SkMath.h revision 69975b0fce6c950a0481a2ddaec3ce0aaa03f90d 
1/*
2 * Copyright (C) 2006 The Android Open Source Project
3 *
4 * Licensed under the Apache License, Version 2.0 (the "License");
5 * you may not use this file except in compliance with the License.
6 * You may obtain a copy of the License at
7 *
8 *      http://www.apache.org/licenses/LICENSE-2.0
9 *
10 * Unless required by applicable law or agreed to in writing, software
11 * distributed under the License is distributed on an "AS IS" BASIS,
12 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
13 * See the License for the specific language governing permissions and
14 * limitations under the License.
15 */
16
17#ifndef SkMath_DEFINED
18#define SkMath_DEFINED
19
20#include "SkTypes.h"
21
22//! Returns the number of leading zero bits (0...32)
23int SkCLZ_portable(uint32_t);
24
25/** Computes the 64bit product of a * b, and then shifts the answer down by
26    shift bits, returning the low 32bits. shift must be [0..63]
27    e.g. to perform a fixedmul, call SkMulShift(a, b, 16)
28*/
29int32_t SkMulShift(int32_t a, int32_t b, unsigned shift);
30
31/** Computes numer1 * numer2 / denom in full 64 intermediate precision.
32    It is an error for denom to be 0. There is no special handling if
33    the result overflows 32bits.
34*/
35int32_t SkMulDiv(int32_t numer1, int32_t numer2, int32_t denom);
36
37/** Computes (numer1 << shift) / denom in full 64 intermediate precision.
38    It is an error for denom to be 0. There is no special handling if
39    the result overflows 32bits.
40*/
41int32_t SkDivBits(int32_t numer, int32_t denom, int shift);
42
43/** Return the integer square root of value, with a bias of bitBias
44*/
45int32_t SkSqrtBits(int32_t value, int bitBias);
46
47/** Return the integer square root of n, treated as a SkFixed (16.16)
48*/
49#define SkSqrt32(n)         SkSqrtBits(n, 15)
50
51/** Return the integer cube root of value, with a bias of bitBias
52 */
53int32_t SkCubeRootBits(int32_t value, int bitBias);
54
55/** Returns -1 if n < 0, else returns 0
56*/
57#define SkExtractSign(n)    ((int32_t)(n) >> 31)
58
59/** If sign == -1, returns -n, else sign must be 0, and returns n.
60    Typically used in conjunction with SkExtractSign().
61*/
62static inline int32_t SkApplySign(int32_t n, int32_t sign) {
63    SkASSERT(sign == 0 || sign == -1);
64    return (n ^ sign) - sign;
65}
66
67/** Returns (value < 0 ? 0 : value) efficiently (i.e. no compares or branches)
68*/
69static inline int SkClampPos(int value) {
70    return value & ~(value >> 31);
71}
72
73/** Given an integer and a positive (max) integer, return the value
74    pinned against 0 and max, inclusive.
75    Note: only works as long as max - value doesn't wrap around
76    @param value    The value we want returned pinned between [0...max]
77    @param max      The positive max value
78    @return 0 if value < 0, max if value > max, else value
79*/
80static inline int SkClampMax(int value, int max) {
81    // ensure that max is positive
82    SkASSERT(max >= 0);
83    // ensure that if value is negative, max - value doesn't wrap around
84    SkASSERT(value >= 0 || max - value > 0);
85
86#ifdef SK_CPU_HAS_CONDITIONAL_INSTR
87    if (value < 0) {
88        value = 0;
89    }
90    if (value > max) {
91        value = max;
92    }
93    return value;
94#else
95
96    int diff = max - value;
97    // clear diff if diff is positive
98    diff &= diff >> 31;
99
100    // clear the result if value < 0
101    return (value + diff) & ~(value >> 31);
102#endif
103}
104
105/** Given a positive value and a positive max, return the value
106    pinned against max.
