y-cruncher

Screenshot of y-cruncher after a calculation of the golden ratio
π can be calculated with any number of digits – for larger calculations, a lot of RAM is necessary. In this case, 25 billion digits of Pi are calculated in 10.4 minutes.

y-cruncher is a computer program used for the calculation of some mathematical constant with theoretical accuracy limited only by computing time and available storage space. It was originally developed to calculate the Euler-Mascheroni constant 𝛾; the y is derived from it in the name.

Since 2010, y-cruncher has been used for all record calculations of the number π and other constants.

The software is downloadable from the website of the developers for Microsoft Windows and Linux. It does not have a graphical interface, but works on the command line. Calculation options are selected or entered via the text menu, the results are saved as a file.

Some popular uses of y-cruncher are running hardware benchmarks to measure performance of a computer system. An example of such benchmark is HWBOT. y-cruncher can also be used for stress-tests, as performed computations are sensitive to RAM errors and the program can automatically detect such errors.[1][2]

Development

Alexander J. Yee started developing in high school a Java library for arbitrary-precision arithmetic called "BigNumber". With this he was able together with his roommate Raymond Chan on 8 December 2006 set the world record for the most number of calculated decimal places for the Euler-Mascheroni constant with 116 580 041 decimal places.[3] In January 2009, they broke their own record and calculated 14 922 244 782 decimal places. At this point, the program was renamed to "y-cruncher" and ported to C and C++.[4]

In the aftermath, Shigeru Kondo with the help of y-cruncher calculated π to 5 trillion digits on 2 August 2010.[5]

Next year, Yee and Kondo calculated 10 trillion decimal places and broke the then-valid world record for decimal places of π.[6] After that, Yee decided to completely overhaul the program and rewrite it from scratch in version v0.6.1.[7] This enabled determining π with 12.1 trillion digits in just 94 days compared to 371 days that were spent for the previous record.[8]

Properties

y-cruncher has the following characteristic properties:[9][10]

  • Multithreading
  • Vector instruction sets (see SIMD)
  • Swapping
  • Using multiple hard drives (in RAID)
  • Automatic detection and correction of smaller arithmetic errors
  • Processor-specific optimization

Calculations

Since 2009, most of the world record-level calculations of mathematical constants have been performed with y-cruncher. The technical challenge does not (any longer) lie in the calculation itself, but in providing an environment that enables a comparatively efficient execution.[11]

Current world records set with y-cruncher[12]
Mathematical constant Digits Number of
decimal places 		Date Carried out by
π 3.14159... 314000000000000 19 Nov 2025 Storage Review[12][13]
√2 1.41421... 28000000000000 8 Jun 2025 Teck Por Lim
√3 1.73205... 4000000000000 23 May 2025 DMAHJEFF
√5 2.23606... 2250000000000 7 Oct 2021 John Kominek
√7 2.64575... 2275000000000 7 Oct 2021 John Kominek
√11 3.31662... 2284000000000 9 Oct 2021 John Kominek
Golden ratio 1.61803... 20000000000000 27 Nov 2023 Jordan Ranous
Euler's number 2.71828... 35000000000000 24 Dec 2023 Jordan Ranous
Euler-Mascheroni constant 0.57721... 1337000000000 7 Sep 2023 Andrew Sun
Apéry constant 1.20205... 2020569031595 22 Dec 2023 Andrew Sun
Lemniscate constant 2.62205... 2000000000000 16 May 2025 Lorenz Milla
Catalan's constant 0.91596... 1200000000100 9 Mar 2022 Seungmin Kim
ln 2 0.69314... 3000000000000 12 Feb 2024 Jordan Ranous
ln 10 2.30258... 2000000000100 6 Jun 2025 Lorenz Milla
Gamma(1/3) 2.67893... 1300000000000 6 Aug 2025 Mamdouh Barakat
Gamma(1/4) 3.62560... 1200000000000 13 Jun 2025 Dmitriy Grigoryev
Gamma(1/5) 4.59084... 220000000000 26 May 2025 Dmitriy Grigoryev
Zeta(5) 1.03692... 506000000000 17 Mar 2025 Ben Hadad
ln 3 1.09861... 600000000000 14 Jun 2025 Dmitriy Grigoryev
ln 5 1.60943... 549755813888 29 Jun 2020 Marco Julian Hummel
ln 7 1.94591... 549755813888 12 Aug 2020 Marco Julian Hummel

Purpose

The tool can serve several purposes. On the one hand, it allows the capabilities of CPUs and RAM to be determined and compared with other models. On the other hand, these hardware components can also be tested for stability and error susceptibility through stress testing. An alternative program for this would be Prime95. The advantage of the program lies in the fact that (partial) calculations can be carried out on an old Pentium PC, an up-to-date workstation, and theoretically even supercomputers, without measured performance falling off a measurement scale (or complex benchmarks becoming incompatible due to new hardware and interfaces). Setting new computing records also represents a contemporary feasibility study and can serve as an indicator of computer performance improvement over time when regularly performed and with similar parameters.

See also

References

  1. ^ Chris (2024-07-28). "Advanced CPU/RAM Overclock Stability Testing".
  2. ^ Yee, Alexander; Kondo, Shigeru (2011). "10 trillion digits of pi: A case study of summing hypergeometric series to high precision on multicore systems" (PDF).
  3. ^ Alexander Jih-Hing Yee. "Euler-Mascheroni Constant - 116 million digits on a laptop". Retrieved 2020-03-18.
  4. ^ Alexander Jih-Hing Yee (2011-03-07). "New World Records on a Gaming Computer". Retrieved 2020-03-18.
  5. ^ Alexander Jih-Hing Yee (2016-09-22). "5 Trillion Digits of Pi - New World Record". Retrieved 2020-03-18.
  6. ^ Yee, Alexander; Kondo, Shigeru (2011). "10 trillion digits of pi: A case study of summing hypergeometric series to high precision on multicore systems" (PDF).
  7. ^ Alexander Jih-Hing Yee (2012-05-28). "A peak into y-cruncher v0.6.1". Retrieved 2020-03-18.
  8. ^ Yee, Alexander; Kondo, Shigeru. "12.1 Trillion Digits of Pi".
  9. ^ Alexander Jih-Hing Yee (2020-03-12). "y-cruncher - A Multi-Threaded Pi Program". Retrieved 2020-03-18.
  10. ^ Alexander Jih-Hing Yee (2019-08-03). "Processor-Specific Optimizations". Retrieved 2020-03-18.
  11. ^ Emma Haruka Iwao (2022-06-09). "Calculating 100 trillion digits of pi on Google Cloud".
  12. ^ a b Yee, Alexander Jih-Hing (11 December 2025). "Records set by y-cruncher". Archived from the original on 28 December 2025. Retrieved 31 December 2025.
  13. ^ O'Brien, Kevin (11 December 2025). "StorageReview Sets New Pi Record: 314 Trillion Digits on a Dell PowerEdge R7725". Storage Review. Archived from the original on 31 December 2025. Retrieved 31 December 2025.
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