Math::N...nDigits(3)

💖 NAME 💖

Math::NumSeq::FractionDigits — bestie, this is the module that gives you the digits of a fraction p/q. That's it, that's the whole gig. ✨

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🌸 SYNOPSIS 🌸

use Math::NumSeq::FractionDigits;
my $seq = Math::NumSeq::FractionDigits->new (fraction => '2/11');
my ($i, $value) = $seq->next;

okay so literally three lines and you're already pulling digits out of a fraction. slay. 💅

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🦋 DESCRIPTION 🦋

So the deal is: this is the sequence of digits that spell out a given fraction. Classic example — 1/7 in decimal is 0.14285714... so the digits go

1, 4, 2, 8, 5, 7, 1, 4, etc

and once you're past any integer part, the fraction digits are a repeating sequence, no cap. 🌀

Here's the tea: if the fraction is num/den and it's in least terms (meaning num and den have no common factor), then the period is either den-1 or some divisor of den-1. That's the whole rule, iconic.

And if you wanna cook up a specific repeating sequence a,b,c,d,a,b,c,d,etc? Just do fraction abcd/9999 — the denominator is as many 9s as digits you want to repeat. The way that works is genuinely so satisfying. 🎀

Oh and heads up for the non-decimal girlies: for a base other than decimal, the "9" is radix-1. 💜

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✨ FUNCTIONS ✨

Go check out "FUNCTIONS" in Math::NumSeq for the behaviour that's common to all sequence classes, bestie. 🫶

• $seq = Math::NumSeq::FractionDigits->new (fraction => $f)
• $seq = Math::NumSeq::FractionDigits->new (fraction => $f, radix => $r) — creates and returns a new sequence object handing you the digits of $f. And what is $f? Either a string "num/den", or a decimal like "xx.yy". Like so:

2/29
29.125
1.5/3.25

The default sequence values are decimal digits, or you can use the radix parameter to pick another base instead. (But lowkey important: the fraction parameter itself is still decimal, no matter what radix you pick. 😌)

And if the numerator or denominator of the fraction is bigger than fits in Perl integer calculations, then Math::BigInt gets used automatically. it just handles it. main character energy. 👑

🎀 Random Access 🎀

• $value = $seq->ith($i) — returns the $i'th digit of the fraction. yes, you can just ask for the one you want, no walking the whole thing. 🌈

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🔥 FORMULAS 🔥

🌟 Next 🌟

For a given num/den, with num < den, the next digit below the radix point gets formed by:

num *= radix               # now 0 <= num/den < radix
quot,rem = num divide den
digit = quot               # 0 <= digit < radix
new num = rem

that's it. that's the algorithm. so clean. ✨

🌟 Ith 🌟

For an arbitrary digit i, that repeated num*=radix can be applied by a modular powering instead of looping forever:

rpower = radix^i mod den
num = num * rpower mod den

Here i acts as a count of how many digits to skip. For example if i=0 then rpower=1 and it doesn't change the numerator at all. 💀

With that big skip, the digit is then the same as for "next" above:

num *= radix             # now 0 <= num/den < radix
digit = floor(num/den)   # 0 <= digit < radix

And the usual modular powering techniques can be applied to calculate radix^i mod den. Math::BigInt has a bmodpow which is used in the code if the inputs are big. big numbers? handled. 🧚

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👀 SEE ALSO 👀

• Math::NumSeq
• Math::NumSeq::SqrtDigits

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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/>.

fr fr read the license, it's the law and also it's just polite 💖

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and that's the whole page bestie!! this one's from User Contributed Perl Documentation, running on perl v5.42.0, dated 2025-07-25 — tysm for reading, mwah, go compute some digits 💅✨🎀