include/core/SkScalar.h - skia - Git at Google

 /*
  * 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 "include/private/SkFloatingPoint.h"

 #undef SK_SCALAR_IS_FLOAT
 #define SK_SCALAR_IS_FLOAT  1

 typedef float SkScalar;

 #define SK_Scalar1                  1.0f
 #define SK_ScalarHalf               0.5f
 #define SK_ScalarSqrt2              SK_FloatSqrt2
 #define SK_ScalarPI                 SK_FloatPI
 #define SK_ScalarTanPIOver8         0.414213562f
 #define SK_ScalarRoot2Over2         0.707106781f
 #define SK_ScalarMax                3.402823466e+38f
 #define SK_ScalarInfinity           SK_FloatInfinity
 #define SK_ScalarNegativeInfinity   SK_FloatNegativeInfinity
 #define SK_ScalarNaN                SK_FloatNaN

 #define SkScalarFloorToScalar(x)    sk_float_floor(x)
 #define SkScalarCeilToScalar(x)     sk_float_ceil(x)
 #define SkScalarRoundToScalar(x)    sk_float_floor((x) + 0.5f)
 #define SkScalarTruncToScalar(x)    sk_float_trunc(x)

 #define SkScalarFloorToInt(x)       sk_float_floor2int(x)
 #define SkScalarCeilToInt(x)        sk_float_ceil2int(x)
 #define SkScalarRoundToInt(x)       sk_float_round2int(x)

 #define SkScalarAbs(x)              sk_float_abs(x)
 #define SkScalarCopySign(x, y)      sk_float_copysign(x, y)
 #define SkScalarMod(x, y)           sk_float_mod(x,y)
 #define SkScalarSqrt(x)             sk_float_sqrt(x)
 #define SkScalarPow(b, e)           sk_float_pow(b, e)

 #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)
 #define SkScalarLog2(x)             (float)sk_float_log2(x)

 //////////////////////////////////////////////////////////////////////////////////////////////////

 #define SkIntToScalar(x)        static_cast<SkScalar>(x)
 #define SkIntToFloat(x)         static_cast<float>(x)
 #define SkScalarTruncToInt(x)   sk_float_saturate2int(x)

 #define SkScalarToFloat(x)      static_cast<float>(x)
 #define SkFloatToScalar(x)      static_cast<SkScalar>(x)
 #define SkScalarToDouble(x)     static_cast<double>(x)
 #define SkDoubleToScalar(x)     sk_double_to_float(x)

 #define SK_ScalarMin            (-SK_ScalarMax)

 static inline bool SkScalarIsNaN(SkScalar x) { return x != x; }

 /** Returns true if x is not NaN and not infinite
  */
 static inline bool SkScalarIsFinite(SkScalar x) { return sk_float_isfinite(x); }

 static inline bool SkScalarsAreFinite(SkScalar a, SkScalar b) {
     return sk_floats_are_finite(a, b);
 }

 static inline bool SkScalarsAreFinite(const SkScalar array[], int count) {
     return sk_floats_are_finite(array, count);
 }

 /**
  *  Variant of SkScalarRoundToInt, that performs the rounding step (adding 0.5) explicitly using
  *  double, to avoid possibly losing the low bit(s) of the answer before calling floor().
  *
  *  This routine will likely be slower than SkScalarRoundToInt(), and should only be used when the
  *  extra precision is known to be valuable.
  *
  *  In particular, this catches the following case:
  *      SkScalar x = 0.49999997;
  *      int ix = SkScalarRoundToInt(x);
  *      SkASSERT(0 == ix);    // <--- fails
  *      ix = SkDScalarRoundToInt(x);
  *      SkASSERT(0 == ix);    // <--- succeeds
  */
 static inline int SkDScalarRoundToInt(SkScalar x) {
     double xx = x;
     xx += 0.5;
     return (int)floor(xx);
 }

 /** Returns the fractional part of the scalar. */
 static inline SkScalar SkScalarFraction(SkScalar x) {
     return x - SkScalarTruncToScalar(x);
 }

 static inline SkScalar SkScalarSquare(SkScalar x) { return x * x; }

 #define SkScalarInvert(x)           sk_ieee_float_divide_TODO_IS_DIVIDE_BY_ZERO_SAFE_HERE(SK_Scalar1, (x))
 #define SkScalarAve(a, b)           (((a) + (b)) * SK_ScalarHalf)
 #define SkScalarHalf(a)             ((a) * SK_ScalarHalf)

 #define SkDegreesToRadians(degrees) ((degrees) * (SK_ScalarPI / 180))
 #define SkRadiansToDegrees(radians) ((radians) * (180 / SK_ScalarPI))

 static inline bool SkScalarIsInt(SkScalar x) {
     return x == SkScalarFloorToScalar(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;
 }

 static inline float SkScalarSinSnapToZero(SkScalar radians) {
     float v = SkScalarSin(radians);
     return SkScalarNearlyZero(v) ? 0.0f : v;
 }

 static inline float SkScalarCosSnapToZero(SkScalar radians) {
     float v = SkScalarCos(radians);
     return SkScalarNearlyZero(v) ? 0.0f : v;
 }

 /** 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 + (B - A) * t;
 }

 /** 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) {
     SkASSERT(n >= 0);
     for (int i = 0; i < n; ++i) {
         if (a[i] != b[i]) {
             return false;
         }
     }
     return true;
 }

