/* * Copyright 2006 The Android Open Source Project * * Use of this source code is governed by a BSD-style license that can be * found in the LICENSE file. */ #ifndef SkScalar_DEFINED #define SkScalar_DEFINED #include "SkFixed.h" #include "SkFloatingPoint.h" /** \file SkScalar.h Types and macros for the data type SkScalar. This is the fractional numeric type that, depending on the compile-time flag SK_SCALAR_IS_FLOAT, may be implemented either as an IEEE float, or as a 16.16 SkFixed. The macros in this file are written to allow the calling code to manipulate SkScalar values without knowing which representation is in effect. */ #ifdef SK_SCALAR_IS_FLOAT /** SkScalar is our type for fractional values and coordinates. Depending on compile configurations, it is either represented as an IEEE float, or as a 16.16 fixed point integer. */ typedef float SkScalar; /** SK_Scalar1 is defined to be 1.0 represented as an SkScalar */ #define SK_Scalar1 (1.0f) /** SK_Scalar1 is defined to be 1/2 represented as an SkScalar */ #define SK_ScalarHalf (0.5f) /** SK_ScalarInfinity is defined to be infinity as an SkScalar */ #define SK_ScalarInfinity SK_FloatInfinity /** SK_ScalarMax is defined to be the largest value representable as an SkScalar */ #define SK_ScalarMax (3.402823466e+38f) /** SK_ScalarMin is defined to be the smallest value representable as an SkScalar */ #define SK_ScalarMin (-SK_ScalarMax) /** SK_ScalarNaN is defined to be 'Not a Number' as an SkScalar */ #define SK_ScalarNaN SK_FloatNaN /** SkScalarIsNaN(n) returns true if argument is not a number */ static inline bool SkScalarIsNaN(float x) { return x != x; } /** Returns true if x is not NaN and not infinite */ static inline bool SkScalarIsFinite(float x) { // We rely on the following behavior of infinities and nans // 0 * finite --> 0 // 0 * infinity --> NaN // 0 * NaN --> NaN float prod = x * 0; // At this point, prod will either be NaN or 0 // Therefore we can return (prod == prod) or (0 == prod). return prod == prod; } #ifdef SK_DEBUG /** SkIntToScalar(n) returns its integer argument as an SkScalar * * If we're compiling in DEBUG mode, and can thus afford some extra runtime * cycles, check to make sure that the parameter passed in has not already * been converted to SkScalar. (A double conversion like this is harmless * for SK_SCALAR_IS_FLOAT, but for SK_SCALAR_IS_FIXED this causes trouble.) * * Note that we need all of these method signatures to properly handle the * various types that we pass into SkIntToScalar() to date: * int, size_t, U8CPU, etc., even though what we really mean is "anything * but a float". */ static inline float SkIntToScalar(signed int param) { return (float)param; } static inline float SkIntToScalar(unsigned int param) { return (float)param; } static inline float SkIntToScalar(signed long param) { return (float)param; } static inline float SkIntToScalar(unsigned long param) { return (float)param; } static inline float SkIntToScalar(float /* param */) { /* If the parameter passed into SkIntToScalar is a float, * one of two things has happened: * 1. the parameter was an SkScalar (which is typedef'd to float) * 2. the parameter was a float instead of an int * * Either way, it's not good. */ SkDEBUGFAIL("looks like you passed an SkScalar into SkIntToScalar"); return (float)0; } #else // not SK_DEBUG /** SkIntToScalar(n) returns its integer argument as an SkScalar */ #define SkIntToScalar(n) ((float)(n)) #endif // not SK_DEBUG /** SkFixedToScalar(n) returns its SkFixed argument as an SkScalar */ #define SkFixedToScalar(x) SkFixedToFloat(x) /** SkScalarToFixed(n) returns its SkScalar argument as an SkFixed */ #define SkScalarToFixed(x) SkFloatToFixed(x) #define SkScalarToFloat(n) (n) #define SkFloatToScalar(n) (n) #define SkScalarToDouble(n) (double)(n) #define SkDoubleToScalar(n) (float)(n) /** SkScalarFraction(x) returns the signed fractional part of the argument */ #define SkScalarFraction(x) sk_float_mod(x, 1.0f) #define SkScalarFloorToScalar(x) sk_float_floor(x) #define SkScalarCeilToScalar(x) sk_float_ceil(x) #define SkScalarRoundToScalar(x) sk_float_floor((x) + 0.5f) #define SkScalarFloorToInt(x) sk_float_floor2int(x) #define SkScalarCeilToInt(x) sk_float_ceil2int(x) #define SkScalarRoundToInt(x) sk_float_round2int(x) /** Returns the absolute value of the specified SkScalar */ #define SkScalarAbs(x) sk_float_abs(x) /** Return x with the sign of y */ #define SkScalarCopySign(x, y) sk_float_copysign(x, y) /** Returns the value pinned between 0 and max inclusive */ inline SkScalar SkScalarClampMax(SkScalar x, SkScalar max) { return x < 0 ? 