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