Colony

#include "fp_math.h"

#include <avr/pgmspace.h>

#include <math.h>

#include <serial.h>

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

#define TABLE_LENGTH 128

#define TABLE_STEP 1621//.160757

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,

        103754, 105375, 106997, 108618, 110239, 111860, 113481, 115102,

        116724, 118345, 119966, 121587, 123208, 124829, 126451, 128072,

        129693, 131314, 132935, 134556, 136178, 137799, 139420, 141041,

        142662, 144283, 145904, 147526, 149147, 150768, 152389, 154010,

        155631, 157253, 158874, 160495, 162116, 163737, 165358, 166980,

        168601, 170222, 171843, 173464, 175085, 176707, 178328, 179949,

        181570, 183191, 184812, 186433, 188055, 189676, 191297, 192918,

        194539, 196160, 197782, 199403, 201024, 202645, 204266, 205887

};

static int32_t 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,

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

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

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

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

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

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

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

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

};

static int32_t sin_table[TABLE_LENGTH] PROGMEM = {

        0, 1621, 3241, 4859, 6474, 8085, 9691, 11292,

        12885, 14470, 16047, 17614, 19169, 20714, 22245, 23763,

        25267, 26755, 28226, 29680, 31117, 32534, 33931, 35307,

        36662, 37995, 39304, 40589, 41849, 43084, 44292, 45473,

        46627, 47751, 48847, 49913, 50948, 51952, 52924, 53864,

        54771, 55644, 56484, 57288, 58058, 58792, 59491, 60152,

        60777, 61365, 61915, 62428, 62902, 63338, 63735, 64093,

        64411, 64691, 64930, 65130, 65291, 65411, 65491, 65531,

        65531, 65491, 65411, 65291, 65130, 64930, 64691, 64411,

        64093, 63735, 63338, 62902, 62428, 61915, 61365, 60777,

        60152, 59491, 58792, 58058, 57288, 56484, 55644, 54771,

        53864, 52924, 51952, 50948, 49913, 48847, 47751, 46627,

        45473, 44292, 43084, 41849, 40589, 39304, 37995, 36662,

        35307, 33931, 32534, 31117, 29680, 28226, 26755, 25267,

        23763, 22245, 20714, 19169, 17614, 16047, 14470, 12885,

        11292, 9691, 8085, 6474, 4859, 3241, 1621, 0

};

//Quadratic interpolation.

int32_t fp_cos(int32_t theta) {

        uint8_t n;

        int32_t x_n, x_np1, x_np2;

        int32_t y_n, y_np1, y_np2;

        int32_t dd_n, dd_np1, second_dd;

        //Move theta into [0, pi]

        theta = ABS(theta) % FP_TWO_PI;

        if(theta > FP_PI)

                theta = FP_TWO_PI - theta;

        //Find the nearest table values. FIXME

        n = theta / TABLE_STEP;

        while((x_np1 = pgm_read_dword(&linspace[n+1])) < theta) n++;

        usb_puti(n);

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

        //Address edge cases.

        if(n == 0) {

                //TODO

        }

        if(n == TABLE_LENGTH - 1) {

                //TODO

        }

        //Address the general case. Quadratic interpolation.

        //Load in the necessary values.

        x_n = pgm_read_dword(&linspace[n]);

        x_np1 = pgm_read_dword(&linspace[n + 1]);

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

        y_n = pgm_read_dword(&cos_table[n]);

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

        y_np2 = pgm_read_dword(&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);

        return fp_mult(fp_mult(second_dd, theta - x_n), theta - x_np1)

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

}

//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;

}