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September 2017 Update

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Ingy döt Net 2017-09-23 10:01:46 +02:00
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commit ba8067c3b7
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Task/Extensible-prime-generator/REXX/extensible-prime-generator.rexx
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/*REXX program calculates and displays primes using an extendible prime number generator*/
parse arg f .; if f=='' then f=20 /*allow specifying number for 1 ──► F.*/
call primes f; do j=1 for f; $=$ @.j; end /*j*/
say 'first' f 'primes are:' $
say
call primes f; do j=1 for f; $=$ @.j; end /*j*/
say 'first' f 'primes are:' $
say
call primes -150; do j=100 to 150; if !.j==0 then iterate; $=$ j; end /*j*/
say 'the primes between 100 to 150 (inclusive) are:' $
say
say 'the primes between 100 to 150 (inclusive) are:' $
say
call primes -8000; do j=7700 to 8000; if !.j==0 then iterate; $=$ j; end /*j*/
say 'the number of primes between 7700 and 8000 (inclusive) is:' words($)
say
say 'the number of primes between 7700 and 8000 (inclusive) is:' words($)
say
call primes 10000
say 'the 10000th prime is:' @.10000
say 'the 10000th prime is:' @.10000
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
primes: procedure expose !. s. @. $ #; parse arg H . 1 m .,,$; H=abs(H)
if symbol('!.0')=='LIT' then /*1st time here? Then initialize stuff*/
do; !.=0; @.=0; s.=0 /*!.x = some prime; @.n = Nth prime. */
_=2 3 5 7 11 13 17 19 23 /*generate a bunch of low primes. */
do #=1 for words(_); p=word(_,#); @.#=p; !.p=1; end
#=#-1; !.0=#; s.#=@.#**2 /*set # to be the number of primes. */
end /* [↑] done with building low primes? */
neg= m<0 /*Negative? Request is for a P value.*/
if neg then if H<=@.# then return /*do we have a high enough P already?*/
else nop /*this is used to match the above THEN.*/
else if H<=# then return /*do we have a enough primes already ? */
primes: procedure expose !. s. @. $ #; parse arg H,,$; Hneg=H<0; H=abs(H)
if symbol('!.0')=="LIT" then do /*1st time here? Then initialize stuff*/
!.=0; @.=0; s.=0 /*!.x=a prime; @.n=Nth prime.*/
L=2 3 5 7 11 13 17 19 23 /*gen some low primes.*/
do #=1 for words(L); p=word(L, #); @.#=p; !.p=1
end /*#*/
#=#-1; !.0=#; s.#=@.#**2 /*set #≡numb. of primes*/
end
if Hneg then if H<=@.# then return /*do we have a high enough P already?*/
else nop /*this is used to match the above THEN.*/
else if H<=# then return /*are there enough primes currently ? */
/* [↓] gen more primes within range. */
do j=@.#+2 by 2 /*find primes until have H Primes. */
if j//3 ==0 then iterate /*is J divisible by three? */
parse var j '' -1 _; if _==5 then iterate /*is the right-most digit a 5?*/
if j//7 ==0 then iterate /*is J divisible by seven? */
if j//11==0 then iterate /*is J divisible by eleven? */
if j//13==0 then iterate /*is J divisible by thirteen? */
if j//17==0 then iterate /*is J divisible by seventeen? */
if j//19==0 then iterate /*is J divisible by nineteen? */
/*[↑] above five lines saves time. */
do k=!.0 while s.k<=j /*divide by the known odd primes. */
if j//@.k==0 then iterate j /*Is J ÷ by a prime? ¬prime. ___*/
end /*k*/ /* [↑] divide by odd primes up to √ j */
#=#+1 /*bump the number of primes found. */
@.#=j; s.#=j*j; !.j=1 /*assign to sparse array; prime²; P#.*/
if neg then if H<=@.# then leave /*do we have a high enough prime? */
do j=@.# + 2 by 2 /*find primes until have H Primes. */
if j//3 ==0 then iterate /*is J divisible by three? */
parse var j '' -1 _; if _==5 then iterate /*is the right─most digit a 5?*/
if j//7 ==0 then iterate /*is J divisible by seven? */
if j//11==0 then iterate /* " " " " eleven? */
if j//13==0 then iterate /* " " " " thirteen? */
if j//17==0 then iterate /* " " " " seventeen? */
if j//19==0 then iterate /* " " " " nineteen? */
/*[↑] above divisors go up to L end.*/
do k=!.0 while s.k<=j /*divide by the known odd primes. */
if j//@.k==0 then iterate j /*Is J ÷ by a prime? ¬prime. ___*/
end /*k*/ /* [↑] divide by odd primes up to √ J */
#=#+1 /*bump the number of primes found. */
@.#=j; s.#=j * j; !.j=1 /*assign to sparse array; prime²; P#.*/
if Hneg then if H<=@.# then leave /*is this a high enough prime? */
else nop /*used to match the above THEN. */
else if H<=# then leave /*do we have enough primes yet? */
end /*j*/ /* [↑] keep generating until enough. */
else if H<=# then leave /*have enough primes been generated? */
end /*j*/ /* [↑] keep generating until enough. */
return /*return to invoker with more primes. */