0 : x > max ? max : x; } /** Returns the value pinned between min and max inclusive */ inline SkScalar SkScalarPin(SkScalar x, SkScalar min, SkScalar max) { return x < min ? min : x > max ? max : x; } /** Returns the specified SkScalar squared (x*x) */ inline SkScalar SkScalarSquare(SkScalar x) { return x * x; } /** Returns the product of two SkScalars */ #define SkScalarMul(a, b) ((float)(a) * (b)) /** Returns the product of two SkScalars plus a third SkScalar */ #define SkScalarMulAdd(a, b, c) ((float)(a) * (b) + (c)) /** Returns the product of a SkScalar and an int rounded to the nearest integer value */ #define SkScalarMulRound(a, b) SkScalarRound((float)(a) * (b)) /** Returns the product of a SkScalar and an int promoted to the next larger int */ #define SkScalarMulCeil(a, b) SkScalarCeil((float)(a) * (b)) /** Returns the product of a SkScalar and an int truncated to the next smaller int */ #define SkScalarMulFloor(a, b) SkScalarFloor((float)(a) * (b)) /** Returns the quotient of two SkScalars (a/b) */ #define SkScalarDiv(a, b) ((float)(a) / (b)) /** Returns the mod of two SkScalars (a mod b) */ #define SkScalarMod(x,y) sk_float_mod(x,y) /** Returns the product of the first two arguments, divided by the third argument */ #define SkScalarMulDiv(a, b, c) ((float)(a) * (b) / (c)) /** Returns the multiplicative inverse of the SkScalar (1/x) */ #define SkScalarInvert(x) (SK_Scalar1 / (x)) #define SkScalarFastInvert(x) (SK_Scalar1 / (x)) /** Returns the square root of the SkScalar */ #define SkScalarSqrt(x) sk_float_sqrt(x) /** Returns b to the e */ #define SkScalarPow(b, e) sk_float_pow(b, e) /** Returns the average of two SkScalars (a+b)/2 */ #define SkScalarAve(a, b) (((a) + (b)) * 0.5f) /** Returns the geometric mean of two SkScalars */ #define SkScalarMean(a, b) sk_float_sqrt((float)(a) * (b)) /** Returns one half of the specified SkScalar */ #define SkScalarHalf(a) ((a) * 0.5f) #define SK_ScalarSqrt2 1.41421356f #define SK_ScalarPI 3.14159265f #define SK_ScalarTanPIOver8 0.414213562f #define SK_ScalarRoot2Over2 0.707106781f #define SkDegreesToRadians(degrees) ((degrees) * (SK_ScalarPI / 180)) float SkScalarSinCos(SkScalar radians, SkScalar* cosValue); #define SkScalarSin(radians) (float)sk_float_sin(radians) #define SkScalarCos(radians) (float)sk_float_cos(radians) #define SkScalarTan(radians) (float)sk_float_tan(radians) #define SkScalarASin(val) (float)sk_float_asin(val) #define SkScalarACos(val) (float)sk_float_acos(val) #define SkScalarATan2(y, x) (float)sk_float_atan2(y,x) #define SkScalarExp(x) (float)sk_float_exp(x) #define SkScalarLog(x) (float)sk_float_log(x) inline SkScalar SkMaxScalar(SkScalar a, SkScalar b) { return a > b ? a : b; } inline SkScalar SkMinScalar(SkScalar a, SkScalar b) { return a < b ? a : b; } static inline bool SkScalarIsInt(SkScalar x) { return x == (float)(int)x; } #else typedef SkFixed SkScalar; #define SK_Scalar1 SK_Fixed1 #define SK_ScalarHalf SK_FixedHalf #define SK_ScalarInfinity SK_FixedMax #define SK_ScalarMax SK_FixedMax #define SK_ScalarMin SK_FixedMin #define SK_ScalarNaN SK_FixedNaN #define SkScalarIsNaN(x) ((x) == SK_FixedNaN) #define SkScalarIsFinite(x) ((x) != SK_FixedNaN) #define SkIntToScalar(n) SkIntToFixed(n) #define SkFixedToScalar(x) (x) #define SkScalarToFixed(x) (x) #define SkScalarToFloat(n) SkFixedToFloat(n) #define SkFloatToScalar(n) SkFloatToFixed(n) #define SkScalarToDouble(n) SkFixedToDouble(n) #define SkDoubleToScalar(n) SkDoubleToFixed(n) #define SkScalarFraction(x) SkFixedFraction(x) #define SkScalarFloorToScalar(x) SkFixedFloorToFixed(x) #define SkScalarCeilToScalar(x) SkFixedCeilToFixed(x) #define SkScalarRoundToScalar(x) SkFixedRoundToFixed(x) #define SkScalarFloorToInt(x) SkFixedFloorToInt(x) #define SkScalarCeilToInt(x) SkFixedCeilToInt(x) #define