///////////////////////////////////////////////////////////////////////////
//
// Copyright (c) 2002, Industrial Light & Magic, a division of Lucas
// Digital Ltd. LLC
//
// All rights reserved.
//
// 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.
// * Neither the name of Industrial Light & Magic nor the names of
// 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
// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
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// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
//
///////////////////////////////////////////////////////////////////////////
#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