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 33 /** SK_Scalar1 is defined to be 1.0 represented as an SkScalar 34 */ 35 #define SK_Scalar1 (1.0f) 36 /** SK_Scalar1 is defined to be 1/2 represented as an SkScalar 37 */ 38 #define SK_ScalarHalf (0.5f) 39 /** SK_ScalarInfinity is defined to be infinity as an SkScalar 40 */ 41 #define SK_ScalarInfinity SK_FloatInfinity 42 /** SK_ScalarNegativeInfinity is defined to be negative infinity as an SkScalar 43 */ 44 #define SK_ScalarNegativeInfinity SK_FloatNegativeInfinity 45 /** SK_ScalarMax is defined to be the largest value representable as an SkScalar 46 */ 47 #define SK_ScalarMax (3.402823466e+38f) 48 /** SK_ScalarMin is defined to be the smallest value representable as an SkScalar 49 */ 50 #define SK_ScalarMin (-SK_ScalarMax) 51 /** SK_ScalarNaN is defined to be 'Not a Number' as an SkScalar 52 */ 53 #define SK_ScalarNaN SK_FloatNaN 54 /** SkScalarIsNaN(n) returns true if argument is not a number 55 */ 56 static inline bool SkScalarIsNaN(float x) { return x != x; } 57 58 /** Returns true if x is not NaN and not infinite */ 59 static inline bool SkScalarIsFinite(float x) { 60 // We rely on the following behavior of infinities and nans 61 // 0 * finite --> 0 62 // 0 * infinity --> NaN 63 // 0 * NaN --> NaN 64 float prod = x * 0; 65 // At this point, prod will either be NaN or 0 66 // Therefore we can return (prod == prod) or (0 == prod). 67 return prod == prod; 68 } 69 70 /** SkIntToScalar(n) returns its integer argument as an SkScalar 71 */ 72 #define SkIntToScalar(n) ((float)(n)) 73 /** SkFixedToScalar(n) returns its SkFixed argument as an SkScalar 74 */ 75 #define SkFixedToScalar(x) SkFixedToFloat(x) 76 /** SkScalarToFixed(n) returns its SkScalar argument as an SkFixed 77 */ 78 #define SkScalarToFixed(x) SkFloatToFixed(x) 79 80 #define SkScalarToFloat(n) (n) 81 #ifndef SK_SCALAR_TO_FLOAT_EXCLUDED 82 #define SkFloatToScalar(n) (n) 83 #endif 84 85 #define SkScalarToDouble(n) (double)(n) 86 #define SkDoubleToScalar(n) (float)(n) 87 88 /** SkScalarFraction(x) returns the signed fractional part of the argument 89 */ 90 #define SkScalarFraction(x) sk_float_mod(x, 1.0f) 91 92 #define SkScalarFloorToScalar(x) sk_float_floor(x) 93 #define SkScalarCeilToScalar(x) sk_float_ceil(x) 94 #define SkScalarRoundToScalar(x) sk_float_floor((x) + 0.5f) 95 96 #define SkScalarFloorToInt(x) sk_float_floor2int(x) 97 #define SkScalarCeilToInt(x) sk_float_ceil2int(x) 98 #define SkScalarRoundToInt(x) sk_float_round2int(x) 99 #define SkScalarTruncToInt(x) static_cast<int>(x) 100 101 /** Returns the absolute value of the specified SkScalar 102 */ 103 #define SkScalarAbs(x) sk_float_abs(x) 104 /** Return x with the sign of y 105 */ 106 #define SkScalarCopySign(x, y) sk_float_copysign(x, y) 107 /** Returns the value pinned between 0 and max inclusive 108 */ 109 inline SkScalar SkScalarClampMax(SkScalar x, SkScalar max) { 110 return x < 0 ? 