I recently sawthis video that explained how to calculate pi, and attempted to build a Python simulation. In theory, it works, but it is much too slow, and I have no idea why.

In theoutput, you can see that the program starts off with hundreds of collisions calculated per second, but quickly slows down to only 40-50 per second, and when I leave it alone for a prolonged amount of time, it decreases to a measly 2 calculations!Here is my code:

#importsfrom time import time, sleepfrom fractions import Fraction#set variablesp = [Fraction(8, 1), Fraction(10, 1)]m = [1, 1]v = [Fraction(0, 1), Fraction(-1, 1)]collisions = 0time_interval = 1#mainprint("The π Calculator\n\nCredits:\nOriginal formula discovered by Gregory Galperin\nSimulation by Te Du\n")sleep(1)m[1] = 100 ** int(input("How many digits would you like to calculate? "))start_time = time()prev_time = start_timewhile not (v[0] <= v[1] and v[0] >= 0):    if time() - prev_time >= time_interval:        try:            print("Seconds elapsed: " + str(time() - start_time) + "\nCollisions: " + str(collisions))        except ValueError:            prev_time = time() + 1000000000        time_interval = 2 - (time() - prev_time)        prev_time = time()    try:        wall_to_one = p[0] / -v[0]    except ZeroDivisionError:        wall_to_one = 0    one_to_two = (p[1] - p[0]) / (v[0] - v[1])    collisions += 1    if one_to_two <= 0 or (0 < wall_to_one and wall_to_one < one_to_two):        p[0] += v[0] * wall_to_one        p[1] += v[1] * wall_to_one        v[0] *= -1    else:        p[0] += v[0] * one_to_two        p[1] += v[1] * one_to_two        v = [Fraction(m[0] - m[1], m[1] + m[0]) * v[0] + Fraction(2 * m[1], m[1] + m[0]) * v[1], Fraction(2 * m[0], m[1] + m[0]) * v[0] + Fraction(m[1] - m[0], m[1] + m[0]) * v[1]]#cleanupdel p, m, v, wall_to_one, one_to_two, start_time, prev_time, time_interval#printing piprint("π: " + str(collisions))

• What is theexcept ValueError: block for? Why would any of the numbers that you print cause a value error?

  Barmar

  – Barmar

  2024-09-21 18:24:15 +00:00

  CommentedSep 21, 2024 at 18:24
• 1
  Calculations with arbitrary-precision numbers slow down as the number of digits increase. Addition and subtraction are O(n), while multiplication and division are O(n^2).

  Barmar

  – Barmar

  2024-09-21 18:26:10 +00:00

  CommentedSep 21, 2024 at 18:26
• That is for if the collision count gets too big. Since now that prev_time is greater than time(), it will never call print() again and raise an error. (if you haven't learned already, I don't do things the normal way)

  meowdog011011

  – meowdog011011

  2024-09-21 18:28:17 +00:00

  CommentedSep 21, 2024 at 18:28
• thanks @Barmar for the info, but is there any way I can speed this up?

  meowdog011011

  – meowdog011011

  2024-09-21 18:30:07 +00:00

  CommentedSep 21, 2024 at 18:30
• Probably not if you need all those digits of precision. This is why we use floating point for ordinary numeric calculations. It's much faster, but not as precise.

  Barmar

  – Barmar

  2024-09-21 18:31:45 +00:00

  CommentedSep 21, 2024 at 18:31

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