include/cinder/CinderMath.h

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/*
 Copyright (c) 2010, The Barbarian Group
 All rights reserved.

 Portions Copyright (c) 2004, Laminar Research.

 Redistribution and use in source and binary forms, with or without modification, are permitted provided that
 the following conditions are met:

    * Redistributions of source code must retain the above copyright notice, this list of conditions and
    the following disclaimer.
    * Redistributions in binary form must reproduce the above copyright notice, this list of conditions and
    the following disclaimer in the documentation and/or other materials provided with the distribution.

 THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED
 WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
 PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR
 ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
 TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
 HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
 NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
 POSSIBILITY OF SUCH DAMAGE.
*/

#pragma once

#include "cinder/Cinder.h"
#include <cmath>
#include <climits>
#if defined( CINDER_MSW )
    #undef min
    #undef max
    #include <float.h>
#endif

namespace cinder {

template<typename T>
struct math
{
    static T    acos  (T x)     {return ::acos (double(x));}
    static T    asin  (T x)     {return ::asin (double(x));}
    static T    atan  (T x)     {return ::atan (double(x));}
    static T    atan2 (T y, T x)    {return ::atan2 (double(y), double(x));}
    static T    cos   (T x)     {return ::cos (double(x));}
    static T    sin   (T x)     {return ::sin (double(x));}
    static T    tan   (T x)     {return ::tan (double(x));}
    static T    cosh  (T x)     {return ::cosh (double(x));}
    static T    sinh  (T x)     {return ::sinh (double(x));}
    static T    tanh  (T x)     {return ::tanh (double(x));}
    static T    exp   (T x)     {return ::exp (double(x));}
    static T    log   (T x)     {return ::log (double(x));}
    static T    log10 (T x)     {return ::log10 (double(x));}
    static T    modf  (T x, T *iptr)
    {
        double ival;
        T rval( ::modf (double(x),&ival));
    *iptr = ival;
    return rval;
    }
    static T    pow   (T x, T y)    {return ::pow (double(x), double(y));}
    static T    sqrt  (T x)     {return ::sqrt (double(x));}
#if defined( _MSC_VER )
    static T    cbrt( T x )     { return ( x > 0 ) ? (::pow( x, 1.0 / 3.0 )) : (- ::pow( -x, 1.0 / 3.0 ) ); }
#else
    static T    cbrt( T x )     { return ::cbrt( x ); }
#endif
    static T    ceil  (T x)     {return ::ceil (double(x));}
    static T    abs  (T x)      {return ::fabs (double(x));}
    static T    floor (T x)     {return ::floor (double(x));}
    static T    fmod  (T x, T y)    {return ::fmod (double(x), double(y));}
    static T    hypot (T x, T y)    {return ::hypot (double(x), double(y));}
    static T    signum (T x)        {return ( x >0.0 ) ? 1.0 : ( ( x < 0.0 ) ? -1.0 : 0.0 ); }
    static T    min(T x, T y)               {return ( x < y ) ? x : y; }
    static T    max(T x, T y)               {return ( x > y ) ? x : y; }
    static T    clamp(T x, T min=0, T max=1)    {return ( x < min ) ? min : ( ( x > max ) ? max : x );}
};


template<>
struct math<float>
{
    static float    acos  (float x)         {return ::acosf (x);}
    static float    asin  (float x)         {return ::asinf (x);}
    static float    atan  (float x)         {return ::atanf (x);}
    static float    atan2 (float y, float x)    {return ::atan2f (y, x);}
    static float    cos   (float x)         {return ::cosf (x);}
    static float    sin   (float x)         {return ::sinf (x);}
    static float    tan   (float x)         {return ::tanf (x);}
    static float    cosh  (float x)         {return ::coshf (x);}
    static float    sinh  (float x)         {return ::sinhf (x);}
    static float    tanh  (float x)         {return ::tanhf (x);}
    static float    exp   (float x)         {return ::expf (x);}
    static float    log   (float x)         {return ::logf (x);}
    static float    log10 (float x)         {return ::log10f (x);}
    static float    modf  (float x, float *y)   {return ::modff (x, y);}
    static float    pow   (float x, float y)    {return ::powf (x, y);}
    static float    sqrt  (float x)         {return ::sqrtf (x);}
#if defined( _MSC_VER )
    static float    cbrt( float x )     { return ( x > 0 ) ? (::powf( x, 1.0f / 3.0f )) : (- ::powf( -x, 1.0f / 3.0f ) ); }
#else
    static float    cbrt  (float x)         { return ::cbrtf( x ); }    
#endif
    static float    ceil  (float x)         {return ::ceilf (x);}
    static float    abs   (float x)         {return ::fabsf (x);}
    static float    floor (float x)         {return ::floorf (x);}
    static float    fmod  (float x, float y)    {return ::fmodf (x, y);}
    #if !defined(_MSC_VER)
    static float    hypot (float x, float y)    {return ::hypotf (x, y);}
    #else
    static float hypot (float x, float y)   {return ::sqrtf(x*x + y*y);}
    #endif
    static float signum (float x)       {return ( x > 0.0f ) ? 1.0f : ( ( x < 0.0f ) ? -1.0f : 0.0f ); }
    static float min(float x, float y)                  {return ( x < y ) ? x : y; }
    static float max(float x, float y)                  {return ( x > y ) ? x : y; }
    static float clamp(float x, float min=0, float max=1)   {return ( x < min ) ? min : ( ( x > max ) ? max : x );}
};