107    Note: only works as long as max - value doesn't wrap around
108    @return max if value >= max, else value
109*/
110static inline unsigned SkClampUMax(unsigned value, unsigned max) {
111#ifdef SK_CPU_HAS_CONDITIONAL_INSTR
112    if (value > max) {
113        value = max;
114    }
115    return value;
116#else
117    int diff = max - value;
118    // clear diff if diff is positive
119    diff &= diff >> 31;
120
121    return value + diff;
122#endif
123}
124
125///////////////////////////////////////////////////////////////////////////////
126
127#if defined(__arm__) && !defined(__thumb__)
128    #define SkCLZ(x)    __builtin_clz(x)
129#endif
130
131#ifndef SkCLZ
132    #define SkCLZ(x)    SkCLZ_portable(x)
133#endif
134
135///////////////////////////////////////////////////////////////////////////////
136
137/** Returns the smallest power-of-2 that is >= the specified value. If value
138    is already a power of 2, then it is returned unchanged. It is undefined
139    if value is <= 0.
140*/
141static inline int SkNextPow2(int value) {
142    SkASSERT(value > 0);
143    return 1 << (32 - SkCLZ(value - 1));
144}
145
146/** Returns the log2 of the specified value, were that value to be rounded up
147    to the next power of 2. It is undefined to pass 0. Examples:
148         SkNextLog2(1) -> 0
149         SkNextLog2(2) -> 1
150         SkNextLog2(3) -> 2
151         SkNextLog2(4) -> 2
152         SkNextLog2(5) -> 3
153*/
154static inline int SkNextLog2(uint32_t value) {
155    SkASSERT(value != 0);
156    return 32 - SkCLZ(value - 1);
157}
158
159///////////////////////////////////////////////////////////////////////////////
160
161/** SkMulS16(a, b) multiplies a * b, but requires that a and b are both int16_t.
162    With this requirement, we can generate faster instructions on some
163    architectures.
164*/
165#if defined(__arm__) \
166  && !defined(__thumb__) \
167  && !defined(__ARM_ARCH_4T__) \
168  && !defined(__ARM_ARCH_5T__)
169    static inline int32_t SkMulS16(S16CPU x, S16CPU y) {
170        SkASSERT((int16_t)x == x);
171        SkASSERT((int16_t)y == y);
172        int32_t product;
173        asm("smulbb %0, %1, %2 \n"
174            : "=r"(product)
175            : "r"(x), "r"(y)
176            );
177        return product;
178    }
179#else
180    #ifdef SK_DEBUG
181        static inline int32_t SkMulS16(S16CPU x, S16CPU y) {
182            SkASSERT((int16_t)x == x);
183            SkASSERT((int16_t)y == y);
184            return x * y;
185        }
186    #else
187        #define SkMulS16(x, y)  ((x) * (y))
188    #endif
189#endif
190
191/** Return a*b/255, truncating away any fractional bits. Only valid if both
192    a and b are 0..255
193*/
194static inline U8CPU SkMulDiv255Trunc(U8CPU a, U8CPU b) {
195    SkASSERT((uint8_t)a == a);
196    SkASSERT((uint8_t)b == b);
197    unsigned prod = SkMulS16(a, b) + 1;
198    return (prod + (prod >> 8)) >> 8;
199}
200
201/** Return a*b/255, rounding any fractional bits. Only valid if both
202    a and b are 0..255
203 */
204static inline U8CPU SkMulDiv255Round(U8CPU a, U8CPU b) {
205    SkASSERT((uint8_t)a == a);
206    SkASSERT((uint8_t)b == b);
207    unsigned prod = SkMulS16(a, b) + 128;
208    return (prod + (prod >> 8)) >> 8;
209}
210
211/** Return a*b/((1 << shift) - 1), rounding any fractional bits.
212    Only valid if a and b are unsigned and <= 32767 and shift is > 0 and <= 8
213*/
214static inline unsigned SkMul16ShiftRound(unsigned a, unsigned b, int shift) {
215    SkASSERT(a <= 32767);
216    SkASSERT(b <= 32767);
217    SkASSERT(shift > 0 && shift <= 8);
218    unsigned prod = SkMulS16(a, b) + (1 << (shift - 1));
219    return (prod + (prod >> shift)) >> shift;
220}
221
222/** Just the rounding step in SkDiv255Round: round(value / 255)
223 */
224static inline unsigned SkDiv255Round(unsigned prod) {
225    prod += 128;
226    return (prod + (prod >> 8)) >> 8;
227}
228
229#endif
230
231