Blame Imath/ImathMath.h

Packit 8dc392
///////////////////////////////////////////////////////////////////////////
Packit 8dc392
//
Packit 8dc392
// Copyright (c) 2002-2012, Industrial Light & Magic, a division of Lucas
Packit 8dc392
// Digital Ltd. LLC
Packit 8dc392
// 
Packit 8dc392
// All rights reserved.
Packit 8dc392
// 
Packit 8dc392
// Redistribution and use in source and binary forms, with or without
Packit 8dc392
// modification, are permitted provided that the following conditions are
Packit 8dc392
// met:
Packit 8dc392
// *       Redistributions of source code must retain the above copyright
Packit 8dc392
// notice, this list of conditions and the following disclaimer.
Packit 8dc392
// *       Redistributions in binary form must reproduce the above
Packit 8dc392
// copyright notice, this list of conditions and the following disclaimer
Packit 8dc392
// in the documentation and/or other materials provided with the
Packit 8dc392
// distribution.
Packit 8dc392
// *       Neither the name of Industrial Light & Magic nor the names of
Packit 8dc392
// its contributors may be used to endorse or promote products derived
Packit 8dc392
// from this software without specific prior written permission. 
Packit 8dc392
// 
Packit 8dc392
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
Packit 8dc392
// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
Packit 8dc392
// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
Packit 8dc392
// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
Packit 8dc392
// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
Packit 8dc392
// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
Packit 8dc392
// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
Packit 8dc392
// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
Packit 8dc392
// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
Packit 8dc392
// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
Packit 8dc392
// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
Packit 8dc392
//
Packit 8dc392
///////////////////////////////////////////////////////////////////////////
Packit 8dc392
Packit 8dc392
Packit 8dc392
Packit 8dc392
#ifndef INCLUDED_IMATHMATH_H
Packit 8dc392
#define INCLUDED_IMATHMATH_H
Packit 8dc392
Packit 8dc392
//----------------------------------------------------------------------------
Packit 8dc392
//
Packit 8dc392
//	ImathMath.h
Packit 8dc392
//
Packit 8dc392
//	This file contains template functions which call the double-
Packit 8dc392
//	precision math functions defined in math.h (sin(), sqrt(),
Packit 8dc392
//	exp() etc.), with specializations that call the faster
Packit 8dc392
//	single-precision versions (sinf(), sqrtf(), expf() etc.)
Packit 8dc392
//	when appropriate.
Packit 8dc392
//
Packit 8dc392
//	Example:
Packit 8dc392
//
Packit 8dc392
//	    double x = Math<double>::sqrt (3);	// calls ::sqrt(double);
Packit 8dc392
//	    float  y = Math<float>::sqrt (3);	// calls ::sqrtf(float);
Packit 8dc392
//
Packit 8dc392
//	When would I want to use this?
