Math::NumSeq::FractionDigits -- the digits of a fraction p/q
use Math::NumSeq::FractionDigits; my $seq = Math::NumSeq::FractionDigits->new (fraction => '2/11'); my ($i, $value) = $seq->next;
The sequence of digits which are a given fraction. For example 1/7 in decimal, being 0.14285714...
1, 4, 2, 8, 5, 7, 1, 4, etc
After any integer part, the fraction digits are a repeating sequence. If the fraction is num/den and is in least terms (num and den have no common factor) then the period is either den-1 or some divisor of den-1.
A particular a repeating sequence a,b,c,d,a,b,c,d,etc can be cooked up with fraction abcd/9999, the denominator being as many 9s as digits to repeat. For a base other than decimal the "9" is radix-1.
See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence classes.
$seq = Math::NumSeq::FractionDigits->new (fraction => $f)
$seq = Math::NumSeq::FractionDigits->new (fraction => $f, radix => $r)
Create and return a new sequence object giving the digits of $f
. $f
is a string "num/den", or a decimal "xx.yy",
2/29 29.125 1.5/3.25
The default sequence values are decimal digits, or the radix
parameter can select another base. (But the fraction
parameter is still decimal.)
If the numerator or denominator of the fraction is bigger than fits Perl integer calculations then Math::BigInt
is used automatically.
$value = $seq->ith($i)
Return the $i
'th digit of the fraction.
For a given num/den, with num < den, the next digit below the radix point is formed by
num *= radix # now 0 <= num/den < radix quot,rem = num divide den digit = quot # 0 <= digit < radix new num = rem
For an arbitrary digit i, the repeated num*=radix can be applied by a modular powering
rpower = radix^i mod den num = num * rpower mod den
i here acts as a count of how many digits to skip. For example if i=0 then rpower=1 and 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
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.
Math::NumSeq, Math::NumSeq::SqrtDigits
http://user42.tuxfamily.org/math-numseq/index.html
Copyright 2010, 2011, 2012, 2013, 2014 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/>.