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MathExtras.h

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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 <stdint.h>-
34#include <stdlib.h>-
35#include <wtf/StdLibExtras.h>-
36-
37#if OS(SOLARIS)-
38#include <ieeefp.h>-
39#endif-
40-
41#if OS(OPENBSD)-
42#include <sys/types.h>-
43#include <machine/ieee.h>-
44#endif-
45-
46#if OS(QNX) && defined(_CPPLIB_VER)-
47// FIXME: Look into a way to have cmath import its functions into both the standard and global-
48// namespace. For now, we include math.h since the QNX cmath header only imports its functions-
49// into the standard namespace.-
50#include <math.h>-
51// These macros from math.h conflict with the real functions in the std namespace.-
52#undef signbit-
53#undef isnan-
54#undef isinf-
55#undef isfinite-
56#endif-
57-
58#ifndef M_PI-
59const double piDouble = 3.14159265358979323846;-
60const float piFloat = 3.14159265358979323846f;-
61#else-
62const double piDouble = M_PI;-
63const float piFloat = static_cast<float>(M_PI);-
64#endif-
65-
66#ifndef M_PI_2-
67const double piOverTwoDouble = 1.57079632679489661923;-
68const float piOverTwoFloat = 1.57079632679489661923f;-
69#else-
70const double piOverTwoDouble = M_PI_2;-
71const float piOverTwoFloat = static_cast<float>(M_PI_2);-
72#endif-
73-
74#ifndef M_PI_4-
75const double piOverFourDouble = 0.785398163397448309616;-
76const float piOverFourFloat = 0.785398163397448309616f;-
77#else-
78const double piOverFourDouble = M_PI_4;-
79const float piOverFourFloat = static_cast<float>(M_PI_4);-
80#endif-
81-
82#if OS(DARWIN)-
83-
84// Work around a bug in the Mac OS X libc where ceil(-0.1) return +0.-
85inline double wtf_ceil(double x) { return copysign(ceil(x), x); }-
86-
87#define ceil(x) wtf_ceil(x)-
88-
89#endif-
90-
91#if OS(SOLARIS) && __cplusplus < 201103L-
92-
93namespace std {-
94-
95#ifndef isfinite-
96inline bool isfinite(double x) { return finite(x) && !isnand(x); }-
97#endif-
98#ifndef signbit-
99inline bool signbit(double x) { return copysign(1.0, x) < 0; }-
100#endif-
101#ifndef isinf-
102inline bool isinf(double x) { return !finite(x) && !isnand(x); }-
103#endif-
104-
105} // namespace std-
106-
107#endif-
108-
109#if OS(OPENBSD) && __cplusplus < 201103L-
110-
111namespace std {-
112-
113#ifndef isfinite-
114inline bool isfinite(double x) { return finite(x); }-
115#endif-
116#ifndef signbit-
117inline bool signbit(double x) { struct ieee_double *p = (struct ieee_double *)&x; return p->dbl_sign; }-
118#endif-
119-
120} // namespace std-
121-
122#endif-
123-
124#if COMPILER(MSVC)-
125-
126#if _MSC_VER < 1800-
127// We must not do 'num + 0.5' or 'num - 0.5' because they can cause precision loss.-
128static double round(double num)-
129{-
130 double integer = ceil(num);-
131 if (num > 0)-
132 return integer - num > 0.5 ? integer - 1.0 : integer;-
133 return integer - num >= 0.5 ? integer - 1.0 : integer;-
134}-
135static float roundf(float num)-
136{-
137 float integer = ceilf(num);-
138 if (num > 0)-
139 return integer - num > 0.5f ? integer - 1.0f : integer;-
140 return integer - num >= 0.5f ? integer - 1.0f : integer;-
141}-
142#endif-
143inline long long llround(double num) { return static_cast<long long>(round(num)); }-
144inline long long llroundf(float num) { return static_cast<long long>(roundf(num)); }-
145inline long lround(double num) { return static_cast<long>(round(num)); }-
