Exploring the Python decimal module and approximations of transcendental numbers

decimalapproximation.py

#!/usr/bin/python2.7
# How many digits can I remember? How good is that approximation?
import math
import decimal

def compute_pi():
    """Compute Pi to the current precision.

    >>> print(pi())
    3.141592653589793238462643383

    """
    decimal.getcontext().prec += 2  # extra digits for intermediate steps
    three = decimal.Decimal(3)      # substitute "three=3.0" for regular floats
    lasts, t, s, n, na, d, da = 0, three, 3, 1, 0, 0, 24
    while s != lasts:
        lasts = s
        n, na = n+na, na+8
        d, da = d+da, da+32
        t = (t * n) / d
        s += t
    decimal.getcontext().prec -= 2
    return +s               # unary plus applies the new precision

D = decimal.Decimal
decimal.getcontext().prec = 30
pi = compute_pi()
mypi = "3.14159265358979"
e = D(1).exp()
mye = "2.718281828459045"
def correct_digits(approximation, truth):
    return -abs((approximation/truth).ln()).log10()

def print_correct_digits(approximation, truth):
    digits = correct_digits(approximation, truth)
    print(str(digits.quantize(D("1.00"))) + " correct digits of " + str(approximation) + ":" + str(truth))

approxlist = [
    (D("3.14"), pi),
    (D(22)/D(7), pi),
    (D(355)/D(113), pi),
    (D(mypi), pi),
    (D(math.pi), pi),

    (D("2.71"), e),
    (D("2.72"), e),
    (D(2721)/D(1001), e),
    (D(mye), e),
    (D(math.e), e),

    (D(7)/D(12), D("1.5").ln()/D(2).ln()),
    (D(31)/D(53), D("1.5").ln()/D(2).ln()),
    ]

for (a, t) in approxlist:
    print_correct_digits(a, t)