xref: /third_party/skia/src/core/SkMathPriv.h (revision cb93a386) 
1/*
2 * Copyright 2012 Google Inc.
3 *
4 * Use of this source code is governed by a BSD-style license that can be
5 * found in the LICENSE file.
6 */
7
8#ifndef SkMathPriv_DEFINED
9#define SkMathPriv_DEFINED
10
11#include "include/core/SkMath.h"
12
13/**
14 *  Return the integer square root of value, with a bias of bitBias
15 */
16int32_t SkSqrtBits(int32_t value, int bitBias);
17
18/** Return the integer square root of n, treated as a SkFixed (16.16)
19 */
20static inline int32_t SkSqrt32(int32_t n) { return SkSqrtBits(n, 15); }
21
22/**
23 *  Returns (value < 0 ? 0 : value) efficiently (i.e. no compares or branches)
24 */
25static inline int SkClampPos(int value) {
26    return value & ~(value >> 31);
27}
28
29/**
30 * Stores numer/denom and numer%denom into div and mod respectively.
31 */
32template <typename In, typename Out>
33inline void SkTDivMod(In numer, In denom, Out* div, Out* mod) {
34#ifdef SK_CPU_ARM32
35    // If we wrote this as in the else branch, GCC won't fuse the two into one
36    // divmod call, but rather a div call followed by a divmod.  Silly!  This
37    // version is just as fast as calling __aeabi_[u]idivmod manually, but with
38    // prettier code.
39    //
40    // This benches as around 2x faster than the code in the else branch.
41    const In d = numer/denom;
42    *div = static_cast<Out>(d);
43    *mod = static_cast<Out>(numer-d*denom);
44#else
45    // On x86 this will just be a single idiv.
46    *div = static_cast<Out>(numer/denom);
47    *mod = static_cast<Out>(numer%denom);
48#endif
49}
50
51/** Returns -1 if n < 0, else returns 0
52 */
53#define SkExtractSign(n)    ((int32_t)(n) >> 31)
54
55/** If sign == -1, returns -n, else sign must be 0, and returns n.
56 Typically used in conjunction with SkExtractSign().
57 */
58static inline int32_t SkApplySign(int32_t n, int32_t sign) {
59    SkASSERT(sign == 0 || sign == -1);
60    return (n ^ sign) - sign;
61}
62
63/** Return x with the sign of y */
64static inline int32_t SkCopySign32(int32_t x, int32_t y) {
65    return SkApplySign(x, SkExtractSign(x ^ y));
66}
67
68/** Given a positive value and a positive max, return the value
69 pinned against max.
70 Note: only works as long as max - value doesn't wrap around
71 @return max if value >= max, else value
72 */
73static inline unsigned SkClampUMax(unsigned value, unsigned max) {
74    if (value > max) {
75        value = max;
76    }
77    return value;
78}
79
80// If a signed int holds min_int (e.g. 0x80000000) it is undefined what happens when
81// we negate it (even though we *know* we're 2's complement and we'll get the same
82// value back). So we create this helper function that casts to size_t (unsigned) first,
83// to avoid the complaint.
84static inline size_t sk_negate_to_size_t(int32_t value) {
85#if defined(_MSC_VER)
86#pragma warning(push)
87#pragma warning(disable : 4146)  // Thanks MSVC, we know what we're negating an unsigned
88#endif
89    return -static_cast<size_t>(value);
90#if defined(_MSC_VER)
91#pragma warning(pop)
92#endif
93}
94
95///////////////////////////////////////////////////////////////////////////////
96
97/** Return a*b/255, truncating away any fractional bits. Only valid if both
98 a and b are 0..255
99 */
100static inline U8CPU SkMulDiv255Trunc(U8CPU a, U8CPU b) {
101    SkASSERT((uint8_t)a == a);
102    SkASSERT((uint8_t)b == b);
103    unsigned prod = a*b + 1;
104    return (prod + (prod >> 8)) >> 8;
105}
106
107/** Return (a*b)/255, taking the ceiling of any fractional bits. Only valid if
108 both a and b are 0..255. The expected result equals (a * b + 254) / 255.