146inline long lroundf(float num) { return static_cast<long>(roundf(num)); }-
147-
148#endif-
149-
150#if COMPILER(MSVC) && COMPILER(MSVC12_OR_LOWER)-
151// MSVC's math.h does not currently supply log2 or log2f.-
152inline double log2(double num)-
153{-
154 // This constant is roughly M_LN2, which is not provided by default on Windows.-
155 return log(num) / 0.693147180559945309417232121458176568;-
156}-
157-
158inline float log2f(float num)-
159{-
160 // This constant is roughly M_LN2, which is not provided by default on Windows.-
161 return logf(num) / 0.693147180559945309417232121458176568f;-
162}-
163#endif-
164-
165#if COMPILER(MSVC)-
166// The 64bit version of abs() is already defined in stdlib.h which comes with VC10-
167#if COMPILER(MSVC9_OR_LOWER)-
168inline long long abs(long long num) { return _abs64(num); }-
169#endif-
170-
171#if COMPILER(MSVC12_OR_LOWER)-
172-
173inline double nextafter(double x, double y) { return _nextafter(x, y); }-
174inline float nextafterf(float x, float y) { return x > y ? x - FLT_EPSILON : x + FLT_EPSILON; }-
175-
176inline double copysign(double x, double y) { return _copysign(x, y); }-
177-
178#endif // COMPILER(MSVC12_OR_LOWER)-
179-
180// Work around a bug in Win, where atan2(+-infinity, +-infinity) yields NaN instead of specific values.-
181inline double wtf_atan2(double x, double y)-
182{-
183 double posInf = std::numeric_limits<double>::infinity();-
184 double negInf = -std::numeric_limits<double>::infinity();-
185 double nan = std::numeric_limits<double>::quiet_NaN();-
186-
187 double result = nan;-
188-
189 if (x == posInf && y == posInf)-
190 result = piOverFourDouble;-
191 else if (x == posInf && y == negInf)-
192 result = 3 * piOverFourDouble;-
193 else if (x == negInf && y == posInf)-
194 result = -piOverFourDouble;-
195 else if (x == negInf && y == negInf)-
196 result = -3 * piOverFourDouble;-
197 else-
198 result = ::atan2(x, y);-
199-
200 return result;-
201}-
202-
203// Work around a bug in the Microsoft CRT, where fmod(x, +-infinity) yields NaN instead of x.-
204inline double wtf_fmod(double x, double y) { return (!std::isinf(x) && std::isinf(y)) ? x : fmod(x, y); }-
205-
206// Work around a bug in the Microsoft CRT, where pow(NaN, 0) yields NaN instead of 1.-
207inline double wtf_pow(double x, double y) { return y == 0 ? 1 : pow(x, y); }-
208-
209#define atan2(x, y) wtf_atan2(x, y)-
210#define fmod(x, y) wtf_fmod(x, y)-
211#define pow(x, y) wtf_pow(x, y)-
212-
213#if COMPILER(MSVC12_OR_LOWER)-
214-
215// MSVC's math functions do not bring lrint.-
216inline long int lrint(double flt)-
217{-
218 int64_t intgr;-
219#if CPU(X86)-
220 __asm {-
221 fld flt-
222 fistp intgr-
223 };-
224#else-
225 ASSERT(std::isfinite(flt));-
226 double rounded = round(flt);-
227 intgr = static_cast<int64_t>(rounded);-
228 // If the fractional part is exactly 0.5, we need to check whether-
229 // the rounded result is even. If it is not we need to add 1 to-
230 // negative values and subtract one from positive values.-
231 if ((fabs(intgr - flt) == 0.5) & intgr)-
232 intgr -= ((intgr >> 62) | 1); // 1 with the sign of result, i.e. -1 or 1.-
233#endif-
234 return static_cast<long int>(intgr);-
235}-
236-
237#endif // COMPILER(MSVC12_OR_LOWER)-
238#endif // COMPILER(MSVC)-
239-
240inline double deg2rad(double d) { return d * piDouble / 180.0; }
