y-cruncher
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y-cruncher is a computer program that can compute 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 .
Development[edit]
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 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 .[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 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[edit]
y-cruncher is characterized by the following computation properties, among others:[6][7]
- Multithreading
- 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[edit]
Since 2009, the program has been used to perform most of the world record level computations for some well-known mathematical constants.
| 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[edit]
- ↑ Alexander Jih-Hing Yee. "Euler-Mascheroni Konstante - 116 Millionen Stellen auf einem Laptop". Retrieved 2020-12-20.
- ↑ Alexander Jih-Hing Yee (2011-03-07). "New World Records on a Gaming Computer". Retrieved 2020-12-20.
- ↑ Alexander Jih-Hing Yee (2016-09-22). "5 Trillion Digits of Pi - New World Record". Retrieved 2020-12-20.
- ↑ Alexander Jih-Hing Yee (2016-09-22). "Round 2... 10 Trillion Digits of Pi". Retrieved 2020-12-20.
- ↑ Alexander Jih-Hing Yee (2012-05-28). "A peak into y-cruncher v0.6.1". Retrieved 2020-12-20.
- ↑ Alexander Jih-Hing Yee (2020-05-12). "y-cruncher - A Multi-Threaded Pi Program". Retrieved 2020-12-20.
- ↑ Alexander Jih-Hing Yee (2019-08-03). "Processor-Specific Optimizations". Retrieved 2020-12-20.
- ↑ Alexander Jih-Hing Yee (2020-12-05). "Records set by y-cruncher". Retrieved 2020-12-20.
External links[edit]
- official website with downloads for various architectures
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