CWE-ou-minkata/Sources/Plasma/CoreLib/hsFastMath.h

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*==LICENSE==*/

#ifndef hsFastMath_inc
#define hsFastMath_inc

#include "hsPoint2.h"
#include "hsGeometry3.h"

class hsFastMath {
protected:
    static const hsPoint2* fCosSinTable;

public:
    static const hsScalar kSqrtTwo;
    static const hsScalar kInvSqrtTwo;
    static const hsScalar kTwoPI;

    static hsScalar IATan2OverTwoPi(hsScalar y, hsScalar x);

    static inline hsScalar InvSqrtAppr(hsScalar x);
    static inline hsScalar InvSqrt(hsScalar x);
    static inline hsVector3& Normalize(hsVector3& v) { return (v *= InvSqrt(v.MagnitudeSquared())); }
    static inline hsVector3& NormalizeAppr(hsVector3& v) { return (v *= InvSqrtAppr(v.MagnitudeSquared())); }

    static inline void SinCosAppr(hsScalar rads, hsScalar& sinRads, hsScalar& cosRads);
    static inline void SinCosInRangeAppr(hsScalar rads, hsScalar& sinRads, hsScalar& cosRads);

    static inline void SinCos(hsScalar rads, hsScalar& sinRads, hsScalar& cosRads);
    static inline void SinCosInRange(hsScalar ang, hsScalar& sinRads, hsScalar& cosRads);

    static inline hsScalar Sin(hsScalar rads);
    static inline hsScalar Cos(hsScalar rads);
    static inline hsScalar SinInRange(hsScalar rads);
    static inline hsScalar CosInRange(hsScalar rads);
};


// One over Square Root - from Graphics Gems
// Interesting combo's are
// NUM_ITER     LOOKUP_BITS         err frac    us per call
// 0            8                   5e-3        0.045
// 1            8                   3e-5        0.082
// 0            6                   1e-2        0.045
// 1            6                   1e-4        0.082
// 2            6                   1e-7        0.11
// 1            4                   2e-3        0.082
// 2            4                   5e-6        0.11
// 2            3                   8e-5        0.11
// Tested on 5000 random numbers from [1.e-6..1.e3] over several runs
// These are tight loops, though, so they don't weigh in a bigger
// table trashing the cache.
#define NUM_ITER        0
#define LOOKUP_BITS     8
#define EXP_POS         23
#define EXP_BIAS        127

#define LOOKUP_POS      (EXP_POS - LOOKUP_BITS)
#define SEED_POS        (EXP_POS - 8)
#define TABLE_SIZE      (2 << LOOKUP_BITS)
#define LOOKUP_MASK     (TABLE_SIZE - 1)
#define GET_EXP(a)      (((a) >> EXP_POS) & 0xff)
#define SET_EXP(a)      ((a) << EXP_POS)
#define GET_EMANT(a)    (((a) >> LOOKUP_POS) & LOOKUP_MASK)

#define SET_MANTSEED(a) (((unsigned long) (a)) << SEED_POS)

inline hsScalar hsFastMath::InvSqrtAppr(hsScalar x)
{
    register unsigned long a = *(long*)&x;
    register float arg = x;
    union {
        long    i;
        float   f;
    } seed;
    register float r;

    extern unsigned char statSeedTable[];

    seed.i = SET_EXP(((3*EXP_BIAS - 1) - GET_EXP(a)) >> 1) | SET_MANTSEED(statSeedTable[GET_EMANT(a)]);

    r = seed.f;

#if NUM_ITER > 0
    r = (3.0f - r * r * arg) * r * 0.5f;

#if NUM_ITER > 1
    r = (3.0f - r * r * arg) * r * 0.5f;
#endif
#endif

    return r;
}

inline hsScalar hsFastMath::InvSqrt(hsScalar x)
{
    register unsigned long a = *(long*)&x;
    register float arg = x;
    union {
        long    i;
        float   f;
    } seed;
    register float r;

    extern unsigned char statSeedTable[];

    seed.i = SET_EXP(((3*EXP_BIAS - 1) - GET_EXP(a)) >> 1) | SET_MANTSEED(statSeedTable[GET_EMANT(a)]);

    r = seed.f;

    r = (3.0f - r * r * arg) * r * 0.5f;

    r = (3.0f - r * r * arg) * r * 0.5f;

    return r;
}


inline void hsFastMath::SinCosAppr(hsScalar rads, hsScalar& sinRads, hsScalar& cosRads)
{
    rads = fmodf(rads, kTwoPI);
    if( rads < 0 )
        rads += kTwoPI;
    SinCosInRangeAppr(rads, sinRads, cosRads);
}

inline void hsFastMath::SinCosInRangeAppr(hsScalar rads, hsScalar& sinRads, hsScalar& cosRads)
{
    const int kNumSinCosEntries = 8;
    const hsScalar kNumEntriesOverTwoPI = kNumSinCosEntries * 0.5f / hsScalarPI;
    hsScalar t = rads * kNumEntriesOverTwoPI;
    int iLo = (int)t;
    t -= iLo;

    const hsPoint2* p = &fCosSinTable[iLo + 1];
    cosRads = p->fX;
    sinRads = p->fY;
    p--;
    cosRads -= p->fX;
    sinRads -= p->fY;
    cosRads *= t;
    sinRads *= t;
    cosRads += p->fX;
    sinRads += p->fY;

