Math::NumSeq::FractionDigits(3pm)

1Math::NumSeq::FractionDUisgeirtsC(o3n)tributed Perl DocuMmaetnht:a:tNiuomnSeq::FractionDigits(3)
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NAME

6       Math::NumSeq::FractionDigits -- the digits of a fraction p/q
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SYNOPSIS

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

14       The sequence of digits which are a given fraction.  For example 1/7 in
15       decimal, being 0.14285714...
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17           1, 4, 2, 8, 5, 7, 1, 4, etc
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19       After any integer part, the fraction digits are a repeating sequence.
20       If the fraction is num/den and is in least terms (num and den have no
21       common factor) then the period is either den-1 or some divisor of
22       den-1.
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24       A particular a repeating sequence a,b,c,d,a,b,c,d,etc can be cooked up
25       with fraction abcd/9999, the denominator being as many 9s as digits to
26       repeat.  For a base other than decimal the "9" is radix-1.
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FUNCTIONS

29       See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence
30       classes.
31
32       "$seq = Math::NumSeq::FractionDigits->new (fraction => $f)"
33       "$seq = Math::NumSeq::FractionDigits->new (fraction => $f, radix =>
34       $r)"
35           Create and return a new sequence object giving the digits of $f.
36           $f is a string "num/den", or a decimal "xx.yy",
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38               2/29
39               29.125
40               1.5/3.25
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42           The default sequence values are decimal digits, or the "radix"
43           parameter can select another base.  (But the "fraction" parameter
44           is still decimal.)
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46           If the numerator or denominator of the fraction is bigger than fits
47           Perl integer calculations then "Math::BigInt" is used
48           automatically.
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50   Random Access
51       "$value = $seq->ith($i)"
52           Return the $i'th digit of the fraction.
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FORMULAS

55   Next
56       For a given num/den, with num < den, the next digit below the radix
57       point is formed by
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59           num *= radix               # now 0 <= num/den < radix
60           quot,rem = num divide den
61           digit = quot               # 0 <= digit < radix
62           new num = rem
63
64   Ith
65       For an arbitrary digit i, the repeated num*=radix can be applied by a
66       modular powering
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68           rpower = radix^i mod den
69           num = num * rpower mod den
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71       i here acts as a count of how many digits to skip.  For example if i=0
72       then rpower=1 and doesn't change the numerator at all.  With that big
73       skip the digit is then the same as for "next" above,
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75           num *= radix             # now 0 <= num/den < radix
76           digit = floor(num/den)   # 0 <= digit < radix
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78       The usual modular powering techniques can be applied to calculate
79       radix^i mod den.  "Math::BigInt" has a bmodpow which is used in the
80       code if the inputs are big.
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HOME PAGE

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

89       Copyright 2010, 2011, 2012, 2013, 2014, 2016, 2019 Kevin Ryde
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91       Math-NumSeq is free software; you can redistribute it and/or modify it
92       under the terms of the GNU General Public License as published by the
93       Free Software Foundation; either version 3, or (at your option) any
94       later version.
95
96       Math-NumSeq is distributed in the hope that it will be useful, but
97       WITHOUT ANY WARRANTY; without even the implied warranty of
98       MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
99       General Public License for more details.
100
101       You should have received a copy of the GNU General Public License along
102       with Math-NumSeq.  If not, see <http://www.gnu.org/licenses/>.
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106perl v5.32.1                      2021-01-27   Math::NumSeq::FractionDigits(3)