tasks a-s

Task/Random-numbers/REXX/random-numbers.rexx

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+/*REXX pgm gens 1,000 normally distributed #s: mean=1, standard dev.=½. */
+call pi                                /*call subroutine to define  pi. */
+parse arg n seed .                     /*allow specification of N | seed*/
+if n=='' | n==','  then n=1000         /*  N  is the size of the array. */
+if seed\=='' then call random ,,seed   /*use seed for repeatable RANDOM#*/
+mean=1                                 /*desired new mean (arith. avg.) */
+sd=1/2                                 /*desired new standard deviation.*/
+          do g=1  for n                /*generate N uniform random nums.*/
+          #.g=random(0,1e5)/1e5        /*REXX gens uniform rand integers*/
+          end   /*g*/
+
+say '              old mean=' mean()
+say 'old standard deviation=' stddev()
+say
+      do j=1  to n-1  by 2
+      m=j+1
+        _=sd*sqrt(-2*ln(#.j))*cos(2*pi*#.m)+mean /*use Box-Muller method*/
+      #.m=sd*sqrt(-2*ln(#.j))*sin(2*pi*#.m)+mean /*rand # must be 0──<E29480>1.*/
+      #.j=_
+      end    /*j*/
+say '              new mean=' mean()
+say 'new standard deviation=' stddev()
+exit                                   /*stick a fork in it, we're done.*/
+/*──────────────────────────────────subroutines─────────────────────────*/
+mean:   _=0; do k=1 for n; _=_+#.k; end; return _/n
+stddev: _avg=mean(); _=0; do k=1 for n; _=_+(#.k-_avg)**2; end; return sqrt(_/n)
+e:      e=2.7182818284590452353602874713526624977572470936999595749669676277240766303535;  return e
+pi:     pi=3.1415926535897932384626433832795028841971693993751058209749445923078164062862; return pi
+r2r:    return arg(1)//(2*pi())
+sqrt:   procedure;parse arg x; if x=0 then return 0; d=digits(); numeric digits 11; g=.sqrtGuess()
+        do j=0 while p>9; m.j=p; p=p%2+1; end; do k=j+5 to 0 by -1; if m.k>11 then numeric digits m.k
+        g=.5*(g+x/g); end; numeric digits d; return g/1
+.sqrtGuess: numeric form;  m.=11;  p=d+d%4+2
+        parse value format(x,2,1,,0) 'E0' with g 'E' _ .; return g*.5'E'_%2
+cos:    procedure; arg x; x=r2r(x); a=abs(x); numeric fuzz min(9,digits()-9); if a=pi() then return -1
+        if a=pi()/2|a=2*pi() then return 0;if a=pi()/3 then return .5;if a=2*pi()/3 then return -.5;return .sincos(1,1,-1)
+sin:    procedure; arg x; x=r2r(x); numeric fuzz min(5,digits()-3); if abs(x)=pi() then return 0; return .sincos(x,x,1)
+.sincos:parse arg z,_,i; x=x*x; p=z; do k=2 by 2; _=-_*x/(k*(k+i)); z=z+_; if z=p then leave; p=z; end; return z
+ln:     procedure; parse arg x,f; call e; ig=x>1.5; is=1-2*(ig\==1); ii=0; xx=x; return .ln_comp()
+.ln_comp: do while ig&xx>1.5|\ig&xx<.5;_=e;do k=-1;iz=xx*_**-is;if k>=0&(ig&iz<1|\ig&iz>.5) then leave;_=_*_;izz=iz;end
+        xx=izz;ii=ii+is*2**k;end;x=x*e**-ii-1;z=0;_=-1;p=z;do k=1;_=-_*x;z=z+_/k;if z=p then leave;p=z;end;return z+ii