Count in factors: Difference between revisions

Content added Content deleted
m (→‎using integer SQRT: used better highlighting for the REXX section header.)
m (→‎{{header|REXX}}: optimized the function, simplified some code, added/changed whitespace and comments.)
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@.=left('', 8); @.0="{unity} "; @.1='[prime] ' /*some tags and handy-dandy literals.*/
@.=left('', 8); @.0="{unity} "; @.1='[prime] ' /*some tags and handy-dandy literals.*/
parse arg low high . /*get optional arguments from the C.L. */
parse arg low high . /*get optional arguments from the C.L. */
if low=='' then do; low=1; high=40; end /*No LOW & HIGH? Then use the default.*/
if low=='' then do; low= 1; high= 40; end /*No LOW & HIGH? Then use the default.*/
if high=='' then high=low; tell= (high>0) /*No HIGH? " " " " */
if high=='' then high= low /*No HIGH? " " " " */
w=length(high); high=abs(high) /*get maximum width for pretty output. */
tell= (high>0) /*if HIGH is positive, then show #'s.*/
numeric digits max(9, w+1) /*maybe bump the precision of numbers. */
high= abs(high) /*use the absolute value for HIGH. */
#=0 /*the number of primes found (so far). */
w= length(high) /*get maximum width for pretty output. */
do n=abs(low) to high; f= factr(n) /*process a single number or a range.*/
numeric digits max(9, w + 1) /*maybe bump the precision of numbers. */
p=words(translate(f,,'x')) - (n==1) /*P: is the number of prime factors. */
#= 0 /*the number of primes found (so far). */
if p==1 then #=#+1 /*bump the primes counter (exclude N=1)*/
do n=abs(low) to high; f= factr(n) /*process a single number or a range.*/
if tell then say right(n, w) '=' @.p space(f, 0) /*show if prime and factors.*/
p= words( translate(f, ,'x') ) - (n==1) /*P: is the number of prime factors. */
if p==1 then #= # + 1 /*bump the primes counter (exclude N=1)*/
⚫
end /*n*/
if tell then say right(n, w) '=' @.p f /*display if a prime, plus its factors.*/
⚫
end /*n*/
say
say
say right(#, w) ' primes found.' /*display the number of primes found. */
say right(#, w) ' primes found.' /*display the number of primes found. */
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/*──────────────────────────────────────────────────────────────────────────────────────*/
/*──────────────────────────────────────────────────────────────────────────────────────*/
factr: procedure; parse arg z 1 n,$; if z<2 then return z /*if Z too small, return Z*/
factr: procedure; parse arg z 1 n,$; if z<2 then return z /*if Z too small, return Z*/
do while z// 2==0; $=$ 'x 2' ; z=z% 2; end /*maybe add factor of 2 */
do while z//2==0; $= $'x2'; z= z % 2; end /*maybe add factor of 2 */
do while z// 3==0; $=$ 'x 3' ; z=z% 3; end /* " " " " 3 */
do while z//3==0; $= $'x3'; z= z % 3; end /* " " " " 3 */
do while z// 5==0; $=$ 'x 5' ; z=z% 5; end /* " " " " 5 */
do while z//5==0; $= $'x5'; z= z % 5; end /* " " " " 5 */
do while z// 7==0; $=$ 'x 7' ; z=z% 7; end /* " " " " 7 */
do while z//7==0; $= $'x7'; z= z % 7; end /* " " " " 7 */


do j=11 by 6 while j<=z /*insure that J isn't divisible by 3.*/
do j=11 by 6 while j<=z /*insure that J isn't divisible by 3.*/
parse var j '' -1 _ /*get the last decimal digit of J. */
parse var j '' -1 _ /*get the last decimal digit of J. */
if _\==5 then do while z//j==0; $=$ 'x' j; z=z%j; end /*maybe reduce Z.*/
if _\==5 then do while z//j==0; $=$'x'j; z= z%j; end /*maybe reduce Z.*/
if _ ==3 then iterate /*if next number will be ÷ by 5, skip.*/
if _ ==3 then iterate /*Next # ÷ by 5? Skip. ___ */
if j*j>n then leave /*are we higher than the √ N ? */
if j*j>n then leave /*are we higher than the √ N ? */
⚫
y= j + 2 /*obtain the next odd divisor. */
y=j+2
do while z//y==0; $=$ 'x' y; z=z%y; end /*maybe reduce Z.*/
do while z//y==0; $=$'x'y; z= z%y; end /*maybe reduce Z.*/
end /*j*/
end /*j*/