#ifndef M_PI
#define M_PI           3.14159265358979323846
#endif

const double EPSILON_VALUE = 4.37114e-05;
#define EPSILON EPSILON_VALUE

inline float toRadians( float x )
{
    return x * 0.017453292519943295769f; // ( x * PI / 180 )
}

inline double toRadians( double x )
{
    return x * 0.017453292519943295769; // ( x * PI / 180 )
}

inline float toDegrees( float x )
{
    return x * 57.295779513082321f; // ( x * 180 / PI )
}

inline double toDegrees( double x )
{
    return x * 57.295779513082321; // ( x * 180 / PI )
}

template<typename T, typename L>
T lerp( const T &a, const T &b, L factor )
{
    return a + ( b - a ) * factor;
}

template<typename T>
T lmap(T val, T inMin, T inMax, T outMin, T outMax)
{
    return outMin + (outMax - outMin) * ((val - inMin) / (inMax - inMin));
}

template<typename T, typename L>
T bezierInterp( T a, T b, T c, T d, L t)
{
    L t1 = static_cast<L>(1.0) - t;
    return a*(t1*t1*t1) + b*(3*t*t1*t1) + c*(3*t*t*t1) + d*(t*t*t);
}

template<typename T, typename L>
T bezierInterpRef( const T &a, const T &b, const T &c, const T &d, L t)
{
    L t1 = static_cast<L>(1.0) - t;
    return a*(t1*t1*t1) + b*(3*t*t1*t1) + c*(3*t*t*t1) + d*(t*t*t);
}

template<typename T>
T constrain( T val, T minVal, T maxVal )
{
    if( val < minVal ) return minVal;
    else if( val > maxVal ) return maxVal;
    else return val;
}

// Don Hatch's version of sin(x)/x, which is accurate for very small x.
// Returns 1 for x == 0.
template <class T>
T sinx_over_x( T x )
{
    if( x * x < 1.19209290E-07F )
    return T( 1 );
    else
    return math<T>::sin( x ) / x;
}

// There are faster techniques for this, but this is portable
inline uint32_t log2floor( uint32_t x )
{
    uint32_t result = 0;
    while( x >>= 1 )
        ++result;

    return result;
}

inline uint32_t log2ceil( uint32_t x )
{
    uint32_t isNotPowerOf2 = (x & (x - 1));
    return ( isNotPowerOf2 ) ? (log2floor( x ) + 1) : log2floor( x );
}

inline uint32_t nextPowerOf2( uint32_t x )
{
    x |= (x >> 1);
    x |= (x >> 2);
    x |= (x >> 4);
    x |= (x >> 8);
    x |= (x >> 16);
    return(x+1);
}

template<typename T>
inline int solveLinear( T a, T b, T result[1] )
{
    if( a == 0 ) return (b == 0 ? -1 : 0 );
    result[0] = -b / a;
    return 1;
}

template<typename T>
inline int solveQuadratic( T a, T b, T c, T result[2] )
{
    if( a == 0 ) return solveLinear( b, c, result );

    T radical = b * b - 4 * a * c;
    if( radical < 0 ) return 0;

    if( radical == 0 ) {
        result[0] = -b / (2 * a);
        return 1;
    }

    T srad = math<T>::sqrt( radical );
    result[0] = ( -b - srad ) / (2 * a);
    result[1] = ( -b + srad ) / (2 * a);
    if( a < 0 ) std::swap( result[0], result[1] );
    return 2;
}

template<typename T>
int solveCubic( T a, T b, T c, T d, T result[3] );

} // namespace cinder

#if defined( _MSC_VER )
namespace std {
    inline bool isfinite( float arg ) { return _finite( arg ) != 0; }
    inline bool isfinite( double arg ) { return _finite( arg ) != 0; }
}
#endif