ImathMath.h

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//
// Copyright (c) 2002, Industrial Light & Magic, a division of Lucas
// Digital Ltd. LLC
// 
// All rights reserved.
// 
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// modification, are permitted provided that the following conditions are
// met:
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// notice, this list of conditions and the following disclaimer.
// *       Redistributions in binary form must reproduce the above
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// in the documentation and/or other materials provided with the
// distribution.
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// its contributors may be used to endorse or promote products derived
// from this software without specific prior written permission. 
// 
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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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 <math.h>

namespace Imath {


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);
}



} // namespace Imath

#endif