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+/* include/corecg/SkScalar.h
+**
+** Copyright 2006, Google Inc.
+**
+** Licensed under the Apache License, Version 2.0 (the "License");
+** you may not use this file except in compliance with the License.
+** You may obtain a copy of the License at
+**
+** http://www.apache.org/licenses/LICENSE-2.0
+**
+** Unless required by applicable law or agreed to in writing, software
+** distributed under the License is distributed on an "AS IS" BASIS,
+** WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+** See the License for the specific language governing permissions and
+** limitations under the License.
+*/
+
+#ifndef SkScalar_DEFINED
+#define SkScalar_DEFINED
+
+#include "SkFixed.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
+ #include "SkFloatingPoint.h"
+
+ /** 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;
+ extern const uint32_t gIEEENotANumber;
+ extern const uint32_t gIEEEInfinity;
+
+ /** 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 (*(const float*)&gIEEEInfinity)
+ /** SK_ScalarMax is defined to be the largest value representable as an SkScalar
+ */
+ #define SK_ScalarMax (3.4028235e+38f)
+ /** SK_ScalarMin is defined to be the smallest value representable as an SkScalar
+ */
+ #define SK_ScalarMin (1.1754944e-38f)
+ /** SK_ScalarNaN is defined to be 'Not a Number' as an SkScalar
+ */
+ #define SK_ScalarNaN (*(const float*)(const void*)&gIEEENotANumber)
+ /** SkScalarIsNaN(n) returns true if argument is not a number
+ */
+ static inline bool SkScalarIsNaN(float x) { return x != x; }
+ /** SkIntToScalar(n) returns its integer argument as an SkScalar
+ */
+ #define SkIntToScalar(n) ((float)(n))
+ /** 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)
+ /** Rounds the SkScalar to the nearest integer value
+ */
+ #define SkScalarRound(x) (int)sk_float_floor((x) + 0.5f)
+ /** Returns the smallest integer that is >= the specified SkScalar
+ */
+ #define SkScalarCeil(x) (int)sk_float_ceil(x)
+ /** Returns the largest integer that is <= the specified SkScalar
+ */
+ #define SkScalarFloor(x) (int)sk_float_floor(x)
+ /** Returns the absolute value of the specified SkScalar
+ */
+ #define SkScalarAbs(x) sk_float_abs(x)
+ /** 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 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; }
+
+#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 SkIntToScalar(n) SkIntToFixed(n)
+ #define SkFixedToScalar(x) (x)
+ #define SkScalarToFixed(x) (x)
+ #ifdef SK_CAN_USE_FLOAT
+ #define SkScalarToFloat(n) SkFixedToFloat(n)
+ #define SkFloatToScalar(n) SkFloatToFixed(n)
+
+ #define SkScalarToDouble(n) SkFixedToDouble(n)
+ #define SkDoubleToScalar(n) SkDoubleToFixed(n)
+ #endif
+ #define SkScalarFraction(x) SkFixedFraction(x)
+ #define SkScalarRound(x) SkFixedRound(x)
+ #define SkScalarCeil(x) SkFixedCeil(x)
+ #define SkScalarFloor(x) SkFixedFloor(x)
+ #define SkScalarAbs(x) SkFixedAbs(x)
+ #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)
+#endif
+
+#ifndef SK_SCALAR_IS_FLOAT
+#define SK_ScalarNearlyZero SK_FixedNearlyZero
+#else
+/* Allow a little more flexibility for floating-point scalars
+ */
+#define SK_ScalarNearlyZero (SK_Scalar1 / (1<<15))
+#endif
+
+/* <= is slower than < for floats, so we use < for our tolerance test
+*/
+
+inline bool SkScalarNearlyZero(SkScalar x, SkScalar tolerance = SK_ScalarNearlyZero)
+{
+ SkASSERT(tolerance > 0);
+ return SkScalarAbs(x) < 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]
+*/
+inline SkScalar SkScalarInterp(SkScalar A, SkScalar B, SkScalar t)
+{
+ SkASSERT(t >= 0 && t <= SK_Scalar1);
+ return A + SkScalarMul(B - A, t);
+}
+
+#endif
+