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 SkScalar_DEFINED 18 #define SkScalar_DEFINED 19 20 #include "SkFixed.h" 21 #include "SkFloatingPoint.h" 22 23 /** \file SkScalar.h 24 25 Types and macros for the data type SkScalar. This is the fractional numeric type 26 that, depending on the compile-time flag SK_SCALAR_IS_FLOAT, may be implemented 27 either as an IEEE float, or as a 16.16 SkFixed. The macros in this file are written 28 to allow the calling code to manipulate SkScalar values without knowing which representation 29 is in effect. 30 */ 31 32 #ifdef SK_SCALAR_IS_FLOAT 33 34 /** SkScalar is our type for fractional values and coordinates. Depending on 35 compile configurations, it is either represented as an IEEE float, or 36 as a 16.16 fixed point integer. 37 */ 38 typedef float SkScalar; 39 extern const uint32_t gIEEENotANumber; 40 extern const uint32_t gIEEEInfinity; 41 42 /** SK_Scalar1 is defined to be 1.0 represented as an SkScalar 43 */ 44 #define SK_Scalar1 (1.0f) 45 /** SK_Scalar1 is defined to be 1/2 represented as an SkScalar 46 */ 47 #define SK_ScalarHalf (0.5f) 48 /** SK_ScalarInfinity is defined to be infinity as an SkScalar 49 */ 50 #define SK_ScalarInfinity (*(const float*)&gIEEEInfinity) 51 /** SK_ScalarMax is defined to be the largest value representable as an SkScalar 52 */ 53 #define SK_ScalarMax (3.402823466e+38f) 54 /** SK_ScalarMin is defined to be the smallest value representable as an SkScalar 55 */ 56 #define SK_ScalarMin (-SK_ScalarMax) 57 /** SK_ScalarNaN is defined to be 'Not a Number' as an SkScalar 58 */ 59 #define SK_ScalarNaN (*(const float*)(const void*)&gIEEENotANumber) 60 /** SkScalarIsNaN(n) returns true if argument is not a number 61 */ 62 static inline bool SkScalarIsNaN(float x) { return x != x; } 63 /** Returns true if x is not NaN and not infinite */ 64 static inline bool SkScalarIsFinite(float x) { 65 uint32_t bits = SkFloat2Bits(x); // need unsigned for our shifts 66 int exponent = bits << 1 >> 24; 67 return exponent != 0xFF; 68 } 69 #ifdef SK_DEBUG 70 /** SkIntToScalar(n) returns its integer argument as an SkScalar 71 * 72 * If we're compiling in DEBUG mode, and can thus afford some extra runtime 73 * cycles, check to make sure that the parameter passed in has not already 74 * been converted to SkScalar. (A double conversion like this is harmless 75 * for SK_SCALAR_IS_FLOAT, but for SK_SCALAR_IS_FIXED this causes trouble.) 76 * 77 * Note that we need all of these method signatures to properly handle the 78 * various types that we pass into SkIntToScalar() to date: 79 * int, size_t, U8CPU, etc., even though what we really mean is "anything 80 * but a float". 