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#!/usr/bin/env python
 
import subprocess
import atexit
from math import pi
 
try:
    from matplotlib import pyplot
except ImportError:
    print "You need matplotlib to run this script!"
    exit(0)
 
children = []
def cleanup():
    for child in children:
        print "Terminating child process"
        child.terminate()
atexit.register(cleanup)
 
def run_c(file_name):
    process = subprocess.Popen(["../c2verilog", "iverilog", "run", str(file_name)])
    children.append(process)
    process.wait()
    children.remove(process)
 
def test():
    run_c("sqrt.c")
    x = [float(i) for i in open("x")]
    sqrt_x = [float(i) for i in open("sqrt_x")]
    pyplot.plot(x, sqrt_x)
    pyplot.xlim(0, 10.1)
    pyplot.title("Square Root of x")
    pyplot.xlabel("x")
    pyplot.ylabel("$\\sqrt{x}$")
    pyplot.savefig("../docs/source/examples/images/example_1.png")
    pyplot.show()
 
def indent(lines):
    return "\n    ".join(lines.splitlines())
 
def generate_docs():
 
    documentation = """
 
Calculate Square Root using Newton's Method
-------------------------------------------
 
In this example, we calculate the sqrt of a number using `Newton's method
<http://en.wikipedia.org/wiki/Newton's_method#Square_root_of_a_number>`_.
The problem of finding the square root can be expressed as:
 
.. math::
 
     n = x^2
 
Which can be rearranged as:
 
.. math::
 
     f(x) = x^2 - n
 
Using Newton's method, we can find numerically the approximate point at which
:math:`f(x) = 0`. Repeated applications of the following expression yield
increasingly accurate approximations of the Square root:
 
.. math::
 
    f(x_k) = x_{k-1} - \\frac{{x_{k-1}}^2 - n}{2x_{k-1}}
 
Turning this into a practical solution, the following code calculates the square
root of a floating point number. An initial approximation is refined using
Newton's method until further refinements agree to within a small degree.
 
.. code-block:: c
 
    %s
 
Note that the code isn't entirely robust, and cannot handle special cases such
as Nans, infinities or negative numbers.  A simple test calculates
:math:`\\sqrt{x}` where :math:`-10 < x < 10`.
 
.. image:: images/example_1.png
 
"""%indent(open("sqrt.c").read())
 
    document = open("../docs/source/examples/example_1.rst", "w").write(documentation)
 
test()
generate_docs()