llmath.h

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#ifndef LLMATH_H
#define LLMATH_H

// work around for Windows & older gcc non-standard function names.
#if LL_WINDOWS
#define llisnan(val)    _isnan(val)
#define llfinite(val)   _finite(val)
#elif (LL_LINUX && __GNUC__ <= 2)
#define llisnan(val)    isnan(val)
#define llfinite(val)   isfinite(val)
#elif LL_SOLARIS
#define llisnan(val)    isnan(val)
#define llfinite(val)   (val <= std::numeric_limits<double>::max())
#else
#define llisnan(val)    std::isnan(val)
#define llfinite(val)   std::isfinite(val)
#endif

// Single Precision Floating Point Routines
#ifndef fsqrtf
#define fsqrtf(x)               ((F32)sqrt((F64)(x)))
#endif
#ifndef sqrtf
#define sqrtf(x)                ((F32)sqrt((F64)(x)))
#endif

#ifndef cosf
#define cosf(x)         ((F32)cos((F64)(x)))
#endif
#ifndef sinf
#define sinf(x)         ((F32)sin((F64)(x)))
#endif
#ifndef tanf
#define tanf(x)         ((F32)tan((F64)(x)))
#endif
#ifndef acosf
#define acosf(x)                ((F32)acos((F64)(x)))
#endif

#ifndef powf
#define powf(x,y) ((F32)pow((F64)(x),(F64)(y)))
#endif

const F32       GRAVITY                 = -9.8f;

// mathematical constants
const F32       F_PI            = 3.1415926535897932384626433832795f;
const F32       F_TWO_PI        = 6.283185307179586476925286766559f;
const F32       F_PI_BY_TWO     = 1.5707963267948966192313216916398f;
const F32       F_SQRT2         = 1.4142135623730950488016887242097f;
const F32       F_SQRT3         = 1.73205080756888288657986402541f;
const F32       OO_SQRT2        = 0.7071067811865475244008443621049f;
const F32       DEG_TO_RAD      = 0.017453292519943295769236907684886f;
const F32       RAD_TO_DEG      = 57.295779513082320876798154814105f;
const F32       F_APPROXIMATELY_ZERO = 0.00001f;
const F32       F_LN2           = 0.69314718056f;
const F32       OO_LN2          = 1.4426950408889634073599246810019f;

// BUG: Eliminate in favor of F_APPROXIMATELY_ZERO above?
const F32 FP_MAG_THRESHOLD = 0.0000001f;

// TODO: Replace with logic like is_approx_equal
inline BOOL is_approx_zero( F32 f ) { return (-F_APPROXIMATELY_ZERO < f) && (f < F_APPROXIMATELY_ZERO); }

inline BOOL is_approx_equal(F32 x, F32 y)
{
        const S32 COMPARE_MANTISSA_UP_TO_BIT = 0x02;
        return (abs((S32) ((U32&)x - (U32&)y) ) < COMPARE_MANTISSA_UP_TO_BIT);
}

inline BOOL is_approx_equal_fraction(F32 x, F32 y, U32 frac_bits)
{
        BOOL ret = TRUE;
        F32 diff = (F32) fabs(x - y);

        S32 diffInt = (S32) diff;
        S32 diffFracTolerance = (S32) ((diff - (F32) diffInt) * (1 << frac_bits));
        
        // if integer portion is not equal, not enough bits were used for packing
        // so error out since either the use case is not correct OR there is
        // an issue with pack/unpack. should fail in either case.
        // for decimal portion, make sure that the delta is no more than 1
        // based on the number of bits used for packing decimal portion.
        if (diffInt != 0 || diffFracTolerance > 1)
        {
                ret = FALSE;
        }

        return ret;
}

inline S32 llabs(const S32 a)
{
        return S32(labs(a));
}

inline F32 llabs(const F32 a)
{
        return F32(fabs(a));
}

inline F64 llabs(const F64 a)
{
        return F64(fabs(a));
}

inline S32 lltrunc( F32 f )
{
#if LL_WINDOWS && !defined( __INTEL_COMPILER )
                // Avoids changing the floating point control word.
                // Add or subtract 0.5 - epsilon and then round
                const static U32 zpfp[] = { 0xBEFFFFFF, 0x3EFFFFFF };
                S32 result;
                __asm {
                        fld             f
                        mov             eax,    f
                        shr             eax,    29
                        and             eax,    4
                        fadd    dword ptr [zpfp + eax]
                        fistp   result
                }
                return result;
#else
                return (S32)f;
#endif
}