81 */ 82 static inline float SkIntToScalar(signed int param) { 83 return (float)param; 84 } 85 static inline float SkIntToScalar(unsigned int param) { 86 return (float)param; 87 } 88 static inline float SkIntToScalar(signed long param) { 89 return (float)param; 90 } 91 static inline float SkIntToScalar(unsigned long param) { 92 return (float)param; 93 } 94 static inline float SkIntToScalar(float param) { 95 /* If the parameter passed into SkIntToScalar is a float, 96 * one of two things has happened: 97 * 1. the parameter was an SkScalar (which is typedef'd to float) 98 * 2. the parameter was a float instead of an int 99 * 100 * Either way, it's not good. 101 */ 102 SkASSERT(!"looks like you passed an SkScalar into SkIntToScalar"); 103 return (float)0; 104 } 105 #else // not SK_DEBUG 106 /** SkIntToScalar(n) returns its integer argument as an SkScalar 107 */ 108 #define SkIntToScalar(n) ((float)(n)) 109 #endif // not SK_DEBUG 110 /** SkFixedToScalar(n) returns its SkFixed argument as an SkScalar 111 */ 112 #define SkFixedToScalar(x) SkFixedToFloat(x) 113 /** SkScalarToFixed(n) returns its SkScalar argument as an SkFixed 114 */ 115 #define SkScalarToFixed(x) SkFloatToFixed(x) 116 117 #define SkScalarToFloat(n) (n) 118 #define SkFloatToScalar(n) (n) 119 120 #define SkScalarToDouble(n) (double)(n) 121 #define SkDoubleToScalar(n) (float)(n) 122 123 /** SkScalarFraction(x) returns the signed fractional part of the argument 124 */ 125 #define SkScalarFraction(x) sk_float_mod(x, 1.0f) 126 /** Rounds the SkScalar to the nearest integer value 127 */ 128 #define SkScalarRound(x) sk_float_round2int(x) 129 /** Returns the smallest integer that is >= the specified SkScalar 130 */ 131 #define SkScalarCeil(x) sk_float_ceil2int(x) 132 /** Returns the largest integer that is <= the specified SkScalar 133 */ 134 #define SkScalarFloor(x) sk_float_floor2int(x) 135 /** Returns the absolute value of the specified SkScalar 136 */ 137 #define SkScalarAbs(x) sk_float_abs(x) 138 /** Return x with the sign of y 139 */ 140 #define SkScalarCopySign(x, y) sk_float_copysign(x, y) 141 /** Returns the value pinned between 0 and max inclusive 142 */ 143 inline SkScalar SkScalarClampMax(SkScalar x, SkScalar max) { 144 return x < 0 ? 0 : x > max ? max : x; 145 } 146 /** Returns the value pinned between min and max inclusive 147 */ 148 inline SkScalar SkScalarPin(SkScalar x, SkScalar min, SkScalar max) { 149 return x < min ? min : x > max ? max : x; 150 } 151 /** Returns the specified SkScalar squared (x*x) 152 */ 153 inline SkScalar SkScalarSquare(SkScalar x) { return x * x; } 154 /** Returns the product of two SkScalars 155 */ 156 #define SkScalarMul(a, b) ((float)(a) * (b)) 157 /** Returns the product of two SkScalars plus a third SkScalar 158 */ 159 #define SkScalarMulAdd(a, b, c) ((float)(a) * (b) + (c)) 160 /** Returns the product of a SkScalar and an int rounded to the nearest integer value 161 */ 162 #define SkScalarMulRound(a, b) SkScalarRound((float)(a) * (b)) 163 /** Returns the product of a SkScalar and an int promoted to the next larger int 164 */ 165 #define SkScalarMulCeil(a, b) SkScalarCeil((float)(a) * (b)) 166 /** Returns the product of a SkScalar and an int truncated to the next smaller int 167 */ 168 #define SkScalarMulFloor(a, b) SkScalarFloor((float)(a) * (b)) 169 /** Returns the quotient of two SkScalars (a/b) 170 */ 171 #define SkScalarDiv(a, b) ((float)(a) / (b)) 172 /** Returns the mod of two SkScalars (a