gets the sign of a value
     * \details Returns -1, 0, or 1 whether value \p x is resp. negative, zero
     * or positive. The function uses operator<() and operator>() to compare
     * the value to 0 (zero). The integer constant zero must make
     * senses for the type of the value, or T must be constructible from
     * integer constant zero.
     * \param[in] x the value to test
     * \tparam T the type of the value
     * \return the sign of the value
     * \see Sign
     */
    template <class T>
    inline Sign geo_sgn(const T& x) {
        return geo_cmp(x, T(0));
    }

    /**
     * \brief Defines numeric types used in Vorpaline.
     * \details
     * These types names have the form (u)int<size> or float<size>,
     * where the (optional) u denotes an unsigned type,
     * and the size is in bits.
     */
    namespace Numeric {

        /** Generic pointer type */
        typedef void* pointer;

        /** Integer type with a width of 8 bits */
        typedef int8_t int8;

        /** Integer type with a width of 16 bits */
        typedef int16_t int16;

        /** Integer type with a width of 32 bits */
        typedef int32_t int32;

        /** Integer type with a width of 64 bits */
        typedef int64_t int64;

        /** Unsigned integer type with a width of 8 bits */
        typedef uint8_t uint8;

        /** Unsigned integer type with a width of 16 bits */
        typedef uint16_t uint16;

        /** Unsigned integer type with a width of 32 bits */
        typedef uint32_t uint32;

        /** Unsigned integer type with a width of 64 bits */
        typedef uint64_t uint64;

        /** Floating point type with a width of 32 bits */
        typedef float float32;

        /** Floating point type with a width of 64 bits */
        typedef double float64;

        /**
         * \brief Gets 32 bits float maximum positive value
         */
        inline float32 max_float32() {
            return std::numeric_limits<float32>::max();
        }

        /**
         * \brief Gets 32 bits float minimum negative value
         */
        inline float32 min_float32() {
            // Note: numeric_limits<>::min() is not
            // what we want (it returns the smallest
            // positive non-denormal).
            return -max_float32();
        }

        /**
         * \brief Gets 64 bits float maximum positive value
         */
        inline float64 max_float64() {
            return std::numeric_limits<float64>::max();
        }

        /**
         * \brief Gets 64 bits float minimum negative value
         */
        inline float64 min_float64() {
            // Note: numeric_limits<>::min() is not
            // what we want (it returns the smallest
            // positive non-denormal).
            return -max_float64();
        }

        /**
         * \brief Checks whether a 32 bits float is "not a number"
         */
        bool GEOGRAM_API is_nan(float32 x);

        /**
         * \brief Checks whether a 64 bits float is "not a number"
         */
        bool GEOGRAM_API is_nan(float64 x);

        /**
         * \brief Resets the random number generator.
         */
        void GEOGRAM_API random_reset();

        /**
         * \brief Returns a 32 bits integer between 0 and RAND_MAX
         */
        int32 GEOGRAM_API random_int32();

        /**
         * \brief Returns a 32 bits float between 0 and 1
         */
        float32 GEOGRAM_API random_float32();

        /**
         * \brief Returns a 64 bits float between 0 and 1
         */
        float64 GEOGRAM_API random_float64();

        /**
         * \brief Limits helper class that extends std::numeric_limits
         * \details LimitsHelper extends std::numeric_limits to provide
         * additional information about numeric types \p T.
         * Template parameter \p is_numeric receives the value \c
         * std::numeric_limits<T>::is_specialized which is \c true for all
         * numeric types and \c false for the other types. The template is
         * specialized for \p is_numeric == \c true to define additional
         * information. For non-numeric types, the default template does not
         * define anything.
         * \tparam T an object type
         * \tparam is_numeric is true if type \p T is a numeric type, false
         * otherwise.
         */
        template <class T, bool is_numeric>
        struct LimitsHelper : std::numeric_limits<T> {
        };