109 */
110static inline U8CPU SkMulDiv255Ceiling(U8CPU a, U8CPU b) {
111    SkASSERT((uint8_t)a == a);
112    SkASSERT((uint8_t)b == b);
113    unsigned prod = a*b + 255;
114    return (prod + (prod >> 8)) >> 8;
115}
116
117/** Just the rounding step in SkDiv255Round: round(value / 255)
118 */
119static inline unsigned SkDiv255Round(unsigned prod) {
120    prod += 128;
121    return (prod + (prod >> 8)) >> 8;
122}
123
124/**
125 * Swap byte order of a 4-byte value, e.g. 0xaarrggbb -> 0xbbggrraa.
126 */
127#if defined(_MSC_VER)
128    #include <stdlib.h>
129    static inline uint32_t SkBSwap32(uint32_t v) { return _byteswap_ulong(v); }
130#else
131    static inline uint32_t SkBSwap32(uint32_t v) { return __builtin_bswap32(v); }
132#endif
133
134//! Returns the number of leading zero bits (0...32)
135// From Hacker's Delight 2nd Edition
136constexpr int SkCLZ_portable(uint32_t x) {
137    int n = 32;
138    uint32_t y = x >> 16; if (y != 0) {n -= 16; x = y;}
139             y = x >>  8; if (y != 0) {n -=  8; x = y;}
140             y = x >>  4; if (y != 0) {n -=  4; x = y;}
141             y = x >>  2; if (y != 0) {n -=  2; x = y;}
142             y = x >>  1; if (y != 0) {return n - 2;}
143    return n - x;
144}
145
146static_assert(32 == SkCLZ_portable(0));
147static_assert(31 == SkCLZ_portable(1));
148static_assert( 1 == SkCLZ_portable(1 << 30));
149static_assert( 1 == SkCLZ_portable((1 << 30) | (1 << 24) | 1));
150static_assert( 0 == SkCLZ_portable(~0U));
151
152#if defined(SK_BUILD_FOR_WIN)
153    #include <intrin.h>
154
155    static inline int SkCLZ(uint32_t mask) {
156        if (mask) {
157            unsigned long index = 0;
158            _BitScanReverse(&index, mask);
159            // Suppress this bogus /analyze warning. The check for non-zero
160            // guarantees that _BitScanReverse will succeed.
161            // #pragma warning(suppress : 6102) // Using 'index' from failed function call
162            return index ^ 0x1F;
163        } else {
164            return 32;
165        }
166    }
167#elif defined(SK_CPU_ARM32) || defined(__GNUC__) || defined(__clang__)
168    static inline int SkCLZ(uint32_t mask) {
169        // __builtin_clz(0) is undefined, so we have to detect that case.
170        return mask ? __builtin_clz(mask) : 32;
171    }
172#else
173    static inline int SkCLZ(uint32_t mask) {
174        return SkCLZ_portable(mask);
175    }
176#endif
177
178//! Returns the number of trailing zero bits (0...32)
179// From Hacker's Delight 2nd Edition
180constexpr int SkCTZ_portable(uint32_t x) {
181    return 32 - SkCLZ_portable(~x & (x - 1));
182}
183
184static_assert(32 == SkCTZ_portable(0));
185static_assert( 0 == SkCTZ_portable(1));
186static_assert(30 == SkCTZ_portable(1 << 30));
187static_assert( 2 == SkCTZ_portable((1 << 30) | (1 << 24) | (1 << 2)));
188static_assert( 0 == SkCTZ_portable(~0U));
189
190#if defined(SK_BUILD_FOR_WIN)
191    #include <intrin.h>
192
193    static inline int SkCTZ(uint32_t mask) {
194        if (mask) {
195            unsigned long index = 0;
196            _BitScanForward(&index, mask);
197            // Suppress this bogus /analyze warning. The check for non-zero
198            // guarantees that _BitScanReverse will succeed.