mod b) 173 */ 174 #define SkScalarMod(x,y) sk_float_mod(x,y) 175 /** Returns the product of the first two arguments, divided by the third argument 176 */ 177 #define SkScalarMulDiv(a, b, c) ((float)(a) * (b) / (c)) 178 /** Returns the multiplicative inverse of the SkScalar (1/x) 179 */ 180 #define SkScalarInvert(x) (SK_Scalar1 / (x)) 181 #define SkScalarFastInvert(x) (SK_Scalar1 / (x)) 182 /** Returns the square root of the SkScalar 183 */ 184 #define SkScalarSqrt(x) sk_float_sqrt(x) 185 /** Returns the average of two SkScalars (a+b)/2 186 */ 187 #define SkScalarAve(a, b) (((a) + (b)) * 0.5f) 188 /** Returns the geometric mean of two SkScalars 189 */ 190 #define SkScalarMean(a, b) sk_float_sqrt((float)(a) * (b)) 191 /** Returns one half of the specified SkScalar 192 */ 193 #define SkScalarHalf(a) ((a) * 0.5f) 194 195 #define SK_ScalarSqrt2 1.41421356f 196 #define SK_ScalarPI 3.14159265f 197 #define SK_ScalarTanPIOver8 0.414213562f 198 #define SK_ScalarRoot2Over2 0.707106781f 199 200 #define SkDegreesToRadians(degrees) ((degrees) * (SK_ScalarPI / 180)) 201 float SkScalarSinCos(SkScalar radians, SkScalar* cosValue); 202 #define SkScalarSin(radians) (float)sk_float_sin(radians) 203 #define SkScalarCos(radians) (float)sk_float_cos(radians) 204 #define SkScalarTan(radians) (float)sk_float_tan(radians) 205 #define SkScalarASin(val) (float)sk_float_asin(val) 206 #define SkScalarACos(val) (float)sk_float_acos(val) 207 #define SkScalarATan2(y, x) (float)sk_float_atan2(y,x) 208 #define SkScalarExp(x) (float)sk_float_exp(x) 209 #define SkScalarLog(x) (float)sk_float_log(x) 210 211 inline SkScalar SkMaxScalar(SkScalar a, SkScalar b) { return a > b ? a : b; } 212 inline SkScalar SkMinScalar(SkScalar a, SkScalar b) { return a < b ? a : b; } 213 214 static inline bool SkScalarIsInt(SkScalar x) { 215 return x == (float)(int)x; 216 } 217 #else 218 typedef SkFixed SkScalar; 219 220 #define SK_Scalar1 SK_Fixed1 221 #define SK_ScalarHalf SK_FixedHalf 222 #define SK_ScalarInfinity SK_FixedMax 223 #define SK_ScalarMax SK_FixedMax 224 #define SK_ScalarMin SK_FixedMin 225 #define SK_ScalarNaN SK_FixedNaN 226 #define SkScalarIsNaN(x) ((x) == SK_FixedNaN) 227 #define SkScalarIsFinite(x) ((x) != SK_FixedNaN) 228 229 #define SkIntToScalar(n) SkIntToFixed(n) 230 #define SkFixedToScalar(x) (x) 231 #define SkScalarToFixed(x) (x) 232 #ifdef SK_CAN_USE_FLOAT 233 #define SkScalarToFloat(n) SkFixedToFloat(n) 234 #define SkFloatToScalar(n) SkFloatToFixed(n) 235 236 #define SkScalarToDouble(n) SkFixedToDouble(n) 237 #define SkDoubleToScalar(n) SkDoubleToFixed(n) 238 #endif 239 #define SkScalarFraction(x) SkFixedFraction(x) 240 #define SkScalarRound(x) SkFixedRound(x) 241 #define SkScalarCeil(x) SkFixedCeil(x) 242 #define SkScalarFloor(x) SkFixedFloor(x) 243 #define SkScalarAbs(x) SkFixedAbs(x) 244 #define SkScalarCopySign(x, y) SkCopySign32(x, y) 245 #define SkScalarClampMax(x, max) SkClampMax(x, max) 246 #define SkScalarPin(x, min, max) SkPin32(x, min, max) 247 #define SkScalarSquare(x) SkFixedSquare(x) 248 #define SkScalarMul(a, b) SkFixedMul(a, b) 