ImathMath.h

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//
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#ifndef INCLUDED_IMATHMATH_H
#define INCLUDED_IMATHMATH_H

//----------------------------------------------------------------------------
//
//      ImathMath.h
//
//      This file contains template functions which call the double-
//      precision math functions defined in math.h (sin(), sqrt(),
//      exp() etc.), with specializations that call the faster
//      single-precision versions (sinf(), sqrtf(), expf() etc.)
//      when appropriate.
//
//      Example:
//
//          double x = Math<double>::sqrt (3);  // calls ::sqrt(double);
//          float  y = Math<float>::sqrt (3);   // calls ::sqrtf(float);
//
//      When would I want to use this?
//
//      You may be writing a template which needs to call some function
//      defined in math.h, for example to extract a square root, but you
//      don't know whether to call the single- or the double-precision
//      version of this function (sqrt() or sqrtf()):
//
//          template <class T>
//          T
//          glorp (T x)
//          {
//              return sqrt (x + 1);            // should call ::sqrtf(float)
//          }                                   // if x is a float, but we
//                                              // don't know if it is
//
//      Using the templates in this file, you can make sure that
//      the appropriate version of the math function is called:
//
//          template <class T>
//          T
//          glorp (T x, T y)
//          {
//              return Math<T>::sqrt (x + 1);   // calls ::sqrtf(float) if x
//          }                                   // is a float, ::sqrt(double)
//                                              // otherwise
//
//----------------------------------------------------------------------------

#include "ImathPlatform.h"
#include "ImathLimits.h"
#include "ImathNamespace.h"
#include <math.h>

IMATH_INTERNAL_NAMESPACE_HEADER_ENTER


template <class 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 x, T y)        {return ::atan2 (double(x), double(y));}
   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));}
   static T     ceil  (T x)             {return ::ceil (double(x));}
   static T     fabs  (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));}
};


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 x, float y)        {return ::atan2f (x, y);}
   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);}
   static float ceil  (float x)                 {return ::ceilf (x);}
   static float fabs  (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
};


//--------------------------------------------------------------------------
// Don Hatch's version of sin(x)/x, which is accurate for very small x.
// Returns 1 for x == 0.
//--------------------------------------------------------------------------

template <class T>
inline T
sinx_over_x (T x)
{
    if (x * x < limits<T>::epsilon())
        return T (1);
    else
        return Math<T>::sin (x) / x;
}


//--------------------------------------------------------------------------
// Compare two numbers and test if they are "approximately equal":
//
// equalWithAbsError (x1, x2, e)
//
//      Returns true if x1 is the same as x2 with an absolute error of
//      no more than e,
//      
//      abs (x1 - x2) <= e
//
// equalWithRelError (x1, x2, e)
//
//      Returns true if x1 is the same as x2 with an relative error of
//      no more than e,
//      
//      abs (x1 - x2) <= e * x1
//
//--------------------------------------------------------------------------

template <class T>
inline bool
equalWithAbsError (T x1, T x2, T e)
{
    return ((x1 > x2)? x1 - x2: x2 - x1) <= e;
}


template <class T>
inline bool
equalWithRelError (T x1, T x2, T e)
{
    return ((x1 > x2)? x1 - x2: x2 - x1) <= e * ((x1 > 0)? x1: -x1);
}


IMATH_INTERNAL_NAMESPACE_HEADER_EXIT

#endif // INCLUDED_IMATHMATH_H