inline S32 lltrunc( F64 f )
{
        return (S32)f;
}

inline S32 llfloor( F32 f )
{
#if LL_WINDOWS && !defined( __INTEL_COMPILER )
                // Avoids changing the floating point control word.
                // Accurate (unlike Stereopsis version) for all values between S32_MIN and S32_MAX and slightly faster than Stereopsis version.
                // Add -(0.5 - epsilon) and then round
                const U32 zpfp = 0xBEFFFFFF;
                S32 result;
                __asm { 
                        fld             f
                        fadd    dword ptr [zpfp]
                        fistp   result
                }
                return result;
#else
                return (S32)floor(f);
#endif
}


inline S32 llceil( F32 f )
{
        // This could probably be optimized, but this works.
        return (S32)ceil(f);
}


#ifndef BOGUS_ROUND
// Use this round.  Does an arithmetic round (0.5 always rounds up)
inline S32 llround(const F32 val)
{
        return llfloor(val + 0.5f);
}

#else // BOGUS_ROUND
// Old llround implementation - does banker's round (toward nearest even in the case of a 0.5.
// Not using this because we don't have a consistent implementation on both platforms, use
// llfloor(val + 0.5f), which is consistent on all platforms.
inline S32 llround(const F32 val)
{
        #if LL_WINDOWS
                // Note: assumes that the floating point control word is set to rounding mode (the default)
                S32 ret_val;
                _asm fld        val
                _asm fistp      ret_val;
                return ret_val;
        #elif LL_LINUX
                // Note: assumes that the floating point control word is set
                // to rounding mode (the default)
                S32 ret_val;
                __asm__ __volatile__( "flds %1    \n\t"
                                                          "fistpl %0  \n\t"
                                                          : "=m" (ret_val)
                                                          : "m" (val) );
                return ret_val;
        #else
                return llfloor(val + 0.5f);
        #endif
}

// A fast arithmentic round on intel, from Laurent de Soras http://ldesoras.free.fr
inline int round_int(double x)
{
        const float round_to_nearest = 0.5f;
        int i;
        __asm
        {
                fld x
                fadd st, st (0)
                fadd round_to_nearest
                fistp i
                sar i, 1
        }
        return (i);
}
#endif // BOGUS_ROUND

inline F32 llround( F32 val, F32 nearest )
{
        return F32(floor(val * (1.0f / nearest) + 0.5f)) * nearest;
}

inline F64 llround( F64 val, F64 nearest )
{
        return F64(floor(val * (1.0 / nearest) + 0.5)) * nearest;
}

// these provide minimum peak error
//
// avg  error = -0.013049 
// peak error = -31.4 dB
// RMS  error = -28.1 dB

const F32 FAST_MAG_ALPHA = 0.960433870103f;
const F32 FAST_MAG_BETA = 0.397824734759f;

// these provide minimum RMS error
//
// avg  error = 0.000003 
// peak error = -32.6 dB
// RMS  error = -25.7 dB
//
//const F32 FAST_MAG_ALPHA = 0.948059448969f;
//const F32 FAST_MAG_BETA = 0.392699081699f;

inline F32 fastMagnitude(F32 a, F32 b)
{ 
        a = (a > 0) ? a : -a;
        b = (b > 0) ? b : -b;
        return(FAST_MAG_ALPHA * llmax(a,b) + FAST_MAG_BETA * llmin(a,b));
}



//
// Fast F32/S32 conversions
//
// Culled from www.stereopsis.com/FPU.html

const F64 LL_DOUBLE_TO_FIX_MAGIC        = 68719476736.0*1.5;     //2^36 * 1.5,  (52-_shiftamt=36) uses limited precisicion to floor
const S32 LL_SHIFT_AMOUNT                       = 16;                    //16.16 fixed point representation,

