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; }
241inline double rad2deg(double r) { return r * 180.0 / piDouble; }
242inline double deg2grad(double d) { return d * 400.0 / 360.0; }
243inline double grad2deg(double g) { return g * 360.0 / 400.0; }
244inline double turn2deg(double t) { return t * 360.0; }
245inline double deg2turn(double d) { return d / 360.0; }
246inline double rad2grad(double r) { return r * 200.0 / piDouble; }
247inline double grad2rad(double g) { return g * piDouble / 200.0; }
248
249inline float deg2rad(float d) { return d * piFloat / 180.0f; }
250inline float rad2deg(float r) { return r * 180.0f / piFloat; }
251inline float deg2grad(float d) { return d * 400.0f / 360.0f; }
252inline float grad2deg(float g) { return g * 360.0f / 400.0f; }
253inline float turn2deg(float t) { return t * 360.0f; }
254inline float deg2turn(float d) { return d / 360.0f; }
255inline float rad2grad(float r) { return r * 200.0f / piFloat; }
256inline float grad2rad(float g) { return g * piFloat / 200.0f; }
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(); }
260template<> inline float defaultMinimumForClamp() { return -std::numeric_limits<float>::max(); }
261template<> inline double defaultMinimumForClamp() { return -std::numeric_limits<double>::max(); }
262template<typename T> inline T defaultMaximumForClamp() { return std::numeric_limits<T>::max(); }
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))
267 return max;
268 if (value <= static_cast<double>(min))
269 return min;
270 return static_cast<T>(value);
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);
277}
278
279inline float clampToFloat(double value)
280{
281 return clampTo<float>(value);
282}
283
284inline int clampToPositiveInteger(double value)
285{
286 return clampTo<int>(value, min: 0);
287}
288
289inline int clampToInteger(float value)
290{
291 return clampTo<int>(value);
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)
299 return std::numeric_limits<int>::max();
300 return static_cast<int>(x);
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());
306}
307
308template<typename T> inline bool hasOneBitSet(T value)
309{
310 return !((value - 1) & value) && value;
311}
312
313template<typename T> inline bool hasZeroOrOneBitsSet(T value)
314{
315 return !((value - 1) & value);
316}
317
318template<typename T> inline bool hasTwoOrMoreBitsSet(T value)
319{
320 return !hasZeroOrOneBitsSet(value);
321}
322
323template <typename T> inline unsigned getLSBSet(T value)
324{
325 unsigned result = 0;
326
327 while (value >>= 1)
328 ++result;
329
330 return result;
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);
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(x: number);
382
383 uint64_t bits = WTF::bitwise_cast<uint64_t>(from: 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)
390 exponent = mantissa ? -0x3fe : 0;
391 else
392 mantissa |= 0x10000000000000ull;
393}
394
395// Calculate d % 2^{64}.
396inline void doubleToInteger(double d, unsigned long long& value)
397{
398 if (std::isnan(x: d) || std::isinf(x: d))
399 value = 0;
400 else {
401 // -2^{64} < fmodValue < 2^{64}.
402 double fmodValue = fmod(x: trunc(x: d), y: -2.0 * std::numeric_limits<long long>::min());
403 if (fmodValue >= 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 {
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 }
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;
431}
432
433inline unsigned fastLog2(unsigned i)
434{
435 unsigned log2 = 0;
436 if (i & (i - 1))
437 log2 += 1;
438 if (i >> 16)
439 log2 += 16, i >>= 16;
440 if (i >> 8)
441 log2 += 8, i >>= 8;
442 if (i >> 4)
443 log2 += 4, i >>= 4;
444 if (i >> 2)
445 log2 += 2, i >>= 2;
446 if (i >> 1)
447 log2 += 1;
448 return log2;
449}
450
451} // namespace WTF
452
453#endif // #ifndef WTF_MathExtras_h
454

source code of qtdeclarative/src/3rdparty/masm/wtf/MathExtras.h