divisorsSieve: Generate Complete Factorization for Numbers in a Range

In RcppAlgos: High Performance Tools for Combinatorics and Computational Mathematics

Generate Complete Factorization for Numbers in a Range

Description

Sieve that generates the complete factorization of all numbers between bound1 and bound2 (if supplied) or all numbers up to bound1.

Usage

divisorsSieve(bound1, bound2 = NULL, namedList = FALSE, nThreads = NULL)

Arguments

bound1	Positive integer or numeric value.
bound2	Positive integer or numeric value.
namedList	Logical flag. If TRUE, a named list is returned. The default is FALSE.
nThreads	Specific number of threads to be used. The default is NULL.

Details

This function is useful when many complete factorizations are needed. Instead of generating the complete factorization on the fly, one can reference the indices/names of the generated list.

This algorithm benefits greatly from the fast integer division library 'libdivide'. The following is from https://libdivide.com/:

• “libdivide allows you to replace expensive integer divides with comparatively cheap multiplication and bitshifts. Compilers usually do this, but only when the divisor is known at compile time. libdivide allows you to take advantage of it at runtime. The result is that integer division can become faster - a lot faster.”

Value

Returns a named/unnamed list of integer vectors if max(bound1, bound2) < 2^{31}, or a list of numeric vectors otherwise.

Note

The maximum value for either of the bounds is 2^{53} - 1.

Author(s)

Joseph Wood

References

• Divisor

• ridiculousfish (author of libdivide)

• github.com/ridiculousfish/libdivide

• 53-bit significand precision

See Also

divisorsRcpp, primeFactorizeSieve

Examples

## Generate some random data
set.seed(33550336)
mySamp <- sample(10^5, 5*10^4)

## Generate complete factorizations up
## to 10^5 (max element from mySamp)
system.time(allFacs <- divisorsSieve(10^5))

## Use generated complete factorization for further
## analysis by accessing the index of allFacs
for (s in mySamp) {
    myFac <- allFacs[[s]]
    ## Continue algorithm
}

## Generating complete factorizations over
## a range is efficient as well
system.time(divisorsSieve(10^12, 10^12 + 10^5))

## Use nThreads for improved efficiency
system.time(divisorsSieve(10^12, 10^12 + 10^5, nThreads = 2))

## Set 'namedList' to TRUE to return a named list
divisorsSieve(27, 30, namedList = TRUE)

## Using nThreads
system.time(divisorsSieve(1e5, 2e5, nThreads = 2))

RcppAlgos documentation built on May 29, 2024, noon