epsilon = 0.0000001
def square_root(a):
    x = a / 2.0
    while True:
        y = (x + a / x) / 2
        if abs(y - x) < epsilon:
            break
        x = y
    return y

def test_square_root():
    import math
    for i in range(1, 10):
        mine = square_root(i)
        theirs = math.sqrt(i)
        delta = abs(mine - theirs)

        # Old style string formatting.
        # %-13.11g
        #  -  = left justified
        #  13 = total number of characters for field
        #  11 = number of characters after decimal point
        #  g  = floating point number or scientific notation (shorter wins)
        # print("%3.1f %-13.11g %-13.11g %.11g"
        #      % (float(i), mine, theirs, delta))

        # New style string formatting.
        # print("{:3.1f} {:<13.11g} {:<13.11g} {:.11g}".format(
        #           float(i), mine, theirs, delta))

        # New style string formatting with named arguments.
        # Note that multiple string constants with no operators
        # between them are concatenated together and treated as
        # a single string constant.
        print("{number:3.1f} {estimate:<13.11g} "
              "{sqrt:<13.11g} {difference:.11g}".format(
                  number=i, estimate=mine, sqrt=theirs, difference=delta))

test_square_root()