fmath.c

#include "flib.h"
#include "fmath.h"

static double atan2_lut[] = {
    3.141592653589793115998e+00,
    3.079082476590802919247e+00,
    3.053175508375344016088e+00,
    3.033286550313302409876e+00,
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    9.999247018391445029906e-01,
    9.999811752826011090889e-01,
};


static double sin_lut[] = {
    0.000000000000000000000e+00,
    6.135884649154475269095e-03,
    1.227153828571992538743e-02,
    1.840672990580482018541e-02,
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    4.293825693494082024193e-02,
    4.906767432741801493457e-02,
    5.519524434968993420458e-02,
    6.132073630220857829443e-02,
    6.744391956366405094236e-02,
    7.356456359966742630796e-02,
    7.968243797143012563389e-02,
    8.579731234443989384975e-02,
    9.190895649713272386183e-02,
    9.801714032956060362878e-02,
    1.041216338720545864227e-01,
    1.102222072938830593758e-01,
    1.163186309119047523453e-01,
    1.224106751992161956633e-01,
    1.284981107937931688046e-01,
    1.345807085071261677278e-01,
    1.406582393328492108786e-01,
    1.467304744553617479319e-01,
    1.527971852584434353517e-01,
    1.588581433338614457007e-01,
    1.649131204899699221222e-01,
    1.709618887603012171716e-01,
    1.770042204121487494639e-01,
    1.830398879551409507815e-01,
    1.890686641498061926203e-01,
    1.950903220161282480838e-01,
    2.011046348420919005484e-01,
    2.071113761922185603215e-01,
    2.131103199160913619359e-01,
    2.191012401568697975929e-01,
    2.250839113597928320409e-01,
    2.310581082806711095134e-01,
    2.370236059943671980133e-01,
    2.429801799032638709441e-01,
    2.489276057457201485335e-01,
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    2.667127574748983653841e-01,
    2.726213554499489766236e-01,
    2.785196893850530597270e-01,
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    2.902846772544623310530e-01,
    2.961508882436237888314e-01,
    3.020059493192280841711e-01,
    3.078496400415348666080e-01,
    3.136817403988915176072e-01,
    3.195020308160156918831e-01,
    3.253102921622629262188e-01,
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    3.426607173119943783313e-01,
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    3.541635254204903437980e-01,
    3.598950365349881108656e-01,
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    3.826834323650897817792e-01,
    3.883450466988262461676e-01,
    3.939920400610480988313e-01,
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    4.052413140049898609973e-01,
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    4.275550934302820849098e-01,
    4.330938188531519572599e-01,
    4.386162385385276585303e-01,
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    4.550835871263438359158e-01,
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    4.659764957679661812051e-01,
    4.713967368259976420397e-01,
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    4.875501601484359959215e-01,
    4.928981922297840378988e-01,
    4.982276669727818685374e-01,
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    6.006164793838689730521e-01,
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    6.103828062763094752796e-01,
    6.152315905806268192535e-01,
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    6.391244448637757313847e-01,
    6.438315428897913861306e-01,
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    6.531728429537767555146e-01,
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    7.572088465064844564623e-01,
    7.612023854842617787142e-01,
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    8.140363297059483027596e-01,
    8.175848131515837113881e-01,
    8.211025149911046483453e-01,
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    8.314696123025452356714e-01,
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};

double sqrt(double x)
{
    double r = 1 / q_rsqrt((float) x);
    return r;
}

double fmod(double dividend, double divisor)
{
#if 0
    double quotient = dividend / divisor;
    double integer = (double)(long long) quotient;
    double remainder = dividend - integer * divisor;
    return remainder;
#else
    double result;
    __asm__ (
             "fldl %1;   \n\t"  // load divisor into st(0)
             "fldl %2;   \n\t"  // load dividend into st(1)
             "fprem;     \n\t"  // compute dividend % divisor
             "fstpl %0;  \n\t"  // store result in output variable
             : "=m" (result)    // output
             : "m" (divisor), "m" (dividend) // inputs
             : "cc", "memory"  // clobbered registers
             );
    return result;
#endif
}

double atan2(double y, double x)
{
    // Calculate the normalized coordinates in the range [-1, 1]
    // double x_norm = x / sqrt(x * x + y * y);
    double x_norm = x * q_rsqrt(x * x + y * y);
    
    // int index = (int)((x_norm + 1.0) / 2.0 * array_length(atan2_lut));
    int index = (int)((x_norm + 1.0) * 0.5 * array_length(atan2_lut));
    
    return atan2_lut[index];
}

double cos(double angle)
{
    // normalize the angle to the lookup table range
    angle = fmod(angle, pi2);
    if (angle < 0.0)
        angle += pi2;
    
    int index = (int)(angle * pi2_inv * array_length(cos_lut));
    // int index = (int)(angle / (pi2) * array_length(cos_lut));
    
    return cos_lut[index];
}

double sin(double angle)
{
    // normalize the angle to the lookup table range
    angle = fmod(angle, pi2);
    if (angle < 0.0)
        angle += pi2;
    
    int index = (int)(angle * pi2_inv * array_length(sin_lut));
    // int index = (int)(angle / (pi2) * array_length(sin_lut));
    
    return sin_lut[index];
}