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 */ 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 */ 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 */ 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 */ 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 */ 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 */ 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 */ 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__) 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 */ 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 */ 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 */ 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 */ 229 static inline unsigned SkDiv255Round(unsigned prod) { 230 prod += 128; 231 return (prod + (prod >> 8)) >> 8; 232 } 233 234 #endif 235 236