}

inline hsScalar hsFastMath::Sin(hsScalar rads)
{
    rads = fmodf(rads, kTwoPI);
    if( rads < 0 )
        rads += kTwoPI;

    return SinInRange(rads);
}

inline hsScalar hsFastMath::Cos(hsScalar rads)
{
    rads = fmodf(rads, kTwoPI);
    if( rads < 0 )
        rads += kTwoPI;

    return CosInRange(rads);
}

inline hsScalar hsFastMath::SinInRange(hsScalar ang)
{
    float sgn = 1.f;

    if(ang >= (0.75f * kTwoPI))
        ang -= kTwoPI;
    else if(ang >= (0.25f * kTwoPI))
    {
        ang -= 3.141592654f;
        sgn = -1.0f;
    }
    
    return (ang - (ang*ang*ang) * (1.0f/6.0f) + (ang*ang*ang*ang*ang) / 120.0f) * sgn;
}

inline hsScalar hsFastMath::CosInRange(hsScalar ang)
{
    float sgn = 1.f;
    
    if(ang >= (0.75f * kTwoPI))
        ang -= kTwoPI;
    else if(ang >= (0.25f * kTwoPI))
    {
        ang -= 3.141592654f;
        sgn = -1.0f;
    }
    
    return (1.0f - (ang*ang / 2.0f) + (ang*ang*ang*ang) / 24.0f) *sgn;
}

inline void hsFastMath::SinCos(hsScalar rads, hsScalar& sinRads, hsScalar& cosRads)
{
    rads = fmodf(rads, kTwoPI);
    if( rads < 0 )
        rads += kTwoPI;
    SinCosInRange(rads, sinRads, cosRads);
}

inline void hsFastMath::SinCosInRange(hsScalar ang, hsScalar& sinRads, hsScalar& cosRads)
{
    float sgn = 1.f;
    
    if(ang >= (0.75f * kTwoPI))
        ang -= kTwoPI;
    else if(ang >= (0.25f * kTwoPI))
    {
        ang -= 3.141592654f;
        sgn = -1.0f;
    }
    
    sinRads = (ang - (ang*ang*ang) * (1.0f/6.0f) + (ang*ang*ang*ang*ang) / 120.0f) * sgn;
    cosRads = (1.0f - (ang*ang / 2.0f) + (ang*ang*ang*ang) / 24.0f) *sgn;
}
//
// Here's an interesting one from GDalgorithms, which doesn't need a LUT
// Not sure how the accuracy compares, but it's probably fine for this purpose.
#if 0 // For future reference
/*
From: "Jason Dorie" <jason.dorie@blackboxgames.com>
To: "GDAlgorithms" <gdalgorithms-list@lists.sourceforge.net>
Date: Wed, 14 Mar 2001 11:43:48 -0800
Subject: [Algorithms] Fast simultaneous Sin() and Cos()
Reply-To: gdalgorithms-list@lists.sourceforge.net


  I know someone (Jason Zisk?) was looking for fast rotation matrix
generation code.  I realize that a Sin/Cos lookup table is the way to go for
absolute speed, but if storage is a concern and the accuracy isn't, this
code is about 5x faster than using the built-in sin and cos instructions,
and accurate to about 4 decimal places.

  If you really want speed, and don't care about accuracy, drop the 2nd
polynomial from each term.  It's less accurate and faster still.  It could
probably be made even faster by replacing the if/else with branchless code,
but I haven't bothered to figure out how yet.


  My angles are 0-65535 so that they can be masked into range easily, stored
as shorts, and converted to normalized floats where necessary using SIMD
instructions.
*/

void FastSinCos(long Angle, float *pSin, float *pCos)
{
float ang, sgn;

        ang = (Angle & 65535) * ((1.0f/65536.0f) * TwoPI);

        sgn = 1.0f;
        if(ang >= (0.75f * TwoPI))
                ang -= TwoPI;
        else if(ang >= (0.25f * TwoPI))
        {
                ang -= 3.141592654f;
                sgn = -1.0f;
        }

        *pSin = (ang - (ang*ang*ang) * (1.0f/6.0f) + (ang*ang*ang*ang*ang) / 120.0f) * sgn;
        *pCos = (1.0f - (ang*ang / 2.0f) + (ang*ang*ang*ang) / 24.0f) *sgn;
}
#endif // For future reference
#endif // hsFastMath_inc