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Ingy döt Net 2023-07-01 11:58:00 -04:00
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Task/Extensible-prime-generator/REXX/extensible-prime-generator.rexx Normal file
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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.*/
_i= ' (inclusive) '; _b= 'between '; _tnp= 'the number of primes' _b; _tn= 'the primes'
call primes f; do j=1 for f; $= $ @.j; end /*j*/
say 'the first ' f " primes are: " $
say
call primes -150; do j=100 to 150; if !.j==1 then $= $ j; end /*j*/
say _tn _b '100 to 150' _i "are: " $
say
call primes -8000; do j=7700 to 8000; if !.j==1 then $= $ j; end /*j*/
say _tnp '7,700 and 8,000' _i "is: " words($)
say
call primes 10000
say 'the 10,000th prime is: ' @.10000
exit 0 /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
primes: procedure expose !. @. $ #; parse arg H,,$; Hneg= H<0; H= abs(H)
if symbol('#')=="LIT" then call .primI /*1st time here? Then initialize stuff*/
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; parse var j '' -1 _ /*find primes until have H Primes. */
if _==5 then iterate /*is the right─most digit a 5 (five)? */
if j// 3==0 then iterate /*is J divisible by three? (& etc.)*/
if j// 7==0 then iterate; if j//11==0 then iterate; if j//13==0 then iterate
if j//17==0 then iterate; if j//19==0 then iterate; if j//23==0 then iterate
if j//29==0 then iterate; if j//31==0 then iterate; if j//37==0 then iterate
if j//41==0 then iterate; if j//43==0 then iterate; if j//47==0 then iterate
if j//53==0 then iterate; if j//59==0 then iterate; if j//61==0 then iterate
if j//67==0 then iterate; if j//71==0 then iterate; if j//73==0 then iterate
if j//79==0 then iterate; if j//83==0 then iterate; if j//89==0 then iterate
if j//97==0 then iterate; if j//101==0 then iterate; if j//103==0 then iterate
x= j; r= 0; q= 1; do while q<=x; q= q*4; end /*R: the sqrt(J).*/
do while q>1; q=q%4; _=x-r-q; r=r%2; if _>=0 then do;x=_;r=r+q; end; end
do k=@.lowP while @.k<=r /*÷ by the known odd primes (hardcoded)*/
if j//@.k==0 then iterate j /*J ÷ by a prime? Then not prime. ___*/
end /*k*/ /* [↑] divide by odd primes up to √ J */
#= # + 1 /*bump the number of primes found. */
@.#= 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 /*have enough primes been generated? */
end /*j*/ /* [↑] keep generating until enough. */
return /*return to invoker with more primes. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
.primI: !.=0; @.=0; /*!.x= a prime or not; @.n= Nth prime.*/
L= 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103
do #=1 for words(L); p= word(L, #); @.#= p; !.p=1; end /*#*/
#= # - 1; @.lowP= #; return /*#: # primes; @.lowP: start of ÷ */