never executed: return d * piDouble / 180.0;
0
241inline double rad2deg(double r) { return r * 180.0 / piDouble; }
never executed: return r * 180.0 / piDouble;
0
242inline double deg2grad(double d) { return d * 400.0 / 360.0; }
never executed: return d * 400.0 / 360.0;
0
243inline double grad2deg(double g) { return g * 360.0 / 400.0; }
never executed: return g * 360.0 / 400.0;
0
244inline double turn2deg(double t) { return t * 360.0; }
never executed: return t * 360.0;
0
245inline double deg2turn(double d) { return d / 360.0; }
never executed: return d / 360.0;
0
246inline double rad2grad(double r) { return r * 200.0 / piDouble; }
never executed: return r * 200.0 / piDouble;
0
247inline double grad2rad(double g) { return g * piDouble / 200.0; }
never executed: return g * piDouble / 200.0;
0
248-
249inline float deg2rad(float d) { return d * piFloat / 180.0f; }
never executed: return d * piFloat / 180.0f;
0
250inline float rad2deg(float r) { return r * 180.0f / piFloat; }
never executed: return r * 180.0f / piFloat;
0
251inline float deg2grad(float d) { return d * 400.0f / 360.0f; }
never executed: return d * 400.0f / 360.0f;
0
252inline float grad2deg(float g) { return g * 360.0f / 400.0f; }
never executed: return g * 360.0f / 400.0f;
0
253inline float turn2deg(float t) { return t * 360.0f; }
never executed: return t * 360.0f;
0
254inline float deg2turn(float d) { return d / 360.0f; }
never executed: return d / 360.0f;
0
255inline float rad2grad(float r) { return r * 200.0f / piFloat; }
never executed: return r * 200.0f / piFloat;
0
256inline float grad2rad(float g) { return g * piFloat / 200.0f; }
never executed: return g * piFloat / 200.0f;
0
257-
258// std::numeric_limits<T>::min() returns the smallest positive value for floating point types-
259template<typename T> inline T defaultMinimumForClamp() { return std::numeric_limits<T>::min(); }
never executed: return std::numeric_limits<T>::min();
0
260template<> inline float defaultMinimumForClamp() { return -std::numeric_limits<float>::max(); }
never executed: return -std::numeric_limits<float>::max();
0
261template<> inline double defaultMinimumForClamp() { return -std::numeric_limits<double>::max(); }
never executed: return -std::numeric_limits<double>::max();
0
262template<typename T> inline T defaultMaximumForClamp() { return std::numeric_limits<T>::max(); }
never executed: return std::numeric_limits<T>::max();
0
263-
264template<typename T> inline T clampTo(double value, T min = defaultMinimumForClamp<T>(), T max = defaultMaximumForClamp<T>())-
265{-
266 if (value >= static_cast<double>(max))
value >= stati...t<double>(max)Description
TRUEnever evaluated
FALSEnever evaluated
0
267 return max;
never executed: return max;
0
268 if (value <= static_cast<double>(min))
value <= stati...t<double>(min)Description
TRUEnever evaluated
FALSEnever evaluated
0
269 return min;
never executed: return min;
0
270 return static_cast<T>(value);
never executed: return static_cast<T>(value);
0
271}-
272template<> long long int clampTo(double, long long int, long long int); // clampTo does not support long long ints.-
273-
274inline int clampToInteger(double value)-
275{-
276 return clampTo<int>(value);
never executed: return clampTo<int>(value);
0
277}-
278-
279inline float clampToFloat(double value)-
280{-
281 return clampTo<float>(value);
never executed: return clampTo<float>(value);
0
282}-
283-