0 : x > max ? max : x; 111 } 112 /** Returns the value pinned between min and max inclusive 113 */ 114 inline SkScalar SkScalarPin(SkScalar x, SkScalar min, SkScalar max) { 115 return x < min ? min : x > max ? max : x; 116 } 117 /** Returns the specified SkScalar squared (x*x) 118 */ 119 inline SkScalar SkScalarSquare(SkScalar x) { return x * x; } 120 /** Returns the product of two SkScalars 121 */ 122 #define SkScalarMul(a, b) ((float)(a) * (b)) 123 /** Returns the product of two SkScalars plus a third SkScalar 124 */ 125 #define SkScalarMulAdd(a, b, c) ((float)(a) * (b) + (c)) 126 /** Returns the product of a SkScalar and an int rounded to the nearest integer value 127 */ 128 #define SkScalarMulRound(a, b) SkScalarRound((float)(a) * (b)) 129 /** Returns the product of a SkScalar and an int promoted to the next larger int 130 */ 131 #define SkScalarMulCeil(a, b) SkScalarCeil((float)(a) * (b)) 132 /** Returns the product of a SkScalar and an int truncated to the next smaller int 133 */ 134 #define SkScalarMulFloor(a, b) SkScalarFloor((float)(a) * (b)) 135 /** Returns the quotient of two SkScalars (a/b) 136 */ 137 #define SkScalarDiv(a, b) ((float)(a) / (b)) 138 /** Returns the mod of two SkScalars (a mod b) 139 */ 140 #define SkScalarMod(x,y) sk_float_mod(x,y) 141 /** Returns the product of the first two arguments, divided by the third argument 142 */ 143 #define SkScalarMulDiv(a, b, c) ((float)(a) * (b) / (c)) 144 /** Returns the multiplicative inverse of the SkScalar (1/x) 145 */ 146 #define SkScalarInvert(x) (SK_Scalar1 / (x)) 147 #define SkScalarFastInvert(x) (SK_Scalar1 / (x)) 148 /** Returns the square root of the SkScalar 149 */ 150 #define SkScalarSqrt(x) sk_float_sqrt(x) 151 /** Returns b to the e 152 */ 153 #define SkScalarPow(b, e) sk_float_pow(b, e) 154 /** Returns the average of two SkScalars (a+b)/2 155 */ 156 #define SkScalarAve(a, b) (((a) + (b)) * 0.5f) 157 /** Returns the geometric mean of two SkScalars 158 */ 159 #define SkScalarMean(a, b) sk_float_sqrt((float)(a) * (b)) 160 /** Returns one half of the specified SkScalar 161 */ 162 #define SkScalarHalf(a) ((a) * 0.5f) 163 164 #define SK_ScalarSqrt2 1.41421356f 165 #define SK_ScalarPI 3.14159265f 166 #define SK_ScalarTanPIOver8 0.414213562f 167 #define SK_ScalarRoot2Over2 0.707106781f 168 169 #define SkDegreesToRadians(degrees) ((degrees) * (SK_ScalarPI / 180)) 170 float SkScalarSinCos(SkScalar radians, SkScalar* cosValue); 171 #define SkScalarSin(radians) (float)sk_float_sin(radians) 172 #define SkScalarCos(radians) (float)sk_float_cos(radians) 173 #define SkScalarTan(radians) (float)sk_float_tan(radians) 174 #define SkScalarASin(val) (float)sk_float_asin(val) 175 #define SkScalarACos(val) (float)sk_float_acos(val) 176 #define SkScalarATan2(y, x) (float)sk_float_atan2(y,x) 177 #define SkScalarExp(x) (float)sk_float_exp(x) 178 #define SkScalarLog(x) (float)sk_float_log(x) 179 180 inline SkScalar SkMaxScalar(SkScalar a, SkScalar