1 /*
2 * Copyright (C) 2006, 2007, 2008, 2009, 2010 Apple Inc. All rights reserved.
3 *
4 * Redistribution and use in source and binary forms, with or without
5 * modification, are permitted provided that the following conditions
6 * are met:
7 * 1. Redistributions of source code must retain the above copyright
8 * notice, this list of conditions and the following disclaimer.
9 * 2. Redistributions in binary form must reproduce the above copyright
10 * notice, this list of conditions and the following disclaimer in the
11 * documentation and/or other materials provided with the distribution.
12 *
13 * THIS SOFTWARE IS PROVIDED BY APPLE COMPUTER, INC. ``AS IS'' AND ANY
14 * EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
15 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
16 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL APPLE COMPUTER, INC. OR
17 * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
18 * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
19 * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
20 * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
21 * OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
22 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
23 * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
24 */
25
26 #ifndef WTF_MathExtras_h
27 #define WTF_MathExtras_h
28
29 #include <algorithm>
30 #include <cmath>
31 #include <float.h>
32 #include <limits>
33 #include <stdlib.h>
34
35 #if OS(SOLARIS)
36 #include <ieeefp.h>
37 #endif
38
39 #if OS(OPENBSD)
40 #include <sys/types.h>
41 #include <machine/ieee.h>
42 #endif
43
44 #if COMPILER(MSVC)
45 #if OS(WINCE)
46 #include <stdlib.h>
47 #endif
48 #include <limits>
49 #endif
50
51 #ifndef M_PI
52 const double piDouble = 3.14159265358979323846;
53 const float piFloat = 3.14159265358979323846f;
54 #else
55 const double piDouble = M_PI;
56 const float piFloat = static_cast<float>(M_PI);
57 #endif
58
59 #ifndef M_PI_2
60 const double piOverTwoDouble = 1.57079632679489661923;
61 const float piOverTwoFloat = 1.57079632679489661923f;
62 #else
63 const double piOverTwoDouble = M_PI_2;
64 const float piOverTwoFloat = static_cast<float>(M_PI_2);
65 #endif
66
67 #ifndef M_PI_4
68 const double piOverFourDouble = 0.785398163397448309616;
69 const float piOverFourFloat = 0.785398163397448309616f;
70 #else
71 const double piOverFourDouble = M_PI_4;
72 const float piOverFourFloat = static_cast<float>(M_PI_4);
73 #endif
74
75 #if OS(DARWIN)
76
77 // Work around a bug in the Mac OS X libc where ceil(-0.1) return +0.
wtf_ceil(double x)78 inline double wtf_ceil(double x) { return copysign(ceil(x), x); }
79
80 #define ceil(x) wtf_ceil(x)
81
82 #endif
83
84 #if OS(SOLARIS)
85
86 #ifndef isfinite
isfinite(double x)87 inline bool isfinite(double x) { return finite(x) && !isnand(x); }
88 #endif
89 #ifndef isinf
isinf(double x)90 inline bool isinf(double x) { return !finite(x) && !isnand(x); }
91 #endif
92 #ifndef signbit
signbit(double x)93 inline bool signbit(double x) { return copysign(1.0, x) < 0; }
94 #endif
95
96 #endif
97
98 #if OS(OPENBSD)
99
100 #ifndef isfinite
isfinite(double x)101 inline bool isfinite(double x) { return finite(x); }
102 #endif
103 #ifndef signbit
signbit(double x)104 inline bool signbit(double x) { struct ieee_double *p = (struct ieee_double *)&x; return p->dbl_sign; }
105 #endif
106
107 #endif
108
109 #if COMPILER(MSVC) || (COMPILER(RVCT) && !(RVCT_VERSION_AT_LEAST(3, 0, 0, 0)))
110
111 // We must not do 'num + 0.5' or 'num - 0.5' because they can cause precision loss.
round(double num)112 static double round(double num)
113 {
114 double integer = ceil(num);
115 if (num > 0)
116 return integer - num > 0.5 ? integer - 1.0 : integer;
117 return integer - num >= 0.5 ? integer - 1.0 : integer;
118 }
roundf(float num)119 static float roundf(float num)
120 {
121 float integer = ceilf(num);
122 if (num > 0)
123 return integer - num > 0.5f ? integer - 1.0f : integer;
124 return integer - num >= 0.5f ? integer - 1.0f : integer;
125 }
llround(double num)126 inline long long llround(double num) { return static_cast<long long>(round(num)); }
llroundf(float num)127 inline long long llroundf(float num) { return static_cast<long long>(roundf(num)); }
lround(double num)128 inline long lround(double num) { return static_cast<long>(round(num)); }
lroundf(float num)129 inline long lroundf(float num) { return static_cast<long>(roundf(num)); }
trunc(double num)130 inline double trunc(double num) { return num > 0 ? floor(num) : ceil(num); }
131
132 #endif
133
134 #if COMPILER(MSVC)
135 // The 64bit version of abs() is already defined in stdlib.h which comes with VC10
136 #if COMPILER(MSVC9_OR_LOWER)
abs(long long num)137 inline long long abs(long long num) { return _abs64(num); }
138 #endif
139
isinf(double num)140 inline bool isinf(double num) { return !_finite(num) && !_isnan(num); }
isnan(double num)141 inline bool isnan(double num) { return !!_isnan(num); }
signbit(double num)142 inline bool signbit(double num) { return _copysign(1.0, num) < 0; }
143
nextafter(double x,double y)144 inline double nextafter(double x, double y) { return _nextafter(x, y); }
nextafterf(float x,float y)145 inline float nextafterf(float x, float y) { return x > y ? x - FLT_EPSILON : x + FLT_EPSILON; }
146
copysign(double x,double y)147 inline double copysign(double x, double y) { return _copysign(x, y); }
isfinite(double x)148 inline int isfinite(double x) { return _finite(x); }
149
150 // MSVC's math.h does not currently supply log2.
log2(double num)151 inline double log2(double num)
152 {
153 // This constant is roughly M_LN2, which is not provided by default on Windows.
