1/* 2 * Copyright 2006 The Android Open Source Project 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#ifndef SkScalar_DEFINED 9#define SkScalar_DEFINED 10 11#include "SkFixed.h" 12#include "../private/SkFloatingPoint.h" 13 14// TODO: move this sort of check into SkPostConfig.h 15#define SK_SCALAR_IS_DOUBLE 0 16#undef SK_SCALAR_IS_FLOAT 17#define SK_SCALAR_IS_FLOAT 1 18 19 20#if SK_SCALAR_IS_FLOAT 21 22typedef float SkScalar; 23 24#define SK_Scalar1 1.0f 25#define SK_ScalarHalf 0.5f 26#define SK_ScalarSqrt2 1.41421356f 27#define SK_ScalarPI 3.14159265f 28#define SK_ScalarTanPIOver8 0.414213562f 29#define SK_ScalarRoot2Over2 0.707106781f 30#define SK_ScalarMax 3.402823466e+38f 31#define SK_ScalarInfinity SK_FloatInfinity 32#define SK_ScalarNegativeInfinity SK_FloatNegativeInfinity 33#define SK_ScalarNaN SK_FloatNaN 34 35#define SkFixedToScalar(x) SkFixedToFloat(x) 36#define SkScalarToFixed(x) SkFloatToFixed(x) 37 38#define SkScalarFloorToScalar(x) sk_float_floor(x) 39#define SkScalarCeilToScalar(x) sk_float_ceil(x) 40#define SkScalarRoundToScalar(x) sk_float_floor((x) + 0.5f) 41 42#define SkScalarFloorToInt(x) sk_float_floor2int(x) 43#define SkScalarCeilToInt(x) sk_float_ceil2int(x) 44#define SkScalarRoundToInt(x) sk_float_round2int(x) 45 46#define SkScalarAbs(x) sk_float_abs(x) 47#define SkScalarCopySign(x, y) sk_float_copysign(x, y) 48#define SkScalarMod(x, y) sk_float_mod(x,y) 49#define SkScalarFraction(x) sk_float_mod(x, 1.0f) 50#define SkScalarSqrt(x) sk_float_sqrt(x) 51#define SkScalarPow(b, e) sk_float_pow(b, e) 52 53#define SkScalarSin(radians) (float)sk_float_sin(radians) 54#define SkScalarCos(radians) (float)sk_float_cos(radians) 55#define SkScalarTan(radians) (float)sk_float_tan(radians) 56#define SkScalarASin(val) (float)sk_float_asin(val) 57#define SkScalarACos(val) (float)sk_float_acos(val) 58#define SkScalarATan2(y, x) (float)sk_float_atan2(y,x) 59#define SkScalarExp(x) (float)sk_float_exp(x) 60#define SkScalarLog(x) (float)sk_float_log(x) 61#define SkScalarLog2(x) (float)sk_float_log2(x) 62 63#else // SK_SCALAR_IS_DOUBLE 64 65typedef double SkScalar; 66 67#define SK_Scalar1 1.0 68#define SK_ScalarHalf 0.5 69#define SK_ScalarSqrt2 1.414213562373095 70#define SK_ScalarPI 3.141592653589793 71#define SK_ScalarTanPIOver8 0.4142135623731 72#define SK_ScalarRoot2Over2 0.70710678118655 73#define SK_ScalarMax 1.7976931348623157+308 74#define SK_ScalarInfinity SK_DoubleInfinity 75#define SK_ScalarNegativeInfinity SK_DoubleNegativeInfinity 76#define SK_ScalarNaN SK_DoubleNaN 77 78#define SkFixedToScalar(x) SkFixedToDouble(x) 79#define SkScalarToFixed(x) SkDoubleToFixed(x) 80 81#define SkScalarFloorToScalar(x) floor(x) 82#define SkScalarCeilToScalar(x) ceil(x) 83#define SkScalarRoundToScalar(x) floor((x) + 0.5) 84 85#define SkScalarFloorToInt(x) (int)floor(x) 86#define SkScalarCeilToInt(x) (int)ceil(x) 87#define SkScalarRoundToInt(x) (int)floor((x) + 0.5) 88 89#define SkScalarAbs(x) abs(x) 90#define SkScalarCopySign(x, y) copysign(x, y) 91#define SkScalarMod(x, y) fmod(x,y) 