Data update
This commit is contained in:
Ingy dot Net
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1045 changed files with 18889 additions and 2777 deletions
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/*REXX pgm does prime decomposition of a range of positive integers (with a prime count)*/
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numeric digits 1000 /*handle thousand digits for the powers*/
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parse arg bot top step base add /*get optional arguments from the C.L. */
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if bot=='' then do; bot=1; top=100; end /*no BOT given? Then use the default.*/
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if top=='' then top=bot /* " TOP? " " " " " */
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if step=='' then step= 1 /* " STEP? " " " " " */
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if add =='' then add= -1 /* " ADD? " " " " " */
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tell= top>0; top=abs(top) /*if TOP is negative, suppress displays*/
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w=length(top) /*get maximum width for aligned display*/
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if base\=='' then w=length(base**top) /*will be testing powers of two later? */
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@.=left('', 7); @.0="{unity}"; @.1='[prime]' /*some literals: pad; prime (or not).*/
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numeric digits max(9, w+1) /*maybe increase the digits precision. */
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#=0 /*#: is the number of primes found. */
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do n=bot to top by step /*process a single number or a range.*/
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?=n; if base\=='' then ?=base**n + add /*should we perform a "Mercenne" test? */
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pf=factr(?); f=words(pf) /*get prime factors; number of factors.*/
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if f==1 then #=#+1 /*Is N prime? Then bump prime counter.*/
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if tell then say right(?,w) right('('f")",9) 'prime factors: ' @.f pf
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end /*n*/
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say
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ps= 'primes'; if p==1 then ps= "prime" /*setup for proper English in sentence.*/
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say right(#, w+9+1) ps 'found.' /*display the number of primes found. */
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exit /*stick a fork in it, we're all done. */
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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factr: procedure; parse arg x 1 d,$ /*set X, D to argument 1; $ to null.*/
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if x==1 then return '' /*handle the special case of X = 1. */
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do while x//2==0; $=$ 2; x=x%2; end /*append all the 2 factors of new X.*/
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do while x//3==0; $=$ 3; x=x%3; end /* " " " 3 " " " " */
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do while x//5==0; $=$ 5; x=x%5; end /* " " " 5 " " " " */
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do while x//7==0; $=$ 7; x=x%7; end /* " " " 7 " " " " */
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/* ___*/
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q=1; do while q<=x; q=q*4; end /*these two lines compute integer √ X */
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r=0; do while q>1; q=q%4; _=d-r-q; r=r%2; if _>=0 then do; d=_; r=r+q; end; end
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do j=11 by 6 to r /*insure that J isn't divisible by 3.*/
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parse var j '' -1 _ /*obtain the last decimal digit of J. */
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if _\==5 then do while x//j==0; $=$ j; x=x%j; end /*maybe reduce by J. */
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if _ ==3 then iterate /*Is next Y is divisible by 5? Skip.*/
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y=j+2; do while x//y==0; $=$ y; x=x%y; end /*maybe reduce by J. */
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end /*j*/
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/* [↓] The $ list has a leading blank.*/
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if x==1 then return $ /*Is residual=unity? Then don't append.*/
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return $ x /*return $ with appended residual. */
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@ -1,48 +1,81 @@
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/*REXX pgm does prime decomposition of a range of positive integers (with a prime count)*/
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numeric digits 1000 /*handle thousand digits for the powers*/
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parse arg bot top step base add /*get optional arguments from the C.L. */
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if bot=='' then do; bot=1; top=100; end /*no BOT given? Then use the default.*/
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if top=='' then top=bot /* " TOP? " " " " " */
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if step=='' then step= 1 /* " STEP? " " " " " */
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if add =='' then add= -1 /* " ADD? " " " " " */
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tell= top>0; top=abs(top) /*if TOP is negative, suppress displays*/
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w=length(top) /*get maximum width for aligned display*/
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if base\=='' then w=length(base**top) /*will be testing powers of two later? */
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@.=left('', 7); @.0="{unity}"; @.1='[prime]' /*some literals: pad; prime (or not).*/
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numeric digits max(9, w+1) /*maybe increase the digits precision. */
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#=0 /*#: is the number of primes found. */
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do n=bot to top by step /*process a single number or a range.*/
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?=n; if base\=='' then ?=base**n + add /*should we perform a "Mercenne" test? */
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pf=factr(?); f=words(pf) /*get prime factors; number of factors.*/
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if f==1 then #=#+1 /*Is N prime? Then bump prime counter.*/
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if tell then say right(?,w) right('('f")",9) 'prime factors: ' @.f pf
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end /*n*/
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say
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ps= 'primes'; if p==1 then ps= "prime" /*setup for proper English in sentence.*/
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say right(#, w+9+1) ps 'found.' /*display the number of primes found. */
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exit /*stick a fork in it, we're all done. */
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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factr: procedure; parse arg x 1 d,$ /*set X, D to argument 1; $ to null.*/
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if x==1 then return '' /*handle the special case of X = 1. */
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do while x// 2==0; $=$ 2; x=x%2; end /*append all the 2 factors of new X.*/
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do while x// 3==0; $=$ 3; x=x%3; end /* " " " 3 " " " " */
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do while x// 5==0; $=$ 5; x=x%5; end /* " " " 5 " " " " */
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do while x// 7==0; $=$ 7; x=x%7; end /* " " " 7 " " " " */
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do while x//11==0; $=$ 11; x=x%11; end /* " " " 11 " " " " */ /* ◄■■■■ added.*/
