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 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 */
SkClampMax(int value,int max)85 static 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 */
SkClampUMax(unsigned value,unsigned max)115 static 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 */
SkNextPow2(int value)146 static 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 */
SkNextLog2(uint32_t value)159 static 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__)
SkMulS16(S16CPU x,S16CPU y)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
SkMulS16(S16CPU x,S16CPU y)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 */
SkMulDiv255Trunc(U8CPU a,U8CPU b)199 static 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 */
SkMulDiv255Round(U8CPU a,U8CPU b)209 static 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 */
SkMul16ShiftRound(unsigned a,unsigned b,int shift)219 static 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 */
SkDiv255Round(unsigned prod)229 static inline unsigned SkDiv255Round(unsigned prod) {
230 prod += 128;
231 return (prod + (prod >> 8)) >> 8;
232 }
233
234 #endif
235
236