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 @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 */ 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 */ 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 */ 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 */ 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 */ 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__) 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 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 */ 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 */ 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 */ 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 */ 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 */ 232 static inline unsigned SkDiv255Round(unsigned prod) { 233 prod += 128; 234 return (prod + (prod >> 8)) >> 8; 235 } 236 237 #endif 238 239
