1 2 /* 3 * Copyright 2006 The Android Open Source Project 4 * 5 * Use of this source code is governed by a BSD-style license that can be 6 * found in the LICENSE file. 7 */ 8 9 10 #ifndef SkScalar_DEFINED 11 #define SkScalar_DEFINED 12 13 #include "SkFixed.h" 14 #include "SkFloatingPoint.h" 15 16 /** \file SkScalar.h 17 18 Types and macros for the data type SkScalar. This is the fractional numeric type 19 that, depending on the compile-time flag SK_SCALAR_IS_FLOAT, may be implemented 20 either as an IEEE float, or as a 16.16 SkFixed. The macros in this file are written 21 to allow the calling code to manipulate SkScalar values without knowing which representation 22 is in effect. 23 */ 24 25 #ifdef SK_SCALAR_IS_FLOAT 26 27 /** SkScalar is our type for fractional values and coordinates. Depending on 28 compile configurations, it is either represented as an IEEE float, or 29 as a 16.16 fixed point integer. 30 */ 31 typedef float SkScalar; 32 extern const uint32_t gIEEENotANumber; 33 extern const uint32_t gIEEEInfinity; 34 35 /** SK_Scalar1 is defined to be 1.0 represented as an SkScalar 36 */ 37 #define SK_Scalar1 (1.0f) 38 /** SK_Scalar1 is defined to be 1/2 represented as an SkScalar 39 */ 40 #define SK_ScalarHalf (0.5f) 41 /** SK_ScalarInfinity is defined to be infinity as an SkScalar 42 */ 43 #define SK_ScalarInfinity (*(const float*)&gIEEEInfinity) 44 /** SK_ScalarMax is defined to be the largest value representable as an SkScalar 45 */ 46 #define SK_ScalarMax (3.402823466e+38f) 47 /** SK_ScalarMin is defined to be the smallest value representable as an SkScalar 48 */ 49 #define SK_ScalarMin (-SK_ScalarMax) 50 /** SK_ScalarNaN is defined to be 'Not a Number' as an SkScalar 51 */ 52 #define SK_ScalarNaN (*(const float*)(const void*)&gIEEENotANumber) 53 /** SkScalarIsNaN(n) returns true if argument is not a number 54 */ 55 static inline bool SkScalarIsNaN(float x) { return x != x; } 56 /** Returns true if x is not NaN and not infinite */ 57 static inline bool SkScalarIsFinite(float x) { 58 uint32_t bits = SkFloat2Bits(x); // need unsigned for our shifts 59 int exponent = bits << 1 >> 24; 60 return exponent != 0xFF; 61 } 62 #ifdef SK_DEBUG 63 /** SkIntToScalar(n) returns its integer argument as an SkScalar 64 * 65 * If we're compiling in DEBUG mode, and can thus afford some extra runtime 66 * cycles, check to make sure that the parameter passed in has not already 67 * been converted to SkScalar. (A double conversion like this is harmless 68 * for SK_SCALAR_IS_FLOAT, but for SK_SCALAR_IS_FIXED this causes trouble.) 69 * 70 * Note that we need all of these method signatures to properly handle the 71 * various types that we pass into SkIntToScalar() to date: 72 * int, size_t, U8CPU, etc., even though what we really mean is "anything 73 * but a float". 74 */ 75 static inline float SkIntToScalar(signed int param) { 76 return (float)param; 77 } 78 static inline float SkIntToScalar(unsigned int param) { 79 return (float)param; 80 } 81 static inline float SkIntToScalar(signed long param) { 82 return (float)param; 83 } 84 static inline float SkIntToScalar(unsigned long param) { 85 return (float)param; 86 } 87 static inline float SkIntToScalar(float param) { 88 /* If the parameter passed into SkIntToScalar is a float, 89 * one of two things has happened: 90 * 1. the parameter was an SkScalar (which is typedef'd to float) 91 * 2. the parameter was a float instead of an int 92 * 93 * Either way, it's not good. 94 */ 95 SkDEBUGFAIL("looks like you passed an SkScalar into SkIntToScalar"); 96 return (float)0; 97 } 98 #else // not SK_DEBUG 99 /** SkIntToScalar(n) returns its integer argument as an SkScalar 100 */ 101 #define SkIntToScalar(n) ((float)(n)) 102 #endif // not SK_DEBUG 103 /** SkFixedToScalar(n) returns its SkFixed argument as an SkScalar 104 */ 105 #define SkFixedToScalar(x) SkFixedToFloat(x) 106 /** SkScalarToFixed(n) returns its SkScalar argument as an SkFixed 107 */ 108 #define SkScalarToFixed(x) SkFloatToFixed(x) 109 110 #define SkScalarToFloat(n) (n) 111 #define SkFloatToScalar(n) (n) 112 113 #define SkScalarToDouble(n) (double)(n) 114 #define SkDoubleToScalar(n) (float)(n) 115 116 /** SkScalarFraction(x) returns the signed fractional part of the argument 117 */ 118 #define SkScalarFraction(x) sk_float_mod(x, 1.0f) 119 120 #define SkScalarFloorToScalar(x) sk_float_floor(x) 121 #define SkScalarCeilToScalar(x) sk_float_ceil(x) 122 #define SkScalarRoundToScalar(x) sk_float_floor((x) + 0.5f) 123 124 #define SkScalarFloorToInt(x) sk_float_floor2int(x) 125 #define SkScalarCeilToInt(x) sk_float_ceil2int(x) 126 #define SkScalarRoundToInt(x) sk_float_round2int(x) 127 128 /** Returns the absolute value of the specified SkScalar 129 */ 130 #define SkScalarAbs(x) sk_float_abs(x) 131 /** Return x with the sign of y 132 */ 133 #define SkScalarCopySign(x, y) sk_float_copysign(x, y) 134 /** Returns the value pinned between 0 and max inclusive 135 */ 136 inline SkScalar SkScalarClampMax(SkScalar x, SkScalar max) { 137 return x < 0 ? 0 : x > max ? max : x; 138 } 139 /** Returns the value pinned between min and max inclusive 140 */ 141 inline SkScalar SkScalarPin(SkScalar x, SkScalar min, SkScalar max) { 142 return x < min ? min : x > max ? max : x; 143 } 144 /** Returns the specified SkScalar squared (x*x) 145 */ 146 inline SkScalar SkScalarSquare(SkScalar x) { return x * x; } 147 /** Returns the product of two SkScalars 148 */ 149 #define SkScalarMul(a, b) ((float)(a) * (b)) 150 /** Returns the product of two SkScalars plus a third SkScalar 151 */ 152 #define SkScalarMulAdd(a, b, c) ((float)(a) * (b) + (c)) 153 /** Returns the product of a SkScalar and an int rounded to the nearest integer value 154 */ 155 #define SkScalarMulRound(a, b) SkScalarRound((float)(a) * (b)) 156 /** Returns the product of a SkScalar and an int promoted to the next larger int 157 */ 158 #define SkScalarMulCeil(a, b) SkScalarCeil((float)(a) * (b)) 159 /** Returns the product of a SkScalar and an int truncated to the next smaller int 160 */ 161 #define SkScalarMulFloor(a, b) SkScalarFloor((float)(a) * (b)) 162 /** Returns the quotient of two SkScalars (a/b) 163 */ 164 #define SkScalarDiv(a, b) ((float)(a) / (b)) 165 /** Returns the mod of two SkScalars (a mod b) 166 */ 167 #define SkScalarMod(x,y) sk_float_mod(x,y) 168 /** Returns the product of the first two arguments, divided by the third argument 169 */ 170 #define SkScalarMulDiv(a, b, c) ((float)(a) * (b) / (c)) 171 /** Returns the multiplicative inverse of the SkScalar (1/x) 172 */ 173 #define SkScalarInvert(x) (SK_Scalar1 / (x)) 174 #define SkScalarFastInvert(x) (SK_Scalar1 / (x)) 175 /** Returns the square root of the SkScalar 176 */ 177 #define