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do while x//13==0; $=$ 13; x=x%13; end /* " " " 13 " " " " */ /* ◄■■■■ added.*/
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do while x//17==0; $=$ 17; x=x%17; end /* " " " 17 " " " " */ /* ◄■■■■ added.*/
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do while x//19==0; $=$ 19; x=x%19; end /* " " " 19 " " " " */ /* ◄■■■■ added.*/
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do while x//23==0; $=$ 23; x=x%23; end /* " " " 23 " " " " */ /* ◄■■■■ added.*/
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/* ___*/
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q=1; do while q<=x; q=q*4; end /*these two lines compute integer √ X */
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r=0; do while q>1; q=q%4; _=d-r-q; r=r%2; if _>=0 then do; d=_; r=r+q; end; end
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Numeric Digits 1000 /*handle thousand digits For the powers*/
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Parse Arg bot top step base add /*get optional arguments from the C.L. */
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If bot='?' Then Do
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Say 'rexx pfoo bot top step base add'
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Exit
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End
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If bot=='' Then /* no arguments given */
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Parse Value 1 100 With bot top /* set default range .*/
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If top=='' Then top=bot /* process one number */
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If step=='' Then step=1 /* step=2 to process only odd numbers */
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If add =='' Then add=-1 /* for Mersenne tests */
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tell=top>0 /*If TOP is negative, suppress displays*/
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top=abs(top)
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w=length(top) /*get maximum width For aligned display*/
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If base\=='' Then
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w=length(base**top) /*will be testing powers of two later? */
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tag.=left('', 7) /*some literals: pad; prime (or not).*/
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tag.0='{unity}'
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tag.1='[prime]'
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Numeric Digits max(9,w+1) /*maybe increase the digits precision. */
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np=0 /*np: is the number of primes found.*/
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Do n=bot To top by step /*process a single number or a range. */
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?=n
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If base\=='' Then /*should we perform a 'Mersenne' test? */
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?=base**n+add
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pf=factr(?) /* get prime factors */
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f=words(pf) /* number of prime factors */
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If f=1 Then /* If the number is prime */
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np=np+1 /* Then bump prime counter */
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If tell Then
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Say right(?,w) right('('f')',9) 'prime factors: ' tag.f pf
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End /*n*/
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Say ''
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ps='prime'
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If f>1 Then ps=ps's' /*setup For proper English in sentence.*/
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Say right(np, w+9+1) ps 'found.' /*display the number of primes found. */
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Exit /*stick a fork in it, we're all done. */
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/*---------------------------------------------------------------------------*/
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factr: Procedure
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Parse Arg x 1 d,pl /*set X, D to argument 1, pl to null */
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If x==1 Then Return '' /*handle the special case of X=1. */
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primes=2 3 5 7 11 13 17 19 23
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Do While primes>'' /* first check the small primes */
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Parse Var primes prime primes
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Do While x//prime==0
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pl=pl prime
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x=x%prime
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End
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End
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r=isqrt(x)
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Do j=29 by 6 To r /*insure that J isn't divisible by 3.*/
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Parse var j '' -1 _ /*obtain the last decimal digit of J. */
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If _\==5 Then Do
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Do While x//j==0
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pl=pl j
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x=x%j
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End /*maybe reduce by J. */
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End
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If _ ==3 Then Iterate /*If next Y is divisible by 5? Skip. */
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y=j+2
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Do While x//y==0
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pl=pl y
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x=x%y
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End /*maybe reduce by y. */
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End /*j*/
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If x==1 Then Return pl /*Is residual=unity? Then don't append.*/
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Return pl x /*return pl with appended residual.*/
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do j=29 by 6 to r /*insure that J isn't divisible by 3.*/ /* ◄■■■■ changed.*/
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parse var j '' -1 _ /*obtain the last decimal digit of J. */
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if _\==5 then do while x//j==0; $=$ j; x=x%j; end /*maybe reduce by J. */
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if _ ==3 then iterate /*Is next Y is divisible by 5? Skip.*/
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y=j+2; do while x//y==0; $=$ y; x=x%y; end /*maybe reduce by J. */
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end /*j*/
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/* [↓] The $ list has a leading blank.*/
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if x==1 then return $ /*Is residual=unity? Then don't append.*/
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return $ x /*return $ with appended residual. */
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isqrt: Procedure
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Parse Arg x
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x=abs(x)
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Parse Value 0 x with lo hi
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Do While lo<=hi
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t=(lo+hi)%2
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If t**2>x Then
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hi=t-1
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Else
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lo=t+1
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End
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Return t
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