Author: Laurence D. Finston

This copyright notice applies to the text and source code of this web site, and the graphics that appear on it. The software described in this text has its own copyright notice and license, which can be found in the distribution itself.

Copyright (C) 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018 The Free Software Foundation

Permission is granted to copy, distribute, and/or modify this document under the terms of the GNU Free Documentation License, Version 1.3 or any later version published by the Free Software Foundation; with no Invariant Sections, with no Front-Cover Texts, and with no Back-Cover Texts. A copy of this license is included in the file COPYING.TXT

Last updated: January 20, 2006.

Top |

Introduction |

Implementation Details |

Contact |

Back to top

Back to main page

2005.12.06.

I have started working on functions and parser rules for prime
numbers. You can find the **n ^{th}** prime number by
using the

`get_prime`

operator:
ulong_long L; L := get_prime 24; show L; --> 89

It's also possible to store a range of prime numbers in a
`ulong_long_vector`

by using the
`get_prime_vector`

operator:

ulong_long_vector LV; LV := get_prime_vector 3 7; show LV; --> >> ulong_long_vector: size: 5 (0) : 5 (1) : 7 (2) : 11 (3) : 13 (4) : 17

In the fullness of time, I plan to add more functions for use with prime numbers. However, testing for primality and finding the prime factors of composite numbers are not easy tasks.

Back to contents

Back to top

Back to main page

The prime number functions involve a considerable amount of overhead.

**get_prime** returns a value of the type **ulong_long**, which
I've added especially for prime numbers. **ulong_long**
corresponds to the **unsigned long long** type in C and C++.
**numeric**, on the other hand, corresponds to either **float**
or **double**, depending on the value of a preprocessor variable
when 3DLDF is built. Currently, the default is **double**.

The problem with the floating point types **float** and
**double** is that they represent integers with limited
precision, whereas the integer types (**char**, **short**,
**int**, **long**, and **long long**, with their
**unsigned** variants) represent integers exactly.
I also wanted to be able to work with the largest possible
prime numbers, so I chose **unsigned long long** rather than
**unsigned int** or **unsigned long**. The prime numbers are
all positive, so there was no need to use **signed long long**.

The objects and functions for the prime numbers are declared in
**namespace Prime_Numbers**.
When **Prime_Numbers::get_prime()** is called for the first time, it causes a table
of prime numbers to be created. It is stored in a
**vector<unsigned long long>** pointed to by the pointer
**Prime_Numbers::primes_table**.
Just before **3dldf** exits, it writes a binary file called
**primes.lbn**, creates a checksum for it (stored in the
file **primes.lsm**), and
compresses it using **gzip** to create **primes.lbn.gz**. The
next time **3dldf** is run, it uncompresses **primes.lbn.gz**,
checks **primes.lbn** against the checksum, and if it hasn't been
corrupted, reads the values it contains into ***primes_table**.

If **get_prime** is called with an argument larger than the number
of primes already stored in **primes_table**, additional primes are
added up to and including the one specified by the argument. If this
occurs, **primes.lbn**, **primes.lbn.gz**, and **primes.lsm**
are regenerated at the end of the run, if they already exist. If they
don't already exist, they will be created. If they don't exist, and
**get_prime** is never called, they won't be created.

Since **3DLDF** uses threads, it's necessary to protect
**primes_table** and the associated files using mutexes.
It's also necessary to determine whether a system provides
**unsigned long long**. If it doesn't, **unsigned long** or
**unsigned int** is used instead. It is very unlikely that a
system wouldn't provide **unsigned long**.
In addition, it's necessary to check what functions are available for
creating checksums, and whether **gzip** is available for compression.

Back to contents

Back to top

Back to main page