Engel expansion: Difference between revisions

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=={{header|J}}==

{{trans|Raku}}<~~lang~~ J>to_engle=: {{ r=. i.0 while. y * 30>:#r do. y=. _1+y*{:r=. r, >.%y end. r }}

{{trans|Raku}}<syntaxhighlight lang="j">to_engle=: {{ r=. i.0 while. y * 30>:#r do. y=. _1+y*{:r=. r, >.%y end. r }}

from_engle=: {{+/%*/\y}}</~~lang~~>

from_engle=: {{+/%*/\y}}</syntaxhighlight>

Task examples:<~~lang~~ J> to_engle 3.14159265358979

Task examples:<syntaxhighlight lang="j"> to_engle 3.14159265358979

1 1 1 8 8 17 19 300 1991 2767 8641 16313 1628438 7702318 25297938 431350188 765676622 776491263 1739733589 2329473788 6871947674 17179869184

from_engle to_engle 3.14159265358979

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1.41421

1.414213562373095-from_engle to_engle 1.414213562373095

0</~~lang~~>

0</syntaxhighlight>

(by default, J displays the first six digits of floating point numbers)

Stretch goal (note that we seem to have a problem here with e, presumably because of the limited length of the series):<~~lang~~ j> pi175=: (%10x^175)*<.@o.10x^175

Stretch goal (note that we seem to have a problem here with e, presumably because of the limited length of the series):<syntaxhighlight lang="j"> pi175=: (%10x^175)*<.@o.10x^175

e101=: +/ %@!@i. 101x

sq2_179=: (10x^179)%~<.@%:2*10x^2*179

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1.25532e_34

0.0+sq2_179-from_engle to_engle sq2_179

9.66281e_196</~~lang~~>

9.66281e_196</syntaxhighlight>

=={{header|Julia}}==

<~~lang~~ ruby>tobigrational(s) = (d = length(s) - something(findfirst(==('.'), s), 0); parse(BigInt, replace(s, '.' => "")) // big"10"^d)

<syntaxhighlight lang="ruby">tobigrational(s) = (d = length(s) - something(findfirst(==('.'), s), 0); parse(BigInt, replace(s, '.' => "")) // big"10"^d)

toEngel(x) = (a = BigInt[]; while x != 0; y = ceil(big"1" // x); push!(a, y); x = x * y - 1; end; a)

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"25.628906",

])

</~~lang~~>{{out}}

</syntaxhighlight>{{out}}

<pre>

Number: 3.14159265358979

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=={{header|Phix}}==

with javascript_semantics

include mpfr.e

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printf(1,"Back to rational: %s\n\n", s)

end for

I could only get pi accurate to 125 decimal places and root2 to 87, so cut the input strings accordingly.

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=={{header|Raku}}==

<lang ~~perl6~~>sub to-engel ($rat is copy) { do while $rat { my $a = ceiling 1 / $rat; $rat = $rat × $a - 1; $a } }

<syntaxhighlight lang="raku" line>sub to-engel ($rat is copy) { do while $rat { my $a = ceiling 1 / $rat; $rat = $rat × $a - 1; $a } }

sub from-engel (@expanded) { sum [\×] @expanded.map: { FatRat.new: 1, $_ } }

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say " Converted back: " ~ @expanded.&from-engel;

put '';

}</~~lang~~>

}</syntaxhighlight>

<pre>Rational number: 3.14159265358979

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However, I've also limited the number of terms accumulated by the 'fromEngel' function to 70 which is just enough to reproduce the high precision rationals in decimal notation. To accumulate all the terms in a reasonable time would require the use of Wren-gmp which I've tried to avoid so the solution will run under Wren-CLI.

<~~lang~~ ecmascript>import "./big" for BigRat

<syntaxhighlight lang="ecmascript">import "./big" for BigRat

import "./fmt" for Fmt

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Fmt.print("Number of terms : $d", engel.count)

Fmt.print("Back to rational: $s\n", fromEngel.call(engel.take(70).toList).toDecimal(places))

}</~~lang~~>

}</syntaxhighlight>