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**Google Cloud Topples the Pi Record:** (March 14, 2019) - permalink

Happy Pi Day everyone!

Guess what? Records are meant to be broken and there is a new one!

From September to January, Emma Haruka Iwao of Google (@Yuryu) ran a computation of Pi to 31.4 trillion digits. The exact number of digits that was computed is 31,415,926,535,897 decimal digits and 26,090,362,246,629 hexadecimal digits. (Pop Quiz: Where do those figures come from?)

The details of the computation can be found in the main article. Below are the official Google blogs:

**Version v0.7.7:** (January 5, 2019) - permalink

Version 0.7.7 is now out and with it are all mathematical features that I've blogged about here months ago.

- The Custom Formula feature along with about 80 prebuilt formulas and constants.
- 3 new built-in algorithms for Catalan's constant: Guilerra, Pilehrood-short, and Pilehrood-long
- A new built-in algorithm for the Lemniscate constant: AGM-Pi

So for the first time in years, this is a major release with almost nothing on the hardware/optimization front.

The defining feature for this release is obviously the custom formulas. As mentioned in the October blog, it allows y-cruncher to evaluate user-input formulas.

The final list of functions for v0.7.7 is:

**Basic Arithmetic:**addition, subtraction, multiplication, division, integer power**Elementary Functions:**square root, arithmetic-geometric mean (AGM), logarithms, ArcCoth() of integer**Special Functions:**ArcSinlemn() of rational, generalized hypergeometric series of rationals**Constants:**Golden Ratio, e, Pi, Zeta(3), Catalan's Constant, Lemniscate, Euler-Mascheroni Constant

The only thing new since the original announcement is that the logarithm has been extended to allow any real input as opposed to just small integers.

All of these operations are fully parallelized and run in quasi-linear time and linear memory. There is also support for swap mode and checkpoint restart. Thus anything that can be represented (or sufficiently approximated) by a reasonably small combination of these operations (subject to restrictions) can be now be feasibly computed to billions or even trillions of digits without being limited by physical memory. This is well beyond the capability of most computer algebra systems. So hopefully it will serve as a useful tool for researchers in search of algorithms for super-high-precision computation of various constants and functions.

The download bundles now include about 80 prebuilt formulas which you can input into y-cruncher to compute. Feel free to contribute more on GitHub.

Documentation for the custom formulas can be found here.

Due to the sheer size and scope of the custom formulas, I expect there to be a lot of bugs. So if you encounter anything that doesn't seem right, let me know either though email or by opening an issue on GitHub.