Provided by: libbobcat-dev_4.08.02-2build1_amd64 
NAME
FBB::PrimeFactors - Performs the prime-number factorization of (BigInt) values
SYNOPSIS
#include <bobcat/primefactors>
Linking option: -lbobcat
DESCRIPTION
Integral values fall into two categories: prime numbers, whose only integral divisors are
their own values and 1, and composite numbers, which also have at least one other (prime
number) integral divisor. All composite integral values can be factorized as the product
of prime numbers. E.g., 6 can be factorized as 2 * 3; 8 can be factorized as 2 * 2 * 2.
Finding these prime factors is called the prime number factorization, or `prime
factorization’. When factorizing a value its prime factors may sometimes repeatedly be
used as integral divisors: 8 is factorized as pow(2, 3), and 36 is factorized as
36 = pow(2, 2) * pow(3, 2)
The class FBB::PrimeFactors performs prime number factorizations of FBB::BigInt values.
When factorizing a value prime numbers up to sqrt(value) must be available, as prime
numbers up to sqrt(value) may be factors of value. Currently PrimeFactors uses the sieve
of Eratosthenes to find these prime numbers. To find the next prime number beyond
lastPrime, the sieve of Eratosthenes must be used repeatedly for lastPrime += 2 until
lastPrime is prime. Once determined, prime numbers can of course be used directly to
determine the next prime number or to factorize an integral value. To accellerate prime
number factorization and Eratosthenes’s sieve PrimeFactors saves all its computed prime
numbers in either a std::vector or in a file. Once determined, these prime numbers may
again be used when factorizing the next integral value.
After factorizing an integral value its prime number factors and associated powers are
made available in a vector of (PrimeFactors::PrimePower) structs, containing the value’s
sorted prime factors and associated powers.
NAMESPACE
FBB
All constructors, members, operators and manipulators, mentioned in this man-page, are
defined in the namespace FBB.
INHERITS FROM
-
TYPEDEFS AND ENUMS
o struct PrimePower:
contains two fields:
struct PrimePower
{
BigInt prime;
size_t power;
};
Here, power represents the number of times prime can be used as an integral divisor
of the value that was factorized by PrimeFactors.
o Factors:
is a synonym for std::vector<PrimePower
CONSTRUCTORS
o PrimeFactors(BigIntVector &primes):
Prime numbers that were determined while factorizing values are collected in the
BigIntVector that is passed as argument to this constructor.
Initially the BigIntVector passed as argument may be empty or may contain at least
two primes (which must be, respectively, 2 and 3). The prime numbers in primes must
be sorted. The constructor does not verify whether the prime numbers are actually
sorted, but if the BigIntVector contains primes it does check whether the first two
prime numbers are indeed 2 and 3. An FBB::Exception is thrown if this condition is
not met.
While numbers are being factorized, new prime numbers may be added to primes, and
primes can be reused by othher PrimeFactors objects.
o PrimeFactors(std::string const &name = "~/.primes", size_t blockSize = 1000):
Prime numbers that are determined while factorizing values are collected on a
stream whose name is passed as argument to this constructor. By default ~/.primes
is used. If name starts with `~/’, then this string is replaced by the user’s home
directory.
Primes are read from the named stream in blocks of at most blockSize, and new
primes are flushed to this stream once blockSize new primes have been generated or
when the PrimeFactors object (i.e., the last PrimeFactors object sharing the
stream) ceases to exist.
If the stream does not yet exist it is created by PrimeFactors. The stream may
either be empty, or it must contain sorted and white-space delimited prime numbers
(inserted as hexadecimal BigInt values). The first two primes on this file must be,
respectively, 2 and 3. The constructor does not verify whether the prime numbers
are actually sorted, but if the stream contains primes it does check whether the
first two prime numbers are indeed 2 and 3. An FBB::Exception is thrown if this
condition is not met.
While numbers are being factorized, new prime numbers may be added to the stream,
and the stream can be reused by other PrimeFactors objects.
The default copy and move constructors are available. FBB::PrimeFactor objects created
using the copy constructor share the prime numbers storage device (the BigIntVector or the
stream containing the primes) with their source objects.
OVERLOADED OPERATORS
The default copy and move assignment operators are available. Left-hand side
FBB::PrimeFactor objects receiving values from right-hand side FBB::PrimeFactor objects
using the copy assignment operator share the prime numbers storage device (the
BigIntVector or the stream containing the primes) with their right-hand side
FBB::PrimeFactors arguments.
MEMBER FUNCTION
o Factors const &factorize(BigInt const &value):
The prime factors of value are determined and returned in the PrimeFactors::Factors
vectors. While the prime factors of value are determined new prime numbers may be
added to the BigIntVector or to the stream that is passed to the PrimeFactors
object. The elements of PrimeFactors::Factors are sorted by their prime numbers.
The first element contains the value’s smallest prime number factor.
EXAMPLE
#include <iostream>
#include <bobcat/primefactors>
using namespace std;
using namespace FBB;
int main(int argc, char **argv)
{
PrimeFactors pf1("/tmp/primes");
PrimeFactors::Factors const *factors = &pf1.factorize(stoull(argv[1]));
cout << "Using /tmp/primes:\n";
for (auto &factor: *factors)
cout << factor.prime << "**" << factor.power << ’ ’;
vector<BigInt> primes;
PrimeFactors pf2(primes);
factors = &pf2.factorize(stoull(argv[1]));
cout << "\n"
"Using BigIntVector:\n";
for (auto &factor: *factors)
cout << factor.prime << "**" << factor.power << ’ ’;
cout << "\n"
"Collected primes: ";
for (auto &prime: primes)
cout << prime << ’ ’;
cout << ’\n’;
}
If this program is run with argument 1950 it produces the following output:
Using /tmp/primes:
2**1 3**1 5**2 13**1
Using BigIntVector:
2**1 3**1 5**2 13**1
Collected primes: 2 3 5 7 11 13
FILES
bobcat/primefactors - defines the class interface
SEE ALSO
bobcat(7), bigint(3bobcat)
BUGS
None Reported.
DISTRIBUTION FILES
o bobcat_4.08.02-x.dsc: detached signature;
o bobcat_4.08.02-x.tar.gz: source archive;
o bobcat_4.08.02-x_i386.changes: change log;
o libbobcat1_4.08.02-x_*.deb: debian package holding the libraries;
o libbobcat1-dev_4.08.02-x_*.deb: debian package holding the libraries, headers and
manual pages;
o http://sourceforge.net/projects/bobcat: public archive location;
BOBCAT
Bobcat is an acronym of `Brokken’s Own Base Classes And Templates’.
COPYRIGHT
This is free software, distributed under the terms of the GNU General Public License
(GPL).
AUTHOR
Frank B. Brokken (f.b.brokken@rug.nl).