        /**
         * \brief Specialization of LimitsHelper for numeric types
         * \details This specialization defines the following values:
         * - size - the size of the numeric type in bytes
         * - numbits - the size of the numeric type in bits
         * \tparam T a numeric type
         */
        template <class T>
        struct LimitsHelper<T, true> : std::numeric_limits<T> {
            /** The size of the numeric type in bytes */
            static const size_t size = sizeof(T);
            /** The size of the numeric type in bits */
            static const size_t numbits = 8 * sizeof(T);
        };

        /**
         * \brief Extends std::numeric_limits with additional information
         * \details Limits provides additional information about numeric types
         * that are not available in std::numeric_limits:
         * - size: the size of the numeric type in bytes
         * - numbits: the size of the numeric type in bits
         * These types are defined in the helper class LimitsHelper for
         * numeric types only. They are not defined for non-numeric types.
         */
        template <class T>
        struct Limits :
            LimitsHelper<T, std::numeric_limits<T>::is_specialized> {
        };

        /**
         * \brief place holder for optimizing internal number representation
         * \details there are specializations for expansion_nt, rational_nt
         */
        template <class T> inline void optimize_number_representation(T& x) {
            geo_argused(x);
        }

        /**
         * \brief Compares two rational numbers given as separate
         *   numerators and denominators.
         * \param[in] a_num , a_denom defines a = \p a_num / \p a_denom
         * \param[in] b_num , b_denom defines b = \p b_num / \p b_denom
         * \return the sign of a - b
         */
        template <class T> inline Sign ratio_compare(
            const T& a_num, const T& a_denom, const T& b_num, const T& b_denom
        ) {
            if(a_denom == b_denom) {
                return Sign(geo_cmp(a_num,b_num)*geo_sgn(a_denom));
            }
            return Sign(
                geo_cmp(a_num*b_denom, b_num*a_denom) *
                geo_sgn(a_denom) * geo_sgn(b_denom)
            );
        }
    }

    /************************************************************************/


    /**
     * \brief Gets the square value of a value
     * \param[in] x a value of type \p T
     * \tparam T the type of the value
     * \return the square value of \p x
     */
    template <class T>
    inline T geo_sqr(T x) {
        return x * x;
    }

    /**
     * \brief Clamps a value to a range
     * \details Clamps the value \p x to a range defined by \p min and \p max.
     * This modifies the value of \p x directly.
     * \param[in,out] x a value of type \p T
     * \param[in] min the lower bound of the clamping range
     * \param[in] max the upper bound of the clamping range
     */
    template <class T>
    inline void geo_clamp(T& x, T min, T max) {
        if(x < min) {
            x = min;
        } else if(x > max) {
            x = max;
        }
    }

    /**
     * \brief The type for storing and manipulating indices.
     * \internal
     * Vorpaline uses 32 bit indices (can be changed to 64 bits
     * if need be, but this will double memory consumption of
     * all combinatorial data structures).
     */
    typedef geo_index_t index_t;

    /**
     * \brief Gets the maximum positive value of type index_t.
     */
    inline index_t max_index_t() {
        return std::numeric_limits<index_t>::max();
    }

    /**
     * \brief The type for storing and manipulating indices differences.
     * \details Can be negative (for instance to indicate special values like
     * borders).
     */
    typedef geo_signed_index_t signed_index_t;

    /**
     * \brief Gets the maximum positive value of type signed_index_t.
     */
    inline signed_index_t max_signed_index_t() {
        return std::numeric_limits<signed_index_t>::max();
    }

    /**
     * \brief Gets the minimum negative value of type signed_index_t.
     */
    inline signed_index_t min_signed_index_t() {
        return std::numeric_limits<signed_index_t>::min();
    }

    /**
     * \brief The type for storing coordinate indices, and iterating on
     *  the coordinates of a point.
     */
    typedef geo_coord_index_t coord_index_t;

    /**
     * \TODOC
     */
    inline double round(double x) {
        return ((x - floor(x)) > 0.5 ? ceil(x) : floor(x));
    }

    /************************************************************************/

    /**
     * \brief The dummy index value.
     * \details Used for instance on the border of a surface, where adjacent
     *  facets are set to NO_INDEX.
     */
    static constexpr index_t NO_INDEX = index_t(-1);

    /************************************************************************/
}

#endif
