I am currently working on a program to calculate 100,000 digits of the first sophomore's dream constant, I1. It's given by the sum below.

After about 10,000 terms in this series it gets quite slow. I opted to write the program so small because I wanted to see how small I could make it

from decimal import *

def sophodream(a):
    s,i,t=0,1,int(a*1.5)
    while i<t:
         print(i)
         n,d=Decimal(pow(-1,i 1)),Decimal(i**i)
         f=n/d
         s =f
         i =1
    return s

I would like to know if there are any ways to speed this up aside from multithreading/multiprocessing. I find that when I do series like these in threaded pieces the accuracy of them gets lower.

CodePudding user response：

There are some minor changes / simplifications that can be made to your code but as has already been noted, you're working (at times) with some very big numbers.

from decimal import getcontext, Decimal

def sophodream(a):
    s, p = 0, 1
    getcontext().prec = a
    for i in range(1, int(a * 1.5)):
        s  = p / Decimal(i**i)
        p = -p
    return s

print(sophodream(100))

Output:

0.7834305107121344070592643865269754694076819901469309582554178227016001845891404456248642049722689389

Obviously just a very short version to prove functionality