2016 Update
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Tina Müller
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7965 changed files with 139854 additions and 31002 deletions
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/*REXX program to implement the Trabb─Pardo-Knuth algorithm for N numbers.*/
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N=11 /*N is the number of numbers to be used*/
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maxValue=400 /*the maximum value f(x) can have. */
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compDigs=200 /*compute with this many decimal digits*/
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showDigs=20 /* ··· but only show this many digits.*/
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numeric digits compDigs /*the number of digits precision to use*/
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say ' _____ ' /*vinculum.*/
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/*REXX program implements the Trabb─Pardo-Knuth algorithm for N numbers (default is 11).*/
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parse arg N .; if N=='' | N=="," then N=11 /*Not specified? Then use the default.*/
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maxValue=400 /*the maximum value f(x) can have. */
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wid= 20 /* ··· but only show this many digits.*/
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frac= 5 /* ··· show this # of fractional digs.*/
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numeric digits 200 /*the number of digits precision to use*/
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say ' _____ ' /* ◄───── display a vinculum.*/
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say 'function: ƒ(x) ≡ √ │x│ + (5 * x^3)'
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prompt= 'enter ' N " numbers for the Trabb─Pardo─Knuth algorithm: (or Quit)"
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prompt= 'enter ' N " numbers for the Trabb─Pardo─Knuth algorithm: (or Quit)"
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/*▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒ */
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do ask=0; say; say prompt; say; pull $; say /* ▒ */
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if abbrev('QUIT',$,1) then exit /*does the user want to QUIT this pgm? */ /* ▒ */
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do ask=0; say; say prompt; say; pull $; say /* ▒ */
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if abbrev('QUIT',$,1) then do; say 'quitting.'; exit 1; end /* ▒ */
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ok=0 /* ▒ */
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select /*validate that there are N numbers. */ /* ▒ */
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when $='' then say 'no numbers entered' /* ▒ */
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when words($)<N then say 'not enough numbers entered' /* ▒ */
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when words($)>N then say 'too many numbers entered' /* ▒ */
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select /*validate there're N numbers.*/ /* ▒ */
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when $='' then say "no numbers entered" /* ▒ */
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when words($)<N then say "not enough numbers entered" /* ▒ */
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when words($)>N then say "too many numbers entered" /* ▒ */
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otherwise ok=1 /* ▒ */
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end /*select*/ /* ▒ */
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if \ok then iterate /* [↓] is max width*/ /* ▒ */
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if \ok then iterate /* [↓] is max width.*/ /* ▒ */
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w=0; do v=1 for N; _=word($,v); w=max(w,length(_)) /* ▒ */
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if datatype(_,'N') then iterate /*numeric ? */ /* ▒ */
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if datatype(_,'N') then iterate /*numeric ? */ /* ▒ */
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say _ "isn't numeric"; iterate ask /* ▒ */
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end /*v*/ /* ▒ */
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leave /* ▒ */
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end /*ask*/ /* ▒ */
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say 'numbers entered: ' $; say /* ▒ */
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/*▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒ */
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do i=N by -1 to 1; #=word($,i)/1 /*process nums in reverse. */
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numeric digits compDigs; g=f(#) /*for func. ƒ, use big digs*/
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numeric digits showdigs; g=g/1 /*scale down output digits.*/
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gw=right('ƒ('#") ",w+7) /*nice formatted ƒ(number)*/
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if g>maxValue then say gw "is > " maxValue ' ['g"]"
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else say gw " = " g /*display the (good) result*/
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end /*i*/
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exit /*stick a fork in it, we're all done. */
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/*────────────────────────────────────────────────────────────────────────────*/
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f: procedure; parse arg x; return sqrt(abs(x)) + 5 * x**3
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/*────────────────────────────────────────────────────────────────────────────*/
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sqrt: procedure; parse arg x; if x=0 then return 0; d=digits(); i=; m.=9
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numeric digits 9; numeric form; h=d+6; if x<0 then do; x=-x; i='i'; end
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parse value format(x,2,1,,0) 'E0' with g 'E' _ .; g=g*.5'e'_%2
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do j=0 while h>9; m.j=h; h=h%2+1; end /*j*/
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do k=j+5 to 0 by -1; numeric digits m.k; g=(g+x/g)*.5; end /*k*/
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numeric digits d; return (g/1)i /*make complex if X < 0.*/
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say 'numbers entered: ' $
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say
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do i=N by -1 to 1; #=word($,i)/1 /*process the numbers in reverse. */
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g = fmt( f( # ) ) /*invoke function ƒ with arg number.*/
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gw=right( 'ƒ('#") ", w+7) /*nicely formatted ƒ(number). */
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if g>maxValue then say gw "is > " maxValue ' ['space(g)"]"
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else say gw " = " g
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end /*i*/ /* [+] display the result to terminal.*/
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exit /*stick a fork in it, we're all done. */
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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f: procedure; parse arg x; return sqrt( abs(x) ) + 5 * x**3
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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fmt: z=right(translate(format(arg(1),wid,frac),'e',"E"),wid) /*right adjust; use e*/
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if pos(.,z)\==0 then z=left(strip(strip(z,'T',0),"T",.),wid) /*strip trailing 0 &.*/
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return right(z,wid-4*(pos('e',z)==0)) /*adjust: no exponent*/
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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sqrt: procedure; parse arg x; if x=0 then return 0; d=digits(); m.=9; numeric form; h=d+6
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numeric digits; parse value format(x,2,1,,0) 'E0' with g 'E' _ .; g=g *.5'e'_ % 2
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do j=0 while h>9; m.j=h; h=h%2+1; end /*j*/
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do k=j+5 to 0 by -1; numeric digits m.k; g=(g+x/g)*.5; end /*k*/
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return g
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