kyle_hw9

kyle_hw9 accepts a list of floating point numbers between 0
and 1 from standard input or by arguments.  It calculates
sines using the CORDIC algorithm, maclaurin approximation,
and the library sine function. The results are sent to
stdout.

The first column shows the inputted value.  The second
column shows the CORDIC value.  The third column shows the
Maclaurin value.  And the fourth column shows the C library
sin() value.

main.c contains a constant MAXINP that defines how many
values can be entered into the program at a time.  You can
adjust this however you please, just keep in mind how much
memory you have on your machine.

EXAMPLE

> ./kyle_hw9 .5 .832 .342
0.500000  0.479426  0.479426  0.479426
0.832000  0.735131  0.739279  0.739280
0.342000  0.335258  0.335372  0.335372
> ./kyle_hw9 < test
0.200000  0.198620  0.198669  0.198669
0.400000  0.389046  0.389418  0.389418
0.583000  0.550460  0.550531  0.550531
0.384000  0.374499  0.374632  0.374632
0.001400  0.001401  0.001400  0.001400
0.938000  0.796402  0.806375  0.806377
0.104800  0.104596  0.104608  0.104608
0.240000  0.237479  0.237703  0.237703
0.010000  0.009999  0.010000  0.010000
0.001000  0.001000  0.001000  0.001000
0.540000  0.514128  0.514136  0.514136
0.230000  0.227802  0.227978  0.227978
0.424000  0.410668  0.411410  0.411410
0.583400  0.550794  0.550865  0.550865
0.384100  0.374590  0.374725  0.374725
0.001500  0.001500  0.001500  0.001500
0.939000  0.796932  0.806966  0.806968
0.108800  0.108570  0.108585  0.108585
0.220000  0.218103  0.218230  0.218230
0.002000  0.002000  0.002000  0.002000
0.005000  0.005000  0.005000  0.005000
0.550000  0.522671  0.522687  0.522687

Elapsed Time: 0 seconds
>

VALIDATION

The binary float values were tested by comparing strings of
1's and 0's created by the function with strings generated
with a binary converter program located at:

	http://www.exploringbinary.com/binary-converter/

Sine values were compared to those calculated by Wolfram
Alpha.

EXECUTION SPEED

Speed tests were done with the file 'test' containing
100,000 values.

Method			Time (seconds)
--------------------------
CORDIC			0.34
Maclaurin		0.07
sin(x)			0.09
_all_				0.37
_none_			0.12
_all_+print 1.28

As you can see, both the C library sin() and the Maclaurin
polynomial were computed so fast, that their computation
time is virtually indistinguishable from the time it took to
process the input.

It makes sense that the maclaurin should be fast given that
it only has to do 7 multiplications, 3 divisions,  2
additions, 1 subtraction and an assignment.  I would
estimate each computation took less than a microsecond.

The CORDIC, on the other hand, had to do a lot more work.
Nevertheless, to complete 100,000 computations in 0.34
seconds requires that each computation take 3.4
microseconds.

ACCURACY

The descrepancies between actual values and calculated
values for CORDIC are probably primarily due to loss of
precision in my precomputed values for sine and cosine.
Error may have also cropped up as an effect of truncation in
the conversion from double to binary array.  

The equivalent of a 32 bit binary number can only represent
so many decimals.  `sizeof(double)` returns 8 on my system,
indicating double is 64 bits, twice the precision I am
storing for my values.