Add all the A tasks

Task/Averages-Mean-angle/REXX/averages-mean-angle.rexx

@@ -0,0 +1,57 @@
+/*REXX program to compute the mean angle  (angles expressed in degrees).*/
+numeric digits 50                      /*use fifty digits of precision. */
+showDigs=10                            /* ... but only show ten digits. */
+#=350 10          ;   say showit(#, meanAngleD(#))
+#=90 180 270 360  ;   say showit(#, meanAngleD(#))
+#=10 20 30        ;   say showit(#, meanAngleD(#))
+exit                                   /*stick a fork in it, we're done.*/
+/*──────────────────────────────────MEANANGD subroutine─────────────────*/
+meanAngleD:   procedure;  arg x;  _sin=0;  _cos=0
+numeric digits $d()+$d()%4
+n=words(x);                            do j=1 for n
+                                       xr = d2r(d2d(word(x,j)))
+                                       _sin = _sin + sin(xr)
+                                       _cos = _cos + cos(xr)
+                                       end   /*j*/
+return r2d(atan2(_sin/n, _cos/n))
+/*═════════════════════════════general 1-line subs══════════════════════*/
+/*The 1-line subs were broken up into multiple lines for easier reading.*/
+d2d:    return arg(1)//360
+d2r:    return r2r(d2d(arg(1))/180*pi())
+r2d:    return d2d((r2r(arg(1))/pi())*180)
+r2r:    return arg(1)//(2*pi())
+p:      return word(arg(1),1)
+$d:     return p(arg(1) digits())
+$fuzz:  return min(arg(1),max(1,$d()-arg(2)))
+showit: procedure expose showDigs;  numeric digits showDigs;  arg a,ma
+        return left('angles='a,30) 'mean angle=' format(ma,,showDigs,0)/1
+acos:   procedure; arg x; if x<-1 | x>1 then call $81r -1,1,x,"ACOS"
+        return .5*pi() - asin(x)   /* $81r subroutine not included here.*/
+atan:   if abs(arg(1))=1 then return pi()*.25*sign(arg(1))
+        return asin(arg(1) / sqrt(1+arg(1)**2))
+asin:   procedure;   arg x;   if x<-1 | x>1 then call $81r -1,1,x,"ASIN"
+        s=x*x;   if abs(x)>=.7 then return sign(x)*acos(sqrt(1-s),'-ASIN')
+        z=x;  o=x;  p=z;        do j=2 by 2;  o=o*s*(j-1)/j;  z=z+o/(j+1)
+        if z=p then leave;  p=z;  end;     return z
+atan2:  procedure;  arg y,x;  pi=pi();  s=sign(y)
+        select;  when x=0 then z=s*pi*.5;  when x<0 then if y=0 then z=pi
+        else z=s*(pi-abs(atan(y/x)));otherwise z=s*atan(y/x);end; return z
+cos:    procedure;  arg x;  x=r2r(x);  a=abs(x);  numeric fuzz $fuzz(5,3)
+        if a=0 then return 1;   if a=pi() then return -1
+        if a=pi()*.5 | a=pi()*1.5 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 $fuzz(5,3)
+        if x=pi()*.5 then return 1;   if x==pi()*1.5 then return -1
+        if abs(x)=pi() | x=0 then return 0;   return .sincos(x,x,1)
+.sincos: parse arg z,_,i; x=x*x; p=z; do k=2 by 2; _=-_*x/(k*(k+i)); z=z+_
+        if z=p then leave; p=z; end; return z
+sqrt:   procedure; parse arg x; if x=0 then return 0; d=digits()
+        numeric digits 11; g=.sqrtGuess(); do j=0 while p>9;m.j=p; p=p%2+1
+        end;     do k=j+5 to 0 by -1;  if m.k>11 then numeric digits m.k
+        g=.5*(g+x/g);  end;      numeric digits d;  return g/1
+.sqrtGuess: if x<0 then call er 02,x p($.ff 'SQRT') "negative"
+        /*The above IF statement was left here to show checking for x<0.*/
+        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
+pi:     return ,
+3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148