b) { return a > b ? a : b; } 181 inline SkScalar SkMinScalar(SkScalar a, SkScalar b) { return a < b ? a : b; } 182 183 static inline bool SkScalarIsInt(SkScalar x) { 184 return x == (float)(int)x; 185 } 186 #else 187 typedef SkFixed SkScalar; 188 189 #define SK_Scalar1 SK_Fixed1 190 #define SK_ScalarHalf SK_FixedHalf 191 #define SK_ScalarInfinity SK_FixedMax 192 #define SK_ScalarNegativeInfinity SK_FixedMin 193 #define SK_ScalarMax SK_FixedMax 194 #define SK_ScalarMin SK_FixedMin 195 #define SK_ScalarNaN SK_FixedNaN 196 #define SkScalarIsNaN(x) ((x) == SK_FixedNaN) 197 #define SkScalarIsFinite(x) ((x) != SK_FixedNaN) 198 199 #define SkIntToScalar(n) SkIntToFixed(n) 200 #define SkFixedToScalar(x) (x) 201 #define SkScalarToFixed(x) (x) 202 #define SkScalarToFloat(n) SkFixedToFloat(n) 203 #ifndef SK_SCALAR_TO_FLOAT_EXCLUDED 204 #define SkFloatToScalar(n) SkFloatToFixed(n) 205 #endif 206 207 #define SkScalarToDouble(n) SkFixedToDouble(n) 208 #define SkDoubleToScalar(n) SkDoubleToFixed(n) 209 #define SkScalarFraction(x) SkFixedFraction(x) 210 211 #define SkScalarFloorToScalar(x) SkFixedFloorToFixed(x) 212 #define SkScalarCeilToScalar(x) SkFixedCeilToFixed(x) 213 #define SkScalarRoundToScalar(x) SkFixedRoundToFixed(x) 214 215 #define SkScalarFloorToInt(x) SkFixedFloorToInt(x) 216 #define SkScalarCeilToInt(x) SkFixedCeilToInt(x) 217 #define SkScalarRoundToInt(x) SkFixedRoundToInt(x) 218 #define SkScalarTruncToInt(x) (((x) < 0) ? SkScalarCeilToInt(x) : SkScalarFloorToInt(x)) 219 220 #define SkScalarAbs(x) SkFixedAbs(x) 221 #define SkScalarCopySign(x, y) SkCopySign32(x, y) 222 #define SkScalarClampMax(x, max) SkClampMax(x, max) 223 #define SkScalarPin(x, min, max) SkPin32(x, min, max) 224 #define SkScalarSquare(x) SkFixedSquare(x) 225 #define SkScalarMul(a, b) SkFixedMul(a, b) 226 #define SkScalarMulAdd(a, b, c) SkFixedMulAdd(a, b, c) 227 #define SkScalarMulRound(a, b) SkFixedMulCommon(a, b, SK_FixedHalf) 228 #define SkScalarMulCeil(a, b) SkFixedMulCommon(a, b, SK_Fixed1 - 1) 229 #define SkScalarMulFloor(a, b) SkFixedMulCommon(a, b, 0) 230 #define SkScalarDiv(a, b) SkFixedDiv(a, b) 231 #define SkScalarMod(a, b) SkFixedMod(a, b) 232 #define SkScalarMulDiv(a, b, c) SkMulDiv(a, b, c) 233 #define SkScalarInvert(x) SkFixedInvert(x) 234 #define SkScalarFastInvert(x) SkFixedFastInvert(x) 235 #define SkScalarSqrt(x) SkFixedSqrt(x) 236 #define SkScalarAve(a, b) SkFixedAve(a, b) 237 #define SkScalarMean(a, b) SkFixedMean(a, b) 238 #define SkScalarHalf(a) ((a) >> 1) 239 240 #define SK_ScalarSqrt2 SK_FixedSqrt2 241 #define SK_ScalarPI SK_FixedPI 242 #define SK_ScalarTanPIOver8 SK_FixedTanPIOver8 243 #define SK_ScalarRoot2Over2 SK_FixedRoot2Over2 244 245 #define SkDegreesToRadians(degrees) SkFractMul(degrees, SK_FractPIOver180) 246 #define SkScalarSinCos(radians, cosPtr) SkFixedSinCos(radians, cosPtr) 247 #define SkScalarSin(radians) SkFixedSin(radians) 248 #define SkScalarCos(radians) SkFixedCos(radians) 