if z==1 then z= /*if residual is unity, then nullify it*/
if z==1 then return strip($ , , 'x') /*if residual is unity, then nullify it*/
return strip( strip($ 'x' z), , "x") /*elide a possible leading (extra) "x".*/</lang>
return strip($'x'z, , 'x') /*elide a possible leading (extra) "x".*/</lang>
{{out|output|text=&nbsp; when using the default inputs:}}
{{out|output|text=&nbsp; when using the default inputs:}}
<pre>
<pre>
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@.=left('', 8); @.0="{unity} "; @.1='[prime] ' /*some tags and handy-dandy literals.*/
@.=left('', 8); @.0="{unity} "; @.1='[prime] ' /*some tags and handy-dandy literals.*/
parse arg low high . /*get optional arguments from the C.L. */
parse arg low high . /*get optional arguments from the C.L. */
if low=='' then do; low= 1; high= 40; end /*No LOW & HIGH? Then use the default.*/
if low=='' then do; low= 1; high= 40; end /*No LOW & HIGH? Then use the default.*/
if high=='' then high= low; tell= (high>0) /*No HIGH? " " " " */
if high=='' then high= low /*No HIGH? " " " " */
high= abs(high); w= length(high) /*get maximum width for pretty output. */
tell= (high>0) /*if HIGH is positive, then show #'s.*/
numeric digits max(9, w+1) /*maybe bump the precision of numbers. */
high= abs(high) /*use the absolute value for HIGH. */
w= length(high) /*get maximum width for pretty output. */
numeric digits max(9, w + 1) /*maybe bump the precision of numbers. */
#= 0 /*the number of primes found (so far). */
#= 0 /*the number of primes found (so far). */
do n=abs(low) to high; f= factr(n) /*process a single number or a range.*/
do n=abs(low) to high; f= factr(n) /*process a single number or a range.*/
p= words( translate(f, , 'x') ) - (n==1) /*P: is the number of prime factors. */
p= words( translate(f, ,'x') ) - (n==1) /*P: is the number of prime factors. */
if p==1 then #= # + 1 /*bump the primes counter (exclude N=1)*/
if p==1 then #= # + 1 /*bump the primes counter (exclude N=1)*/
if tell then say right(n, w) '= ' @.p space(f, 0) /*show if prime and factors.*/
if tell then say right(n, w) '=' @.p f /*display if a prime, plus its factors.*/
end /*n*/
end /*n*/
say
say
say right(#, w) ' primes found.' /*display the number of primes found. */
say right(#, w) ' primes found.' /*display the number of primes found. */
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/*──────────────────────────────────────────────────────────────────────────────────────*/
/*──────────────────────────────────────────────────────────────────────────────────────*/
factr: procedure; parse arg z 1 n,$; if z<2 then return z /*if Z too small, return Z*/
factr: procedure; parse arg z 1 n,$; if z<2 then return z /*if Z too small, return Z*/
do while z// 2==0; $= $ 'x 2' ; z= z % 2; end /*maybe add factor of 2 */
do while z// 2==0; $= $'x2' ; z= z%2 ; end /*maybe add factor of 2 */
do while z// 3==0; $= $ 'x 3' ; z= z % 3; end /* " " " " 3 */
do while z// 3==0; $= $'x3' ; z= z%3 ; end /* " " " " 3 */
do while z// 5==0; $= $ 'x 5' ; z= z % 5; end /* " " " " 5 */
do while z// 5==0; $= $'x5' ; z= z%5 ; end /* " " " " 5 */
do while z// 7==0; $= $ 'x 7' ; z= z % 7; end /* " " " " 7 */
do while z// 7==0; $= $'x7' ; z= z%7 ; end /* " " " " 7 */
do while z//11==0; $= $ 'x 11' ; z= z % 11; end /* " " " " 11 */
do while z//11==0; $= $'x11'; z= z%11; end /* " " " " 11 */
do while z//13==0; $= $ 'x 13' ; z= z % 13; end /* " " " " 13 */
do while z//13==0; $= $'x13'; z= z%13; end /* " " " " 13 */
do while z//17==0; $= $ 'x 17' ; z= z % 17; end /* " " " " 17 */
do while z//17==0; $= $'x17'; z= z%17; end /* " " " " 17 */
do while z//19==0; $= $ 'x 19' ; z= z % 19; end /* " " " " 19 */
do while z//19==0; $= $'x19'; z= z%19; end /* " " " " 19 */
do while z//23==0; $= $ 'x 23' ; z= z % 23; end /* " " " " 23 */
do while z//23==0; $= $'x23'; z= z%23; end /* " " " " 23 */
do while z//29==0; $= $ 'x 29' ; z= z % 29; end /* " " " " 29 */
do while z//29==0; $= $'x29'; z= z%29; end /* " " " " 29 */
do while z//31==0; $= $ 'x 31' ; z= z % 31; end /* " " " " 31 */
do while z//31==0; $= $'x31'; z= z%31; end /* " " " " 31 */
do while z//37==0; $= $ 'x 37' ; z= z % 37; end /* " " " " 37 */
do while z//37==0; $= $'x37'; z= z%37; end /* " " " " 37 */
r= 0 /*R: will be integer SQRT of Z.*/

