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"

/** \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;
    }

    /** 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)

    #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)

    /** 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 SkScalarTruncToInt(x)       (((x) < 0) ? SkScalarCeilToInt(x) : SkScalarFloorToInt(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