199            // #pragma warning(suppress : 6102) // Using 'index' from failed function call
200            return index;
201        } else {
202            return 32;
203        }
204    }
205#elif defined(SK_CPU_ARM32) || defined(__GNUC__) || defined(__clang__)
206    static inline int SkCTZ(uint32_t mask) {
207        // __builtin_ctz(0) is undefined, so we have to detect that case.
208        return mask ? __builtin_ctz(mask) : 32;
209    }
210#else
211    static inline int SkCTZ(uint32_t mask) {
212        return SkCTZ_portable(mask);
213    }
214#endif
215
216/**
217 *  Returns the log2 of the specified value, were that value to be rounded up
218 *  to the next power of 2. It is undefined to pass 0. Examples:
219 *  SkNextLog2(1) -> 0
220 *  SkNextLog2(2) -> 1
221 *  SkNextLog2(3) -> 2
222 *  SkNextLog2(4) -> 2
223 *  SkNextLog2(5) -> 3
224 */
225static inline int SkNextLog2(uint32_t value) {
226    SkASSERT(value != 0);
227    return 32 - SkCLZ(value - 1);
228}
229
230constexpr int SkNextLog2_portable(uint32_t value) {
231    SkASSERT(value != 0);
232    return 32 - SkCLZ_portable(value - 1);
233}
234
235/**
236*  Returns the log2 of the specified value, were that value to be rounded down
237*  to the previous power of 2. It is undefined to pass 0. Examples:
238*  SkPrevLog2(1) -> 0
239*  SkPrevLog2(2) -> 1
240*  SkPrevLog2(3) -> 1
241*  SkPrevLog2(4) -> 2
242*  SkPrevLog2(5) -> 2
243*/
244static inline int SkPrevLog2(uint32_t value) {
245    SkASSERT(value != 0);
246    return 32 - SkCLZ(value >> 1);
247}
248
249constexpr int SkPrevLog2_portable(uint32_t value) {
250    SkASSERT(value != 0);
251    return 32 - SkCLZ_portable(value >> 1);
252}
253
254/**
255 *  Returns the smallest power-of-2 that is >= the specified value. If value
256 *  is already a power of 2, then it is returned unchanged. It is undefined
257 *  if value is <= 0.
258 */
259static inline int SkNextPow2(int value) {
260    SkASSERT(value > 0);
261    return 1 << SkNextLog2(value);
262}
263
264constexpr int SkNextPow2_portable(int value) {
265    SkASSERT(value > 0);
266    return 1 << SkNextLog2_portable(value);
267}
268
269/**
270*  Returns the largest power-of-2 that is <= the specified value. If value
271*  is already a power of 2, then it is returned unchanged. It is undefined
272*  if value is <= 0.
273*/
274static inline int SkPrevPow2(int value) {
275    SkASSERT(value > 0);
276    return 1 << SkPrevLog2(value);
277}
278
279constexpr int SkPrevPow2_portable(int value) {
280    SkASSERT(value > 0);
281    return 1 << SkPrevLog2_portable(value);
282}
283
284///////////////////////////////////////////////////////////////////////////////
285
286/**
287 *  Return the smallest power-of-2 >= n.
288 */
289static inline uint32_t GrNextPow2(uint32_t n) {
290    return n ? (1 << (32 - SkCLZ(n - 1))) : 1;
291}
292
293/**
294 * Returns the next power of 2 >= n or n if the next power of 2 can't be represented by size_t.
295 */
296static inline size_t GrNextSizePow2(size_t n) {
297    constexpr int kNumSizeTBits = 8 * sizeof(size_t);
298    constexpr size_t kHighBitSet = size_t(1) << (kNumSizeTBits - 1);
299
300    if (!n) {
301        return 1;
302    } else if (n >= kHighBitSet) {
303        return n;
304    }
305
306    n--;
307    uint32_t shift = 1;
308    while (shift < kNumSizeTBits) {
309        n |= n >> shift;
310        shift <<= 1;
311    }
312    return n + 1;
313}
314
315// conservative check. will return false for very large values that "could" fit
316template <typename T> static inline bool SkFitsInFixed(T x) {
317    return SkTAbs(x) <= 32767.0f;
318}
319
320#endif
321