 #endif
	/*
	* 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 "include/private/SkFloatingPoint.h"

	#undef SK_SCALAR_IS_FLOAT
	#define SK_SCALAR_IS_FLOAT 1

	typedef float SkScalar;

	#define SK_Scalar1 1.0f
	#define SK_ScalarHalf 0.5f
	#define SK_ScalarSqrt2 SK_FloatSqrt2
	#define SK_ScalarPI SK_FloatPI
	#define SK_ScalarTanPIOver8 0.414213562f
	#define SK_ScalarRoot2Over2 0.707106781f
	#define SK_ScalarMax 3.402823466e+38f
	#define SK_ScalarInfinity SK_FloatInfinity
	#define SK_ScalarNegativeInfinity SK_FloatNegativeInfinity
	#define SK_ScalarNaN SK_FloatNaN

	#define SkScalarFloorToScalar(x) sk_float_floor(x)
	#define SkScalarCeilToScalar(x) sk_float_ceil(x)
	#define SkScalarRoundToScalar(x) sk_float_floor((x) + 0.5f)
	#define SkScalarTruncToScalar(x) sk_float_trunc(x)

	#define SkScalarFloorToInt(x) sk_float_floor2int(x)
	#define SkScalarCeilToInt(x) sk_float_ceil2int(x)
	#define SkScalarRoundToInt(x) sk_float_round2int(x)

	#define SkScalarAbs(x) sk_float_abs(x)
	#define SkScalarCopySign(x, y) sk_float_copysign(x, y)
	#define SkScalarMod(x, y) sk_float_mod(x,y)
	#define SkScalarSqrt(x) sk_float_sqrt(x)
	#define SkScalarPow(b, e) sk_float_pow(b, e)

	#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)
	#define SkScalarLog2(x) (float)sk_float_log2(x)

	//////////////////////////////////////////////////////////////////////////////////////////////////

	#define SkIntToScalar(x) static_cast<SkScalar>(x)
	#define SkIntToFloat(x) static_cast<float>(x)
	#define SkScalarTruncToInt(x) sk_float_saturate2int(x)

	#define SkScalarToFloat(x) static_cast<float>(x)
	#define SkFloatToScalar(x) static_cast<SkScalar>(x)
	#define SkScalarToDouble(x) static_cast<double>(x)
	#define SkDoubleToScalar(x) sk_double_to_float(x)

	#define SK_ScalarMin (-SK_ScalarMax)

	static inline bool SkScalarIsNaN(SkScalar x) { return x != x; }

	/** Returns true if x is not NaN and not infinite
	*/
	static inline bool SkScalarIsFinite(SkScalar x) { return sk_float_isfinite(x); }

	static inline bool SkScalarsAreFinite(SkScalar a, SkScalar b) {
	return sk_floats_are_finite(a, b);
	}

	static inline bool SkScalarsAreFinite(const SkScalar array[], int count) {
	return sk_floats_are_finite(array, count);
	}

	/**
	* Variant of SkScalarRoundToInt, that performs the rounding step (adding 0.5) explicitly using
	* double, to avoid possibly losing the low bit(s) of the answer before calling floor().
	*
	* This routine will likely be slower than SkScalarRoundToInt(), and should only be used when the
	* extra precision is known to be valuable.
	*
	* In particular, this catches the following case:
	* SkScalar x = 0.49999997;
	* int ix = SkScalarRoundToInt(x);
	* SkASSERT(0 == ix); // <--- fails
	* ix = SkDScalarRoundToInt(x);
	* SkASSERT(0 == ix); // <--- succeeds
	*/
	static inline int SkDScalarRoundToInt(SkScalar x) {
	double xx = x;
	xx += 0.5;
	return (int)floor(xx);
	}

	/** Returns the fractional part of the scalar. */
	static inline SkScalar SkScalarFraction(SkScalar x) {
	return x - SkScalarTruncToScalar(x);
	}

	static inline SkScalar SkScalarSquare(SkScalar x) { return x * x; }

	#define SkScalarInvert(x) sk_ieee_float_divide_TODO_IS_DIVIDE_BY_ZERO_SAFE_HERE(SK_Scalar1, (x))
	#define SkScalarAve(a, b) (((a) + (b)) * SK_ScalarHalf)
	#define SkScalarHalf(a) ((a) * SK_ScalarHalf)

	#define SkDegreesToRadians(degrees) ((degrees) * (SK_ScalarPI / 180))
	#define SkRadiansToDegrees(radians) ((radians) * (180 / SK_ScalarPI))

	static inline bool SkScalarIsInt(SkScalar x) {
	return x == SkScalarFloorToScalar(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;
	}

	static inline float SkScalarSinSnapToZero(SkScalar radians) {
	float v = SkScalarSin(radians);
	return SkScalarNearlyZero(v) ? 0.0f : v;
	}

	static inline float SkScalarCosSnapToZero(SkScalar radians) {
	float v = SkScalarCos(radians);
	return SkScalarNearlyZero(v) ? 0.0f : v;
	}

	/** 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 + (B - A) * t;
	}

	/** 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) {
	SkASSERT(n >= 0);
	for (int i = 0; i < n; ++i) {
	if (a[i] != b[i]) {
	return false;
	}
	}
	return true;
	}

	#endif