with ELEMENTARY_FUNCTIONS ; use ELEMENTARY_FUNCTIONS ;

function SPIRAL ( X : FLOAT ;
                  Y : FLOAT ) return FLOAT is

  -- return Z as SPIRAL(X,Y) such that a surface is generated with a spiral
  -- trough running down a side of a cone with vertex at 0,0
  -- typical use X in -16..16  Y in -16..16  step size 0.5
  -- then Z, the return, runs about 0..10 for interesting plot
  --  Z runs from -0.1 to 18.0 full scale

    HALFPI : FLOAT := 1.57079 ;
    R : FLOAT;
    THETA : FLOAT;
    TZ : FLOAT;

begin

    R := SQRT ( X * X + Y * Y ) ;
    if R < 0.01 then
      THETA := 0.0 ;
    else
      THETA := ARCTAN ( Y , X ) ;
    end if ;
    TZ := THETA / HALFPI ;
    if TZ < 0.0 then
      TZ := TZ + 4.0 ;
    end if ;
    return 0.75 * R + SIN (( R + TZ ) * HALFPI );
end SPIRAL ;

with TEXT_IO; use TEXT_IO;
with FLOAT_TEXT_IO; use FLOAT_TEXT_IO;
with SPIRAL;
procedure TEST_SPIRAL is
  X : FLOAT;
  Y : FLOAT;
  Z : FLOAT;
begin
  for I in INTEGER(-6) .. 6 loop
    for J in INTEGER(-6) .. 6 loop
      X := FLOAT(I)/2.0;
      Y := FLOAT(J)/2.0;
      Z := SPIRAL(X,Y);
      PUT(X,3,1,0); PUT("  "); PUT(Y,3,1,0); PUT("  "); PUT(Z,3,1,0); NEW_LINE;
    end loop;
  end loop;
  X := 16.0;
  Y := 16.0;
  Z := SPIRAL(X,Y);
  PUT(X,3,1,0); PUT("  "); PUT(Y,3,1,0); PUT("  "); PUT(Z,3,1,0); NEW_LINE;
  Y := -16.0;
  Z := SPIRAL(X,Y);
  PUT(X,3,1,0); PUT("  "); PUT(Y,3,1,0); PUT("  "); PUT(Z,3,1,0); NEW_LINE;
  X := -16.0;
  Z := SPIRAL(X,Y);
  PUT(X,3,1,0); PUT("  "); PUT(Y,3,1,0); PUT("  "); PUT(Z,3,1,0); NEW_LINE;
  Y := 16.0;
  Z := SPIRAL(X,Y);
  PUT(X,3,1,0); PUT("  "); PUT(Y,3,1,0); PUT("  "); PUT(Z,3,1,0); NEW_LINE;
end TEST_SPIRAL;