SkScalarSqrt(x) sk_float_sqrt(x) 178 /** Returns the average of two SkScalars (a+b)/2 179 */ 180 #define SkScalarAve(a, b) (((a) + (b)) * 0.5f) 181 /** Returns the geometric mean of two SkScalars 182 */ 183 #define SkScalarMean(a, b) sk_float_sqrt((float)(a) * (b)) 184 /** Returns one half of the specified SkScalar 185 */ 186 #define SkScalarHalf(a) ((a) * 0.5f) 187 188 #define SK_ScalarSqrt2 1.41421356f 189 #define SK_ScalarPI 3.14159265f 190 #define SK_ScalarTanPIOver8 0.414213562f 191 #define SK_ScalarRoot2Over2 0.707106781f 192 193 #define SkDegreesToRadians(degrees) ((degrees) * (SK_ScalarPI / 180)) 194 float SkScalarSinCos(SkScalar radians, SkScalar* cosValue); 195 #define SkScalarSin(radians) (float)sk_float_sin(radians) 196 #define SkScalarCos(radians) (float)sk_float_cos(radians) 197 #define SkScalarTan(radians) (float)sk_float_tan(radians) 198 #define SkScalarASin(val) (float)sk_float_asin(val) 199 #define SkScalarACos(val) (float)sk_float_acos(val) 200 #define SkScalarATan2(y, x) (float)sk_float_atan2(y,x) 201 #define SkScalarExp(x) (float)sk_float_exp(x) 202 #define SkScalarLog(x) (float)sk_float_log(x) 203 204 inline SkScalar SkMaxScalar(SkScalar a, SkScalar b) { return a > b ? a : b; } 205 inline SkScalar SkMinScalar(SkScalar a, SkScalar b) { return a < b ? a : b; } 206 207 static inline bool SkScalarIsInt(SkScalar x) { 208 return x == (float)(int)x; 209 } 210 #else 211 typedef SkFixed SkScalar; 212 213 #define SK_Scalar1 SK_Fixed1 214 #define SK_ScalarHalf SK_FixedHalf 215 #define SK_ScalarInfinity SK_FixedMax 216 #define SK_ScalarMax SK_FixedMax 217 #define SK_ScalarMin SK_FixedMin 218 #define SK_ScalarNaN SK_FixedNaN 219 #define SkScalarIsNaN(x) ((x) == SK_FixedNaN) 220 #define SkScalarIsFinite(x) ((x) != SK_FixedNaN) 221 222 #define SkIntToScalar(n) SkIntToFixed(n) 223 #define SkFixedToScalar(x) (x) 224 #define SkScalarToFixed(x) (x) 225 #ifdef SK_CAN_USE_FLOAT 226 #define SkScalarToFloat(n) SkFixedToFloat(n) 227 #define SkFloatToScalar(n) SkFloatToFixed(n) 228 229 #define SkScalarToDouble(n) SkFixedToDouble(n) 230 #define SkDoubleToScalar(n) SkDoubleToFixed(n) 231 #endif 232 #define SkScalarFraction(x) SkFixedFraction(x) 233 234 #define SkScalarFloorToScalar(x) SkFixedFloorToFixed(x) 235 #define SkScalarCeilToScalar(x) SkFixedCeilToFixed(x) 236 #define SkScalarRoundToScalar(x) SkFixedRoundToFixed(x) 237 238 #define SkScalarFloorToInt(x) SkFixedFloorToInt(x) 239 #define SkScalarCeilToInt(x) SkFixedCeilToInt(x) 240 #define SkScalarRoundToInt(x) SkFixedRoundToInt(x) 241 242 #define SkScalarAbs(x) SkFixedAbs(x) 243 #define SkScalarCopySign(x, y) SkCopySign32(x, y) 244 #define SkScalarClampMax(x, max) SkClampMax(x, max) 245 #define SkScalarPin(x, min, max) SkPin32(x, min, max) 246 #define SkScalarSquare(x) SkFixedSquare(x) 247 #define SkScalarMul(a, b) SkFixedMul(a, b) 248 #define SkScalarMulAdd(a, b, c) SkFixedMulAdd(a, b, c) 249 #define SkScalarMulRound(a, b) SkFixedMulCommon(a, b, SK_FixedHalf) 250 #define SkScalarMulCeil(a, b) SkFixedMulCommon(a, b, SK_Fixed1 - 1) 251 #define SkScalarMulFloor(a, b) SkFixedMulCommon(a, b, 0) 252 #define SkScalarDiv(a, b) SkFixedDiv(a, b) 253 #define SkScalarMod(a, b) SkFixedMod(a, b) 254 #define SkScalarMulDiv(a, b, c) SkMulDiv(a, b, c) 255 #define SkScalarInvert(x) SkFixedInvert(x) 256 #define SkScalarFastInvert(x) SkFixedFastInvert(x) 