This code computes sin using three ways.

FIRST:	cordic algorithm
		sin(a+b) = sin(a) cos(b) + cos(a) sin (b)
		cos(a+b) = cos(a) cos(b) - sin(a) sin(b)

SECOND:	Truncated Maclaurin polynomial of order 6  
			sin(x) = x - (x^3)/6 + x^5/120

THIRD:	C-library sin function


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================ The three ways =================

---------------- cordic algorithm ---------------
1. Convert float to binary as (unsigned int)
	example:
		x = .25   ---->   bin = 2 base10     its binary representation (0000 0000 0000 0000 0000 0000 0000 0010) base2 
		x = .125  ---->   bin = 4 base10     its binary representation (0000 0000 0000 0000 0000 0000 0000 0100) base2


2. calculate sin of the binary number recursivly

		sin(a+b) = sin(a) cos(b) + cos(a) sin(b)
		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

	example:
		sin(0.1101) = sin(0.1 + 0.0101) = sin(0.1) cos(0.0101) + cos(0.1) sin(0.0101)
										= sins[1]  cosRec(0.0101) + coss[1] sinRec(0.0101)
										and so on.... where sins and coss are arrays of pre-calculated sines and cosines
														of values sin(1/2^i) where 1 <= i <= 32

---------------- Maclaurin Polynomial -----------
By simply applaying this function
		sin(x) = x - (x^3)/6 + x^5/120
		

--------------- C-library -----------------------
Using the sin() function from math.h

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================ INPUT  =========================

Float numbers. Any number that is out of range is going to stop the program
RANGE (0 <= x < 1)

to stop the program, just enter any number that is out of range for example (1).

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================ OUTPUT =========================

interpreting output:
"x-value         CORDIC         Maclaurin      c-library      Duration for CORDIC"
  x            cordicSin(x)      macSin(x)        sin(x)       ##.######  seconds
 
 
----------------  Sample input/output -----------
terminal command: Haytham_HW_09 < in > out
++++++++++++++++ in +++++++++++++++++++
0.5
0.25
0.125
0.1
0.01
0.001
0.04
0.03
+++++++++++++++++++++++++++++++++++++++
++++++++++++++++ out ++++++++++++++++++
x-value         CORDIC         Maclaurin      c-library      Duration for CORDIC
0.5            0.479425       0.479427       0.479426       1.90735e-06 seconds
0.25           0.247404       0.247404       0.247404       4.05312e-06 seconds
0.125          0.124675       0.124675       0.124675       2.14577e-06 seconds
0.1            0.0998334      0.0998334      0.0998334      0.000983 seconds
0.01           0.00999983     0.00999983     0.00999983     0.00048399 seconds
0.001          0.001          0.001          0.001          0.000133038 seconds
0.04           0.0399893      0.0399893      0.0399893      0.000442028 seconds
0.03           0.0299955      0.0299955      0.0299955      0.00190592 seconds

+++++++++++++++++++++++++++++++++++++++
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