92#define SkScalarFraction(x) fmod(x, 1.0) 93#define SkScalarSqrt(x) sqrt(x) 94#define SkScalarPow(b, e) pow(b, e) 95 96#define SkScalarSin(radians) sin(radians) 97#define SkScalarCos(radians) cos(radians) 98#define SkScalarTan(radians) tan(radians) 99#define SkScalarASin(val) asin(val) 100#define SkScalarACos(val) acos(val) 101#define SkScalarATan2(y, x) atan2(y,x) 102#define SkScalarExp(x) exp(x) 103#define SkScalarLog(x) log(x) 104#define SkScalarLog2(x) log2(x) 105 106#endif 107 108////////////////////////////////////////////////////////////////////////////////////////////////// 109 110#define SkIntToScalar(x) static_cast<SkScalar>(x) 111#define SkScalarTruncToInt(x) static_cast<int>(x) 112 113#define SkScalarToFloat(x) static_cast<float>(x) 114#define SkFloatToScalar(x) static_cast<SkScalar>(x) 115#define SkScalarToDouble(x) static_cast<double>(x) 116#define SkDoubleToScalar(x) static_cast<SkScalar>(x) 117 118#define SK_ScalarMin (-SK_ScalarMax) 119 120static inline bool SkScalarIsNaN(SkScalar x) { return x != x; } 121 122/** Returns true if x is not NaN and not infinite 123 */ 124static inline bool SkScalarIsFinite(SkScalar x) { 125 // We rely on the following behavior of infinities and nans 126 // 0 * finite --> 0 127 // 0 * infinity --> NaN 128 // 0 * NaN --> NaN 129 SkScalar prod = x * 0; 130 // At this point, prod will either be NaN or 0 131 return !SkScalarIsNaN(prod); 132} 133 134static inline bool SkScalarsAreFinite(SkScalar a, SkScalar b) { 135 SkScalar prod = 0; 136 prod *= a; 137 prod *= b; 138 // At this point, prod will either be NaN or 0 139 return !SkScalarIsNaN(prod); 140} 141 142static inline bool SkScalarsAreFinite(const SkScalar array[], int count) { 143 SkScalar prod = 0; 144 for (int i = 0; i < count; ++i) { 145 prod *= array[i]; 146 } 147 // At this point, prod will either be NaN or 0 148 return !SkScalarIsNaN(prod); 149} 150 151/** 152 * Variant of SkScalarRoundToInt, that performs the rounding step (adding 0.5) explicitly using 153 * double, to avoid possibly losing the low bit(s) of the answer before calling floor(). 154 * 155 * This routine will likely be slower than SkScalarRoundToInt(), and should only be used when the 156 * extra precision is known to be valuable. 157 * 158 * In particular, this catches the following case: 159 * SkScalar x = 0.49999997; 160 * int ix = SkScalarRoundToInt(x); 161 * SkASSERT(0 == ix); // <--- fails 162 * ix = SkDScalarRoundToInt(x); 163 * SkASSERT(0 == ix); // <--- succeeds 164 */ 165static inline int SkDScalarRoundToInt(SkScalar x) { 166 double xx = x; 167 xx += 0.5; 168 return (int)floor(xx); 169} 170 171static inline SkScalar SkScalarClampMax(SkScalar x, SkScalar max) { 172 x = SkTMin(x, max); 173 x = SkTMax<SkScalar>(x, 0); 174 return x; 175} 176 177static inline SkScalar SkScalarPin(SkScalar x, SkScalar min, SkScalar max) { 178 return SkTPin(x, min, max); 179} 180 181SkScalar SkScalarSinCos(SkScalar radians, SkScalar* cosValue); 182 183static inline SkScalar SkScalarSquare(SkScalar x) { return x * x; } 184 185#define SkScalarMul(a, b) ((SkScalar)(a) * (b)) 186#define SkScalarMulAdd(a, b, c) ((SkScalar)(a) * (b) + (c)) 187#define SkScalarMulDiv(a, b, c) ((SkScalar)(a) * (b) / (c)) 188#define SkScalarInvert(x) (SK_Scalar1 / (x)) 189#define SkScalarFastInvert(x) (SK_Scalar1 / (x)) 190#define SkScalarAve(a, b) (((a) + (b)) * SK_ScalarHalf) 191#define SkScalarHalf(a) ((a) * SK_ScalarHalf) 192 193#define SkDegreesToRadians(degrees) ((degrees) * (SK_ScalarPI / 180)) 194#define SkRadiansToDegrees(radians) ((radians) * (180 / SK_ScalarPI)) 195 196static inline SkScalar SkMaxScalar(SkScalar a, SkScalar b) { return a > b ? a : b; } 197static inline SkScalar SkMinScalar(SkScalar a, SkScalar b) { return a < b ? a : b; } 198 199static inline bool SkScalarIsInt(SkScalar x) { 200 return x == (SkScalar)(int)x; 201} 202 203/** 204 * Returns -1 || 0 || 1 depending on the sign of value: 205 * -1 if x < 0 206 * 0 if x == 0 207 * 1 if x > 0 208 */ 209static inline int SkScalarSignAsInt(SkScalar x) { 210 return x < 0 ? -1 : (x > 0); 211} 212 213// Scalar result version of above 214static inline SkScalar SkScalarSignAsScalar(SkScalar x) { 215 return x < 0 ? -SK_Scalar1 : ((x > 0) ? SK_Scalar1 : 0); 216} 217 218#define SK_ScalarNearlyZero (SK_Scalar1 / (1 << 12)) 219 220static inline bool SkScalarNearlyZero(SkScalar x, 221 SkScalar tolerance = SK_ScalarNearlyZero) { 222 SkASSERT(tolerance >= 0); 223 return SkScalarAbs(x) <= tolerance; 224} 225 226static inline bool SkScalarNearlyEqual(SkScalar x, SkScalar y, 227 SkScalar tolerance = SK_ScalarNearlyZero) { 228 SkASSERT(tolerance >= 0); 229 return SkScalarAbs(x-y) <= tolerance; 230} 231 232/** Linearly interpolate between A and B, based on t. 233 If t is 0, return A 234 If t is 1, return B 235 else interpolate. 236 t must be [0..SK_Scalar1] 237*/ 238static inline SkScalar SkScalarInterp(SkScalar A, SkScalar B, SkScalar t) { 239 SkASSERT(t >= 0 && t <= SK_Scalar1); 240 return A + (B - A) * t; 241} 242 243/** Interpolate along the function described by (keys[length], values[length]) 244 for the passed searchKey. SearchKeys outside the range keys[0]-keys[Length] 245 clamp to the min or max value. This function was inspired by a desire 246 to change the multiplier for thickness in fakeBold; therefore it assumes 247 the number of pairs (length) will be small, and a linear search is used. 248 Repeated keys are allowed for discontinuous functions (so long as keys is 249 monotonically increasing), and if key is the value of a repeated scalar in 250 keys, the first one will be used. However, that may change if a binary 251 search is used. 252*/ 253SkScalar SkScalarInterpFunc(SkScalar searchKey, const SkScalar keys[], 254 const SkScalar values[], int length); 255 256/* 257 * Helper to compare an array of scalars. 258 */ 259static inline bool SkScalarsEqual(const SkScalar a[], const SkScalar b[], int n) { 260 SkASSERT(n >= 0); 261 for (int i = 0; i < n; ++i) { 262 if (a[i] != b[i]) { 263 return false; 264 } 265 } 266 return true; 267} 268 269#endif 270