Pi digits (again) - an unbounded spigot program

[DavidM]

(05-18-2024 01:55 PM)John Keith Wrote:  

(05-18-2024 08:03 AM)EdS2 Wrote:  How fast is a Prime, or an HP49 or HP50, in computing say 1000 digits of pi this way?

Not very fast on the HP 50. I haven't tested up to 1000 digits on a physical calculator but 302 digits (the number returned by Gibbons' original program with input of 1000) takes about 198 seconds. I timed 1000 digits on EMU48 but I'm not at home now and i don't remember the exact time.

Here's some timings for completing 1000 digits of PI:
\begin{array}{|l|r|}
\hline
\textbf{Platform} & \textbf{Time (seconds)} \\
\hline
\text{John's } \textbf{piG3 } \text{on real 50g} & 1960 \\
\text{SysRPL version based on John's } \textbf{piG3} & 1520 \\
\text{Emu48 on Desktop running } \textbf{SysRPL piG3} & 7 \\
\text{LongFloat's } \textbf{FPI } \text{on real 50g} & 43 \\
\text{LongFloat's } \textbf{FPI } \text{on Emu48} & 0.2 \\
\hline
\end{array}

(05-18-2024 01:55 PM)John Keith Wrote:  By way of comparison, the LongFloat function FPI is between 25 and 50 times as fast depending on the number of digits. Gibbons' paper does mention that spigot algorithms are not competitive with state-of-the-art conventional algorithms.

FWIW: the documentation for the LongFloat library attributes the computation of FPI to Werner Huysegom's implementation of Chudnovsky.