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 "wtf/CPU.h"
30#include <cmath>
31#include <limits>
32
33#if COMPILER(MSVC)
34#include "wtf/Assertions.h"
35#include <stdint.h>
36#endif
37
38#if OS(OPENBSD)
39#include <sys/types.h>
40#include <machine/ieee.h>
41#endif
42
43const double piDouble = M_PI;
44const float piFloat = static_cast<float>(M_PI);
45
46const double piOverTwoDouble = M_PI_2;
47const float piOverTwoFloat = static_cast<float>(M_PI_2);
48
49const double piOverFourDouble = M_PI_4;
50const float piOverFourFloat = static_cast<float>(M_PI_4);
51
52const double twoPiDouble = piDouble * 2.0;
53const float twoPiFloat = piFloat * 2.0f;
54
55#if OS(MACOSX)
56
57// Work around a bug in the Mac OS X libc where ceil(-0.1) return +0.
58inline double wtf_ceil(double x) { return copysign(ceil(x), x); }
59
60#define ceil(x) wtf_ceil(x)
61
62#endif
63
64#if OS(OPENBSD)
65
66namespace std {
67
68#ifndef isfinite
69inline bool isfinite(double x) { return finite(x); }
70#endif
71#ifndef signbit
72inline bool signbit(double x) { struct ieee_double *p = (struct ieee_double *)&x; return p->dbl_sign; }
73#endif
74
75} // namespace std
76
77#endif
78
79#if COMPILER(MSVC) && (_MSC_VER < 1800)
80
81// We must not do 'num + 0.5' or 'num - 0.5' because they can cause precision loss.
82static double round(double num)
83{
84    double integer = ceil(num);
85    if (num > 0)
86        return integer - num > 0.5 ? integer - 1.0 : integer;
87    return integer - num >= 0.5 ? integer - 1.0 : integer;
88}
89static float roundf(float num)
90{
91    float integer = ceilf(num);
92    if (num > 0)
93        return integer - num > 0.5f ? integer - 1.0f : integer;
94    return integer - num >= 0.5f ? integer - 1.0f : integer;
95}
96inline long long llround(double num) { return static_cast<long long>(round(num)); }
97inline long long llroundf(float num) { return static_cast<long long>(roundf(num)); }
98inline long lround(double num) { return static_cast<long>(round(num)); }
99inline long lroundf(float num) { return static_cast<long>(roundf(num)); }
100inline double trunc(double num) { return num > 0 ? floor(num) : ceil(num); }
101
102#endif
103
104#if OS(ANDROID) || COMPILER(MSVC)
105// ANDROID and MSVC's math.h does not currently supply log2 or log2f.
106inline double log2(double num)
107{
108    // This constant is roughly M_LN2, which is not provided by default on Windows and Android.
109    return log(num) / 0.693147180559945309417232121458176568;
110}
111
112inline float log2f(float num)
113{
114    // This constant is roughly M_LN2, which is not provided by default on Windows and Android.
115    return logf(num) / 0.693147180559945309417232121458176568f;
116}
117#endif
118
119#if COMPILER(MSVC)
120
121// VS2013 has most of the math functions now, but we still need to work
122// around various differences in behavior of Inf.
123
124#if _MSC_VER < 1800
125
126namespace std {
127
128inline bool isinf(double num) { return !_finite(num) && !_isnan(num); }
129inline bool isnan(double num) { return !!_isnan(num); }
130inline bool isfinite(double x) { return _finite(x); }
131inline bool signbit(double num) { return _copysign(1.0, num) < 0; }
132
133} // namespace std
134
135inline double nextafter(double x, double y) { return _nextafter(x, y); }
136inline float nextafterf(float x, float y) { return x > y ? x - FLT_EPSILON : x + FLT_EPSILON; }
137
138inline double copysign(double x, double y) { return _copysign(x, y); }
139
140#endif // _MSC_VER
141
142// Work around a bug in Win, where atan2(+-infinity, +-infinity) yields NaN instead of specific values.
