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+-- --------------------------------------------------------------------
+--
+-- Copyright © 2008 by IEEE. All rights reserved.
+--
+-- This source file is an essential part of IEEE Std 1076-2008,
+-- IEEE Standard VHDL Language Reference Manual. This source file may not be
+-- copied, sold, or included with software that is sold without written
+-- permission from the IEEE Standards Department. This source file may be
+-- copied for individual use between licensed users. This source file is
+-- provided on an AS IS basis. The IEEE disclaims ANY WARRANTY EXPRESS OR
+-- IMPLIED INCLUDING ANY WARRANTY OF MERCHANTABILITY AND FITNESS FOR USE
+-- FOR A PARTICULAR PURPOSE. The user of the source file shall indemnify
+-- and hold IEEE harmless from any damages or liability arising out of the
+-- use thereof.
+--
+-- Title : Standard VHDL Mathematical Packages
+-- : (MATH_COMPLEX package body)
+-- :
+-- Library : This package shall be compiled into a library
+-- : symbolically named IEEE.
+-- :
+-- Developers: IEEE DASC VHDL Mathematical Packages Working Group
+-- :
+-- Purpose : This package defines a standard for designers to use in
+-- : describing VHDL models that make use of common COMPLEX
+-- : constants and common COMPLEX mathematical functions and
+-- : operators.
+-- :
+-- Limitation: The values generated by the functions in this package
+-- : may vary from platform to platform, and the precision
+-- : of results is only guaranteed to be the minimum required
+-- : by IEEE Std 1076-2008.
+-- :
+-- Note : This package may be modified to include additional data
+-- : required by tools, but it must in no way change the
+-- : external interfaces or simulation behavior of the
+-- : description. It is permissible to add comments and/or
+-- : attributes to the package declarations, but not to change
+-- : or delete any original lines of the package declaration.
+-- : The package body may be changed only in accordance with
+-- : the terms of Clause 16 of this standard.
+-- :
+-- --------------------------------------------------------------------
+-- $Revision: 1220 $
+-- $Date: 2008-04-10 17:16:09 +0930 (Thu, 10 Apr 2008) $
+-- --------------------------------------------------------------------
+
+use WORK.MATH_REAL.all;
+
+package body MATH_COMPLEX is
+
+ --
+ -- Equality and Inequality Operators for COMPLEX_POLAR
+ --
+ function "=" ( L: in COMPLEX_POLAR; R: in COMPLEX_POLAR ) return BOOLEAN
+ is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- a) Returns FALSE on error
+ begin
+ -- Check validity of input arguments
+ if ( L.ARG = -MATH_PI ) then
+ assert FALSE
+ report "L.ARG = -MATH_PI in =(L,R)"
+ severity ERROR;
+ return FALSE;
+ end if;
+
+ if ( R.ARG = -MATH_PI ) then
+ assert FALSE
+ report "R.ARG = -MATH_PI in =(L,R)"
+ severity ERROR;
+ return FALSE;
+ end if;
+
+ -- Get special values
+ if ( L.MAG = 0.0 and R.MAG = 0.0 ) then
+ return TRUE;
+ end if;
+
+ -- Get value for general case
+ if ( L.MAG = R.MAG and L.ARG = R.ARG ) then
+ return TRUE;
+ end if;
+
+ return FALSE;
+ end function "=";
+
+
+ function "/=" ( L: in COMPLEX_POLAR; R: in COMPLEX_POLAR ) return BOOLEAN
+ is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- a) Returns FALSE on error
+ begin
+ -- Check validity of input arguments
+ if ( L.ARG = -MATH_PI ) then
+ assert FALSE
+ report "L.ARG = -MATH_PI in /=(L,R)"
+ severity ERROR;
+ return FALSE;
+ end if;
+
+ if ( R.ARG = -MATH_PI ) then
+ assert FALSE
+ report "R.ARG = -MATH_PI in /=(L,R)"
+ severity ERROR;
+ return FALSE;
+ end if;
+
+ -- Get special values
+ if ( L.MAG = 0.0 and R.MAG = 0.0 ) then
+ return FALSE;
+ end if;
+
+ -- Get value for general case
+ if ( L.MAG = R.MAG and L.ARG = R.ARG ) then