154 return log(num) / 0.693147180559945309417232121458176568;
155 }
156
157 // Work around a bug in Win, where atan2(+-infinity, +-infinity) yields NaN instead of specific values.
wtf_atan2(double x,double y)158 inline double wtf_atan2(double x, double y)
159 {
160 double posInf = std::numeric_limits<double>::infinity();
161 double negInf = -std::numeric_limits<double>::infinity();
162 double nan = std::numeric_limits<double>::quiet_NaN();
163
164 double result = nan;
165
166 if (x == posInf && y == posInf)
167 result = piOverFourDouble;
168 else if (x == posInf && y == negInf)
169 result = 3 * piOverFourDouble;
170 else if (x == negInf && y == posInf)
171 result = -piOverFourDouble;
172 else if (x == negInf && y == negInf)
173 result = -3 * piOverFourDouble;
174 else
175 result = ::atan2(x, y);
176
177 return result;
178 }
179
180 // Work around a bug in the Microsoft CRT, where fmod(x, +-infinity) yields NaN instead of x.
wtf_fmod(double x,double y)181 inline double wtf_fmod(double x, double y) { return (!isinf(x) && isinf(y)) ? x : fmod(x, y); }
182
183 // Work around a bug in the Microsoft CRT, where pow(NaN, 0) yields NaN instead of 1.
wtf_pow(double x,double y)184 inline double wtf_pow(double x, double y) { return y == 0 ? 1 : pow(x, y); }
185
186 #define atan2(x, y) wtf_atan2(x, y)
187 #define fmod(x, y) wtf_fmod(x, y)
188 #define pow(x, y) wtf_pow(x, y)
189
190 #endif // COMPILER(MSVC)
191
deg2rad(double d)192 inline double deg2rad(double d) { return d * piDouble / 180.0; }
rad2deg(double r)193 inline double rad2deg(double r) { return r * 180.0 / piDouble; }
deg2grad(double d)194 inline double deg2grad(double d) { return d * 400.0 / 360.0; }
grad2deg(double g)195 inline double grad2deg(double g) { return g * 360.0 / 400.0; }
turn2deg(double t)196 inline double turn2deg(double t) { return t * 360.0; }
deg2turn(double d)197 inline double deg2turn(double d) { return d / 360.0; }
rad2grad(double r)198 inline double rad2grad(double r) { return r * 200.0 / piDouble; }
grad2rad(double g)199 inline double grad2rad(double g) { return g * piDouble / 200.0; }
200
deg2rad(float d)201 inline float deg2rad(float d) { return d * piFloat / 180.0f; }
rad2deg(float r)202 inline float rad2deg(float r) { return r * 180.0f / piFloat; }
deg2grad(float d)203 inline float deg2grad(float d) { return d * 400.0f / 360.0f; }
grad2deg(float g)204 inline float grad2deg(float g) { return g * 360.0f / 400.0f; }
turn2deg(float t)205 inline float turn2deg(float t) { return t * 360.0f; }
deg2turn(float d)206 inline float deg2turn(float d) { return d / 360.0f; }
rad2grad(float r)207 inline float rad2grad(float r) { return r * 200.0f / piFloat; }
grad2rad(float g)208 inline float grad2rad(float g) { return g * piFloat / 200.0f; }
209
clampToInteger(double d)210 inline int clampToInteger(double d)
211 {
212 const double minIntAsDouble = std::numeric_limits<int>::min();
213 const double maxIntAsDouble = std::numeric_limits<int>::max();
214 return static_cast<int>(std::max(std::min(d, maxIntAsDouble), minIntAsDouble));
215 }
216
clampToPositiveInteger(double d)217 inline int clampToPositiveInteger(double d)
218 {
219 const double maxIntAsDouble = std::numeric_limits<int>::max();
220 return static_cast<int>(std::max<double>(std::min(d, maxIntAsDouble), 0));
221 }
222
clampToInteger(float x)223 inline int clampToInteger(float x)
224 {
225 static const int s_intMax = std::numeric_limits<int>::max();
226 static const int s_intMin = std::numeric_limits<int>::min();
227
228 if (x >= static_cast<float>(s_intMax))
229 return s_intMax;
230 if (x < static_cast<float>(s_intMin))
231 return s_intMin;
232 return static_cast<int>(x);
233 }
234
clampToPositiveInteger(float x)235 inline int clampToPositiveInteger(float x)
236 {
237 static const int s_intMax = std::numeric_limits<int>::max();
238
239 if (x >= static_cast<float>(s_intMax))
240 return s_intMax;
241 if (x < 0)
242 return 0;
243 return static_cast<int>(x);
244 }
245
clampToInteger(unsigned value)246 inline int clampToInteger(unsigned value)
247 {
248 return static_cast<int>(std::min(value, static_cast<unsigned>(std::numeric_limits<int>::max())));
249 }
250
251 #if !COMPILER(MSVC) && !(COMPILER(RVCT) && PLATFORM(BREWMP)) && !OS(SOLARIS) && !OS(SYMBIAN)
252 using std::isfinite;
253 using std::isinf;
254 using std::isnan;
255 using std::signbit;
256 #endif
257
258 #endif // #ifndef WTF_MathExtras_h
259