SkScalarRoundToInt(x) SkFixedRoundToInt(x) #define SkScalarAbs(x) SkFixedAbs(x) #define SkScalarCopySign(x, y) SkCopySign32(x, y) #define SkScalarClampMax(x, max) SkClampMax(x, max) #define SkScalarPin(x, min, max) SkPin32(x, min, max) #define SkScalarSquare(x) SkFixedSquare(x) #define SkScalarMul(a, b) SkFixedMul(a, b) #define SkScalarMulAdd(a, b, c) SkFixedMulAdd(a, b, c) #define SkScalarMulRound(a, b) SkFixedMulCommon(a, b, SK_FixedHalf) #define SkScalarMulCeil(a, b) SkFixedMulCommon(a, b, SK_Fixed1 - 1) #define SkScalarMulFloor(a, b) SkFixedMulCommon(a, b, 0) #define SkScalarDiv(a, b) SkFixedDiv(a, b) #define SkScalarMod(a, b) SkFixedMod(a, b) #define SkScalarMulDiv(a, b, c) SkMulDiv(a, b, c) #define SkScalarInvert(x) SkFixedInvert(x) #define SkScalarFastInvert(x) SkFixedFastInvert(x) #define SkScalarSqrt(x) SkFixedSqrt(x) #define SkScalarAve(a, b) SkFixedAve(a, b) #define SkScalarMean(a, b) SkFixedMean(a, b) #define SkScalarHalf(a) ((a) >> 1) #define SK_ScalarSqrt2 SK_FixedSqrt2 #define SK_ScalarPI SK_FixedPI #define SK_ScalarTanPIOver8 SK_FixedTanPIOver8 #define SK_ScalarRoot2Over2 SK_FixedRoot2Over2 #define SkDegreesToRadians(degrees) SkFractMul(degrees, SK_FractPIOver180) #define SkScalarSinCos(radians, cosPtr) SkFixedSinCos(radians, cosPtr) #define SkScalarSin(radians) SkFixedSin(radians) #define SkScalarCos(radians) SkFixedCos(radians) #define SkScalarTan(val) SkFixedTan(val) #define SkScalarASin(val) SkFixedASin(val) #define SkScalarACos(val) SkFixedACos(val) #define SkScalarATan2(y, x) SkFixedATan2(y,x) #define SkScalarExp(x) SkFixedExp(x) #define SkScalarLog(x) SkFixedLog(x) #define SkMaxScalar(a, b) SkMax32(a, b) #define SkMinScalar(a, b) SkMin32(a, b) static inline bool SkScalarIsInt(SkFixed x) { return 0 == (x & 0xffff); } #endif // DEPRECATED : use ToInt or ToScalar variant #define SkScalarFloor(x) SkScalarFloorToInt(x) #define SkScalarCeil(x) SkScalarCeilToInt(x) #define SkScalarRound(x) SkScalarRoundToInt(x) /** * Returns -1 || 0 || 1 depending on the sign of value: * -1 if x < 0 * 0 if x == 0 * 1 if x > 0 */ static inline int SkScalarSignAsInt(SkScalar x) { return x < 0 ? -1 : (x > 0); } // Scalar result version of above static inline SkScalar SkScalarSignAsScalar(SkScalar x) { return x < 0 ? -SK_Scalar1 : ((x > 0) ? SK_Scalar1 : 0); } #define SK_ScalarNearlyZero (SK_Scalar1 / (1 << 12)) static inline bool SkScalarNearlyZero(SkScalar x, SkScalar tolerance = SK_ScalarNearlyZero) { SkASSERT(tolerance >= 0); return SkScalarAbs(x) <= tolerance; } static inline bool SkScalarNearlyEqual(SkScalar x, SkScalar y, SkScalar tolerance = SK_ScalarNearlyZero) { SkASSERT(tolerance >= 0); return SkScalarAbs(x-y) <= tolerance; } /** Linearly interpolate between A and B, based on t. If t is 0, return A If t is 1, return B else interpolate. t must be [0..SK_Scalar1] */ static inline SkScalar SkScalarInterp(SkScalar A, SkScalar B, SkScalar t) { SkASSERT(t >= 0 && t <= SK_Scalar1); return A + SkScalarMul(B - A, t); } static inline SkScalar SkScalarLog2(SkScalar x) { static const SkScalar log2_conversion_factor = SkScalarDiv(1, SkScalarLog(2)); return SkScalarMul(SkScalarLog(x), log2_conversion_factor); } /** Interpolate along the function described by (keys[length], values[length]) for the passed searchKey. SearchKeys outside the range keys[0]-keys[Length] clamp to the min or max value. This function was inspired by a desire to change the multiplier for thickness in fakeBold; therefore it assumes the number of pairs (length) will be small, and a linear search is used. Repeated keys are allowed for discontinuous functions (so long as keys is monotonically increasing), and if key is the value of a repeated scalar in keys, the first one will be used. However, that may change if a binary search is used. */ SkScalar SkScalarInterpFunc(SkScalar searchKey, const SkScalar keys[], const SkScalar values[], int length); /* * Helper to compare an array of scalars. */ static inline bool SkScalarsEqual(const SkScalar a[], const SkScalar b[], int n) { #ifdef SK_SCALAR_IS_FLOAT SkASSERT(n >= 0); for (int i = 0; i < n; ++i) { if (a[i] != b[i]) { return false; } } return true; #else return 0 == memcmp(a, b, n * sizeof(SkScalar)); #endif } #endif