Colony

#include "fp_math.h"

#include <avr/pgmspace.h>

#include <math.h>

#include <serial.h>

#define ABS(x) (x > 0 ? x : -x)

#define FP_PI_OVER_TWO 102944

#define FP_TWO_PI 411775

#define TABLE_LENGTH 64

#define TABLE_STEP 1621//.160757

#define EXP_MAGICONSTANT

static int32_t linspace[TABLE_LENGTH] PROGMEM = { 

        0, 1621, 3242, 4863, 6485, 8106, 9727, 11348, 

        12969, 14590, 16212, 17833, 19454, 21075, 22696, 24317, 

        25939, 27560, 29181, 30802, 32423, 34044, 35666, 37287, 

        38908, 40529, 42150, 43771, 45393, 47014, 48635, 50256, 

        51877, 53498, 55119, 56741, 58362, 59983, 61604, 63225, 

        64846, 66468, 68089, 69710, 71331, 72952, 74573, 76195, 

        77816, 79437, 81058, 82679, 84300, 85922, 87543, 89164, 

        90785, 92406, 94027, 95648, 97270, 98891, 100512, 102133

};

static int32_t fp_cos_table[TABLE_LENGTH] PROGMEM = {

        65536, 65516, 65456, 65356, 65215, 65035, 64815, 64556, 

        64257, 63919, 63541, 63125, 62670, 62176, 61645, 61076, 

        60470, 59826, 59146, 58430, 57678, 56890, 56068, 55212, 

        54322, 53398, 52442, 51454, 50434, 49384, 48303, 47193, 

        46053, 44886, 43691, 42470, 41222, 39949, 38652, 37331, 

        35988, 34622, 33235, 31828, 30401, 28956, 27492, 26013, 

        24517, 23006, 21481, 19943, 18393, 16831, 15260, 13679, 

        12089, 10492, 8889, 7280, 5667, 4050, 2431, 811

};

//FIXME Lazy implementations of tangent and sine.

int32_t fp_tan(int32_t theta) { 

        return fp_div(fp_sin(theta), fp_cos(theta));

}

int32_t fp_sin(int32_t theta) { 

        return fp_cos(theta + FP_PI_OVER_TWO);

}

int32_t fp_exp(int32_t x) { 

        //Try with partial fractions for now.

        int32_t xsquare = fp_mult(x,x);

        int32_t result, i;

        if(theta > EXP_MAGICONSTANT) { 

                usb_puts("Output value is out of range.\n\r");

                return -1;

        }

        //This is again, massive amounts of lazyness.

        //The approximation fails outside this range (approximately).

        if(theta < -17)

                return 0;

        result = xsquare;

        for(i= (22 << 16); i > (2 << 16); i-= (4 << 16)) { 

                result += i;

                result = fp_div(xsquare, result);

        }

        result += (2 << 16) - x;

        return (1 << 16) + fp_div(fp_mult((2 << 16), x), result);

}

//Quadratic interpolation.

int32_t fp_cos(int32_t theta) { 

        uint8_t n;        

        int8_t negative;

        int32_t x_n, x_np1, x_np2;

        int32_t y_n, y_np1, y_np2;

        int32_t dd_n, dd_np1, second_dd, result;

        //Move theta into [0, pi/2] w/ appropriate sign.

        theta = ABS(theta) % FP_TWO_PI; 

        if(theta > FP_PI) 

                theta = FP_TWO_PI - theta;

        if(theta > FP_PI_OVER_TWO) {

                theta = FP_PI - theta;

                negative = 1;

        }

        //Find the nearest table values. FIXME

        n = theta / TABLE_STEP;

        while( n < TABLE_LENGTH - 1 && (x_np1 = pgm_read_dword(&linspace[n+1]))) 

                n++;

        //theta is between x_{n} and x_{n+1}

        if(n == TABLE_LENGTH - 1) { 

                //Perform linear interpolation, since we're close to zero anyway.

                x_n = pgm_read_dword(&linspace[TABLE_LENGTH - 1]);

                y_n = pgm_read_dword(&fp_cos_table[TABLE_LENGTH - 1]);

                result = fp_mult(fp_div(FP_PI_OVER_TWO - x_n, 0 - y_n), theta - x_n) + y_n;

                return negative ? -result : result;

        }

        if(n == TABLE_LENGTH) { 

                //We didn't find a value! Oh no!

                usb_puts("fp_math: We couldn't find surrounding table values! \n\r

                                  This should never happen!!!\n\r\n\r");

                return 0;

        }

        //Address the general case. Quadratic interpolation.

        //Load in the necessary values.

        x_n = pgm_read_dword(&linspace[n]);

        x_np2  = pgm_read_dword(&linspace[n + 2]);

        y_n = pgm_read_dword(&fp_cos_table[n]);

        y_np1 = pgm_read_dword(&fp_cos_table[n + 1]);

        y_np2 = pgm_read_dword(&fp_cos_table[n + 2]);

        //Calculate first divided differences.

        dd_n = fp_div(y_np1 - y_n, x_np1 - x_n);

        dd_np1 = fp_div(y_np2 - y_np1, x_np2 - x_np1);

        //Calculate the second divided difference.

        second_dd = fp_div(dd_np1 - dd_n, x_np2 - x_n);

        result = fp_mult(fp_mult(second_dd, theta - x_n), theta - x_np1)  

                           + fp_mult(dd_n, theta - x_n) + y_n;

        return negative ? -result : result;

}

//FIXME I didn't write these functions very carefully...

int32_t fp_mult(int32_t a, int32_t b) { 

        return (int32_t) (((int64_t)a) * ((int64_t)b)) >>  16;

}

int32_t fp_div(int32_t a, int32_t b) { 

        return (int32_t) ((int64_t)a << 16) / (int64_t)b;

}