249 #define SkScalarMulAdd(a, b, c) SkFixedMulAdd(a, b, c) 250 #define SkScalarMulRound(a, b) SkFixedMulCommon(a, b, SK_FixedHalf) 251 #define SkScalarMulCeil(a, b) SkFixedMulCommon(a, b, SK_Fixed1 - 1) 252 #define SkScalarMulFloor(a, b) SkFixedMulCommon(a, b, 0) 253 #define SkScalarDiv(a, b) SkFixedDiv(a, b) 254 #define SkScalarMod(a, b) SkFixedMod(a, b) 255 #define SkScalarMulDiv(a, b, c) SkMulDiv(a, b, c) 256 #define SkScalarInvert(x) SkFixedInvert(x) 257 #define SkScalarFastInvert(x) SkFixedFastInvert(x) 258 #define SkScalarSqrt(x) SkFixedSqrt(x) 259 #define SkScalarAve(a, b) SkFixedAve(a, b) 260 #define SkScalarMean(a, b) SkFixedMean(a, b) 261 #define SkScalarHalf(a) ((a) >> 1) 262 263 #define SK_ScalarSqrt2 SK_FixedSqrt2 264 #define SK_ScalarPI SK_FixedPI 265 #define SK_ScalarTanPIOver8 SK_FixedTanPIOver8 266 #define SK_ScalarRoot2Over2 SK_FixedRoot2Over2 267 268 #define SkDegreesToRadians(degrees) SkFractMul(degrees, SK_FractPIOver180) 269 #define SkScalarSinCos(radians, cosPtr) SkFixedSinCos(radians, cosPtr) 270 #define SkScalarSin(radians) SkFixedSin(radians) 271 #define SkScalarCos(radians) SkFixedCos(radians) 272 #define SkScalarTan(val) SkFixedTan(val) 273 #define SkScalarASin(val) SkFixedASin(val) 274 #define SkScalarACos(val) SkFixedACos(val) 275 #define SkScalarATan2(y, x) SkFixedATan2(y,x) 276 #define SkScalarExp(x) SkFixedExp(x) 277 #define SkScalarLog(x) SkFixedLog(x) 278 279 #define SkMaxScalar(a, b) SkMax32(a, b) 280 #define SkMinScalar(a, b) SkMin32(a, b) 281 282 static inline bool SkScalarIsInt(SkFixed x) { 283 return 0 == (x & 0xffff); 284 } 285 #endif 286 287 #define SK_ScalarNearlyZero (SK_Scalar1 / (1 << 12)) 288 289 /* <= is slower than < for floats, so we use < for our tolerance test 290 */ 291 292 static inline bool SkScalarNearlyZero(SkScalar x, 293 SkScalar tolerance = SK_ScalarNearlyZero) { 294 SkASSERT(tolerance > 0); 295 return SkScalarAbs(x) < tolerance; 296 } 297 298 /** Linearly interpolate between A and B, based on t. 299 If t is 0, return A 300 If t is 1, return B 301 else interpolate. 302 t must be [0..SK_Scalar1] 303 */ 304 static inline SkScalar SkScalarInterp(SkScalar A, SkScalar B, SkScalar t) { 305 SkASSERT(t >= 0 && t <= SK_Scalar1); 306 return A + SkScalarMul(B - A, t); 307 } 308 309 /** Interpolate along the function described by (keys[length], values[length]) 310 for the passed searchKey. SearchKeys outside the range keys[0]-keys[Length] 311 clamp to the min or max value. This function was inspired by a desire 312 to change the multiplier for thickness in fakeBold; therefore it assumes 313 the number of pairs (length) will be small, and a linear search is used. 314 Repeated keys are allowed for discontinuous functions (so long as keys is 315 monotonically increasing), and if key is the value of a repeated scalar in 316 keys, the first one will be used. However, that may change if a binary 317 search is used. 318 */ 319 SkScalar SkScalarInterpFunc(SkScalar searchKey, const SkScalar keys[], 320 const SkScalar values[], int length); 321 322 #endif 323
