skia2/include/core/SkScalar.h

/*
 * 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"

//#define SK_SUPPORT_DEPRECATED_SCALARROUND

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;
}

/** 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)
#ifndef SK_SCALAR_TO_FLOAT_EXCLUDED
#define SkFloatToScalar(n)      (n)
#endif

#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)
#define SkScalarTruncToInt(x)       static_cast<int>(x)

/**
 *  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 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 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 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))
#define SkRadiansToDegrees(radians) ((radians) * (180 / SK_ScalarPI))
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;
}

// DEPRECATED : use ToInt or ToScalar variant
#ifdef SK_SUPPORT_DEPRECATED_SCALARROUND
#   define SkScalarFloor(x)    SkScalarFloorToInt(x)
#   define SkScalarCeil(x)     SkScalarCeilToInt(x)
#   define SkScalarRound(x)    SkScalarRoundToInt(x)
#endif

/**
 *  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 + (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