-- math_pkg.vhd
-- by Toshio Iwata May/10/00
-- for sin(x) and cos(x)

library ieee;
use ieee.std_logic_1164.all;
use ieee.std_logic_arith.all;

package math_pkg is
  type realarray is array(natural range <>) of real;

  constant pai 	: real := 3.1415927;
  constant delta: real := 0.01;

  function sin( x : real ) return real;
  function cos( x : real ) return real;
end math_pkg;
    
package body math_pkg is

-- calculate sin(x) by Taylor Tenkai
  function sin(x : real) return real is
    variable alpha, beta : real;
    variable result : real;
    variable thita : real;
    variable temp, temp2 : real;
    constant kaijo : realarray(0 to 11) := (
      -6.0, -- -3!
      +120.0, -- 5!
      -5040.0, -- -7!
      +362880.0, -- 9!
      -39916800.0, -- -11!
      +6.227021e9, --  13!
      -1.307674e12, -- -15!
      +3.556874e14, -- 17!
      -1.216451e17, -- -19!
      +5.109094e19, -- 21!
      -2.585201e22, -- -23!
      +1.551121e25  -- 25!
    );
  begin
    thita := x/(2.0*pai);
    thita := thita - real(integer(thita));
    alpha := 2.0*pai*thita;
    if (abs(alpha) < delta) then return alpha;
    end if;
    beta := alpha * alpha;
    temp := alpha;
    result := alpha;
    for i in 0 to 11 loop
      temp := temp * beta;
      temp2 := temp / kaijo(i);
      result := result + temp2;
    end loop;
    return result;
  end sin;

    
-- cos(x) = sin(x+pai/2);
  function cos(x : real) return real is
  begin
    return sin(x+pai/2.0);
  end cos;

end math_pkg;