Packit 8dc392
//
Packit 8dc392
//	You may be writing a template which needs to call some function
Packit 8dc392
//	defined in math.h, for example to extract a square root, but you
Packit 8dc392
//	don't know whether to call the single- or the double-precision
Packit 8dc392
//	version of this function (sqrt() or sqrtf()):
Packit 8dc392
//
Packit 8dc392
//	    template <class T>
Packit 8dc392
//	    T
Packit 8dc392
//	    glorp (T x)
Packit 8dc392
//	    {
Packit 8dc392
//		return sqrt (x + 1);		// should call ::sqrtf(float)
Packit 8dc392
//	    }					// if x is a float, but we
Packit 8dc392
//						// don't know if it is
Packit 8dc392
//
Packit 8dc392
//	Using the templates in this file, you can make sure that
Packit 8dc392
//	the appropriate version of the math function is called:
Packit 8dc392
//
Packit 8dc392
//	    template <class T>
Packit 8dc392
//	    T
Packit 8dc392
//	    glorp (T x, T y)
Packit 8dc392
//	    {
Packit 8dc392
//		return Math<T>::sqrt (x + 1);	// calls ::sqrtf(float) if x
Packit 8dc392
//	    }					// is a float, ::sqrt(double)
Packit 8dc392
//	    					// otherwise
Packit 8dc392
//
Packit 8dc392
//----------------------------------------------------------------------------
Packit 8dc392
Packit 8dc392
#include "ImathPlatform.h"
Packit 8dc392
#include "ImathLimits.h"
Packit 8dc392
#include "ImathNamespace.h"
Packit 8dc392
#include <math.h>
Packit 8dc392
Packit 8dc392
IMATH_INTERNAL_NAMESPACE_HEADER_ENTER
Packit 8dc392
Packit 8dc392
Packit 8dc392
template <class T>
Packit 8dc392
struct Math
Packit 8dc392
{
Packit 8dc392
   static T	acos  (T x)		{return ::acos (double(x));}	
Packit 8dc392
   static T	asin  (T x)		{return ::asin (double(x));}
Packit 8dc392
   static T	atan  (T x)		{return ::atan (double(x));}
Packit 8dc392
   static T	atan2 (T x, T y)	{return ::atan2 (double(x), double(y));}
Packit 8dc392
   static T	cos   (T x)		{return ::cos (double(x));}
Packit 8dc392
   static T	sin   (T x)		{return ::sin (double(x));}
Packit 8dc392
   static T	tan   (T x)		{return ::tan (double(x));}
Packit 8dc392
   static T	cosh  (T x)		{return ::cosh (double(x));}
Packit 8dc392
   static T	sinh  (T x)		{return ::sinh (double(x));}
Packit 8dc392
   static T	tanh  (T x)		{return ::tanh (double(x));}
Packit 8dc392
   static T	exp   (T x)		{return ::exp (double(x));}
Packit 8dc392
   static T	log   (T x)		{return ::log (double(x));}
Packit 8dc392
   static T	log10 (T x)		{return ::log10 (double(x));}
Packit 8dc392
   static T	modf  (T x, T *iptr)
Packit 8dc392
   {
Packit 8dc392
        double ival;
Packit 8dc392
        T rval( ::modf (double(x),&ival));
Packit 8dc392
	*iptr = ival;
Packit 8dc392
	return rval;
Packit 8dc392
   }
Packit 8dc392
   static T	pow   (T x, T y)	{return ::pow (double(x), double(y));}
Packit 8dc392
   static T	sqrt  (T x)		{return ::sqrt (double(x));}
Packit 8dc392
   static T	ceil  (T x)		{return ::ceil (double(x));}
Packit 8dc392
   static T	fabs  (T x)		{return ::fabs (double(x));}
Packit 8dc392
   static T	floor (T x)		{return ::floor (double(x));}
Packit 8dc392
   static T	fmod  (T x, T y)	{return ::fmod (double(x), double(y));}
Packit 8dc392
   static T	hypot (T x, T y)	{return ::hypot (double(x), double(y));}
Packit 8dc392
};
Packit 8dc392
Packit 8dc392
Packit 8dc392
template <>
Packit 8dc392
struct Math<float>
Packit 8dc392
{
Packit 8dc392
   static float	acos  (float x)			{return ::acosf (x);}	
Packit 8dc392
   static float	asin  (float x)			{return ::asinf (x);}
Packit 8dc392
   static float	atan  (float x)			{return ::atanf (x);}
