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/* This is a very incomplete version of libc math.h

 * Not all the funtions and Macros are implemented.

 * It has not been tested.

 * Special cases have not been catered for*/

/* globals */

const float M_PI=3.14159265359;

/*Taylor series approximation of Cosine function*/

float taylor(float angle){

    float old, approximation, sign, power, fact;

    unsigned count, i;

    approximation = 1.0;

    old = 0.0;

    sign = -1.0;

    count = 1;

    power = 1.0;

    fact = 1.0;

    for(i=2; approximation!=old; i+=2){

        old = approximation;

        while(count<=i){

            power*=angle;

            fact*=count;

            count++;

        }

        approximation += sign*(power/fact);

        sign = -sign;

    }

    return approximation;

}

/*return cos of angle in radians*/

float cos(float angle){

    return taylor(angle);

}

/*return sin of angle in radians*/

float sin(float angle){

    return cos(angle-(M_PI/2));

}

/*return tan of angle in radians*/

float tan(float n){

    return sin(n) / cos(n);

}

/* Return absolute value of a float n*/

float fabs(float n){

    if (n < 0.0) {

        return - n;

    } else {

        return n;

    }

}

/* Return absolute value of integer n*/

int abs(int n){

    if (n < 0) {

        return - n;

    } else {

        return n;

    }

}

/* return e ** x */

float exp(float x){

    float result = 1.0;

    unsigned n = 1;

    float power = 1.0;

    float factorial = 1.0;

    float old = 0.0;

    while(fabs(old - result) > 0.000001){

        old = result;

        power *= x;

        factorial *= n;

        result += (power/factorial);

        n++;

    }

    return result;

}

/* return log_e(n) */

float log(float n){

    float antilog, x, old;

    x = 10.0;

    old = 0.0;

    while(fabs(old - x) > 0.000001){

        old = x;

        antilog = exp(x);

        x -= (antilog - n)/antilog;

    }

    return x;

}

/* return log_10(n) */

float log10(float n){

    return log(n)/log(10);

}

/* return log_2(n) */

float log2(float n){

    return log(n)/log(2);

}