Continued fraction/Arithmetic/Construct from rational number: Difference between revisions

Content added Content deleted
(→‎{{header|REXX}}: changed/added comments and whitespace, changed indentations, reformatted some functions, reinstated original glyphs for readability.)
(→‎{{header|REXX}}: re-added the REXX program source text.)
Line 797: Line 797:
*   Checks were included to verify that the arguments being passed to   '''r2cf''''   are indeed numeric and also not zero.
*   Checks were included to verify that the arguments being passed to   '''r2cf''''   are indeed numeric and also not zero.
*   This version also handles negative numbers.
*   This version also handles negative numbers.
<lang rexx>/*REXX program converts a decimal or rational fraction to a continued fraction. */
<lang rexx></lang>
numeric digits 230 /*determines how many terms to be gened*/
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 pi'
say 'pi ──► CF: ' r2cf( pi() )
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
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: return 3.1415926535897932384626433832795028841971693993751058209749445923078164062862,
|| 089986280348253421170679821480865132823066470938446095505822317253594081284,
|| 811174502841027019385211055596446229489549303819644288109756659334461284756,
|| 48233786783165271 /* ··· should ≥ NUMERIC DIGITS */
/*──────────────────────────────────────────────────────────────────────────────────────*/
serr: say; say '***error!***'; say; say arg(1); say; exit 13
/*──────────────────────────────────────────────────────────────────────────────────────*/
sqrt: procedure; parse arg x; if x=0 then return 0; d=digits(); h=d+6; numeric form
m.=9; numeric digits; parse value format(x,2,1,,0) 'E0' with g 'E' _ .; g=g*.5'e'_%2
do j=0 while h>9; m.j=h; h=h%2+1; end /*j*/
do k=j+5 to 0 by -1; numeric digits m.k; g=(g+x/g)*.5; end /*k*/
numeric digits d; return g/1
/*──────────────────────────────────────────────────────────────────────────────────────*/
$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'''
'''output'''
<pre>
<pre>
Retrieved from "https://rosettacode.org/wiki/Continued_fraction/Arithmetic/Construct_from_rational_number"