// Endian dependent code
#ifdef LL_LITTLE_ENDIAN
        #define LL_EXP_INDEX                            1
        #define LL_MAN_INDEX                            0
#else
        #define LL_EXP_INDEX                            0
        #define LL_MAN_INDEX                            1
#endif

/* Deprecated: use llround(), lltrunc(), or llfloor() instead
// ================================================================================================
// Real2Int
// ================================================================================================
inline S32 F64toS32(F64 val)
{
        val             = val + LL_DOUBLE_TO_FIX_MAGIC;
        return ((S32*)&val)[LL_MAN_INDEX] >> LL_SHIFT_AMOUNT; 
}

// ================================================================================================
// Real2Int
// ================================================================================================
inline S32 F32toS32(F32 val)
{
        return F64toS32 ((F64)val);
}
*/

//
// Fast exp and log
//

// Implementation of fast exp() approximation (from a paper by Nicol N. Schraudolph
// http://www.inf.ethz.ch/~schraudo/pubs/exp.pdf
static union
{
        double d;
        struct
        {
#ifdef LL_LITTLE_ENDIAN
                S32 j, i;
#else
                S32 i, j;
#endif
        } n;
} LLECO; // not sure what the name means

#define LL_EXP_A (1048576 * OO_LN2) // use 1512775 for integer
#define LL_EXP_C (60801)                        // this value of C good for -4 < y < 4

#define LL_FAST_EXP(y) (LLECO.n.i = llround(F32(LL_EXP_A*(y))) + (1072693248 - LL_EXP_C), LLECO.d)



inline F32 llfastpow(const F32 x, const F32 y)
{
        return (F32)(LL_FAST_EXP(y * log(x)));
}


inline F32 snap_to_sig_figs(F32 foo, S32 sig_figs)
{
        // compute the power of ten
        F32 bar = 1.f;
        for (S32 i = 0; i < sig_figs; i++)
        {
                bar *= 10.f;
        }

        foo = (F32)llround(foo * bar);

        // shift back
        foo /= bar;
        return foo;
}

inline F32 lerp(F32 a, F32 b, F32 u) 
{
        return a + ((b - a) * u);
}

inline F32 lerp2d(F32 x00, F32 x01, F32 x10, F32 x11, F32 u, F32 v)
{
        F32 a = x00 + (x01-x00)*u;
        F32 b = x10 + (x11-x10)*u;
        F32 r = a + (b-a)*v;
        return r;
}

inline F32 ramp(F32 x, F32 a, F32 b)
{
        return (a == b) ? 0.0f : ((a - x) / (a - b));
}

inline F32 rescale(F32 x, F32 x1, F32 x2, F32 y1, F32 y2)
{
        return lerp(y1, y2, ramp(x, x1, x2));
}

inline F32 clamp_rescale(F32 x, F32 x1, F32 x2, F32 y1, F32 y2)
{
        if (y1 < y2)
        {
                return llclamp(rescale(x,x1,x2,y1,y2),y1,y2);
        }
        else
        {
                return llclamp(rescale(x,x1,x2,y1,y2),y2,y1);
        }
}


inline F32 cubic_step( F32 x, F32 x0, F32 x1, F32 s0, F32 s1 )
{
        if (x <= x0)
                return s0;

        if (x >= x1)
                return s1;

        F32 f = (x - x0) / (x1 - x0);

        return  s0 + (s1 - s0) * (f * f) * (3.0f - 2.0f * f);
}

inline F32 cubic_step( F32 x )
{
        x = llclampf(x);

        return  (x * x) * (3.0f - 2.0f * x);
}

inline F32 quadratic_step( F32 x, F32 x0, F32 x1, F32 s0, F32 s1 )
{
        if (x <= x0)
                return s0;

        if (x >= x1)
                return s1;

        F32 f = (x - x0) / (x1 - x0);
        F32 f_squared = f * f;

        return  (s0 * (1.f - f_squared)) + ((s1 - s0) * f_squared);
}

inline F32 llsimple_angle(F32 angle)
{
        while(angle <= -F_PI)
                angle += F_TWO_PI;
        while(angle >  F_PI)
                angle -= F_TWO_PI;
        return angle;
}

#endif

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