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Primes.h
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//# Primes.h: This class provides some prime number operations using a cached table
//# Copyright (C) 1994,1995,1999,2001
//# Associated Universities, Inc. Washington DC, USA.
//#
//# This library is free software; you can redistribute it and/or modify it
//# under the terms of the GNU Library General Public License as published by
//# the Free Software Foundation; either version 2 of the License, or (at your
//# option) any later version.
//#
//# This library is distributed in the hope that it will be useful, but WITHOUT
//# ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
//# FITNESS FOR A PARTICULAR PURPOSE. See the GNU Library General Public
//# License for more details.
//#
//# You should have received a copy of the GNU Library General Public License
//# along with this library; if not, write to the Free Software Foundation,
//# Inc., 675 Massachusetts Ave, Cambridge, MA 02139, USA.
//#
//# Correspondence concerning AIPS++ should be addressed as follows:
//# Internet email: casa-feedback@nrao.edu.
//# Postal address: AIPS++ Project Office
//# National Radio Astronomy Observatory
//# 520 Edgemont Road
//# Charlottesville, VA 22903-2475 USA
#ifndef SCIMATH_PRIMES_H
#define SCIMATH_PRIMES_H
#include <casacore/casa/aips.h>
#include <casacore/casa/Containers/Block.h>
#include <mutex>
namespace casacore { //# NAMESPACE CASACORE - BEGIN
// <summary> Creates a reference table of prime numbers, and some functions </summary>
//
// <reviewed reviewer="Gareth Hunt" date="94/08/19" tests="tPrimes">
//
// <prerequisite>
// <li>Understanding Block is only peripherally important.
// </prerequisite>
//
// <etymology>
// Prime has its usual definition (a number whose only factors are
// itself and one.) Zero and one are not considered to be prime.
// </etymology>
//
// <synopsis>
// The primary function of the Primes class is to create and maintain a list of
// prime numbers. This class has no constructors; all member functions are
// therefore declared static. The class maintains an internal cache table of
// prime numbers. There are also several member functions of more general use,
// which do not access the cached table.
//
// The table is initialized to contain the next prime greater than each power
// of two. The function "aLargerPrimeThan" accepts a number and returns a
// larger prime number from the table of prime numbers. The function
// "nextLargerPrimeThan" finds the next greater integer that is a prime,
// returns it, and inserts it into the table. There are also functions to
// initialize and examine the table.
//
// The basic prime number operations are done in three functions: "isPrime"
// determines whether a given number is a prime; "smallestPrimeFactor" finds
// the smallest factor of a given number; and "factor" returns a Block<uInt>
// containing a number's factors.
// </synopsis>
//
// <example>
// <srcblock>
// #include <casacore/scimath/Mathematics/Primes.h>
// #include <casacore/casa/Utilities/Assert.h>
// #include <iostream>
//
// // Refer also to tPrimes.cc
//
// int main() {
// Block<uInt> BB, DD;
// uInt C, i;
// if(! Primes::isPrime(4)) { //if this number
// cout<<"Four is not a prime number"<<endl; //is not prime
// BB = Primes::factor(4); //than factor it
//
// if( BB[0] != Primes::smallestPrimeFactor(4) ){ //check that first
// //factor equals
// cerr<<"something is wrong"<<endl; //the smallest
// }
// cout<<"4 factored:"<<endl;
// for ( i = 0; i < BB.nelements(); i++ ) {
// cout<<BB[i]<<endl;
// }
//
// C = Primes::aLargerPrimeThan(4);
// if ( (C-5) > 4 ) { //if difference is more
// //than five, then
// C = Primes::nextLargerPrimeThan(4); //find next lprime
// }
// DebugAssertExit( C == Primes::aLargerPrimeThan(4)); //now the prime resides
// } //in the cache table
// if( Primes::nCachedPrimes() > 50 ) {
// Primes::initializeCache();
// }
// DD = Primes::cachedPrimes();
// cout<<"The Table of Primes"<<endl;
// for ( i = 0; i < Primes::nCachedPrimes(); i++ ) {
// cout<<DD[i]<<endl;
// }
// return 0;
// }
//
// </srcblock>
// </example>
//
// <motivation>
// This class was conceived during the coding of a class that creates hash
// tables. The hash table class works best with a table whose size is prime.
// It uses the Primes class's function "nextLargerPrimeThan" to find a prime
// number that is close to an appropriate size. This prime number becomes the
// size of the hash table.
// </motivation>
//
// <todo asof="$DATE:$">
// <li> This class should not be used to generate large sets of prime
// numbers - it is not designed for efficiency at this.
// The algorithm checks 2, 3, and (6n +/- 1) up to the square
// root of the candidate prime.
// <li> The size of the prime numbers are restricted by the size of an
// unsigned integer (2^31-1 on 32 bit machines).
// </todo>
class Primes {
public:
//This function takes number and returns "True" if number is prime, "False"
//if it is not.
static Bool isPrime(uInt number);
//This function returns the closest integer larger than number from the
//table of primes. If there is no entry in the table of primes which is
//larger than number, a zero is returned.
static uInt aLargerPrimeThan(uInt number);
//This function finds the next largest prime than number, returns that
//value and stores it in the table of primes.
static uInt nextLargerPrimeThan(uInt number); // adds to cache
//This function returns the smallest factor of number.
static uInt smallestPrimeFactor(uInt number);
//This function returns a block, of variable length, with each factor
//indexed. For example, if number equaled 4, then the return block would
//have a length of two, and have a two stored in each cell. One and zero
//are special cases; this function returns a one-cell block which holds
//one or zero, respectively.
static Block<uInt> factor(uInt number);
// This function returns the number of primes stored in the primes table.
// static uInt nCachedPrimes()
// { return cacheTable.nelements(); }
//This function returns the table of prime numbers.
//static Block<uInt> cachedPrimes()
// { return cacheTable; }
private:
//This function resets the table of prime numbers to contain 31 prime
//numbers to avoid consuming too much memory.
static void initializeCache();
//This is the table which stores the prime numbers.
static Block<uInt> cacheTable;
static std::mutex theirMutex;
};
} //# NAMESPACE CASACORE - END
#endif
casacore::Block
simple 1-D array
Definition Block.h:198
casacore::Primes
Definition Primes.h:131
casacore::Primes::factor
static Block< uInt > factor(uInt number)
This function returns a block, of variable length, with each factor indexed.
casacore::Primes::aLargerPrimeThan
static uInt aLargerPrimeThan(uInt number)
This function returns the closest integer larger than number from the table of primes.
casacore::Primes::initializeCache
static void initializeCache()
This function returns the number of primes stored in the primes table.
casacore::Primes::smallestPrimeFactor
static uInt smallestPrimeFactor(uInt number)
This function returns the smallest factor of number.
casacore::Primes::cacheTable
static Block< uInt > cacheTable
This is the table which stores the prime numbers.
Definition Primes.h:172
casacore::Primes::theirMutex
static std::mutex theirMutex
Definition Primes.h:173
casacore::Primes::nextLargerPrimeThan
static uInt nextLargerPrimeThan(uInt number)
This function finds the next largest prime than number, returns that value and stores it in the table...
casacore::Primes::isPrime
static Bool isPrime(uInt number)
This function takes number and returns "True" if number is prime, "False" if it is not.
casacore
this file contains all the compiler specific defines
Definition mainpage.dox:28
casacore::uInt
unsigned int uInt
Definition aipstype.h:49
casacore::Bool
bool Bool
Define the standard types used by Casacore.
Definition aipstype.h:40