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资源说明：prime counting function for maxima, the CAS
Copyright (C) 2012 John Lapeyre This program is free software; you
can redistribute it and/or modify it under the terms of the GNU
General Public License as published by the Free Software Foundation;
either version 3 of the License, or (at your option) any later
version.
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prime_pi provides a Common Lisp, as well as a maxima function
that computes the prime counting function (also number of prime
twins). The function is an interface to a C++ library written by Kim
Walisch and tables compiled by Tom\'as Oliveira e Silva.
Using this package directly requires 1) maxima/lisp that supports
quicklisp and cffi (e.g. yes sbcl, but no gcl). 2) installing the mext
third party maxima package system. 3) a c++ compiler that supports
threads. If you don't want mext, it would be possible to hack this to
work with maxima without mext.
Implemented are:
* A lisp (via cffi) interface to the C++ sieve library.
* A lisp interface to the prime pi tables.
* A lisp function that combines lookup and sieving to
return a value of the prime pi function
* A maxima interface to the lisp interface.
At the time this maxima package was written, it was significantly
faster than both the Mathematica and Sage prime pi implementations.
Building this package will use quicklisp to download and install
the asdf package cffi, as well as supporting packages. So only
maxima/lisp implementations that support quicklisp and cffi
will work.
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To build and install this package, you must:
1) install the mext package manager, and packages defmfun1 and
maxdoc. These are all in the github repository 'mext'.
2) build the C++ library. Instructions are in
primesieve-for-maxima/README-maxima.lisp Under linux:
cd primesieve-for-maxima
make lib
3) start maxima and load ibuild.mac. Eg
(%i1) load("./ibuild.mac");
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Use the package as follows:
(%i1) showtime:true$
(%i2) load(mext);
Evaluation took 0.0500 seconds (0.0480 elapsed) using 5.215 MB.
(%o2) /home/jlapeyre/.maxima/mext.lisp
(%i3) require(prime_pi)$
Evaluation took 0.9600 seconds (1.0980 elapsed) using 148.503 MB.
(%i4) prime_pi(10^19+10^9,threads->8);
Evaluation took 56.3700 seconds (7.4140 elapsed) using 0 bytes.
(%o4) 234057667299198865
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Get help online with
?? prime
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Online documentation:
-- Function: prime_pi: prime_pi()
Section: Functions and Variables for Number Theory
mext package: prime_pi; filename: max-ql.lisp
Calling:
prime_pi()
returns the number of primes less than or equal to .
Description:
Computes the prime counting function. The option specifies the
maximum number of cpu threads to use. The routine may use fewer threads,
depending on the value of . The value of is limited to 2^64, that is,
about 1.84e+18.
The percent of the calculation that is finished is printed during the
calculation if the option is true. The status will only work under
some terminals.
Arguments:
`prime_pi' requires one argument , which must be equivalent
to an unsigned 64 bit integer (that is, an integer
between 0 and 2 to the power 64).
Options: prime_pi takes options with default values: status->false, threads->1.
Implementation:
This algorithm is fast, especially for a general purpose mathematics
program. It combines a segmented sieve implemented as a C library with
tables.
Authors: Kim Walisch (C library), Tomas Oliveira e Silva (tables), and John Lapeyre (lisp).
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-- Function: prime_twins: prime_twins( :optional )
Section: Functions and Variables for Number Theory
mext package: prime_pi; filename: max-ql.lisp
Calling:
prime_twins()
returns the number of prime twins less than or equal to .
prime_twins(, )
returns the number of prime twins between and .
Description:
The option counts the -constellation rather than the
twins. must be an integer between 1 and 7.
Arguments:
`prime_twins' requires either one or two arguments.
The first argument must be equivalent to an unsigned 64 bit integer
(that is, an integer between 0 and 2 to the power 64).
The second argument must be equivalent to an unsigned 64 bit integer
(that is, an integer between 0 and 2 to the power 64).
Options: prime_twins takes options with default values:
ktuplet->2, status->false, threads->1.
See also: prime_pi, next_prime, prev_prime, and primep.
Implementation:
No tables are used in this algorithm.
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