Jitted function returning 0s, instead of intended digits of pi?

Numba Community Support
1

I’m relatively new to Numba, so I’m not sure if I’m doing something wrong.
I’d been tinkering with some simpler math functions, trying out using numba’s @njit on them, which was interesting. Then out of curiosity, I figured I’d try it on a generator function which outputs digits of pi, just to see how fast it could go…
Normally this script works fine, outputs the correct digits, even colors 0-9 differently for fun. However, adding the @njit decorator to the function causes it to only output 0s. (I’m on Python 3.8.10, numba 0.56.0, numpy 1.22.4)

from numba import njit

@njit
def calcPi(n):
    "function from: https://gist.github.com/deeplook/4947835"
    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

colors = ('\033[90m','\033[37m','\033[36m','\033[96m','\033[94m','\033[32m','\033[93m','\033[31m','\033[91m','\033[95m')
pi_digits = calcPi(1000000)
lastDigit = 0

try:
    for d in pi_digits:
        print(colors[d] + str(d), end='', flush=True)
        lastDigit += 1
except KeyboardInterrupt:
    print("\n\033[0mDigits calculated:", lastDigit)

If I comment out all the math in the calcPi function, and replace it with a simple addition-counter that cycles through 1-9, outputting those as the digits, that works fine with numba…
I’ve even tried swapping out that pi function for an alternate one, which uses a slightly different formula, and while that is able to output the first 5 digits accurately, after that it crashes with an error, cause the formula starts spitting out weird -1 values or something… So I assume either I’m just missing something simple, or I’ve run into some bug/limitation that prevents calculating pi, for some reason?

314150-1-11Traceback (most recent call last):
  File "calcpi_alt.py", line 32, in <module>
    print(colors[d] + str(d), end='', flush=True)
IndexError: tuple index out of range

@njit
def calcPi():
    q, r, t, k, n, l = 1, 0, 1, 1, 3, 3
    while True:
        if 4*q+r-t < n*t:
            yield n
            nr = 10*(r-n*t)
            n = ((10*(3*q+r))//t)-10*n
            q *= 10
            r = nr
        else:
            nr = (2*q+r)*l
            nn = (q*(7*k)+2+(r*l))//(t*l)
            q *= k
            t *= l
            l += 2
            k += 1
            n = nn
            r = nr
2

Okay, I was asking around, and someone suggested that it may be the internal math of the formula is reaching numbers too large for numba… Which if so, that’s a bummer…

However, I did just come across a simpler and significantly faster version of the function, which might now possibly be fast enough for the pi-related ideas I was thinking of tinkering with. So at least there’s that:

def gospers_pi_unproven():
    q,r,t,i = 1, 180, 60, 2
    while True:
        u,y = 3*(3*i+1)*(3*i+2), (q*(27*i-12)+5*r)//(5*t)
        yield y
        q,r,t,i = 10*q*i*(2*i-1),10*u*(q*(5*i-2)+r-y*t),t*u,i+1