--------------------------------------------------------------- ---- This source file may be used and distributed without restriction.-- No declarations or definitions shall be included in this package.-- This package cannot be sold or distributed for profit. ----   ****************************************************************--   *                                                              *--   *                      W A R N I N G		 	    *--   *								    *--   *   This DRAFT version IS NOT endorsed or approved by IEEE     *--   *								    *--   ****************************************************************---- Title:    PACKAGE BODY MATH_COMPLEX---- Purpose:  VHDL declarations for mathematical package MATH_COMPLEX--	     which contains common complex constants and basic complex--	     functions and operations.---- Author:   IEEE VHDL Math Package Study Group ---- Notes:     --	The package body uses package IEEE.MATH_REAL---- 	The package body shall be considered the formal definition of -- 	the semantics of this package. Tool developers may choose to implement -- 	the package body in the most efficient manner available to them.----   Source code for this package body comes from the following--	following sources: --		IEEE VHDL Math Package Study Group participants,--		U. of Mississippi, Mentor Graphics, Synopsys,--		Viewlogic/Vantage, Communications of the ACM (June 1988, Vol--		31, Number 6, pp. 747, Pierre L'Ecuyer, Efficient and Portable--		Random Number Generators, Handbook of Mathematical Functions--	        by Milton Abramowitz and Irene A. Stegun (Dover).---- History:-- 	Version	0.1	Jose A. Torres	4/23/93	First draft-- 	Version	0.2	Jose A. Torres	5/28/93	Fixed potentially illegal code---------------------------------------------------------------Library IEEE;Use IEEE.MATH_REAL.all;		-- real trascendental operationsPackage body MATH_COMPLEX is    function CABS(Z: in complex ) return real is    	-- returns absolute value (magnitude) of Z	variable ztemp : complex_polar;    begin		ztemp := COMPLEX_TO_POLAR(Z);		return ztemp.mag;    end CABS;    function CARG(Z: in complex ) return real is    	-- returns argument (angle) in radians of a complex number     variable ztemp : complex_polar;    begin    		ztemp := COMPLEX_TO_POLAR(Z);		return ztemp.arg;    end CARG;    function CMPLX(X: in real;  Y: in real := 0.0 ) return complex is    	-- returns complex number X + iY    begin		return COMPLEX'(X, Y);    end CMPLX;    function "-" (Z: in complex ) return complex is    	-- unary minus; returns -x -jy for z= x + jy    begin    		return COMPLEX'(-z.Re, -z.Im);    end "-";    function "-" (Z: in complex_polar ) return complex_polar is    	-- unary minus; returns (z.mag, z.arg + MATH_PI)    begin    		return COMPLEX_POLAR'(z.mag, z.arg + MATH_PI);    end "-";    function CONJ (Z: in complex) return complex is    	-- returns complex conjugate (x-jy for z = x+ jy)    begin    		return COMPLEX'(z.Re, -z.Im);    end CONJ;    function CONJ (Z: in complex_polar) return complex_polar is    	-- returns complex conjugate (z.mag, -z.arg)    begin    		return COMPLEX_POLAR'(z.mag, -z.arg);    end CONJ;    function CSQRT(Z: in complex ) return complex_vector is    	-- returns square root of Z; 2 values		variable ztemp : complex_polar;		variable zout : complex_vector (0 to 1);		variable temp : real;    begin		ztemp := COMPLEX_TO_POLAR(Z);		temp := SQRT(ztemp.mag);		zout(0).re := temp*COS(ztemp.arg/2.0);		zout(0).im := temp*SIN(ztemp.arg/2.0);     				zout(1).re := temp*COS(ztemp.arg/2.0 + MATH_PI);		zout(1).im := temp*SIN(ztemp.arg/2.0 + MATH_PI);				return zout;    end CSQRT;    function CEXP(Z: in complex ) return complex is    	-- returns e**Z    begin		return COMPLEX'(EXP(Z.re)*COS(Z.im), EXP(Z.re)*SIN(Z.im));    end CEXP;    function COMPLEX_TO_POLAR(Z: in complex ) return complex_polar is    	-- converts complex to complex_polar    begin    		return COMPLEX_POLAR'(sqrt(z.re**2 + z.im**2),atan2(z.re,z.im));    end COMPLEX_TO_POLAR;    function POLAR_TO_COMPLEX(Z: in complex_polar ) return complex is    	-- converts complex_polar to complex    begin    		return COMPLEX'( z.mag*cos(z.arg), z.mag*sin(z.arg) );     end POLAR_TO_COMPLEX;    		    --    -- arithmetic operators    --    function "+" ( L: in complex;  R: in complex ) return complex is    begin    		return COMPLEX'(L.Re + R.Re, L.Im + R.Im);    end "+";    function "+" (L: in complex_polar; R: in complex_polar) return complex is		variable zL, zR : complex;    begin		zL := POLAR_TO_COMPLEX( L );		zR := POLAR_TO_COMPLEX( R );		return COMPLEX'(zL.Re + zR.Re, zL.Im + zR.Im);    end "+";    function "+" ( L: in complex_polar; R: in complex ) return complex is    		variable zL : complex;    begin    		zL := POLAR_TO_COMPLEX( L );		return COMPLEX'(zL.Re + R.Re, zL.Im + R.Im);    end "+";    function "+" ( L: in complex;  R: in complex_polar) return complex is    		variable zR : complex;    begin    		zR := POLAR_TO_COMPLEX( R );		return COMPLEX'(L.Re + zR.Re, L.Im + zR.Im);    end "+";    function "+" ( L: in real;     R: in complex ) return complex is    begin    		return COMPLEX'(L + R.Re, R.Im);    end "+";    function "+" ( L: in complex;  R: in real )    return complex is    begin    		return COMPLEX'(L.Re + R, L.Im);    end "+";    function "+" ( L: in real;  R: in complex_polar) return complex is    		variable zR : complex;    begin    		zR := POLAR_TO_COMPLEX( R );		return COMPLEX'(L + zR.Re, zR.Im);    end "+";    function "+" ( L: in complex_polar;  R: in real) return complex is    		variable zL : complex;    begin    		zL := POLAR_TO_COMPLEX( L );		return COMPLEX'(zL.Re + R, zL.Im);    end "+";    function "-" ( L: in complex;  R: in complex ) return complex is    begin    		return COMPLEX'(L.Re - R.Re, L.Im - R.Im);    end "-";    function "-" ( L: in complex_polar; R: in complex_polar) return complex is    		variable zL, zR : complex;    begin    		zL := POLAR_TO_COMPLEX( L );		zR := POLAR_TO_COMPLEX( R );		return COMPLEX'(zL.Re - zR.Re, zL.Im - zR.Im);    end "-";    function "-" ( L: in complex_polar; R: in complex ) return complex is    		variable zL : complex;    begin    		zL := POLAR_TO_COMPLEX( L );		return COMPLEX'(zL.Re - R.Re, zL.Im - R.Im);    end "-";    function "-" ( L: in complex;  R: in complex_polar) return complex is    		variable zR : complex;    begin    		zR := POLAR_TO_COMPLEX( R );		return COMPLEX'(L.Re - zR.Re, L.Im - zR.Im);    end "-";    function "-" ( L: in real;     R: in complex ) return complex is    begin    		return COMPLEX'(L - R.Re, -1.0 * R.Im);    end "-";    function "-" ( L: in complex;  R: in real )    return complex is    begin    		return COMPLEX'(L.Re - R, L.Im);    end "-";    function "-" ( L: in real;  R: in complex_polar) return complex is    		variable zR : complex;    begin    		zR := POLAR_TO_COMPLEX( R );		return COMPLEX'(L - zR.Re, -1.0*zR.Im);    end "-";    function "-" ( L: in complex_polar;  R: in real) return complex is    		variable zL : complex;    begin    		zL := POLAR_TO_COMPLEX( L );		return COMPLEX'(zL.Re - R, zL.Im);    end "-";    function "*" ( L: in complex;  R: in complex ) return complex is    begin        return COMPLEX'(L.Re * R.Re - L.Im * R.Im, L.Re * R.Im + L.Im * R.Re);    end "*";    function "*" ( L: in complex_polar; R: in complex_polar) return complex is		variable zout : complex_polar;    begin		zout.mag := L.mag * R.mag;		zout.arg := L.arg + R.arg;		return POLAR_TO_COMPLEX(zout);    end "*";    function "*" ( L: in complex_polar; R: in complex ) return complex is		variable zL : complex;    begin	zL := POLAR_TO_COMPLEX( L );	return COMPLEX'(zL.Re*R.Re - zL.Im * R.Im, zL.Re * R.Im + zL.Im*R.Re);    end "*";    function "*" ( L: in complex;  R: in complex_polar) return complex is    		variable zR : complex;    begin    	zR := POLAR_TO_COMPLEX( R );	return COMPLEX'(L.Re*zR.Re - L.Im * zR.Im, L.Re * zR.Im + L.Im*zR.Re);    end "*";    function "*" ( L: in real;     R: in complex ) return complex is    begin    		return COMPLEX'(L * R.Re, L * R.Im);    end "*";    function "*" ( L: in complex;  R: in real )    return complex is    begin    		return COMPLEX'(L.Re * R, L.Im * R);    end "*";    function "*" ( L: in real;  R: in complex_polar) return complex is    		variable zR : complex;    begin    		zR := POLAR_TO_COMPLEX( R );    		return COMPLEX'(L * zR.Re, L * zR.Im);    end "*";    function "*" ( L: in complex_polar;  R: in real) return complex is    		variable zL : complex;    begin    		zL := POLAR_TO_COMPLEX( L );    		return COMPLEX'(zL.Re * R, zL.Im * R);    end "*";    function "/" ( L: in complex;  R: in complex ) return complex is    		variable magrsq : REAL := R.Re ** 2 + R.Im ** 2;   begin       if (magrsq = 0.0) then         assert FALSE report "Attempt to divide by (0,0)"         	severity ERROR;         return COMPLEX'(REAL'RIGHT, REAL'RIGHT);      else          return COMPLEX'( (L.Re * R.Re + L.Im * R.Im) / magrsq,                    (L.Im * R.Re - L.Re * R.Im) / magrsq);      end if;    end "/";    function "/" ( L: in complex_polar; R: in complex_polar) return complex is		variable zout : complex_polar;    begin    	if (R.mag = 0.0) then         	assert FALSE report "Attempt to divide by (0,0)"         		severity ERROR;         	return COMPLEX'(REAL'RIGHT, REAL'RIGHT);      	else          	zout.mag := L.mag/R.mag;		zout.arg := L.arg - R.arg;		return POLAR_TO_COMPLEX(zout);      	end if;    end "/";    function "/" ( L: in complex_polar; R: in complex ) return complex is		variable zL : complex;		variable temp : REAL := R.Re ** 2 + R.Im ** 2;    begin    	if (temp = 0.0) then         	assert FALSE report "Attempt to divide by (0.0,0.0)"         		severity ERROR;         	return COMPLEX'(REAL'RIGHT, REAL'RIGHT);      	else          	zL := POLAR_TO_COMPLEX( L );         	return COMPLEX'( (zL.Re * R.Re + zL.Im * R.Im) / temp,                    (zL.Im * R.Re - zL.Re * R.Im) / temp);      	end if;     end "/";    function "/" ( L: in complex;  R: in complex_polar) return complex is    		variable zR : complex := POLAR_TO_COMPLEX( R );		variable temp : REAL := zR.Re ** 2 + zR.Im ** 2;    begin    	if (R.mag = 0.0) or (temp = 0.0) then         	assert FALSE report "Attempt to divide by (0.0,0.0)"         		severity ERROR;         	return COMPLEX'(REAL'RIGHT, REAL'RIGHT);      	else          	return COMPLEX'( (L.Re * zR.Re + L.Im * zR.Im) / temp,                    (L.Im * zR.Re - L.Re * zR.Im) / temp);      	end if;     end "/";    function "/" ( L: in real;     R: in complex ) return complex is    		variable temp : REAL := R.Re ** 2 + R.Im ** 2;    begin       	if (temp = 0.0) then         	assert FALSE report "Attempt to divide by (0.0,0.0)"         		severity ERROR;         	return COMPLEX'(REAL'RIGHT, REAL'RIGHT);      	else          	temp := L / temp;         	return  COMPLEX'( temp * R.Re, -temp * R.Im );      	end if;     end "/";    function "/" ( L: in complex;  R: in real )    return complex is    begin    	if (R = 0.0) then         	assert FALSE report "Attempt to divide by (0.0,0.0)"         		severity ERROR;         	return COMPLEX'(REAL'RIGHT, REAL'RIGHT);      	else          	return COMPLEX'(L.Re / R, L.Im / R);      	end if;     end "/";    function "/" ( L: in real;  R: in complex_polar) return complex is    		variable zR : complex := POLAR_TO_COMPLEX( R );		variable temp : REAL := zR.Re ** 2 + zR.Im ** 2;    begin    	if (R.mag = 0.0) or (temp = 0.0) then         	assert FALSE report "Attempt to divide by (0.0,0.0)"         		severity ERROR;         	return COMPLEX'(REAL'RIGHT, REAL'RIGHT);      	else          	temp := L / temp;         	return  COMPLEX'( temp * zR.Re, -temp * zR.Im );      	end if;     end "/";    function "/" ( L: in complex_polar;  R: in real) return complex is    		variable zL : complex := POLAR_TO_COMPLEX( L );    begin    	if (R = 0.0) then         	assert FALSE report "Attempt to divide by (0.0,0.0)"         		severity ERROR;         	return COMPLEX'(REAL'RIGHT, REAL'RIGHT);      	else          	return COMPLEX'(zL.Re / R, zL.Im / R);      	end if;     end "/";end  MATH_COMPLEX;