284inline int clampToPositiveInteger(double value)-
285{-
286 return clampTo<int>(value, 0);
never executed: return clampTo<int>(value, 0);
0
287}-
288-
289inline int clampToInteger(float value)-
290{-
291 return clampTo<int>(value);
never executed: return clampTo<int>(value);
0
292}-
293-
294inline int clampToInteger(unsigned x)-
295{-
296 const unsigned intMax = static_cast<unsigned>(std::numeric_limits<int>::max());-
297-
298 if (x >= intMax)
x >= intMaxDescription
TRUEnever evaluated
FALSEnever evaluated
0
299 return std::numeric_limits<int>::max();
never executed: return std::numeric_limits<int>::max();
0
300 return static_cast<int>(x);
never executed: return static_cast<int>(x);
0
301}-
302-
303inline bool isWithinIntRange(float x)-
304{-
305 return x > static_cast<float>(std::numeric_limits<int>::min()) && x < static_cast<float>(std::numeric_limits<int>::max());
never executed: return x > static_cast<float>(std::numeric_limits<int>::min()) && x < static_cast<float>(std::numeric_limits<int>::max());
0
306}-
307-
308template<typename T> inline bool hasOneBitSet(T value)-
309{-
310 return !((value - 1) & value) && value;
never executed: return !((value - 1) & value) && value;
0
311}-
312-
313template<typename T> inline bool hasZeroOrOneBitsSet(T value)-
314{-
315 return !((value - 1) & value);
never executed: return !((value - 1) & value);
0
316}-
317-
318template<typename T> inline bool hasTwoOrMoreBitsSet(T value)-
319{-
320 return !hasZeroOrOneBitsSet(value);
never executed: return !hasZeroOrOneBitsSet(value);
0
321}-
322-
323template <typename T> inline unsigned getLSBSet(T value)-
324{-
325 unsigned result = 0;-
326-
327 while (value >>= 1)
value >>= 1Description
TRUEnever evaluated
FALSEnever evaluated
0
328 ++result;
never executed: ++result;
0
329-
330 return result;
never executed: return result;
0
331}-
332-
333template<typename T> inline T timesThreePlusOneDividedByTwo(T value)-
334{-
335 // Mathematically equivalent to:-
336 // (value * 3 + 1) / 2;-
337 // or:-
338 // (unsigned)ceil(value * 1.5));-
339 // This form is not prone to internal overflow.-
340 return value + (value >> 1) + (value & 1);
never executed: return value + (value >> 1) + (value & 1);
0
341}-
342-
343#ifndef UINT64_C-
344#if COMPILER(MSVC)-
345#define UINT64_C(c) c ## ui64-
346#else-
347#define UINT64_C(c) c ## ull-
348#endif-
349#endif-
350-
351#if COMPILER(MINGW64) && (!defined(__MINGW64_VERSION_RC) || __MINGW64_VERSION_RC < 1)-
352inline double wtf_pow(double x, double y)-
353{-
354 // MinGW-w64 has a custom implementation for pow.-
355 // This handles certain special cases that are different.-
356 if ((x == 0.0 || std::isinf(x)) && std::isfinite(y)) {-
357 double f;-
358 if (modf(y, &f) != 0.0)-
359 return ((x == 0.0) ^ (y > 0.0)) ? std::numeric_limits<double>::infinity() : 0.0;-
360 }-
361-
362 if (x == 2.0) {-
363 int yInt = static_cast<int>(y);-
364 if (y == yInt)-
365 return ldexp(1.0, yInt);-
366 }-
367-
368 return pow(x, y);-
369}-
370#define pow(x, y) wtf_pow(x, y)-
371#endif // COMPILER(MINGW64) && (!defined(__MINGW64_VERSION_RC) || __MINGW64_VERSION_RC < 1)-
372-
373-
374// decompose 'number' to its sign, exponent, and mantissa components.-
375// The result is interpreted as:-
376// (sign ? -1 : 1) * pow(2, exponent) * (mantissa / (1 << 52))-
377inline void decomposeDouble(double number, bool& sign, int32_t& exponent, uint64_t& mantissa)-
