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;

}

space = int32(round(linspace(0,pi,128) * 2^16))

costable = int32(round(cos(linspace(0,pi,128)) * 2^16));

sintable = int32(round(sin(linspace(0,pi,128)) * 2^16));

space_file = fopen('space_table.txt', 'w');

cos_file = fopen('cos_table.txt', 'w');

sin_file = fopen('sin_table.txt', 'w');

for i=1:length(space)

	fprintf(space_file, '%d, ', space(i));

	if ~mod(i,8)

		fprintf(space_file, '\n');

	end

end

for i=1:length(costable)

	fprintf(cos_file, '%d, ', costable(i));

	if ~mod(i,8)

		fprintf(cos_file, '\n');

	end

end

for i=1:length(sintable)

	fprintf(sin_file, '%d, ', sintable(i));

	if ~mod(i,8)

		fprintf(sin_file, '\n');

	end

end

#ifndef _FP_MATH_H_

#define _FP_MATH_H_

#define FP_PI 205887

#define FP_TWO_PI 411775

#include <stdint.h>

int32_t fp_cos(int32_t theta);

int32_t fp_sin(int32_t theta);

int32_t fp_mult(int32_t a, int32_t b);

int32_t fp_div(int32_t a, int32_t b);

#endif

#include <serial.h>

#include <stdint.h>

#include "fp_math.h"

int main(int argc, char** argv) { 

	int32_t i,j;

	char buf[128];

	usb_init();

	usb_puts("USB Initialized\n\r");

	for(i=10000; i < 11000; i+=5) { 

		sprintf(buf, "fp_cos(%ld) = %ld\n\r", i,  fp_cos(i));

		usb_puts(buf);

	}

}

# this is a local makefile

# Relative path to the root directory (containing lib directory)

ifndef COLONYROOT

COLONYROOT := ..

# Target file name (without extension).

TARGET=main

# Uncomment this to use the wireless library

USE_WIRELESS = 1

# com1 = serial port. Use lpt1 to connect to parallel port.

AVRDUDE_PORT = $(shell if uname -s |grep -i w32 >/dev/null; then echo 'COM4:'; else echo '/dev/ttyUSB0'; fi)

AVRDUDE_PORT = /dev/tty.usbserial-A4001gUV

else

COLONYROOT := ../$(COLONYROOT)

endif

include $(COLONYROOT)/Makefile