#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include <sys/time.h>

#define PI 3.14159265358979
#define LENGTH 32
#define MILLISECOND 1000000.0

//computes sin(x) using the CORDIC algorithm
float cordicSin(float x);

//computes sin(x) using a truncated Maclaurin polynomial of order 6
// sin(x) = x - (x^3)/6 + x^5/120
double maclaurinPoly(double x);

//converts a float to binary
unsigned int floatToBin(float x);

//prints bin as binary 0's and 1's
int binPrint(unsigned int bin);

//recursive method for solving sin
// argument "bin" is binary representing floating point number
//     example  if float is 0.5  then   bin =  1
//				if float is 0.25 then   bin = 2
//
//  sin(a+b) = sin(a) cos(b) + cos(a) sin (b)
//     where sin(a), and cos(a) are retrieved from a table of pre-calculated sines and cosines
//     cos(b), and sin(b) are called recursivly
float sinRec(unsigned int bin);

//recursive method for solving cos
// argument "bin" is binary representing floating point number
//     example  if float is 0.75   then   bin =  3
//				if float is 0.125  then   bin =  4
//
//  cos(a+b) = cos(a) cos(b) - sin(a) sin(b)
//     where sin(a), and cos(a) are retrieved from a table of pre-calculated sines and cosines
//     cos(b), and sin(b) are called recursivly
float cosRec(unsigned int bin);