378{-
379 ASSERT(std::isfinite(number));-
380-
381 sign = std::signbit(number);-
382-
383 uint64_t bits = WTF::bitwise_cast<uint64_t>(number);-
384 exponent = (static_cast<int32_t>(bits >> 52) & 0x7ff) - 0x3ff;-
385 mantissa = bits & 0xFFFFFFFFFFFFFull;-
386-
387 // Check for zero/denormal values; if so, adjust the exponent,-
388 // if not insert the implicit, omitted leading 1 bit.-
389 if (exponent == -0x3ff)
exponent == -0x3ffDescription
TRUEnever evaluated
FALSEnever evaluated
0
390 exponent = mantissa ? -0x3fe : 0;
never executed: exponent = mantissa ? -0x3fe : 0;
mantissaDescription
TRUEnever evaluated
FALSEnever evaluated
0
391 else-
392 mantissa |= 0x10000000000000ull;
never executed: mantissa |= 0x10000000000000ull;
0
393}-
394-
395// Calculate d % 2^{64}.-
396inline void doubleToInteger(double d, unsigned long long& value)-
397{-
398 if (std::isnan(d) || std::isinf(d))
std::isnan(d)Description
TRUEnever evaluated
FALSEnever evaluated
std::isinf(d)Description
TRUEnever evaluated
FALSEnever evaluated
0
399 value = 0;
never executed: value = 0;
0
400 else {-
401 // -2^{64} < fmodValue < 2^{64}.-
402 double fmodValue = fmod(trunc(d), std::numeric_limits<unsigned long long>::max() + 1.0);-
403 if (fmodValue >= 0) {
fmodValue >= 0Description
TRUEnever evaluated
FALSEnever evaluated
0
404 // 0 <= fmodValue < 2^{64}.-
405 // 0 <= value < 2^{64}. This cast causes no loss.-
406 value = static_cast<unsigned long long>(fmodValue);-
407 } else {
never executed: end of block
0
408 // -2^{64} < fmodValue < 0.-
409 // 0 < fmodValueInUnsignedLongLong < 2^{64}. This cast causes no loss.-
410 unsigned long long fmodValueInUnsignedLongLong = static_cast<unsigned long long>(-fmodValue);-
411 // -1 < (std::numeric_limits<unsigned long long>::max() - fmodValueInUnsignedLongLong) < 2^{64} - 1.-
412 // 0 < value < 2^{64}.-
413 value = std::numeric_limits<unsigned long long>::max() - fmodValueInUnsignedLongLong + 1;-
414 }
never executed: end of block
0
415 }-
416}-
417-
418namespace WTF {-
419-
420// From http://graphics.stanford.edu/~seander/bithacks.html#RoundUpPowerOf2-
421inline uint32_t roundUpToPowerOfTwo(uint32_t v)-
422{-
423 v--;-
424 v |= v >> 1;-
425 v |= v >> 2;-
426 v |= v >> 4;-
427 v |= v >> 8;-
428 v |= v >> 16;-
429 v++;-
430 return v;
never executed: return v;
0
431}-
432-
433inline unsigned fastLog2(unsigned i)-
434{-
435 unsigned log2 = 0;-
436 if (i & (i - 1))
i & (i - 1)Description
TRUEnever evaluated
FALSEnever evaluated
0
437 log2 += 1;
never executed: log2 += 1;
0
438 if (i >> 16)
i >> 16Description
TRUEnever evaluated
FALSEnever evaluated
0
439 log2 += 16, i >>= 16;
never executed: log2 += 16, i >>= 16;
0
440 if (i >> 8)
i >> 8Description
TRUEnever evaluated
FALSEnever evaluated
0
441 log2 += 8, i >>= 8;
never executed: log2 += 8, i >>= 8;
0
442 if (i >> 4)
i >> 4Description
TRUEnever evaluated
FALSEnever evaluated
0
443 log2 += 4, i >>= 4;
never executed: log2 += 4, i >>= 4;
0
444 if (i >> 2)
i >> 2Description
TRUEnever evaluated
FALSEnever evaluated
0
445 log2 += 2, i >>= 2;
never executed: log2 += 2, i >>= 2;
0
446 if (i >> 1)
i >> 1Description
TRUEnever evaluated
FALSEnever evaluated
0
447 log2 += 1;
never executed: log2 += 1;
0
448 return log2;
never executed: return log2;
0
449}-
450-
451} // namespace WTF-
452-
453#endif // #ifndef WTF_MathExtras_h-
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