+ return FALSE;
+ end if;
+
+ return TRUE;
+ end function "/=";
+
+ --
+ -- Other Functions Start Here
+ --
+
+ function CMPLX(X: in REAL; Y: in REAL := 0.0 ) return COMPLEX is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- None
+ begin
+ return COMPLEX'(X, Y);
+ end function CMPLX;
+
+
+ function GET_PRINCIPAL_VALUE(X: in REAL ) return PRINCIPAL_VALUE is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- None
+ variable TEMP: REAL;
+ begin
+ -- Check if already a principal value
+ if ( X > -MATH_PI and X <= MATH_PI ) then
+ return PRINCIPAL_VALUE'(X);
+ end if;
+
+ -- Get principal value
+ TEMP := X;
+ while ( TEMP <= -MATH_PI ) loop
+ TEMP := TEMP + MATH_2_PI;
+ end loop;
+ while (TEMP > MATH_PI ) loop
+ TEMP := TEMP - MATH_2_PI;
+ end loop;
+
+ return PRINCIPAL_VALUE'(TEMP);
+ end function GET_PRINCIPAL_VALUE;
+
+ function COMPLEX_TO_POLAR(Z: in COMPLEX ) return COMPLEX_POLAR is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- None
+ variable TEMP: REAL;
+ begin
+ -- Get value for special cases
+ if ( Z.RE = 0.0 ) then
+ if ( Z.IM = 0.0 ) then
+ return COMPLEX_POLAR'(0.0, 0.0);
+ elsif ( Z.IM > 0.0 ) then
+ return COMPLEX_POLAR'(Z.IM, MATH_PI_OVER_2);
+ else
+ return COMPLEX_POLAR'(-Z.IM, -MATH_PI_OVER_2);
+ end if;
+ end if;
+
+ if ( Z.IM = 0.0 ) then
+ if ( Z.RE = 0.0 ) then
+ return COMPLEX_POLAR'(0.0, 0.0);
+ elsif ( Z.RE > 0.0 ) then
+ return COMPLEX_POLAR'(Z.RE, 0.0);
+ else
+ return COMPLEX_POLAR'(-Z.RE, MATH_PI);
+ end if;
+ end if;
+
+ -- Get principal value for general case
+ TEMP := ARCTAN(Z.IM, Z.RE);
+
+ return COMPLEX_POLAR'(SQRT(Z.RE*Z.RE + Z.IM*Z.IM),
+ GET_PRINCIPAL_VALUE(TEMP));
+ end function COMPLEX_TO_POLAR;
+
+ function POLAR_TO_COMPLEX(Z: in COMPLEX_POLAR ) return COMPLEX is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- a) Returns MATH_CZERO on error
+ begin
+ -- Check validity of input arguments
+ if ( Z.ARG = -MATH_PI ) then
+ assert FALSE
+ report "Z.ARG = -MATH_PI in POLAR_TO_COMPLEX(Z)"
+ severity ERROR;
+ return MATH_CZERO;
+ end if;
+
+ -- Get value for general case
+ return COMPLEX'( Z.MAG*COS(Z.ARG), Z.MAG*SIN(Z.ARG) );
+ end function POLAR_TO_COMPLEX;
+
+
+ function "ABS"(Z: in COMPLEX ) return POSITIVE_REAL is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- a) ABS(Z) = SQRT(Z.RE*Z.RE + Z.IM*Z.IM)
+
+ begin
+ -- Get value for general case
+ return POSITIVE_REAL'(SQRT(Z.RE*Z.RE + Z.IM*Z.IM));
+ end function "ABS";
+
+ function "ABS"(Z: in COMPLEX_POLAR ) return POSITIVE_REAL is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- a) ABS(Z) = Z.MAG
+ -- b) Returns 0.0 on error
+
+ begin
+ -- Check validity of input arguments
+ if ( Z.ARG = -MATH_PI ) then
+ assert FALSE
+ report "Z.ARG = -MATH_PI in ABS(Z)"
+ severity ERROR;
+ return 0.0;
+ end if;
+
+ -- Get value for general case
+ return Z.MAG;
+ end function "ABS";
+
+
+ function ARG(Z: in COMPLEX ) return PRINCIPAL_VALUE is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- a) ARG(Z) = ARCTAN(Z.IM, Z.RE)
+
+ variable ZTEMP : COMPLEX_POLAR;
+ begin
+ -- Get value for general case
+ ZTEMP := COMPLEX_TO_POLAR(Z);
+ return ZTEMP.ARG;
+ end function ARG;
+
+ function ARG(Z: in COMPLEX_POLAR ) return PRINCIPAL_VALUE is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- a) ARG(Z) = Z.ARG
+ -- b) Returns 0.0 on error
+
+ begin
+ -- Check validity of input arguments
+ if ( Z.ARG = -MATH_PI ) then
+ assert FALSE
+ report "Z.ARG = -MATH_PI in ARG(Z)"
+ severity ERROR;
+ return 0.0;
+ end if;
+
+ -- Get value for general case
+ return Z.ARG;
+ end function ARG;
+
+ function "-" (Z: in COMPLEX ) return COMPLEX is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- a) Returns -x -jy for Z = x + jy
+ begin
+ -- Get value for general case
