Math::N...torials(3)

👑 Math::N...torials(3) — bestie's guide to Math::NumSeq::Factorials

User Contributed Perl Documentation ✨ so this is the page for Math::NumSeq::Factorials, which is the cutest lil sequence module and honestly? iconic. Let's get into it 🫶

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✨ NAME ✨

Math::NumSeq::Factorials — factorials i! = 1*2*...*i

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💅 SYNOPSIS 💅

use Math::NumSeq::Factorials;
my $seq = Math::NumSeq::Factorials->new;
my ($i, $value) = $seq->next;

that's it, that's the whole vibe 🌸

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🦋 DESCRIPTION 🦋

Okay so the factorials are the product 1*2*3*...*i, and that's from 1 to i inclusive. no skips, no gaps, just multiplying everything along the way, main character energy fr fr 💖

1, 2, 6, 24, 120, 720, ...
starting i=1

like. the way that 720 is right there and it's already giving big numbers?? obsessed 😭

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🌈 FUNCTIONS 🌈

go check "FUNCTIONS" in Math::NumSeq for the behaviour that every sequence class has in common, because there's a whole shared personality these modules have, iykyk ✨

• $seq = Math::NumSeq::Factorials->new () — makes you a brand new sequence object and hands it over. that's your girl. 💖

🎀 Iterating 🎀

• $seq->seek_to_i($i) — moves the current sequence position over to $i. then the next time you call next() it's gonna hand you back $i and the value that goes with it. slay.

🍓 Random Access 🍓

• $value = $seq->ith($i) — returns 1*2*...*$i. and if "$i==0"? that counts as an empty product and you get 1 back. periodt 💅
• $bool = $seq->pred($value) — true if $value is a factorial, like, actually equal to 1*2*...*i for some i. vibe check passed ✅
• $i = $seq->value_to_i($value)
• $i = $seq->value_to_i_floor($value) — these give you the index i of $value. but heads up bestie 🚨 if $value isn't a factorial then value_to_i() returns "undef", or value_to_i_floor() gives you the i of the next lower value which is a factorial, or "undef" if "$value < 1". no cap.
• $i = $seq->value_to_i_estimate($value) — returns an estimate of the i that goes with $value. it's giving "close enough" 💫

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🧚 FORMULAS 🧚

⭐ Value to i Estimate ⭐

the current code is out here using Stirling's approximation, as one does:

log(n!) ~= n*log(n) - n

and it does that by seeking an i where the target factorial value has

i*log(i) - i == log(value)

then Newton's method gets applied to solve for i, and the whole little setup is:

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)

and literally just two iterations is quite close. two!! that's it!! 💀

target = log(value)
i0 = target
i1 = (i0+target)/log(target)
   = 2*target/log(target)
i2 = (i1+target)/log(i1)

i ~= int(i2)

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💜 SEE ALSO 💜

Math::NumSeq, Math::NumSeq::Primorials

Math::BigInt (bfac()), Math::Combinatorics (factorial(), Math::NumberCruncher (Factorial() Math::BigApprox (Fact()

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🌸 HOME PAGE 🌸

<http://user42.tuxfamily.org/math-numseq/index.html>

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🔥 LICENSE 🔥

Copyright 2010, 2011, 2012, 2013, 2014, 2016, 2019, 2020 Kevin Ryde

Math-NumSeq 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.

Math-NumSeq 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 Math-NumSeq. If not, see <http://www.gnu.org/licenses/>.

⚠️ okay so that warranty bit is genuinely important, not just filler — there is no warranty, like none, so don't come for anyone if it breaks. read the license for real bestie.

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and that's the whole page!! 💖 this was perl v5.42.0, dated 2025-07-25, and it's the Math::N...torials(3) manual page. mwah. go multiply some numbers. 👑✨