257 #define SkScalarSqrt(x) SkFixedSqrt(x) 258 #define SkScalarAve(a, b) SkFixedAve(a, b) 259 #define SkScalarMean(a, b) SkFixedMean(a, b) 260 #define SkScalarHalf(a) ((a) >> 1) 261 262 #define SK_ScalarSqrt2 SK_FixedSqrt2 263 #define SK_ScalarPI SK_FixedPI 264 #define SK_ScalarTanPIOver8 SK_FixedTanPIOver8 265 #define SK_ScalarRoot2Over2 SK_FixedRoot2Over2 266 267 #define SkDegreesToRadians(degrees) SkFractMul(degrees, SK_FractPIOver180) 268 #define SkScalarSinCos(radians, cosPtr) SkFixedSinCos(radians, cosPtr) 269 #define SkScalarSin(radians) SkFixedSin(radians) 270 #define SkScalarCos(radians) SkFixedCos(radians) 271 #define SkScalarTan(val) SkFixedTan(val) 272 #define SkScalarASin(val) SkFixedASin(val) 273 #define SkScalarACos(val) SkFixedACos(val) 274 #define SkScalarATan2(y, x) SkFixedATan2(y,x) 275 #define SkScalarExp(x) SkFixedExp(x) 276 #define SkScalarLog(x) SkFixedLog(x) 277 278 #define SkMaxScalar(a, b) SkMax32(a, b) 279 #define SkMinScalar(a, b) SkMin32(a, b) 280 281 static inline bool SkScalarIsInt(SkFixed x) { 282 return 0 == (x & 0xffff); 283 } 284 #endif 285 286 // DEPRECATED : use ToInt or ToScalar variant 287 #define SkScalarFloor(x) SkScalarFloorToInt(x) 288 #define SkScalarCeil(x) SkScalarCeilToInt(x) 289 #define SkScalarRound(x) SkScalarRoundToInt(x) 290 291 /** 292 * Returns -1 || 0 || 1 depending on the sign of value: 293 * -1 if x < 0 294 * 0 if x == 0 295 * 1 if x > 0 296 */ 297 static inline int SkScalarSignAsInt(SkScalar x) { 298 return x < 0 ? -1 : (x > 0); 299 } 300 301 // Scalar result version of above 302 static inline SkScalar SkScalarSignAsScalar(SkScalar x) { 303 return x < 0 ? -SK_Scalar1 : ((x > 0) ? SK_Scalar1 : 0); 304 } 305 306 #define SK_ScalarNearlyZero (SK_Scalar1 / (1 << 12)) 307 308 /* <= is slower than < for floats, so we use < for our tolerance test 309 */ 310 311 static inline bool SkScalarNearlyZero(SkScalar x, 312 SkScalar tolerance = SK_ScalarNearlyZero) { 313 SkASSERT(tolerance > 0); 314 return SkScalarAbs(x) < tolerance; 315 } 316 317 static inline bool SkScalarNearlyEqual(SkScalar x, SkScalar y, 318 SkScalar tolerance = SK_ScalarNearlyZero) { 319 SkASSERT(tolerance > 0); 320 return SkScalarAbs(x-y) < tolerance; 321 } 322 323 /** Linearly interpolate between A and B, based on t. 324 If t is 0, return A 325 If t is 1, return B 326 else interpolate. 327 t must be [0..SK_Scalar1] 328 */ 329 static inline SkScalar SkScalarInterp(SkScalar A, SkScalar B, SkScalar t) { 330 SkASSERT(t >= 0 && t <= SK_Scalar1); 331 return A + SkScalarMul(B - A, t); 332 } 333 334 /** Interpolate along the function described by (keys[length], values[length]) 335 for the passed searchKey. SearchKeys outside the range keys[0]-keys[Length] 336 clamp to the min or max value. This function was inspired by a desire 337 to change the multiplier for thickness in fakeBold; therefore it assumes 338 the number of pairs (length) will be small, and a linear search is used. 339 Repeated keys are allowed for discontinuous functions (so long as keys is 340 monotonically increasing), and if key is the value of a repeated scalar in 341 keys, the first one will be used. However, that may change if a binary 342 search is used. 343 */ 344 SkScalar SkScalarInterpFunc(SkScalar searchKey, const SkScalar keys[], 345 const SkScalar values[], int length); 346 347 #endif 348