Packit 8dc392
   static float	atan2 (float x, float y)	{return ::atan2f (x, y);}
Packit 8dc392
   static float	cos   (float x)			{return ::cosf (x);}
Packit 8dc392
   static float	sin   (float x)			{return ::sinf (x);}
Packit 8dc392
   static float	tan   (float x)			{return ::tanf (x);}
Packit 8dc392
   static float	cosh  (float x)			{return ::coshf (x);}
Packit 8dc392
   static float	sinh  (float x)			{return ::sinhf (x);}
Packit 8dc392
   static float	tanh  (float x)			{return ::tanhf (x);}
Packit 8dc392
   static float	exp   (float x)			{return ::expf (x);}
Packit 8dc392
   static float	log   (float x)			{return ::logf (x);}
Packit 8dc392
   static float	log10 (float x)			{return ::log10f (x);}
Packit 8dc392
   static float	modf  (float x, float *y)	{return ::modff (x, y);}
Packit 8dc392
   static float	pow   (float x, float y)	{return ::powf (x, y);}
Packit 8dc392
   static float	sqrt  (float x)			{return ::sqrtf (x);}
Packit 8dc392
   static float	ceil  (float x)			{return ::ceilf (x);}
Packit 8dc392
   static float	fabs  (float x)			{return ::fabsf (x);}
Packit 8dc392
   static float	floor (float x)			{return ::floorf (x);}
Packit 8dc392
   static float	fmod  (float x, float y)	{return ::fmodf (x, y);}
Packit 8dc392
#if !defined(_MSC_VER)
Packit 8dc392
   static float	hypot (float x, float y)	{return ::hypotf (x, y);}
Packit 8dc392
#else
Packit 8dc392
   static float hypot (float x, float y)	{return ::sqrtf(x*x + y*y);}
Packit 8dc392
#endif
Packit 8dc392
};
Packit 8dc392
Packit 8dc392
Packit 8dc392
//--------------------------------------------------------------------------
Packit 8dc392
// Don Hatch's version of sin(x)/x, which is accurate for very small x.
Packit 8dc392
// Returns 1 for x == 0.
Packit 8dc392
//--------------------------------------------------------------------------
Packit 8dc392
Packit 8dc392
template <class T>
Packit 8dc392
inline T
Packit 8dc392
sinx_over_x (T x)
Packit 8dc392
{
Packit 8dc392
    if (x * x < limits<T>::epsilon())
Packit 8dc392
	return T (1);
Packit 8dc392
    else
Packit 8dc392
	return Math<T>::sin (x) / x;
Packit 8dc392
}
Packit 8dc392
Packit 8dc392
Packit 8dc392
//--------------------------------------------------------------------------
Packit 8dc392
// Compare two numbers and test if they are "approximately equal":
Packit 8dc392
//
Packit 8dc392
// equalWithAbsError (x1, x2, e)
Packit 8dc392
//
Packit 8dc392
//	Returns true if x1 is the same as x2 with an absolute error of
Packit 8dc392
//	no more than e,
Packit 8dc392
//	
Packit 8dc392
//	abs (x1 - x2) <= e
Packit 8dc392
//
Packit 8dc392
// equalWithRelError (x1, x2, e)
Packit 8dc392
//
Packit 8dc392
//	Returns true if x1 is the same as x2 with an relative error of
Packit 8dc392
//	no more than e,
Packit 8dc392
//	
Packit 8dc392
//	abs (x1 - x2) <= e * x1
Packit 8dc392
//
Packit 8dc392
//--------------------------------------------------------------------------
Packit 8dc392
Packit 8dc392
template <class T>
Packit 8dc392
inline bool
Packit 8dc392
equalWithAbsError (T x1, T x2, T e)
Packit 8dc392
{
Packit 8dc392
    return ((x1 > x2)? x1 - x2: x2 - x1) <= e;
Packit 8dc392
}
Packit 8dc392
Packit 8dc392
Packit 8dc392
template <class T>
Packit 8dc392
inline bool
Packit 8dc392
equalWithRelError (T x1, T x2, T e)
Packit 8dc392
{
Packit 8dc392
    return ((x1 > x2)? x1 - x2: x2 - x1) <= e * ((x1 > 0)? x1: -x1);
Packit 8dc392
}
Packit 8dc392
Packit 8dc392
Packit 8dc392
IMATH_INTERNAL_NAMESPACE_HEADER_EXIT
Packit 8dc392
Packit 8dc392
#endif // INCLUDED_IMATHMATH_H