1 | /////////////////////////////////////////////////////////////////////////// |
2 | // |
3 | // Copyright (c) 2002-2012, 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 |
10 | // met: |
11 | // * Redistributions of source code must retain the above copyright |
12 | // notice, this list of conditions and the following disclaimer. |
13 | // * Redistributions in binary form must reproduce the above |
14 | // copyright notice, this list of conditions and the following disclaimer |
15 | // in the documentation and/or other materials provided with the |
16 | // distribution. |
17 | // * Neither the name of Industrial Light & Magic nor the names of |
18 | // its contributors may be used to endorse or promote products derived |
19 | // from this software without specific prior written permission. |
20 | // |
21 | // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS |
22 | // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT |
23 | // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR |
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30 | // (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE |
31 | // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. |
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 "ImathNamespace.h" |
86 | #include <math.h> |
87 | |
88 | IMATH_INTERNAL_NAMESPACE_HEADER_ENTER |
89 | |
90 | |
91 | template <class T> |
92 | struct Math |
93 | { |
94 | static T acos (T x) {return ::acos (x: double(x));} |
95 | static T asin (T x) {return ::asin (x: double(x));} |
96 | static T atan (T x) {return ::atan (x: double(x));} |
97 | static T atan2 (T x, T y) {return ::atan2 (y: double(x), x: double(y));} |
98 | static T cos (T x) {return ::cos (x: double(x));} |
99 | static T sin (T x) {return ::sin (x: double(x));} |
100 | static T tan (T x) {return ::tan (x: double(x));} |
101 | static T cosh (T x) {return ::cosh (x: double(x));} |
102 | static T sinh (T x) {return ::sinh (x: double(x));} |
103 | static T tanh (T x) {return ::tanh (x: double(x));} |
104 | static T exp (T x) {return ::exp (x: double(x));} |
105 | static T log (T x) {return ::log (x: double(x));} |
106 | static T log10 (T x) {return ::log10 (x: double(x));} |
107 | static T modf (T x, T *iptr) |
108 | { |
109 | double ival; |
110 | T rval( ::modf (x: double(x),iptr: &ival)); |
111 | *iptr = ival; |
112 | return rval; |
113 | } |
114 | static T pow (T x, T y) {return ::pow (x: double(x), y: double(y));} |
115 | static T sqrt (T x) {return ::sqrt (x: double(x));} |
116 | static T ceil (T x) {return ::ceil (x: double(x));} |
117 | static T fabs (T x) {return ::fabs (x: double(x));} |
118 | static T floor (T x) {return ::floor (x: double(x));} |
119 | static T fmod (T x, T y) {return ::fmod (x: double(x), y: double(y));} |
120 | static T hypot (T x, T y) {return ::hypot (x: double(x), y: double(y));} |
121 | }; |
122 | |
123 | |
124 | template <> |
125 | struct Math<float> |
126 | { |
127 | static float acos (float x) {return ::acosf (x: x);} |
128 | static float asin (float x) {return ::asinf (x: x);} |
129 | static float atan (float x) {return ::atanf (x: x);} |
130 | static float atan2 (float x, float y) {return ::atan2f (y: x, x: y);} |
131 | static float cos (float x) {return ::cosf (x: x);} |
132 | static float sin (float x) {return ::sinf (x: x);} |
133 | static float tan (float x) {return ::tanf (x: x);} |
134 | static float cosh (float x) {return ::coshf (x: x);} |
135 | static float sinh (float x) {return ::sinhf (x: x);} |
136 | static float tanh (float x) {return ::tanhf (x: x);} |
137 | static float exp (float x) {return ::expf (x: x);} |
138 | static float log (float x) {return ::logf (x: x);} |
139 | static float log10 (float x) {return ::log10f (x: x);} |
140 | static float modf (float x, float *y) {return ::modff (x: x, iptr: y);} |
141 | static float pow (float x, float y) {return ::powf (x: x, y: y);} |
142 | static float sqrt (float x) {return ::sqrtf (x: x);} |
143 | static float ceil (float x) {return ::ceilf (x: x);} |
144 | static float fabs (float x) {return ::fabsf (x: x);} |
145 | static float floor (float x) {return ::floorf (x: x);} |
146 | static float fmod (float x, float y) {return ::fmodf (x: x, y: y);} |
147 | #if !defined(_MSC_VER) |
148 | static float hypot (float x, float y) {return ::hypotf (x: x, y: y);} |
149 | #else |
150 | static float hypot (float x, float y) {return ::sqrtf(x*x + y*y);} |
151 | #endif |
152 | }; |
153 | |
154 | |
155 | //-------------------------------------------------------------------------- |
156 | // Don Hatch's version of sin(x)/x, which is accurate for very small x. |
157 | // Returns 1 for x == 0. |
158 | //-------------------------------------------------------------------------- |
159 | |
160 | template <class T> |
161 | inline T |
162 | sinx_over_x (T x) |
163 | { |
164 | if (x * x < limits<T>::epsilon()) |
165 | return T (1); |
166 | else |
167 | return Math<T>::sin (x) / x; |
168 | } |
169 | |
170 | |
171 | //-------------------------------------------------------------------------- |
172 | // Compare two numbers and test if they are "approximately equal": |
173 | // |
174 | // equalWithAbsError (x1, x2, e) |
175 | // |
176 | // Returns true if x1 is the same as x2 with an absolute error of |
177 | // no more than e, |
178 | // |
179 | // abs (x1 - x2) <= e |
180 | // |
181 | // equalWithRelError (x1, x2, e) |
182 | // |
183 | // Returns true if x1 is the same as x2 with an relative error of |
184 | // no more than e, |
185 | // |
186 | // abs (x1 - x2) <= e * x1 |
187 | // |
188 | //-------------------------------------------------------------------------- |
189 | |
190 | template <class T> |
191 | inline bool |
192 | equalWithAbsError (T x1, T x2, T e) |
193 | { |
194 | return ((x1 > x2)? x1 - x2: x2 - x1) <= e; |
195 | } |
196 | |
197 | |
198 | template <class T> |
199 | inline bool |
200 | equalWithRelError (T x1, T x2, T e) |
201 | { |
202 | return ((x1 > x2)? x1 - x2: x2 - x1) <= e * ((x1 > 0)? x1: -x1); |
203 | } |
204 | |
205 | |
206 | IMATH_INTERNAL_NAMESPACE_HEADER_EXIT |
207 | |
208 | #endif // INCLUDED_IMATHMATH_H |
209 | |