143inline double wtf_atan2(double x, double y)
144{
145    double posInf = std::numeric_limits<double>::infinity();
146    double negInf = -std::numeric_limits<double>::infinity();
147    double nan = std::numeric_limits<double>::quiet_NaN();
148
149    double result = nan;
150
151    if (x == posInf && y == posInf)
152        result = piOverFourDouble;
153    else if (x == posInf && y == negInf)
154        result = 3 * piOverFourDouble;
155    else if (x == negInf && y == posInf)
156        result = -piOverFourDouble;
157    else if (x == negInf && y == negInf)
158        result = -3 * piOverFourDouble;
159    else
160        result = ::atan2(x, y);
161
162    return result;
163}
164
165// Work around a bug in the Microsoft CRT, where fmod(x, +-infinity) yields NaN instead of x.
166inline double wtf_fmod(double x, double y) { return (!std::isinf(x) && std::isinf(y)) ? x : fmod(x, y); }
167
168// Work around a bug in the Microsoft CRT, where pow(NaN, 0) yields NaN instead of 1.
169inline double wtf_pow(double x, double y) { return y == 0 ? 1 : pow(x, y); }
170
171#define atan2(x, y) wtf_atan2(x, y)
172#define fmod(x, y) wtf_fmod(x, y)
173#define pow(x, y) wtf_pow(x, y)
174
175#if _MSC_VER < 1800
176
177// MSVC's math functions do not bring lrint.
178inline long int lrint(double flt)
179{
180    int64_t intgr;
181#if CPU(X86)
182    __asm {
183        fld flt
184        fistp intgr
185    };
186#else
187    ASSERT(std::isfinite(flt));
188    double rounded = round(flt);
189    intgr = static_cast<int64_t>(rounded);
190    // If the fractional part is exactly 0.5, we need to check whether
191    // the rounded result is even. If it is not we need to add 1 to
192    // negative values and subtract one from positive values.
193    if ((fabs(intgr - flt) == 0.5) & intgr)
194        intgr -= ((intgr >> 62) | 1); // 1 with the sign of result, i.e. -1 or 1.
195#endif
196    return static_cast<long int>(intgr);
197}
198
199#endif // _MSC_VER
200
201#endif // COMPILER(MSVC)
202
203inline double deg2rad(double d)  { return d * piDouble / 180.0; }
204inline double rad2deg(double r)  { return r * 180.0 / piDouble; }
205inline double deg2grad(double d) { return d * 400.0 / 360.0; }
206inline double grad2deg(double g) { return g * 360.0 / 400.0; }
207inline double turn2deg(double t) { return t * 360.0; }
208inline double deg2turn(double d) { return d / 360.0; }
209inline double rad2grad(double r) { return r * 200.0 / piDouble; }
210inline double grad2rad(double g) { return g * piDouble / 200.0; }
211inline double turn2grad(double t) { return t * 400; }
212inline double grad2turn(double g) { return g / 400; }
213
214inline float deg2rad(float d)  { return d * piFloat / 180.0f; }
215inline float rad2deg(float r)  { return r * 180.0f / piFloat; }
216inline float deg2grad(float d) { return d * 400.0f / 360.0f; }
217inline float grad2deg(float g) { return g * 360.0f / 400.0f; }
218inline float turn2deg(float t) { return t * 360.0f; }
219inline float deg2turn(float d) { return d / 360.0f; }
220inline float rad2grad(float r) { return r * 200.0f / piFloat; }
221inline float grad2rad(float g) { return g * piFloat / 200.0f; }
222inline float turn2grad(float t) { return t * 400; }
223inline float grad2turn(float g) { return g / 400; }
224
225// std::numeric_limits<T>::min() returns the smallest positive value for floating point types
226template<typename T> inline T defaultMinimumForClamp() { return std::numeric_limits<T>::min(); }
227template<> inline float defaultMinimumForClamp() { return -std::numeric_limits<float>::max(); }
228template<> inline double defaultMinimumForClamp() { return -std::numeric_limits<double>::max(); }
229template<typename T> inline T defaultMaximumForClamp() { return std::numeric_limits<T>::max(); }
230
231template<typename T> inline T clampTo(double value, T min = defaultMinimumForClamp<T>(), T max = defaultMaximumForClamp<T>())
232{
233    if (value >= static_cast<double>(max))
234        return max;
235    if (value <= static_cast<double>(min))
236        return min;
237    return static_cast<T>(value);
238}
239template<> inline long long int clampTo(double, long long int, long long int); // clampTo does not support long long ints.
