# y-cruncher

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Screenshot of y-cruncher after a computation of the golden ratio.

y-cruncher is a computer program that can compute ${\displaystyle \pi }$ and many other mathematical constants to several trillion decimal places. The original goal was to accurately compute the Euler–Mascheroni constant, hence the y in the name, which is derived from the Greek letter ${\displaystyle \gamma }$.

## Development

Alexander J. Yee started developing a Java library for arbitrary-precision arithmetic called "BigNumber" in high school. With this, he and his roommate Raymond Chan were able to set the world record for the most decimal places computed for the Euler-Mascheroni constant on December 8, 2006, with 116,580,041 decimal places.[1] In January 2009 they broke the record again and computed 14,922,244,782 decimal places, but he has now renamed his program to "y-cruncher" and has reprogrammed it to C or some parts to C++.[2]

Then, on August 2, 2010, Shigeru Kondo computed ${\displaystyle \pi }$ to 5,000,000,000 decimal places using y-cruncher. The computation was verified by Yee.[3]

The next year, Yee and Kondo computed 10,000,000,000,050 decimal places, again breaking the world record for ${\displaystyle \pi }$.[4] As a result, Yee decided that he wanted to completely overhaul the program once, rewriting most of it. This is due to the fact that for the computations of ${\displaystyle \pi }$ he had to make the program compatible for numbers with several trillion decimal places and thereby the code became more and more confusing and inefficient.[5]

## Features

y-cruncher is characterized by the following computation properties, among others:[6][7]

• Vector instruction sets (see SIMD)
• Swap space
• Use of multiple hard disks (in RAID)
• Automatic detection and correction of minor computational errors
• Processor specific optimization

## Computations

Since 2009, the program has been used to perform most of the world record level computations for some well-known mathematical constants.

Currently valid world records set with y-cruncher[8]
Mathematical constant First three decimal places Date Number of decimal places Computation performed by
Pi 3.141 January 29, 2020 50,000,000,000,000 Timothy Mullican
Square root of 2 1.414 June 19, 2016 10,000,000,000,000 Ron Watkins
Square root of 3 1.732 June 9, 2019 2,000,000,000,000 Hiroyuki Oodaira (大平 寛之)
Square root of 5 2.236 July 4, 2019 2,000,000,000,000 Hiroyuki Oodaira (大平 寛之)
Golden ratio 1.618 July 20, 2020 6,000,000,000,000 Damien Debin
Eulers number 2.718 November 22, 2020 31,415,926,535,897 David Christle
Euler–Mascheroni constant 0.577 May 26, 2020 600,000,000,100 Seungmin Kim & Ian Cutress
Apéry's constant 1.202 July 26, 2020 1,200,000,000,100 Seungmin Kim
Lemniscate constant 2.622 May 21, 2019 600,000,000,000 Seungmin Kim & Ian Cutress
Catalan's constant 0.915 September 6, 2020 1,000,000,001,337 Andrew Sun
Natural logarithm of 2 0.693 August 19, 2020 1,200,000,000,100 Seungmin Kim
Natural logarithm of 10 2.302 September 6, 2020 1,200,000,000,100 Seungmin Kim

## References

1. Alexander Jih-Hing Yee. "Euler-Mascheroni Konstante - 116 Millionen Stellen auf einem Laptop". Retrieved 2020-12-20.
2. Alexander Jih-Hing Yee (2011-03-07). "New World Records on a Gaming Computer". Retrieved 2020-12-20.
3. Alexander Jih-Hing Yee (2016-09-22). "5 Trillion Digits of Pi - New World Record". Retrieved 2020-12-20.
4. Alexander Jih-Hing Yee (2016-09-22). "Round 2... 10 Trillion Digits of Pi". Retrieved 2020-12-20.
5. Alexander Jih-Hing Yee (2012-05-28). "A peak into y-cruncher v0.6.1". Retrieved 2020-12-20.
6. Alexander Jih-Hing Yee (2020-05-12). "y-cruncher - A Multi-Threaded Pi Program". Retrieved 2020-12-20.
7. Alexander Jih-Hing Yee (2019-08-03). "Processor-Specific Optimizations". Retrieved 2020-12-20.
8. Alexander Jih-Hing Yee (2020-12-05). "Records set by y-cruncher". Retrieved 2020-12-20.