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Ingy döt Net 2023-07-01 11:58:00 -04:00
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Task/Trabb-Pardo-Knuth-algorithm/REXX/trabb-pardo-knuth-algorithm.rexx Normal file
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/*REXX program implements the Trabb─Pardo-Knuth algorithm for N numbers (default is 11).*/
numeric digits 200 /*the number of digits precision to use*/
parse arg N .; if N=='' | N=="," then N=11 /*Not specified? Then use the default.*/
maxValue= 400 /*the maximum value f(x) can have. */
wid= 20 /* ··· but only show this many digits.*/
frac= 5 /* ··· show this # of fractional digs.*/
say ' _____' /* ◄─── this SAY displays a vinculum.*/
say 'function: ƒ(x) ≡ √ │x│ + (5 * x^3)'
prompt= 'enter ' N " numbers for the Trabb─Pardo─Knuth algorithm: (or Quit)"
do ask=0; say; /*░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░*/
say prompt; say; pull $; say /*░*/
if abbrev('QUIT',$,1) then do; say 'quitting.'; exit 1; end /*░*/
ok=0 /*░*/
select /*validate there're N numbers.*/ /*░*/
when $='' then say "no numbers entered" /*░*/
when words($)<N then say "not enough numbers entered" /*░*/
when words($)>N then say "too many numbers entered" /*░*/
otherwise ok=1 /*░*/
end /*select*/ /*░*/
if \ok then iterate /* [↓] W=max width. */ /*░*/
w=0; do v=1 for N; _=word($, v); w=max(w, length(_) ) /*░*/
if datatype(_, 'N') then iterate /*numeric ?*/ /*░*/
say _ "isn't numeric"; iterate ask /*░*/
end /*v*/ /*░*/
leave /*░*/
end /*ask*/ /*░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░*/
say 'numbers entered: ' $
say
do i=N by -1 for N; #=word($, i) / 1 /*process the numbers in reverse. */
g = fmt( f( # ) ) /*invoke function ƒ with arg number.*/
gw=right( 'ƒ('#") ", w+7) /*nicely formatted ƒ(number). */
if g>maxValue then say gw "is > " maxValue ' ['space(g)"]"
else say gw " = " g
end /*i*/ /* [↑] display the result to terminal.*/
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
f: procedure; parse arg x; return sqrt( abs(x) ) + 5 * x**3
/*──────────────────────────────────────────────────────────────────────────────────────*/
fmt: z=right(translate(format(arg(1), wid, frac), 'e', "E"), wid) /*right adjust; use e*/
if pos(.,z)\==0 then z=left(strip(strip(z,'T',0),"T",.),wid) /*strip trailing 0 &.*/
return right(z, wid - 4*(pos('e', z)==0) ) /*adjust: no exponent*/
/*──────────────────────────────────────────────────────────────────────────────────────*/
sqrt: procedure; parse arg x; if x=0 then return 0; d=digits(); m.=9; numeric form; h=d+6
numeric digits; parse value format(x,2,1,,0) 'E0' with g 'E' _ .; g=g *.5'e'_ % 2
do j=0 while h>9; m.j=h; h=h % 2 + 1; end /*j*/
do k=j+5 to 0 by -1; numeric digits m.k; g=(g+x/g)*.5; end /*k*/; return g