Print Pi To A Number Of Decimal Places

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('

Solution 1:

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...

Solution 2:

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.

Solution 3:

For example the mpmath package

from mpmath import mp
defa(n):
   mp.dps=n+1return(mp.pi)

Solution 4:

Great answers! there are so many ways to achieve this. Check out this method I used below, it works any number of decimal places till infinity:

#import multp-precision modulefrom mpmath import mp
#define PI functiondefpi_func():
    whileTrue:
        #request input from usertry:
             entry = input("Please enter an number of decimal places to which the value of PI should be calculated\nEnter 'quit' to cancel: ")
             #condition for quitif entry == 'quit':
                 break#modify input for computation
             mp.dps = int(entry) +1#condition for input errorexcept:
                print("Looks like you did not enter an integer!")
                continue#execute and print resultelse:
              print(mp.pi)
              continue

Good luck Pal!

Solution 5:

Your solution appears to be looping over the wrong thing:

fornumber_of_placesin 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 inrange(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 ofdecimal places you want to see: 100
Traceback (most recent calllast):
  File "test.py", line 10, in<module>
    length_of_pi.append(str(fraser[places]))
IndexError: string index outofrange>

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

# Rewrite of Henrik Johansson's (Henrik.Johansson@Nexus.Comm.SE)# 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 Gaussdefarctan(talj, kvot):

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

    summation = 0

    talj *= product

    qfactor = 1while talj:
        talj //= kvot
        summation += (talj // qfactor)
        qfactor += 2return 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 = 0for 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 => 3.14159265358979print(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
>