249 #define SkScalarTan(val) SkFixedTan(val) 250 #define SkScalarASin(val) SkFixedASin(val) 251 #define SkScalarACos(val) SkFixedACos(val) 252 #define SkScalarATan2(y, x) SkFixedATan2(y,x) 253 #define SkScalarExp(x) SkFixedExp(x) 254 #define SkScalarLog(x) SkFixedLog(x) 255 256 #define SkMaxScalar(a, b) SkMax32(a, b) 257 #define SkMinScalar(a, b) SkMin32(a, b) 258 259 static inline bool SkScalarIsInt(SkFixed x) { 260 return 0 == (x & 0xffff); 261 } 262 #endif 263 264 // DEPRECATED : use ToInt or ToScalar variant 265 #define SkScalarFloor(x) SkScalarFloorToInt(x) 266 #define SkScalarCeil(x) SkScalarCeilToInt(x) 267 #define SkScalarRound(x) SkScalarRoundToInt(x) 268 269 /** 270 * Returns -1 || 0 || 1 depending on the sign of value: 271 * -1 if x < 0 272 * 0 if x == 0 273 * 1 if x > 0 274 */ 275 static inline int SkScalarSignAsInt(SkScalar x) { 276 return x < 0 ? -1 : (x > 0); 277 } 278 279 // Scalar result version of above 280 static inline SkScalar SkScalarSignAsScalar(SkScalar x) { 281 return x < 0 ? -SK_Scalar1 : ((x > 0) ? SK_Scalar1 : 0); 282 } 283 284 #define SK_ScalarNearlyZero (SK_Scalar1 / (1 << 12)) 285 286 static inline bool SkScalarNearlyZero(SkScalar x, 287 SkScalar tolerance = SK_ScalarNearlyZero) { 288 SkASSERT(tolerance >= 0); 289 return SkScalarAbs(x) <= tolerance; 290 } 291 292 static inline bool SkScalarNearlyEqual(SkScalar x, SkScalar y, 293 SkScalar tolerance = SK_ScalarNearlyZero) { 294 SkASSERT(tolerance >= 0); 295 return SkScalarAbs(x-y) <= 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 static inline SkScalar SkScalarLog2(SkScalar x) { 310 static const SkScalar log2_conversion_factor = SkScalarDiv(1, SkScalarLog(2)); 311 312 return SkScalarMul(SkScalarLog(x), log2_conversion_factor); 313 } 314 315 /** Interpolate along the function described by (keys[length], values[length]) 316 for the passed searchKey. SearchKeys outside the range keys[0]-keys[Length] 317 clamp to the min or max value. This function was inspired by a desire 318 to change the multiplier for thickness in fakeBold; therefore it assumes 319 the number of pairs (length) will be small, and a linear search is used. 320 Repeated keys are allowed for discontinuous functions (so long as keys is 321 monotonically increasing), and if key is the value of a repeated scalar in 322 keys, the first one will be used. However, that may change if a binary 323 search is used. 324 */ 325 SkScalar SkScalarInterpFunc(SkScalar searchKey, const SkScalar keys[], 326 const SkScalar values[], int length); 327 328 /* 329 * Helper to compare an array of scalars. 330 */ 331 static inline bool SkScalarsEqual(const SkScalar a[], const SkScalar b[], int n) { 332 #ifdef SK_SCALAR_IS_FLOAT 333 SkASSERT(n >= 0); 334 for (int i = 0; i < n; ++i) { 335 if (a[i] != b[i]) { 336 return false; 337 } 338 } 339 return true; 340 #else 341 return 0 == memcmp(a, b, n * sizeof(SkScalar)); 342 #endif 343 } 344 345 #endif 346
