1///////////////////////////////////////////////////////////////////////////
2//
3// Copyright (c) 2002, Industrial Light & Magic, a division of Lucas
4// Digital Ltd. LLC
5//
6// All rights reserved.
7//
8// Redistribution and use in source and binary forms, with or without
9// modification, are permitted provided that the following conditions are
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13// *       Redistributions in binary form must reproduce the above
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15// in the documentation and/or other materials provided with the
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20//
21// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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32//
33///////////////////////////////////////////////////////////////////////////
34
35
36
37#ifndef INCLUDED_IMATHMATH_H
38#define INCLUDED_IMATHMATH_H
39
40//----------------------------------------------------------------------------
41//
42//	ImathMath.h
43//
44//	This file contains template functions which call the double-
45//	precision math functions defined in math.h (sin(), sqrt(),
46//	exp() etc.), with specializations that call the faster
47//	single-precision versions (sinf(), sqrtf(), expf() etc.)
48//	when appropriate.
49//
50//	Example:
51//
52//	    double x = Math<double>::sqrt (3);	// calls ::sqrt(double);
53//	    float  y = Math<float>::sqrt (3);	// calls ::sqrtf(float);
54//
55//	When would I want to use this?
56//
57//	You may be writing a template which needs to call some function
58//	defined in math.h, for example to extract a square root, but you
59//	don't know whether to call the single- or the double-precision
60//	version of this function (sqrt() or sqrtf()):
61//
62//	    template <class T>
63//	    T
64//	    glorp (T x)
65//	    {
66//		return sqrt (x + 1);		// should call ::sqrtf(float)
67//	    }					// if x is a float, but we
68//						// don't know if it is
69//
70//	Using the templates in this file, you can make sure that
71//	the appropriate version of the math function is called:
72//
73//	    template <class T>
74//	    T
75//	    glorp (T x, T y)
76//	    {
77//		return Math<T>::sqrt (x + 1);	// calls ::sqrtf(float) if x
78//	    }					// is a float, ::sqrt(double)
79//	    					// otherwise
80//
81//----------------------------------------------------------------------------
82
83#include "ImathPlatform.h"
84#include "ImathLimits.h"
85#include <math.h>
86
87namespace Imath {
88
89
90template <class T>
91struct Math
92{
93   static T	acos  (T x)		{return ::acos (double(x));}
94   static T	asin  (T x)		{return ::asin (double(x));}
95   static T	atan  (T x)		{return ::atan (double(x));}
96   static T	atan2 (T x, T y)	{return ::atan2 (double(x), double(y));}
97   static T	cos   (T x)		{return ::cos (double(x));}
98   static T	sin   (T x)		{return ::sin (double(x));}
99   static T	tan   (T x)		{return ::tan (double(x));}
100   static T	cosh  (T x)		{return ::cosh (double(x));}
101   static T	sinh  (T x)		{return ::sinh (double(x));}
102   static T	tanh  (T x)		{return ::tanh (double(x));}
103   static T	exp   (T x)		{return ::exp (double(x));}
104   static T	log   (T x)		{return ::log (double(x));}
105   static T	log10 (T x)		{return ::log10 (double(x));}
106   static T	modf  (T x, T *iptr)
107   {
108        double ival;
109        T rval( ::modf (double(x),&ival));
110	*iptr = ival;
111	return rval;
112   }
113   static T	pow   (T x, T y)	{return ::pow (double(x), double(y));}
114   static T	sqrt  (T x)		{return ::sqrt (double(x));}
115   static T	ceil  (T x)		{return ::ceil (double(x));}
116   static T	fabs  (T x)		{return ::fabs (double(x));}
117   static T	floor (T x)		{return ::floor (double(x));}
118   static T	fmod  (T x, T y)	{return ::fmod (double(x), double(y));}
119   static T	hypot (T x, T y)	{return ::hypot (double(x), double(y));}
120};
121
122
123template <>
124struct Math<float>
125{
126   static float	acos  (float x)			{return ::acosf (x);}
127   static float	asin  (float x)			{return ::asinf (x);}
128   static float	atan  (float x)			{return ::atanf (x);}
129   static float	atan2 (float x, float y)	{return ::atan2f (x, y);}
130   static float	cos   (float x)			{return ::cosf (x);}
131   static float	sin   (float x)			{return ::sinf (x);}
132   static float	tan   (float x)			{return ::tanf (x);}
133   static float	cosh  (float x)			{return ::coshf (x);}
134   static float	sinh  (float x)			{return ::sinhf (x);}
135   static float	tanh  (float x)			{return ::tanhf (x);}
136   static float	exp   (float x)			{return ::expf (x);}
137   static float	log   (float x)			{return ::logf (x);}
138   static float	log10 (float x)			{return ::log10f (x);}
139   static float	modf  (float x, float *y)	{return ::modff (x, y);}
140   static float	pow   (float x, float y)	{return ::powf (x, y);}
141   static float	sqrt  (float x)			{return ::sqrtf (x);}
142   static float	ceil  (float x)			{return ::ceilf (x);}
143   static float	fabs  (float x)			{return ::fabsf (x);}
144   static float	floor (float x)			{return ::floorf (x);}
145   static float	fmod  (float x, float y)	{return ::fmodf (x, y);}
146#if !defined(_MSC_VER)
147   static float	hypot (float x, float y)	{return ::hypotf (x, y);}
148#else
149   static float hypot (float x, float y)	{return ::sqrtf(x*x + y*y);}
150#endif
151};
152
153
154//--------------------------------------------------------------------------
155// Don Hatch's version of sin(x)/x, which is accurate for very small x.
156// Returns 1 for x == 0.
157//--------------------------------------------------------------------------
158
159template <class T>
160inline T
161sinx_over_x (T x)
162{
163    if (x * x < limits<T>::epsilon())
164	return T (1);
165    else
166	return Math<T>::sin (x) / x;
167}
168
169
170//--------------------------------------------------------------------------
171// Compare two numbers and test if they are "approximately equal":
172//
173// equalWithAbsError (x1, x2, e)
174//
175//	Returns true if x1 is the same as x2 with an absolute error of
176//	no more than e,
177//
178//	abs (x1 - x2) <= e
179//
180// equalWithRelError (x1, x2, e)
181//
182//	Returns true if x1 is the same as x2 with an relative error of
183//	no more than e,
184//
185//	abs (x1 - x2) <= e * x1
186//
187//--------------------------------------------------------------------------
188
189template <class T>
190inline bool
191equalWithAbsError (T x1, T x2, T e)
192{
193    return ((x1 > x2)? x1 - x2: x2 - x1) <= e;
194}
195
196
197template <class T>
198inline bool
199equalWithRelError (T x1, T x2, T e)
200{
201    return ((x1 > x2)? x1 - x2: x2 - x1) <= e * ((x1 > 0)? x1: -x1);
202}
203
204
205
206} // namespace Imath
207
208#endif
209