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pi

Calculating pi without arbitrary precision and only basic arithmetic

I want to calculate pi. But, I have quite a few limits. Variables can only hold up to 5 decimal places, and I only have the following operators:

Addition
Subtraction
Multiplication
Division
Exponents
Square roots
Sin
Cos
Basic Loops, Conditionals, and relational operators.

The BBP algorithm seems useless here, because even though it would not need arbitrary precision, I cannot convert between bases. I'm not aware of any other formulas that can find the nth digit of pi in base 10. Would it even be possible to calculate pi using these constraints?

Solution

  • BBP can be modified to give π in Base 10. There's a Java implementation on Github. (I believe that the screenshot of the algorithm description is taken from Pi - Unleashed by Arndt/Haenel.)

    You'll need the modulo operation and a means to calculate the closest integer to the logarithm of a number, but you can perform them using the operations you have and loops.