#include "Header.h"

// sins[i] = sin(1/2^(i+1))
// 32 values
float sins[] = {
4.794255e-01, 2.474040e-01, 1.246747e-01, 6.245932e-02, 
3.124491e-02, 1.562436e-02, 7.812420e-03, 3.906240e-03, 
1.953124e-03, 9.765623e-04, 4.882812e-04, 2.441406e-04, 
1.220703e-04, 6.103516e-05, 3.051758e-05, 1.525879e-05, 
7.629395e-06, 3.814697e-06, 1.907349e-06, 9.536743e-07, 
4.768372e-07, 2.384186e-07, 1.192093e-07, 5.960464e-08, 
2.980232e-08, 1.490116e-08, 7.450581e-09, 3.725290e-09, 
1.862645e-09, 9.313226e-10, 4.656613e-10, 2.328306e-10};

// coss[i] = cos(1/2^(i+1))
// 32 values
float coss[] = {
8.775826e-01, 9.689124e-01, 9.921977e-01, 9.980475e-01, 
9.995118e-01, 9.998779e-01, 9.999695e-01, 9.999924e-01, 
9.999981e-01, 9.999995e-01, 9.999999e-01, 1.0,
1.0,          1.0,          1.0,          1.0,
1.0,          1.0,          1.0,          1.0,
1.0,          1.0,          1.0,          1.0,
1.0,          1.0,          1.0,          1.0,
1.0,          1.0,          1.0,          1.0};
				
//converts a float to binary
unsigned int floatToBin(float x)
{
	int i;
	unsigned int bit, bin =0;
	float reminder = x;
	if(x <0.0 || x>=1.0)
	{
		printf("input (%g) is out of range. Input must be >= 0 and < 1\n", x);
		exit(1);
	}
	for(i =0; i < LENGTH; i++)
	{
		reminder *= 2.0;
		bit = (unsigned int) reminder;
		bin |= (bit<<i);
		reminder -= bit;
	}
	return bin;
}

//prints bin as binary 0's and 1's
int binPrint(unsigned int bin)
{
	int i;
	unsigned int bit, mask =1;
	for(i=0; i < LENGTH; i++)
	{
		bit = (bin>>i) & mask;
		if(i%4 ==0) printf("  ");
		printf("%u", bit);
	}
	printf("\n");
	
	return 0;
}

//recursive method for solving sin
//  sin(a+b) = sin(a) cos(b) + cos(a) sin (b)
//
// see Header.h for more details...
float sinRec(unsigned int bin)
{
	//base case when there is no more bits
	if(bin == 0)
		return 0;
	else //there are still bits
	{
		unsigned int i = 1;
		int j = 0;
		//find the first bit
		while((bin & i) == 0)
		{
			i = i << 1;
			j++;
		}
		//remove the bit from bin
		bin = bin ^ i;
		return (sins[j] * cosRec(bin)) + (coss[j] * sinRec(bin));
	}
}

//recursive method for solving cos
//  cos(a+b) = cos(a) cos(b) - sin(a) sin(b)
//
// see Header.h for more details...
float cosRec(unsigned int bin)
{
	//base case when there is no more bits
	if(bin == 0)
		return 1;
	else //there are still bits
	{
		unsigned int i = 1;
		int j = 0;
		//find the first bit
		while((bin & i) == 0)
		{
			i = i << 1;
			j++;
		}
		//remove the bit from bin
		bin = bin ^ i;
		return (coss[j] * cosRec(bin)) - (sins[j] * sinRec(bin));
	}
}

//computes sin of num using cordic
float cordicSin(float num)
{
	//convert float to binary, then computes sin
	return sinRec(floatToBin(num));
}