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Abundant, deficient and perfect number classifications: Difference between revisions

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Abundant, deficient and perfect number classifications (view source)

Revision as of 18:20, 1 August 2015

272 bytes added ,  8 years ago
m
→‎{{header|REXX}}: added/changed whitespace and comments, added optimization.
m (→‎{{header|REXX}}: added/changed whitespace and comments, added optimization.)
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=={{header|REXX}}==
===version 1===
<lang rexx>/*REXX pgm counts the #number of abundant/deficient/perfect numbers in a range.*/
parse arg low high . /*get optional argumentsargs from C.L. */
high=word(high low 20000,1); low=word(low 1,1) /*get the LOW and HIGH. values.*/
say center('integers from ' low " to " high, 45, "═")
a!.=0; d=0; p=0 /*setdefine all types of sums to bupkiszero. */
do j=low to high; $=sigma(j) /*find the sigma for an integer range. */
 
do if $<j=low tothen high; $ !.d=sigma(j)!.d+1 /*find theit's sigmaa for andeficient int rangenumber.*/
if $<j then else if $>j then d!.a=d!.a+1 /*it's a " " abundant deficient number. " */
else if $>j then a else !.p=a!.p+1 /* " " perfect abundant " */
end /*j*/▼
else p=p+1 /* " " perfect " */
▲ end /*j*/
 
say ' the number of perfect numbers: ' right(!.p, length(high))
say ' the number of abundant numbers: ' right(!.a, length(high))
say ' the number of deficient numbers: ' right(!.d, length(high))
exit /*stick a fork in it, we're all done. */
/*────────────────────────────────────────────────────────────────────────────*/
/*──────────────────────────────────SIGMA subroutine────────────────────*/
sigma: procedure; parse arg x; if x<2 then return 0; odd=x//2 /*odd? */
s=1 /* [↓] use only use EVEN| or ODD integers.*/
do j=2+odd by 1+odd while j*j<x /*divide by all integers up to √x. */
if x//j==0 then s=s+j+ x%j /*add the two divisors to the(sigma) sum. */
end /*j*/ /* [↑] % is the REXX integer dividedivision*/
/* [↓] adjust for a square. _ ___ */
if j*j==x then s=s+j /*Was X a square? If so, add √x. √ x */
return s /*return the(sigma) sum of the divisors. */</lang>
'''output''' &nbsp; when using the default inputs:
<pre>
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===version 1.5===
This version is pretty much the same as the 1<sup>st</sup> version but uses an &nbsp; ''integer square root'' &nbsp; function to calculate the limit of the &nbsp; '''do''' &nbsp; loop in the &nbsp; '''sigma''' &nbsp; function.
<lang rexx>/*REXX pgm counts the #number of abundant/deficient/perfect numbers in a range.*/
parse arg low high . /*get optional argumentsargs from C.L. */
high=word(high low 20000,1); low=word(low 1,1) /*get the LOW and HIGH. values.*/
say center('integers from ' low " to " high, 45, "═")
!.=0 /*setdefine all types of sums to zero. */
do j=low to high; $=sigma(j) /*find the sigma for an intinteger range. */
if $<j then !.d=!.d+1 /*it's a deficient number.*/
else if $>j then !.a=!.a+1 /* " " abundant " */
else !.p=!.p+1 /* " " perfect " */
end /*j*/
 
say ' the number of perfect numbers: ' right(!.p, length(high))
say ' the number of abundant numbers: ' right(!.a, length(high))
say ' the number of deficient numbers: ' right(!.d, length(high))
exit /*stick a fork in it, we're all done. */
/*────────────────────────────────────────────────────────────────────────────*/
/*──────────────────────────────────ISQRT subroutine────────────────────*/
iSqrt: procedure; parse arg x; q=1; r=0; do while q<=x; q=q*4; end
do while q>1; q=q%4; _=x-r-q; r=r%2; if _>=0 then do; x=_; r=r+q; end
end /*while q>1···*/
return r
/*────────────────────────────────────────────────────────────────────────────*/
/*──────────────────────────────────SIGMA subroutine────────────────────*/
sigma: procedure; parse arg x; odd=if x//2<5 then return /*max(0,x-1); [↓] some special cases.*/sqX=iSqrt(x)
s=1; odd=x//2 /* [↓] use only use EVEN| or ODD integers.*/▼
if x<5 then do; if x==0 then return 0; return x-1; end
sqX=iSqrt(x) do j=2+odd by 1+odd to sqX /*divide by all integers up to √ x /*calculate the integer square rt*/
if x//j==0 then s=s+j+ x%j /*add the two divisors to (sigma) sum. */
▲s=1 /* [↓] use only EVEN|ODD integers*/
do end /*j=2+odd*/ by 1+odd to sqX /*divide by[↑] % allis integersthe upREXX tointeger √xdivision*/
if x//j==0 then s=s+j+ x%j /*add the[↓] adjust for a square. two divisors to the sum___*/
if sqx*sqx==x then end /*s=s-j*/ /*Was X a square? If so, subtract √ x /* [↑] % is REXX integer divide*/
return s /*return [↓](sigma) sum adjustof forthe squaredivisors. _ */</lang>
if sqX*sqX==x then s=s-j /*Is X a square? If so, sub √x.*/
return s /*return the sum of the divisors.*/</lang>
'''output''' is the same as the 1<sup>st</sup> version.
 
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