aparler/RosettaCodeData
1
0
Fork 0
Code Issues 12 Pull requests 3 Projects Releases Packages Wiki Activity Actions

Data update

Browse source
This commit is contained in:
Ingy döt Net 2024-07-13 15:19:22 -07:00
parent 29a5eea0d4
commit 5c1bb7bfa9
2011 changed files with 35081 additions and 3229 deletions
Download patch file Download diff file Expand all files Collapse all files

74
Task/Tau-function/REXX/tau-function.rexx
View file

@ -1,32 +1,42 @@
/*REXX program counts the number of divisors (tau, or sigma_0) up to and including N.*/
parse arg LO HI cols . /*obtain optional argument from the CL.*/
if LO=='' | LO=="," then LO= 1 /*Not specified? Then use the default.*/
if HI=='' | HI=="," then HI= LO + 100 - 1 /*Not specified? Then use the default.*/
if cols=='' | cols=="," then cols= 20 /* " " " " " " */
w= 2 + (HI>45359) /*W: used to align the output columns.*/
say 'The number of divisors (tau) for integers up to ' n " (inclusive):"; say
say '─index─' center(" tau (number of divisors) ", cols * (w+1) + 1, '─')
$=; c= 0 /*$: the output list, shown ROW/line.*/
do j=LO to HI; c= c + 1 /*list # proper divisors (tau) 1 ──► N */
$= $ right( tau(j), w) /*add a tau number to the output list. */
if c//cols \== 0 then iterate /*Not a multiple of ROW? Don't display.*/
idx= j - cols + 1 /*calculate index value (for this row).*/
say center(idx, 7) $; $= /*display partial list to the terminal.*/
end /*j*/
if $\=='' then say center(idx+cols, 7) $ /*there any residuals left to display ?*/
exit 0 /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
tau: procedure; parse arg x 1 y /*X and $ are both set from the arg.*/
if x<6 then return 2 + (x==4) - (x==1) /*some low #s should be handled special*/
odd= x // 2 /*check if X is odd (remainder of 1).*/
if odd then #= 2 /*Odd? Assume divisor count of 2. */
else do; #= 4; y= x % 2; end /*Even? " " " " 4. */
/* [↑] start with known number of divs*/
do j=3 for x%2-3 by 1+odd while j<y /*for odd number, skip even numbers. */
if x//j==0 then do /*if no remainder, then found a divisor*/
#= # + 2; y= x % j /*bump # of divisors; calculate limit.*/
if j>=y then do; #= # - 1; leave; end /*reached limit?*/
end /* ___ */
else if j*j>x then leave /*only divide up to √ x */
end /*j*/; return # /* [↑] this form of DO loop is faster.*/
/* REXX program counts the number of divisors (tau,cr sigma_0) */
/* for a range of numbers */
Parse Arg lo hi cols . /*obtain optional argument from the CL.*/
If lo=='' | lo==',' Then lo=1 /*Not specified? Then use the default.*/
If hi=='' | hi==',' Then hi=lo+100-1 /*Not specified? Then use the default.*/
If cols=='' Then cols=20 /* " " " " " " */
w=2+(hi>45359) /* width of columns tau(4mns5360)=100 */
Say 'The number of divisors (tau) from' lo 'to' hi '(inclusive):'
Say ''
Say '-number' center(' tau (number of divisors) ',cols*(w+1)+1,'-')
line=''
c=0
index=lo
Do j=lo To hi
c=c+1
line=line right(tau(j),w) /* add a tau number to the output line. */
If c//cols=0 Then Do /* line has cols numbers */
Say center(index,7) line
line=''
cnt=0
Index=index+cols
End
End /*j*/
If line\=='' Then
Say center(index,7) line /*there any residuals left To display ? */
Exit 0 /*stick a fork in it, we're all done. */
/*---------------------------------------------------------------------------------*/
tau: Procedure
Parse Arg x
If x<6 Then /* some low numbers are handled special */
Return 2+(x==4)-(x==1)
tau=0
odd=x//2
Do j=1 by 1 While j*j<x
If odd & j//2=0 Then /* even j can't be a divisor of an odd x*/
Iterate
If x//j==0 Then /* if no remainder, then found a divisor*/
tau=tau+2 /* bump n of divisors */
End
If j*j=x Then /* x is a square */
tau=tau+1 /* its root is a divisor */
Return tau