if z>40 then do; t= z; q= 1; do while q<=t; q= q * 4; end /*while*/
if z>40 then do; t= z; q= 1; do while q<=t; q= q * 4; end /*while*/
r= 0 /*R: will be integer SQRT of Z.*/
do while q>1; q= q%4; _= t-r-q; r= r%2; if _>=0 then do; t=_; r=r+q
do while q>1; q= q%4; _= t-r-q; r= r%2; if _>=0 then do; t=_; r=r+q
end
end
end /*while*/ /* [↑] find integer SQRT(z). */
⚫
end /*while*/ /* [↑] find integer SQRT(z). */


do j=41 by 6 to r while j<=z /*insure J isn't divisible by 3*/
do j=41 by 6 to r while j<=z /*insure J isn't divisible by 3*/
parse var j '' -1 _ /*get last decimal digit of J.*/
parse var j '' -1 _ /*get last decimal digit of J.*/
if _\==5 then do while z//j==0; $=$ 'x' j; z= z % j
if _\==5 then do while z//j==0; $=$'x'j; z= z%j; end
end /*while*/ /* [↑] reduce Z by J ? */
if _ ==3 then iterate /*Next number ÷ by 5 ? Skip.*/
if _ ==3 then iterate /*Next number ÷ by 5 ? Skip.*/
y= j + 2 /*use the next (odd) divisor. */
y= j + 2 /*use the next (odd) divisor. */
do while z//y==0; $=$'x'y; z= z%y; end
do while z//y==0; $=$ 'x' y; z= z % y
end /*j*/ /* [↑] reduce Z by Y ? */
end /*while*/ /* [↑] reduce Z by Y ? */
end /*if z>40*/
end /*j*/
end /*if z>40*/


if z==1 then z= /*if residual is unity, nullify it.*/
if z==1 then return strip($ , , 'x') /*if residual is unity, then nullify it*/
return strip(strip( $ 'x' z), , "x") /*elide a possible leading "x" */</lang>
return strip($'x'z, , 'x') /*elide a possible leading (extra) "x".*/</lang>
{{out|output|text=&nbsp; is identical to the 1<sup>st</sup> REXX version.}}<br><br>
{{out|output|text=&nbsp; is identical to the 1<sup>st</sup> REXX version.}}<br><br>


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