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June 2018 Update

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Ingy döt Net 2018-06-22 20:57:24 +00:00
parent ba8067c3b7
commit 22f33d4004
5278 changed files with 84726 additions and 14379 deletions
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36
Task/Aliquot-sequence-classifications/REXX/aliquot-sequence-classifications.rexx
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@ -2,10 +2,10 @@
parse arg low high L /*obtain optional arguments from the CL*/
high=word(high low 10,1); low=word(low 1,1) /*obtain the LOW and HIGH (range). */
if L='' then L=11 12 28 496 220 1184 12496 1264460 790 909 562 1064 1488 15355717786080
numeric digits 20 /*be able to handle the number: BIG */
big=2**47; NTlimit=16+1 /*limits for a non─terminating sequence*/
numeric digits 100 /*be able to compute the number: BIG */
big= 2**47; NTlimit= 16 + 1 /*limits for a non─terminating sequence*/
numeric digits max(9, 1 + length(big) ) /*be able to handle big numbers for // */
#.=.; #.0=0; #.1=0 /*#. are the proper divisor sums. */
#.=.; #.0=0; #.1=0 /*#. are the proper divisor sums. */
say center('numbers from ' low " to " high, 79, "═")
do n=low to high; call classify n /*call a subroutine to classify number.*/
end /*n*/ /* [↑] process a range of integers. */
@ -14,13 +14,13 @@ say center('first numbers for each classification', 79, "═")
class.=0 /* [↓] ensure one number of each class*/
do q=1 until class.sociable\==0 /*the only one that has to be counted. */
call classify -q /*minus (-) sign indicates don't tell. */
_=what; upper _; class._=class._+1 /*bump counter for this class sequence.*/
_=what; upper _; class._= class._ +1 /*bump counter for this class sequence.*/
if class._==1 then say right(q, digits()) 'is' center(what, 15) $
end /*q*/ /* [↑] only display the 1st occurrence*/
say /* [↑] process until all classes found*/
say center('classifications for specific numbers', 79, "═")
do i=1 for words(L) /*L: is a list of "special numbers".*/
call classify word(L,i) /*call a subroutine to classify number.*/
call classify word(L, i) /*call a subroutine to classify number.*/
end /*i*/ /* [↑] process a list of integers. */
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
@ -28,29 +28,29 @@ classify: parse arg a 1 aa; a=abs(a) /*obtain number that's to be cl
if #.a\==. then s=#.a /*Was this number been summed before?*/
else s=sigma(a) /*No, then classify number the hard way*/
#.a=s; $=s /*define sum of the proper divisors. */
what='terminating' /*assume this kind of classification. */
c.=0; c.s=1 /*clear all cyclic sequences; set 1st.*/
if $==a then what='perfect' /*check for a "perfect" number. */
what= 'terminating' /*assume this kind of classification. */
c.=0; c.s=1 /*clear all cyclic sequences; set 1st.*/
if $==a then what= 'perfect' /*check for a "perfect" number. */
else do t=1 while s\==0 /*loop until sum isn't 0 or > big.*/
m=s /*obtain the last number in sequence. */
if #.m==. then s=sigma(m) /*Not defined? Then sum proper divisors*/
else s=#.m /*use the previously found integer. */
if m==s & m\==0 then do; what='aspiring' ; leave; end
parse var $ . word2 . /* " " 2nd " " " */
if word2==a then do; what='amicable' ; leave; end
if m==s & m\==0 then do; what= 'aspiring' ; leave; end
parse var $ . word2 . /*obtain the 2nd number in sequence. */
if word2==a then do; what= 'amicable' ; leave; end
$=$ s /*append a sum to the integer sequence.*/
if s==a & t>3 then do; what='sociable' ; leave; end
if c.s & m\==0 then do; what='cyclic' ; leave; end
if s==a & t>3 then do; what= 'sociable' ; leave; end
if c.s & m\==0 then do; what= 'cyclic' ; leave; end
c.s=1 /*assign another possible cyclic number*/
/* [↓] Rosetta Code task's limit: >16 */
if t>NTlimit then do; what='non-terminating'; leave; end
if s>big then do; what='NON-TERMINATING'; leave; end
if t>NTlimit then do; what= 'non-terminating'; leave; end
if s>big then do; what= 'NON-TERMINATING'; leave; end
end /*t*/ /* [↑] only permit within reason. */
if aa>0 then say right(a, digits() ) 'is' center(what, 15) $
return /* [↑] only display if A is positive.*/
return /* [↑] only display if AA is positive*/
/*──────────────────────────────────────────────────────────────────────────────────────*/
sigma: procedure expose #.; parse arg x; if x<2 then return 0; odd=x//2
s=1 /* [↓] use only EVEN | ODD ints. ___*/
sigma: procedure expose #. !.; parse arg x; if x<2 then return 0; odd=x//2
s=1 /* [↓] use EVEN or ODD integers. ___*/
do j=2+odd by 1+odd while j*j<x /*divide by all the integers up to √ X */
if x//j==0 then s=s + j + x%j /*add the two divisors to the sum. */
end /*j*/ /* [↓] adjust for square. ___*/