NAME
Math::NumSeq::Factorials  factorials i! = 1*2*...*i
SYNOPSIS
use Math::NumSeq::Factorials;
my $seq = Math::NumSeq::Factorials>new;
my ($i, $value) = $seq>next;
DESCRIPTION
The factorials being product 1*2*3*...*i, 1 to i inclusive.
1, 2, 6, 24, 120, 720, ...
starting i=1
FUNCTIONS
See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence classes.
Iterating
$seq>seek_to_i($i)

Move the current sequence position to
$i
. The next call tonext()
will return$i
and corresponding value.
Random Access
$value = $seq>ith($i)

Return
1*2*...*$i
. For$i==0
this is considered an empty product and the return is 1. $bool = $seq>pred($value)

Return true if
$value
is a factorial, ie. equal to1*2*...*i
for some i. $i = $seq>value_to_i($value)
$i = $seq>value_to_i_floor($value)

Return the index i of
$value
. If$value
is not a factorial thenvalue_to_i()
returnsundef
, orvalue_to_i_floor()
the i of the next lower value which is orundef
if$value < 1
. $i = $seq>value_to_i_estimate($value)

Return an estimate of the i corresponding to
$value
.
FORMULAS
Value to i Estimate
The current code uses Stirling's approximation
log(n!) ~= n*log(n)  n
by seeking an i for which the target factorial "value" has
i*log(i)  i == log(value)
Newton's method is applied to solve for i,
target=log(value)
f(x) = x*log(x)  x  target wanting f(x)=0
f'(x) = log(x)
iterate next_x = x  f(x)/f'(x)
= (x+target)/log(x)
Just two iterations is quite close
target = log(value)
i0 = target
i1 = (i0+target)/log(target)
= 2*target/log(target)
i2 = (i1+target)/log(i1)
i ~= int(i2)
SEE ALSO
Math::NumSeq, Math::NumSeq::Primorials
Math::BigInt (bfac()
), Math::Combinatorics (factorial()
, Math::NumberCruncher (Factorial()
Math::BigApprox (Fact()
HOME PAGE
http://user42.tuxfamily.org/mathnumseq/index.html
LICENSE
Copyright 2010, 2011, 2012, 2013, 2014, 2016, 2019 Kevin Ryde
MathNumSeq 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, or (at your option) any later version.
MathNumSeq 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 General Public License for more details.
You should have received a copy of the GNU General Public License along with MathNumSeq. If not, see <http://www.gnu.org/licenses/>.