CODEWITHSUNDEEP
pythonwhile-loopseries
Bob Unger
Bob Unger

Reputation: 341

Needing to calculate pi to 30 digits, but after the 15th digit they all fail

I am having a problem with series calculations in python where they all fail after the 15th digit. I am using Canopy.

For example

3.1415926535897932384626433832795028841971693993751 Actual pi 3.14159265358979444826559301873203366994857788085938 My result 3.1415926535897932384626433832795028841971XXXXXXXXXX The question

The equation 16arctan(1/5) - 4arctan(1/239):

    # For Machin
    mm = 0.
    totalm1 = 0.
    while mm <= 100:
        machin1 = (16.)*(-1)**(mm)*((1./5)**(1+2.*mm))/(2.*mm+1) -(4.)*(-1)**(mm)*((1./239)**(1+2.*mm))/(2.*mm+1)
        totalm1 += machin1
        mm += 1
    print "%50.50f" %totalm1

How to solve this?

Upvotes: 2

Views: 286

Answers (1)

user2357112
user2357112

Reputation: 280554

Floating-point numbers only have about 15 digits of precision. If you need more significant digits, use an arbitrary-precision math library. The built-in decimal module may be suitable, or you could try mpmath, which seems to have a lot more features.

An example of computing the square root of 2 with the decimal module:

>>> import decimal
>>> decimal.getcontext().prec = 50 # Compute with 50 digits of precision
>>> decimal.Decimal('2') ** decimal.Decimal('0.5')
Decimal('1.4142135623730950488016887242096980785696718753769')

Upvotes: 2

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