Y-cruncher
y-cruncher is a computer program that can calculate the number of circles and many other mathematical constants to several trillion decimal places . The original goal was the exact calculation of the Euler-Mascheroni constant , hence the y in the name, which is derived from the Greek letter .
development
Alexander J. Yee began developing a Java long number arithmetic library called BigNumber in high school . With this, he and his roommate Raymond Chan set the world record on December 8, 2006 for the most calculated decimal places for the Euler-Mascheroni constant with 116,580,041 decimal places. In January 2009 they broke the record again and calculated 14,922,244,782 decimal places, but he has now renamed his program to "y-cruncher" and reprogrammed it to C or C ++ .
Then on August 2, 2010 Shigeru Kondo calculated with the help of y-cruncher to 5,000,000,000,000 decimal places. The calculation was verified by Alexander J. Yee.
In the next year, Alexander J. Yee and Shigeru Kondo calculated 10,000,000,000,050 decimal places and thus broke the world record for again. Thereupon Alexander J. Yee decided that he wanted to completely revise the program once and would like to rewrite most of it. This is due to the fact that he had to make the program compatible for numbers with several trillion decimal places for the calculations , and the code became more and more confusing and inefficient.
properties
y-cruncher is characterized by the following calculation properties:
- Multithreading
- Vector instruction sets (see SIMD )
- Swapping
- Use of multiple hard drives (in RAID )
- automatic detection and elimination of minor calculation errors
- Processor-specific optimization
Calculations
Since 2009, the program has performed most of the world record level calculations for the known mathematical constants.
| mathematical constant | first three decimal places | date | Number of decimal places | Calculation performed by |
|---|---|---|---|---|
| Circle number | 3.141 | January 29, 2020 | 50,000,000,000,000 | Timothy Mullican |
| Square root of 2 | 1.414 | 19th June 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 | 4th July 2019 | 2,000,000,000,000 | Hiroyuki Oodaira (大平 寛 之) |
| Golden cut | 1.618 | 23 September 2019 | 5,000,000,000,000 | Hiroyuki Oodaira (大平 寛 之) |
| Euler's number | 2.718 | 3rd January 2019 | 8,000,000,000,000 | Gerald Hofmann |
| Euler-Mascheroni constant | 0.577 | May 26, 2020 | 600,000,000,100 | Seungmin Kim & Ian Cutress |
| Apéry constant | 1.202 | May 26, 2019 | 1,000,000,000,000 | Ian Cutress |
| Lemniscatic constant | 2.622 | May 21, 2019 | 600,000,000,000 | Seungmin Kim & Ian Cutress |
| Catalan's constant | 0.915 | 16th July 2019 | 600,000,000,000 | Seungmin Kim |
| Natural logarithm of 2 | 0.693 | April 26, 2019 | 1,000,000,000,000 | Jacob Riffee |
| Natural logarithm of 10 | 2.302 | August 31, 2019 | 1,000,000,000,000 | Hiroyuki Oodaira (大平 寛 之) |
Web links
Individual evidence
- ↑ Alexander Jih-Hing Yee: Euler-Mascheroni Constant - 116 million digits on a laptop. Retrieved March 18, 2020 (English).
- ↑ Alexander Jih-Hing Yee: New World Records on a Gaming Computer. March 7, 2011, accessed March 18, 2020 .
- ↑ Alexander Jih-Hing Yee: 5 Trillion Digits of Pi - New World Record. September 22, 2016, accessed March 18, 2020 .
- ↑ Alexander Jih-Hing Yee: Round 2 ... 10 Trillion Digits of Pi. September 22, 2016, accessed on March 18, 2020 (English).
- ↑ Alexander Jih-Hing Yee: A peak into y-cruncher v0.6.1. May 28, 2012, accessed March 18, 2020 .
- ↑ Alexander Jih-Hing Yee: y-cruncher - A Multi-Threaded Pi Program. March 12, 2020, accessed on March 18, 2020 .
- ↑ Alexander Jih-Hing Yee: Processor-Specific Optimizations. August 3, 2019, accessed on March 18, 2020 .
- ↑ Alexander Jih-Hing Yee: Records set by y-cruncher. May 28, 2020, accessed on May 28, 2020 .