SkMath.h revision 1c980e0d7772f05f570ae0227d91635f017c2227 
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/** Return x with the sign of y */
68static inline int32_t SkCopySign32(int32_t x, int32_t y) {
69    return SkApplySign(x, SkExtractSign(x ^ y));
70}
71
72/** Returns (value < 0 ? 0 : value) efficiently (i.e. no compares or branches)
73*/
74static inline int SkClampPos(int value) {
75    return value & ~(value >> 31);
76}
77
78/** Given an integer and a positive (max) integer, return the value
79    pinned against 0 and max, inclusive.
80    Note: only works as long as max - value doesn't wrap around
81    @param value    The value we want returned pinned between [0...max]
82    @param max      The positive max value
83    @return 0 if value < 0, max if value > max, else value
84*/
85static inline int SkClampMax(int value, int max) {
86    // ensure that max is positive
87    SkASSERT(max >= 0);
88    // ensure that if value is negative, max - value doesn't wrap around
89    SkASSERT(value >= 0 || max - value > 0);
90
91#ifdef SK_CPU_HAS_CONDITIONAL_INSTR
92    if (value < 0) {
93        value = 0;
94    }
95    if (value > max) {
96        value = max;
97    }
98    return value;
99#else
100
101    int diff = max - value;
102    // clear diff if diff is positive
103    diff &= diff >> 31;
104
105    // clear the result if value < 0
106    return (value + diff) & ~(value >> 31);
107#endif
108}
109
110/** Given a positive value and a positive max, return the value
111    pinned against max.
112    Note: only works as long as max - value doesn't wrap around
113    @return max if value >= max, else value
114*/
115static inline unsigned SkClampUMax(unsigned value, unsigned max) {
116#ifdef SK_CPU_HAS_CONDITIONAL_INSTR
117    if (value > max) {
118        value = max;
119    }
120    return value;
121#else
122    int diff = max - value;
123    // clear diff if diff is positive
124    diff &= diff >> 31;
125
126    return value + diff;
127#endif
128}
129
130///////////////////////////////////////////////////////////////////////////////
131
132#if defined(__arm__) && !defined(__thumb__)
133    #define SkCLZ(x)    __builtin_clz(x)
134#endif
135
136#ifndef SkCLZ
137    #define SkCLZ(x)    SkCLZ_portable(x)
138#endif
139
140///////////////////////////////////////////////////////////////////////////////
141
142/** Returns the smallest power-of-2 that is >= the specified value. If value
143    is already a power of 2, then it is returned unchanged. It is undefined
144    if value is <= 0.
145*/
146static inline int SkNextPow2(int value) {
147    SkASSERT(value > 0);
148    return 1 << (32 - SkCLZ(value - 1));
149}
150
151/** Returns the log2 of the specified value, were that value to be rounded up
152    to the next power of 2. It is undefined to pass 0. Examples:
153         SkNextLog2(1) -> 0
154         SkNextLog2(2) -> 1
155         SkNextLog2(3) -> 2
156         SkNextLog2(4) -> 2
157         SkNextLog2(5) -> 3
158*/
159static inline int SkNextLog2(uint32_t value) {
160    SkASSERT(value != 0);
161    return 32 - SkCLZ(value - 1);
162}
163
164///////////////////////////////////////////////////////////////////////////////
165
166/** SkMulS16(a, b) multiplies a * b, but requires that a and b are both int16_t.
167    With this requirement, we can generate faster instructions on some
168    architectures.
169*/
170#if defined(__arm__) \
171  && !defined(__thumb__) \
172  && !defined(__ARM_ARCH_4T__) \
173  && !defined(__ARM_ARCH_5T__)
174    static inline int32_t SkMulS16(S16CPU x, S16CPU y) {
175        SkASSERT((int16_t)x == x);
176        SkASSERT((int16_t)y == y);
177        int32_t product;
178        asm("smulbb %0, %1, %2 \n"
179            : "=r"(product)
180            : "r"(x), "r"(y)
181            );
182        return product;
183    }
184#else
185    #ifdef SK_DEBUG
186        static inline int32_t SkMulS16(S16CPU x, S16CPU y) {
187            SkASSERT((int16_t)x == x);
188            SkASSERT((int16_t)y == y);
189            return x * y;
190        }
191    #else
192        #define SkMulS16(x, y)  ((x) * (y))
193    #endif
194#endif
195
196/** Return a*b/255, truncating away any fractional bits. Only valid if both
197    a and b are 0..255
198*/
199static inline U8CPU SkMulDiv255Trunc(U8CPU a, U8CPU b) {
200    SkASSERT((uint8_t)a == a);
201    SkASSERT((uint8_t)b == b);
202    unsigned prod = SkMulS16(a, b) + 1;
203    return (prod + (prod >> 8)) >> 8;
204}
205
206/** Return a*b/255, rounding any fractional bits. Only valid if both
207    a and b are 0..255
208 */
209static inline U8CPU SkMulDiv255Round(U8CPU a, U8CPU b) {
210    SkASSERT((uint8_t)a == a);
211    SkASSERT((uint8_t)b == b);
212    unsigned prod = SkMulS16(a, b) + 128;
213    return (prod + (prod >> 8)) >> 8;
214}
215
216/** Return a*b/((1 << shift) - 1), rounding any fractional bits.
217    Only valid if a and b are unsigned and <= 32767 and shift is > 0 and <= 8
218*/
219static inline unsigned SkMul16ShiftRound(unsigned a, unsigned b, int shift) {
220    SkASSERT(a <= 32767);
221    SkASSERT(b <= 32767);
222    SkASSERT(shift > 0 && shift <= 8);
223    unsigned prod = SkMulS16(a, b) + (1 << (shift - 1));
224    return (prod + (prod >> shift)) >> shift;
225}
226
227/** Just the rounding step in SkDiv255Round: round(value / 255)
228 */
229static inline unsigned SkDiv255Round(unsigned prod) {
230    prod += 128;
231    return (prod + (prod >> 8)) >> 8;
232}
233
234#endif
235
236