Print pi to a number of decimal places - Python

问题:

One of the challenges on w3resources is to print pi to 'n' decimal places. Here is my code:

from math import pi

fraser = str(pi)

length_of_pi = []

number_of_places = raw_input("Enter the number of decimal places you want to 
see: ")

for number_of_places in fraser:
    length_of_pi.append(str(number_of_places))

print "".join(length_of_pi)

For whatever reason, it automatically prints pi without taking into account of any inputs. Any help would be great :)

回答1:

Why not just format using number_of_places:

''.format(pi)
>>> format(pi, '.4f')
'3.1416'
>>> format(pi, '.14f')
'3.14159265358979'

And more generally:

>>> number_of_places = 6
>>> '{:.{}f}'.format(pi, number_of_places)
'3.141593'

In your original approach, I guess you're trying to pick a number of digits using number_of_places as the control variable of the loop, which is quite hacky but does not work in your case because the initial number_of_digits entered by the user is never used. It is instead being replaced by the iteratee values from the pi string.

回答2:

The proposed solutions using np.pi, math.pi, etc only only work to double precision (~14 digits), to get higher precision you need to use multi-precision, for example the mpmath package

>>> from mpmath import mp
>>> mp.dps = 20    # set number of digits
>>> print(mp.pi)
3.1415926535897932385

Using np.pi gives the wrong result

>>> format(np.pi, '.20f')
3.14159265358979311600

Compare to the true value:

3.14159265358979323846264338327...

回答3:

Your solution appears to be looping over the wrong thing:

for number_of_places in fraser:

For 9 places, this turns out be something like:

for "9" in "3.141592653589793":

Which loops three times, one for each "9" found in the string. We can fix your code:

from math import pi

fraser = str(pi)

length_of_pi = []

number_of_places = int(raw_input("Enter the number of decimal places you want: "))

for places in range(number_of_places + 1):  # +1 for decimal point
    length_of_pi.append(str(fraser[places]))

print "".join(length_of_pi)

But this still limits n to be less than the len(str(math.pi)), less than 15 in Python 2. Given a serious n, it breaks:

> python test.py
Enter the number of decimal places you want to see: 100
Traceback (most recent call last):
  File "test.py", line 10, in <module>
    length_of_pi.append(str(fraser[places]))
IndexError: string index out of range
> 

To do better, we have to calculate PI ourselves -- using a series evaluation is one approach:

# Rewrite of Henrik Johansson's ([e-mail])
# pi.c example from his bignum package for Python 3
#
# Terms based on Gauss' refinement of Machin's formula:
#
# arctan(x) = x - (x^3)/3 + (x^5)/5 - (x^7)/7 + ...

from decimal import Decimal, getcontext

TERMS = [(12, 18), (8, 57), (-5, 239)]  # ala Gauss

def arctan(talj, kvot):

    """Compute arctangent using a series approximation"""

    summation = 0

    talj *= product

    qfactor = 1

    while talj:
        talj //= kvot
        summation += (talj // qfactor)
        qfactor += 2

    return summation

number_of_places = int(input("Enter the number of decimal places you want: "))
getcontext().prec = number_of_places
product = 10 ** number_of_places

result = 0

for multiplier, denominator in TERMS:
    denominator = Decimal(denominator)
    result += arctan(- denominator * multiplier, - (denominator ** 2))

result *= 4  # pi == atan(1) * 4
string = str(result)

# 3.14159265358979E+15 => 3.14159265358979
print(string[0:string.index("E")])

Now we can take on a large value of n:

> python3 test2.py
Enter the number of decimal places you want: 100
3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067
> 

回答4:

As this question already has useful answers, I would just like to share how i created a program for the same purpose, which is very similar to the one in the question.

from math import pi
i = int(input("Enter the number of decimal places: "))
h = 0
b = list()
for x in str(pi):
    h += 1
    b.append(x)
    if h == i+2:
        break

h = ''.join(b)
print(h)

Thanks for Reading.