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Proper divisors: Difference between revisions

Proper divisors (view source)

Revision as of 18:49, 15 October 2015

266 bytes removed ,  8 years ago
→‎{{header|REXX}}: added/changed whitespace and comments, moved the iSqrt function in-line, changed wording in the REXX section header.
m (→‎version 2: updated the output to reflect the highest number of Pdivs for 20k instead of 2k.)
(→‎{{header|REXX}}: added/changed whitespace and comments, moved the iSqrt function in-line, changed wording in the REXX section header.)
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do i=1 for words(xtra); n=word(xtra,i)
numeric digits max(9,length(n)+1); q=Pdivs(n); #=words(q)
say right(n,max(20,digits()w)) 'has' center(#,4) "proper divisors."
end /*i*/ /* [↑] support extra specified integers*/
exit /*stick a fork in it, we're all done. */
/*────────────────────────────────────────────────────────────────────────────*/
Pdivs: procedure; parse arg x,b; x=abs(x); if x==1 then return ''
odd=x//2; if x==0 then return '∞'
a=1 /* [↓] douse only EVENall or ODDonly odd #s. ___ */
do j=2+odd by 1+odd while j*j<x /*divide by all thesome integers up to √ xX */
if x//j==0 then do; a=a j; b=x%j b; end /*if ÷, add both divisors to α&ß*/
end /*j*/ /* [↑] % is the REXX integer division*/
/* [↓] adjust for a square. ___ */
if j*j==x then return a j b /*Was X a square? If so, add √ xX */
return a b /*return the divisors (both lists). */</lang>
'''output''' &nbsp; when using the following input: &nbsp; <tt> 0 &nbsp; 10 &nbsp; 1 &nbsp; &nbsp; &nbsp; 20000 &nbsp; &nbsp; &nbsp; 166320 &nbsp; 1441440 &nbsp; 11796480000 </tt>
<pre>
0 has ∞ proper divisors: ∞
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===version 3===
This REXX version is slightlyabout 10% faster than the REXX version 2 &nbsp; (especially when specifying larger numbers).
 
It accomplishes a faster speed by incorporating the usecalculation of thean &nbsp; '''iSqrt'integer square root'' &nbsp; functionof whichan computes theinteger &nbsp; (without using any floating point arithmetic).
<br>''integer square root'' &nbsp; of an integer &nbsp; (without using any floating point arithmetic).
<lang rexx>/*REXX program finds proper divisors (& count) of integer ranges; & max count.*/
parse arg bot top inc range xtra /*get optional arguments from CL.*/
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do i=1 for words(xtra); n=word(xtra,i)
numeric digits max(9,length(n)+1); q=Pdivs(n); #=words(q)
say right(n,max(20,digits()w)) 'has' center(#,4) "proper divisors."
end /*i*/ /* [↑] support extra specified integers*/
exit /*stick a fork in it, we're all done. */
/*────────────────────────────────────────────────────────────────────────────*/
iSqrtPdivs: procedure; parse arg x,b; rx=0abs(x); qif x==1; then return do while q<=x; q=q*4; end''
aodd=1x//2; if /*x==0 [↓] then doreturn only'∞' EVEN or ODD/* #s.___ ___*/▼
do while q>1;q=q%4;_=x-r-q;r=r%2;if _>=0 then do;x=_;r=r+q;end;end;return r
z=x; r=0; q=1; do while q<=z; q=q*4; end /*R will be the integer √ X */
/*────────────────────────────────────────────────────────────────────────────*/
Pdivs: procedure; parse arg x,b; do while xq>1; q=abs(x)q%4; _=z-r-q; r=r%2; if x_>==10 then returndo; z=_; r=r+q; end; ''end
odda=x//2;1 /* [↓] if x==0use all thenor returnonly '∞'odd #s. ___ */
do j=2+odd by 1+odd while j<iqxr /*divide by all thesome integers up to √ xX */▼
iqx=iSqrt(x)
▲a=1 /* [↓] do only EVEN or ODD #s. ___*/
▲ do j=2+odd by 1+odd while j<iqx /*divide by all the integers up to √ x */
if x//j==0 then do; a=a j; b=x%j b; end /*if ÷, add both divisors to α&ß*/
end /*j*/ /* [↑] % is the REXX integer division*/
/* [↓] adjust for a square. ___ */
if j*j==x then return a j b /*Was X a square? If so, add √ xX */
return a b /*return the divisors (both lists). */</lang>
'''output''' &nbsp; is identical to the 2<sup>nd</sup> REXX version. <br><br>
Retrieved from "https://rosettacode.org/wiki/Special:MobileDiff/252436"
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