/*
* 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_ScalarNegativeInfinity is defined to be negative infinity as an SkScalar
*/
#define SK_ScalarNegativeInfinity SK_FloatNegativeInfinity
/** 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;
}
#if defined(SK_DEBUG) && !defined(SK_BUILD_FOR_ANDROID)
/** 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_ScalarNegativeInfinity SK_FixedMin
#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