240
241inline int clampToInteger(double value)
242{
243    return clampTo<int>(value);
244}
245
246inline unsigned clampToUnsigned(double value)
247{
248    return clampTo<unsigned>(value);
249}
250
251inline float clampToFloat(double value)
252{
253    return clampTo<float>(value);
254}
255
256inline int clampToPositiveInteger(double value)
257{
258    return clampTo<int>(value, 0);
259}
260
261inline int clampToInteger(float value)
262{
263    return clampTo<int>(value);
264}
265
266inline int clampToInteger(unsigned x)
267{
268    const unsigned intMax = static_cast<unsigned>(std::numeric_limits<int>::max());
269
270    if (x >= intMax)
271        return std::numeric_limits<int>::max();
272    return static_cast<int>(x);
273}
274
275inline bool isWithinIntRange(float x)
276{
277    return x > static_cast<float>(std::numeric_limits<int>::min()) && x < static_cast<float>(std::numeric_limits<int>::max());
278}
279
280static size_t greatestCommonDivisor(size_t a, size_t b)
281{
282    return b ? greatestCommonDivisor(b, a % b) : a;
283}
284
285inline size_t lowestCommonMultiple(size_t a, size_t b)
286{
287    return a && b ? a / greatestCommonDivisor(a, b) * b : 0;
288}
289
290#ifndef UINT64_C
291#if COMPILER(MSVC)
292#define UINT64_C(c) c ## ui64
293#else
294#define UINT64_C(c) c ## ull
295#endif
296#endif
297
298// Calculate d % 2^{64}.
299inline void doubleToInteger(double d, unsigned long long& value)
300{
301    if (std::isnan(d) || std::isinf(d))
302        value = 0;
303    else {
304        // -2^{64} < fmodValue < 2^{64}.
305        double fmodValue = fmod(trunc(d), std::numeric_limits<unsigned long long>::max() + 1.0);
306        if (fmodValue >= 0) {
307            // 0 <= fmodValue < 2^{64}.
308            // 0 <= value < 2^{64}. This cast causes no loss.
309            value = static_cast<unsigned long long>(fmodValue);
310        } else {
311            // -2^{64} < fmodValue < 0.
312            // 0 < fmodValueInUnsignedLongLong < 2^{64}. This cast causes no loss.
313            unsigned long long fmodValueInUnsignedLongLong = static_cast<unsigned long long>(-fmodValue);
314            // -1 < (std::numeric_limits<unsigned long long>::max() - fmodValueInUnsignedLongLong) < 2^{64} - 1.
315            // 0 < value < 2^{64}.
316            value = std::numeric_limits<unsigned long long>::max() - fmodValueInUnsignedLongLong + 1;
317        }
318    }
319}
320
321namespace WTF {
322
323inline unsigned fastLog2(unsigned i)
324{
325    unsigned log2 = 0;
326    if (i & (i - 1))
327        log2 += 1;
328    if (i >> 16)
329        log2 += 16, i >>= 16;
330    if (i >> 8)
331        log2 += 8, i >>= 8;
332    if (i >> 4)
333        log2 += 4, i >>= 4;
334    if (i >> 2)
335        log2 += 2, i >>= 2;
336    if (i >> 1)
337        log2 += 1;
338    return log2;
339}
340
341} // namespace WTF
342
343#endif // #ifndef WTF_MathExtras_h
344