Instantly share code, notes, and snippets.

# deeplook/pi_digits.py

Created February 13, 2013 20:16
Show Gist options
• Save deeplook/4947835 to your computer and use it in GitHub Desktop.
Generate digits of Pi using a spigot algorithm.
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters. Learn more about bidirectional Unicode characters
 """ Run the algorithm below using CPython, Cython, PyPy and Numba and compare their performance. (This is implementing a spigot algorithm by A. Sale, D. Saada, S. Rabinowitz, mentioned on http://mail.python.org/pipermail/edu-sig/2012-December/010721.html). """ def pi_digits(n): "Generate n digits of Pi." k, a, b, a1, b1 = 2, 4, 1, 12, 4 while n > 0: p, q, k = k * k, 2 * k + 1, k + 1 a, b, a1, b1 = a1, b1, p * a + q * a1, p * b + q * b1 d, d1 = a / b, a1 / b1 while d == d1 and n > 0: yield int(d) n -= 1 a, a1 = 10 * (a % b), 10 * (a1 % b1) d, d1 = a / b, a1 / b1 # >>> list(pi_digits(20)) # [3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 8, 9, 7, 9, 3, 2, 3, 8, 4]

### Anderson-Cooper commented Jun 21, 2023

Hello and apologies if this is a rather stupid question.

I've been trying to wrap my head around changing this algorithm to return a specific digit but not have it use a list to read off of (if this makes sense of course). I would really appreciate any help that I can get.

Cheers.

### deeplook commented Jun 22, 2023

I've been trying to wrap my head around changing this algorithm to return a specific digit but not have it use a list to read off of (if this makes sense of course). I would really appreciate any help that I can get.

You can replace the `yield int(d)` above with `if n == 1: return int(d)` to get the nth digit only (renaming it to `pi_digit(i)` would then be more appropriate, too):

```>>> pi_digit(5)
5
>>> pi_digit(1)
3```

If you want to follow Python's 0-based indexing giving the first digit for i=0 you'd also need to take care of that.

### Anderson-Cooper commented Jun 23, 2023

I've been trying to wrap my head around changing this algorithm to return a specific digit but not have it use a list to read off of (if this makes sense of course). I would really appreciate any help that I can get.

You can replace the `yield int(d)` above with `if n == 1: return int(d)` to get the nth digit only (renaming it to `pi_digit(i)` would then be more appropriate, too):

```>>> pi_digit(5)
5
>>> pi_digit(1)
3```

If you want to follow Python's 0-based indexing giving the first digit for i=0 you'd also need to take care of that.

Thanks a lot man.
:)