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Continued fraction/Arithmetic/Construct from rational number: Difference between revisions
Continued fraction/Arithmetic/Construct from rational number (view source)
Revision as of 22:41, 11 February 2013
, 11 years ago→{{header|REXX}}: added the REXX language. -- ~~~~
(corrected one of the numbers which appeared to have it's first digit clipped (probably while cut&pasting). -- ~~~~) |
(→{{header|REXX}}: added the REXX language. -- ~~~~) |
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print(list(real2cf(Fraction(13, 11)))) # => [1, 5, 2]
print(list(islice(real2cf(2 ** 0.5), 20))) # => [1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]</lang>
=={{header|REXX}}==
Programming notes:
<br><br>The '''numeric digits''' can be increased to a higher value to generate more terms.
<br>Two subroutines '''sqrt''' & '''pi''' were included here to demonstrate terms for √2 and π.
<br>The subroutine '''$maxfact''' was included and is only needed if the number used for '''r2cf''' is a decimal fraction.
<br>Checks were included to verify that the arguments being passed to '''r2cf''' are indeed numeric and also not zero.
<br>This version handles negative numbers.
<lang rexx>/*REXX pgm converts decimal or rational fraction to a continued fraction*/
numeric digits 230 /*this determines how many terms */
/*can be generated for dec fracts*/
say ' 1/2 ──► CF: ' r2cf( '1/2' )
say ' 3 ──► CF: ' r2cf( 3 )
say '23/8 ──► CF: ' r2cf( '23/8' )
say '13/11 ──► CF: ' r2cf( '13/11' )
say '22/7 ──► CF: ' r2cf( '22/7 ' )
say
say '───────── attempts at √2.'
say '14142/1e4 ──► CF: ' r2cf( '14142/1e4 ' )
say '141421/1e5 ──► CF: ' r2cf( '141421/1e5 ' )
say '1414214/1e6 ──► CF: ' r2cf( '1414214/1e6 ' )
say '14142136/1e7 ──► CF: ' r2cf( '14142136/1e7 ' )
say '141421356/1e8 ──► CF: ' r2cf( '141421356/1e8 ' )
say '1414213562/1e9 ──► CF: ' r2cf( '1414213562/1e9 ' )
say '14142135624/1e10 ──► CF: ' r2cf( '14142135624/1e10 ' )
say '141421356237/1e11 ──► CF: ' r2cf( '141421356237/1e11 ' )
say '1414213562373/1e12 ──► CF: ' r2cf( '1414213562373/1e12 ' )
say '√2 ──► CF: ' r2cf( sqrt(2) )
say
say '───────── an attempt at π'
say 'π ──► CF: ' r2cf( pi() )
exit /*stick a fork in it, we're done.*/
/*────────────────────────────────R2CF subroutine───────────────────────*/
r2cf: procedure; parse arg g 1 s 2; $=; if s=='-' then g = substr(g,2)
else s =
if pos('.',g)\==0 then do
if \datatype(g,'N') then call serr 'not numeric:' g
g = $maxfact(g)
end
if pos('/',g)==0 then g = g"/"1
parse var g n '/' d
if \datatype(n,'W') then call serr "a numerator isn't an integer:" n
if \datatype(d,'W') then call serr "a denominator isn't an integer:" d
n = abs(n) /*ensure numerator is positive. */
if d=0 then call serr 'a denominator is zero'
do while d\==0 /*where the rubber meets the road*/
$ = $ s || (n%d) /*append another number to list. */
_ = d
d = n // d /* % is int div, // is modulus.*/
n = _
end /*while*/
return strip($)
/*─────────────────────────────PI subroutine────────────────────────────*/
pi: return, /*a bit of overkill, but hey !! */
3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271
/* ··· should ≥ NUMERIC DIGITS */
/*─────────────────────────────SERR subroutine──────────────────────────*/
serr: say; say '***error!***'; say; say arg(1); say; exit
/*─────────────────────────────SQRT subroutine──────────────────────────*/
sqrt: procedure; parse arg x; if x=0 then return 0; d=digits();numeric digits 11
g=.sqrtGuess(); do j=0 while p>9; m.j=p; p=p%2+1; end
do k=j+5 to 0 by -1; if m.k>11 then numeric digits m.k; g=.5*(g+x/g); end
numeric digits d; return g/1
.sqrtGuess: if x<0 then call sqrtErr; numeric form; m.=11; p=d+d%4+2
parse value format(x,2,1,,0) 'E0' with g 'E' _ .; return g*.5'E'_%2
/*─────────────────────────────MAXFACT subroutine───────────────────────*/
$maxFact: procedure; parse arg x 1 _x,y; y=10**(digits()-1); b=0; h=1
a=1; g=0; do while a<=y & g<=y; n=trunc(_x); _=a; a=n*a+b; b=_; _=g
g=n*g+h; h=_; if n=_x | a/g=x then do; if a>y | g>y then iterate; b=a
h=g; leave; end; _x=1/(_x-n); end; return b'/'h
</lang>
'''output'''
<pre style="overflow:scroll">
1/2 ──► CF: 0 2
3 ──► CF: 3
23/8 ──► CF: 2 1 7
13/11 ──► CF: 1 5 2
22/7 ──► CF: 3 7
───────── attempts at √2.
14142/1e4 ──► CF: 1 2 2 2 2 2 1 1 29
141421/1e5 ──► CF: 1 2 2 2 2 2 2 3 1 1 3 1 7 2
1414214/1e6 ──► CF: 1 2 2 2 2 2 2 2 3 6 1 2 1 12
14142136/1e7 ──► CF: 1 2 2 2 2 2 2 2 2 2 6 1 2 4 1 1 2
141421356/1e8 ──► CF: 1 2 2 2 2 2 2 2 2 2 2 3 4 1 1 2 6 8
1414213562/1e9 ──► CF: 1 2 2 2 2 2 2 2 2 2 2 2 1 1 14 1 238 1 3
14142135624/1e10 ──► CF: 1 2 2 2 2 2 2 2 2 2 2 2 2 2 5 4 1 8 4 2 1 4
141421356237/1e11 ──► CF: 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 1 4 1 2 1 63 2 1 1 1 4 2
1414213562373/1e12 ──► CF: 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 1 11 2 3 2 1 1 1 25 1 2 3
√2 ──► CF: 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3
───────── an attempt at π
π ──► CF: 3 7 15 1 292 1 1 1 2 1 3 1 14 2 1 1 2 2 2 2 1 84 2 1 1 15 3 13 1 4 2 6 6 99 1 2 2 6 3 5 1 1 6 8 1 7 1 2 3 7 1 2 1 1 12 1 1 1 3 1 1 8 1 1 2 1 6 1 1 5 2 2 3 1 2 4 4 16 1 161 45 1 22 1 2 2 1 4 1 2 24 1 2 1 3 1 2 1 1 10 2 5 4 1 2 2 8 1 5 2 2 26 1 4 1 1 8 2 42 2 1 7 3 3 1 1 7 2 4 9 7 2 3 1 57 1 18 1 9 19 1 2 18 1 3 7 30 1 1 1 3 3 3 1 2 8 1 1 2 1 15 1 2 13 1 2 1 4 1 12 1 1 3 3 28 1 10 3 2 20 1 1 1 1 4 1 1 1 5 3 2 1 6 1 4 1 120 2 1 1 3 1 23 1 15 1 3 7 1 16 1 2 1 21 2 1 1 2 9 1 6 4
</pre>
=={{header|Ruby}}==
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