Increasing floating point precision in Python

Question

I was working on a project to compute the Leibniz approximation for pi with the below code:

def pi(precision):
    sign = True
    ret = 0
    for i in range(1,precision+1):
        odd = 2 * i - 1
        if sign:
            ret += 1.0 / odd
        else:
            ret -= 1.0 / odd
        sign = not sign
    return ret

However, the output value was always was 12 digits long. How can I increase the precision (e.g. more digits) of the calculation? Does Python support more precise floating points, or will I have to use some external library?

What a strange value for pi: ``>>> repr(pi(17))`` yields ``'0.8000913788523872'`` — alko, Jan 12 '14 at 19:37
@alko Yes, this approximates one fourth of pi. see here: http://en.wikipedia.org/wiki/Leibniz_formula_for_%CF%80 — hkk, Jan 12 '14 at 19:38
What a strange method for pi evaluation, it converges **so slow**. — alko, Jan 12 '14 at 19:40

score 8 · Accepted Answer · edited Jul 03 '16 at 17:27

8

Try using Decimal.

Read Arbitrary-precision elementary mathematical functions (Python)^original for more information

edited Jul 03 '16 at 17:27

grooveplex

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answered Jan 12 '14 at 19:38

albusshin

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Link is expired – Majo_Jose Oct 11 '19 at 08:20

score 6 · Answer 2 · answered Jan 12 '14 at 19:37

Python's float type maps to whatever your platform's C compiler calls a double (see http://en.wikipedia.org/wiki/IEEE_floating_point_number).

The Python standard library also comes with an arbitrary-precision decimal module, called decimal: http://docs.python.org/2/library/decimal.html

score 4 · Answer 3 · edited May 23 '17 at 12:26

4

The Leibniz formula converges extremely slowly - honestly, you won't live long enough for it get 12 digits of accuracy. Click here for one way to accelerate it enormously.

edited May 23 '17 at 12:26

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answered Jan 12 '14 at 20:19

Tim Peters

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score 3 · Answer 4 · edited May 23 '17 at 10:28

3

With Python's float, you get 15–17 digits of precision (if you are seeing fewer, you may need to use a different format specifier when printing).

If you need more, you'll need to use a different method (one that only uses integer arithmetic), or a different way to represent floating-point numbers.

See Python floating point arbitrary precision available?

edited May 23 '17 at 10:28

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answered Jan 12 '14 at 19:35

NPE

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12 is almost sertanly is raw print result, `float.__str__` trims up to 12 digits. – alko Jan 12 '14 at 19:38

Increasing floating point precision in Python

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