You can use exp(x) function of math library, which is same as e^x. Hence you may write your code as:

import math
x.append(1 - math.exp( -0.5 * (value1*value2)**2))

I have modified the equation by replacing 1/2 as 0.5. Else for Python <2.7, we'll have to explicitly type cast the division value to float because Python round of the result of division of two int as integer. For example: 1/2 gives 0 in python 2.7 and below.

This one is a little tricky.

The math module is implemented in a C module, mathmodule.c. At the end of that file there is a specific Python library structure that defines exp as implemented by math_exp:

static PyMethodDef math_methods[] = {
    # ...
    {"exp",             math_exp,       METH_O,         math_exp_doc},

but math_exp itself is actually defined via the FUNC1 macro, using the math_1 wrapper function to call the C library exp function with some error handling and type conversion:

FUNC1(exp, exp, 1,
     "exp(x)\n\nReturn e raised to the power of x.")

However, the C function implementation itself is entirely platform dependent, and on modern hardware is usually taken care of in hardware. You would have to turn to a software version of the function to find a starting point to implement this in Python.

You could use the fdlibm implementation as such a starting point, perhaps, here is a link to the exp function implementation in C from that library:

• http://www.netlib.org/fdlibm/e_exp.c

or you could refer to this implementation instead:

• http://fossies.org/dox/glibc-2.17/sysdeps_2ieee754_2ldbl-128ibm_2e__expl_8c_source.html#l00135