1 /* 2 * Copyright 2011 Google Inc. 3 * 4 * Use of this source code is governed by a BSD-style license that can be 5 * found in the LICENSE file. 6 */ 7 8 #include "SkFloatBits.h" 9 #include "SkMathPriv.h" 10 11 /****************************************************************************** 12 SkFloatBits_toInt[Floor, Round, Ceil] are identical except for what they 13 do right before they return ... >> exp; 14 Floor - adds nothing 15 Round - adds 1 << (exp - 1) 16 Ceil - adds (1 << exp) - 1 17 18 Floor and Cast are very similar, but Cast applies its sign after all other 19 computations on value. Also, Cast does not need to check for negative zero, 20 as that value (0x80000000) "does the right thing" for Ceil. Note that it 21 doesn't for Floor/Round/Ceil, hence the explicit check. 22 ******************************************************************************/ 23 24 #define EXP_BIAS (127+23) 25 #define MATISSA_MAGIC_BIG (1 << 23) 26 27 static inline int unpack_exp(uint32_t packed) { 28 return (packed << 1 >> 24); 29 } 30 31 #if 0 32 // the ARM compiler generates an extra BIC, so I use the dirty version instead 33 static inline int unpack_matissa(uint32_t packed) { 34 // we could mask with 0x7FFFFF, but that is harder for ARM to encode 35 return (packed & ~0xFF000000) | MATISSA_MAGIC_BIG; 36 } 37 #endif 38 39 // returns the low 24-bits, so we need to OR in the magic_bit afterwards 40 static inline int unpack_matissa_dirty(uint32_t packed) { 41 return packed & ~0xFF000000; 42 } 43 44 // same as (int)float 45 int32_t SkFloatBits_toIntCast(int32_t packed) { 46 int exp = unpack_exp(packed) - EXP_BIAS; 47 int value = unpack_matissa_dirty(packed) | MATISSA_MAGIC_BIG; 48 49 if (exp >= 0) { 50 if (exp > 7) { // overflow 51 value = SK_MaxS32; 52 } else { 53 value <<= exp; 54 } 55 } else { 56 exp = -exp; 57 if (exp > 25) { // underflow 58 exp = 25; 59 } 60 value >>= exp; 61 } 62 return SkApplySign(value, SkExtractSign(packed)); 63 } 64 65 // same as (int)floor(float) 66 int32_t SkFloatBits_toIntFloor(int32_t packed) { 67 // curse you negative 0 68 if (SkLeftShift(packed, 1) == 0) { 69 return 0; 70 } 71 72 int exp = unpack_exp(packed) - EXP_BIAS; 73 int value = unpack_matissa_dirty(packed) | MATISSA_MAGIC_BIG; 74 75 if (exp >= 0) { 76 if (exp > 7) { // overflow 77 value = SK_MaxS32; 78 } else { 79 value <<= exp; 80 } 81 // apply the sign after we check for overflow 82 return SkApplySign(value, SkExtractSign(packed)); 83 } else { 84 // apply the sign before we right-shift 85 value = SkApplySign(value, SkExtractSign(packed)); 86 exp = -exp; 87 if (exp > 25) { // underflow 88 #ifdef SK_CPU_FLUSH_TO_ZERO 89 // The iOS ARM processor discards small denormalized numbers to go faster. 90 // The comparision below empirically causes the result to agree with the 91 // tests in MathTest test_float_floor 92 if (exp > 149) { 93 return 0; 94 } 95 #else 96 exp = 25; 97 #endif 98 } 99 // int add = 0; 100 return value >> exp; 101 } 102 } 103 104 // same as (int)floor(float + 0.5) 105 int32_t SkFloatBits_toIntRound(int32_t packed) { 106 // curse you negative 0 107 if (SkLeftShift(packed, 1) == 0) { 108 return 0; 109 } 110 111 int exp = unpack_exp(packed) - EXP_BIAS; 112 int value = unpack_matissa_dirty(packed) | MATISSA_MAGIC_BIG; 113 114 if (exp >= 0) { 115 if (exp > 7) { // overflow 116 value = SK_MaxS32; 117 } else { 118 value <<= exp; 119 } 120 // apply the sign after we check for overflow 121 return SkApplySign(value, SkExtractSign(packed)); 122 } else { 123 // apply the sign before we right-shift 124 value = SkApplySign(value, SkExtractSign(packed)); 125 exp = -exp; 126 if (exp > 25) { // underflow 127 exp = 25; 128 } 129 int add = 1 << (exp - 1); 130 return (value + add) >> exp; 131 } 132 } 133 134 // same as (int)ceil(float) 135 int32_t SkFloatBits_toIntCeil(int32_t packed) { 136 // curse you negative 0 137 if (SkLeftShift(packed, 1) == 0) { 138 return 0; 139 } 140 141 int exp = unpack_exp(packed) - EXP_BIAS; 142 int value = unpack_matissa_dirty(packed) | MATISSA_MAGIC_BIG; 143 144 if (exp >= 0) { 145 if (exp > 7) { // overflow 146 value = SK_MaxS32; 147 } else { 148 value <<= exp; 149 } 150 // apply the sign after we check for overflow 151 return SkApplySign(value, SkExtractSign(packed)); 152 } else { 153 // apply the sign before we right-shift 154 value = SkApplySign(value, SkExtractSign(packed)); 155 exp = -exp; 156 if (exp > 25) { // underflow 157 #ifdef SK_CPU_FLUSH_TO_ZERO 158 // The iOS ARM processor discards small denormalized numbers to go faster. 159 // The comparision below empirically causes the result to agree with the 160 // tests in MathTest test_float_ceil 161 if (exp > 149) { 162 return 0; 163 } 164 return 0 < value; 165 #else 166 exp = 25; 167 #endif 168 } 169 int add = (1 << exp) - 1; 170 return (value + add) >> exp; 171 } 172 } 173 174 float SkIntToFloatCast(int32_t value) { 175 if (0 == value) { 176 return 0; 177 } 178 179 int shift = EXP_BIAS; 180 181 // record the sign and make value positive 182 int sign = SkExtractSign(value); 183 value = SkApplySign(value, sign); 184 185 if (value >> 24) { // value is too big (has more than 24 bits set) 186 int bias = 8 - SkCLZ(value); 187 SkDebugf("value = %d, bias = %d\n", value, bias); 188 SkASSERT(bias > 0 && bias < 8); 189 value >>= bias; // need to round? 190 shift += bias; 191 } else { 192 int zeros = SkCLZ(value << 8); 193 SkASSERT(zeros >= 0 && zeros <= 23); 194 value <<= zeros; 195 shift -= zeros; 196 } 197 198 // now value is left-aligned to 24 bits 199 SkASSERT((value >> 23) == 1); 200 SkASSERT(shift >= 0 && shift <= 255); 201 202 SkFloatIntUnion data; 203 data.fSignBitInt = SkLeftShift(sign, 31) | SkLeftShift(shift, 23) | (value & ~MATISSA_MAGIC_BIG); 204 return data.fFloat; 205 } 206
