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)
23 int 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 */
29 int32_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 */
35 int32_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 */
41 int32_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 */
45 int32_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 */
53 int32_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 */
SkApplySign(int32_t n,int32_t sign)62 static 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 */
SkCopySign32(int32_t x,int32_t y)68 static 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 */
SkClampPos(int value)74 static 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 @param value The value we want returned pinned between [0...max]
81 @param max The positive max value
82 @return 0 if value < 0, max if value > max, else value
83 */
SkClampMax(int value,int max)84 static inline int SkClampMax(int value, int max) {
85 // ensure that max is positive
86 SkASSERT(max >= 0);
87 if (value < 0) {
88 value = 0;
89 }
90 if (value > max) {
91 value = max;
92 }
93 return value;
94 }
95
96 /** Given a positive value and a positive max, return the value
97 pinned against max.
98 Note: only works as long as max - value doesn't wrap around
99 @return max if value >= max, else value
100 */
SkClampUMax(unsigned value,unsigned max)101 static inline unsigned SkClampUMax(unsigned value, unsigned max) {
102 #ifdef SK_CPU_HAS_CONDITIONAL_INSTR
103 if (value > max) {
104 value = max;
105 }
106 return value;
107 #else
108 int diff = max - value;
109 // clear diff if diff is positive
110 diff &= diff >> 31;
111
112 return value + diff;
113 #endif
114 }
115
116 ///////////////////////////////////////////////////////////////////////////////
117
118 #if defined(__arm__)
119 #define SkCLZ(x) __builtin_clz(x)
120 #endif
121
122 #ifndef SkCLZ
123 #define SkCLZ(x) SkCLZ_portable(x)
124 #endif
125
126 ///////////////////////////////////////////////////////////////////////////////
127
128 /** Returns the smallest power-of-2 that is >= the specified value. If value
129 is already a power of 2, then it is returned unchanged. It is undefined
130 if value is <= 0.
131 */
SkNextPow2(int value)132 static inline int SkNextPow2(int value) {
133 SkASSERT(value > 0);
134 return 1 << (32 - SkCLZ(value - 1));
135 }
136
137 /** Returns the log2 of the specified value, were that value to be rounded up
138 to the next power of 2. It is undefined to pass 0. Examples:
139 SkNextLog2(1) -> 0
140 SkNextLog2(2) -> 1
141 SkNextLog2(3) -> 2
142 SkNextLog2(4) -> 2
143 SkNextLog2(5) -> 3
144 */
SkNextLog2(uint32_t value)145 static inline int SkNextLog2(uint32_t value) {
146 SkASSERT(value != 0);
147 return 32 - SkCLZ(value - 1);
148 }
149
150 /** Returns true if value is a power of 2. Does not explicitly check for
151 value <= 0.
152 */
SkIsPow2(int value)153 static inline bool SkIsPow2(int value) {
154 return (value & (value - 1)) == 0;
155 }
156
157 ///////////////////////////////////////////////////////////////////////////////
158
159 /** SkMulS16(a, b) multiplies a * b, but requires that a and b are both int16_t.
160 With this requirement, we can generate faster instructions on some
161 architectures.
162 */
163 #if defined(__arm__) \
164 && !defined(__thumb__) \
165 && !defined(__ARM_ARCH_4T__) \
166 && !defined(__ARM_ARCH_5T__)
SkMulS16(S16CPU x,S16CPU y)167 static inline int32_t SkMulS16(S16CPU x, S16CPU y) {
168 SkASSERT((int16_t)x == x);
169 SkASSERT((int16_t)y == y);
170 int32_t product;
171 asm("smulbb %0, %1, %2 \n"
172 : "=r"(product)
173 : "r"(x), "r"(y)
174 );
175 return product;
176 }
177 #else
178 #ifdef SK_DEBUG
SkMulS16(S16CPU x,S16CPU y)179 static inline int32_t SkMulS16(S16CPU x, S16CPU y) {
180 SkASSERT((int16_t)x == x);
181 SkASSERT((int16_t)y == y);
182 return x * y;
183 }
184 #else
185 #define SkMulS16(x, y) ((x) * (y))
186 #endif
187 #endif
188
189 /** Return a*b/255, truncating away any fractional bits. Only valid if both
190 a and b are 0..255
191 */
SkMulDiv255Trunc(U8CPU a,U8CPU b)192 static inline U8CPU SkMulDiv255Trunc(U8CPU a, U8CPU b) {
193 SkASSERT((uint8_t)a == a);
194 SkASSERT((uint8_t)b == b);
195 unsigned prod = SkMulS16(a, b) + 1;
196 return (prod + (prod >> 8)) >> 8;
197 }
198
199 /** Return a*b/255, rounding any fractional bits. Only valid if both
200 a and b are 0..255
201 */
SkMulDiv255Round(U8CPU a,U8CPU b)202 static inline U8CPU SkMulDiv255Round(U8CPU a, U8CPU b) {
203 SkASSERT((uint8_t)a == a);
204 SkASSERT((uint8_t)b == b);
205 unsigned prod = SkMulS16(a, b) + 128;
206 return (prod + (prod >> 8)) >> 8;
207 }
208
209 /** Return (a*b)/255, taking the ceiling of any fractional bits. Only valid if
210 both a and b are 0..255. The expected result equals (a * b + 254) / 255.
211 */
SkMulDiv255Ceiling(U8CPU a,U8CPU b)212 static inline U8CPU SkMulDiv255Ceiling(U8CPU a, U8CPU b) {
213 SkASSERT((uint8_t)a == a);
214 SkASSERT((uint8_t)b == b);
215 unsigned prod = SkMulS16(a, b) + 255;
216 return (prod + (prod >> 8)) >> 8;
217 }
218
219 /** Return a*b/((1 << shift) - 1), rounding any fractional bits.
220 Only valid if a and b are unsigned and <= 32767 and shift is > 0 and <= 8
221 */
SkMul16ShiftRound(unsigned a,unsigned b,int shift)222 static inline unsigned SkMul16ShiftRound(unsigned a, unsigned b, int shift) {
223 SkASSERT(a <= 32767);
224 SkASSERT(b <= 32767);
225 SkASSERT(shift > 0 && shift <= 8);
226 unsigned prod = SkMulS16(a, b) + (1 << (shift - 1));
227 return (prod + (prod >> shift)) >> shift;
228 }
229
230 /** Just the rounding step in SkDiv255Round: round(value / 255)
231 */
SkDiv255Round(unsigned prod)232 static inline unsigned SkDiv255Round(unsigned prod) {
233 prod += 128;
234 return (prod + (prod >> 8)) >> 8;
235 }
236
237 #endif
238
239