Continued fraction/Arithmetic/Construct from rational number: Difference between revisions
Continued fraction/Arithmetic/Construct from rational number (view source)
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314285714 / 100000000 = 3 7 7142857
</pre>
=={{header|m4}}==
Being able to do such things in m4, without much trouble, makes it very useful as a program-source preprocessor. There may be better macroprocessors, but having ''some'' version of m4 is standard for POSIX platforms.
<syntaxhighlight lang="m4">divert(-1)
# m4 is a recursive macro language with eager evaluation. Generally
# there is no tail-call optimization. I shall define r2cf in a natural
# way, rather than try to mimic call-by-reference or lazy evaluation.
define(`r2cf',`$1/$2 => [_$0($1,$2,`')]')
define(`_r2cf',
`ifelse(eval($2 != 0),1,
`$3eval($1 / $2)$0($2,eval($1 % $2),ifelse($3,,`; ',```,'' '))')')
divert`'dnl
dnl
r2cf(1, 2)
r2cf(3, 1)
r2cf(23, 8)
r2cf(13, 11)
r2cf(22, 7)
r2cf(-151, 77)
dnl
r2cf(14142, 10000)
r2cf(141421, 100000)
r2cf(1414214, 1000000)
r2cf(14142136, 10000000)
dnl
r2cf(31, 10)
r2cf(314, 100)
r2cf(3142, 1000)
r2cf(31428, 10000)
r2cf(314285, 100000)
r2cf(3142857, 1000000)
r2cf(31428571, 10000000)
r2cf(314285714, 100000000)
</syntaxhighlight>
{{out}}
<pre>$ m4 continued-fraction-from-rational.m4
1/2 => [0; 2]
3/1 => [3]
23/8 => [2; 1, 7]
13/11 => [1; 5, 2]
22/7 => [3; 7]
-151/77 => [-1; -1, -24, -1, -2]
14142/10000 => [1; 2, 2, 2, 2, 2, 1, 1, 29]
141421/100000 => [1; 2, 2, 2, 2, 2, 2, 3, 1, 1, 3, 1, 7, 2]
1414214/1000000 => [1; 2, 2, 2, 2, 2, 2, 2, 3, 6, 1, 2, 1, 12]
14142136/10000000 => [1; 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 1, 2, 4, 1, 1, 2]
31/10 => [3; 10]
314/100 => [3; 7, 7]
3142/1000 => [3; 7, 23, 1, 2]
31428/10000 => [3; 7, 357]
314285/100000 => [3; 7, 2857]
3142857/1000000 => [3; 7, 142857]
31428571/10000000 => [3; 7, 476190, 3]
314285714/100000000 => [3; 7, 7142857]</pre>
=={{header|Mathematica}} / {{header|Wolfram Language}}==
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