+ return COMPLEX'(-Z.RE, -Z.IM);
+ end function "-";
+
+ function "-" (Z: in COMPLEX_POLAR ) return COMPLEX_POLAR is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- a) Returns (Z.MAG, Z.ARG + MATH_PI)
+ -- b) Returns Z on error
+ variable TEMP: REAL;
+ begin
+ -- Check validity of input arguments
+ if ( Z.ARG = -MATH_PI ) then
+ assert FALSE
+ report "Z.ARG = -MATH_PI in -(Z)"
+ severity ERROR;
+ return Z;
+ end if;
+
+ -- Get principal value for general case
+ TEMP := REAL'(Z.ARG) + MATH_PI;
+
+ return COMPLEX_POLAR'(Z.MAG, GET_PRINCIPAL_VALUE(TEMP));
+ end function "-";
+
+ function CONJ (Z: in COMPLEX) return COMPLEX is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- a) Returns x - jy for Z = x + jy
+ begin
+ -- Get value for general case
+ return COMPLEX'(Z.RE, -Z.IM);
+ end function CONJ;
+
+ function CONJ (Z: in COMPLEX_POLAR) return COMPLEX_POLAR is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- a) Returns COMPLEX conjugate (Z.MAG, -Z.ARG)
+ -- b) Returns Z on error
+ --
+ variable TEMP: PRINCIPAL_VALUE;
+ begin
+ -- Check validity of input arguments
+ if ( Z.ARG = -MATH_PI ) then
+ assert FALSE
+ report "Z.ARG = -MATH_PI in CONJ(Z)"
+ severity ERROR;
+ return Z;
+ end if;
+
+ -- Get principal value for general case
+ if ( Z.ARG = MATH_PI or Z.ARG = 0.0 ) then
+ TEMP := Z.ARG;
+ else
+ TEMP := -Z.ARG;
+ end if;
+
+ return COMPLEX_POLAR'(Z.MAG, TEMP);
+ end function CONJ;
+
+ function SQRT(Z: in COMPLEX ) return COMPLEX is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- None
+ variable ZTEMP : COMPLEX_POLAR;
+ variable ZOUT : COMPLEX;
+ variable TMAG : REAL;
+ variable TARG : REAL;
+ begin
+ -- Get value for special cases
+ if ( Z = MATH_CZERO ) then
+ return MATH_CZERO;
+ end if;
+
+ -- Get value for general case
+ ZTEMP := COMPLEX_TO_POLAR(Z);
+ TMAG := SQRT(ZTEMP.MAG);
+ TARG := 0.5*ZTEMP.ARG;
+
+ if ( COS(TARG) > 0.0 ) then
+ ZOUT.RE := TMAG*COS(TARG);
+ ZOUT.IM := TMAG*SIN(TARG);
+ return ZOUT;
+ end if;
+
+ if ( COS(TARG) < 0.0 ) then
+ ZOUT.RE := TMAG*COS(TARG + MATH_PI);
+ ZOUT.IM := TMAG*SIN(TARG + MATH_PI);
+ return ZOUT;
+ end if;
+
+ if ( SIN(TARG) > 0.0 ) then
+ ZOUT.RE := 0.0;
+ ZOUT.IM := TMAG*SIN(TARG);
+ return ZOUT;
+ end if;
+
+ ZOUT.RE := 0.0;
+ ZOUT.IM := TMAG*SIN(TARG + MATH_PI);
+ return ZOUT;
+ end function SQRT;
+
+ function SQRT(Z: in COMPLEX_POLAR ) return COMPLEX_POLAR is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- a) Returns Z on error
+
+ variable ZOUT : COMPLEX_POLAR;
+ variable TMAG : REAL;
+ variable TARG : REAL;
+ begin
+ -- Check validity of input arguments
+ if ( Z.ARG = -MATH_PI ) then
+ assert FALSE
+ report "Z.ARG = -MATH_PI in SQRT(Z)"
+ severity ERROR;
+ return Z;
+ end if;
+
+ -- Get value for special cases
+ if ( Z.MAG = 0.0 and Z.ARG = 0.0 ) then
+ return Z;
+ end if;
+
+ -- Get principal value for general case
+ TMAG := SQRT(Z.MAG);
+ TARG := 0.5*Z.ARG;
+
+ ZOUT.MAG := POSITIVE_REAL'(TMAG);
+
+ if ( COS(TARG) < 0.0 ) then
+ TARG := TARG + MATH_PI;
+ end if;
+
+ if ( (COS(TARG) = 0.0) and (SIN(TARG) < 0.0) ) then
+ TARG := TARG + MATH_PI;
+ end if;
+
+ ZOUT.ARG := GET_PRINCIPAL_VALUE(TARG);
+ return ZOUT;
+ end function SQRT;
+
+ function EXP(Z: in COMPLEX ) return COMPLEX is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- None
+
+ variable TEMP: REAL;
+ begin
+ -- Get value for special cases
+ if ( Z = MATH_CZERO ) then
+ return MATH_CBASE_1;
+ end if;
+
+ if ( Z.RE = 0.0 ) then
+ if ( Z.IM = MATH_PI or Z.IM = -MATH_PI ) then
+ return COMPLEX'(-1.0, 0.0);
+ end if;
+
+ if ( Z.IM = MATH_PI_OVER_2 ) then
+ return MATH_CBASE_J;
+ end if;
+
+ if ( Z.IM = -MATH_PI_OVER_2 ) then
+ return COMPLEX'(0.0, -1.0);
+ end if;
+ end if;
+
+ -- Get value for general case
+ TEMP := EXP(Z.RE);
+ return COMPLEX'(TEMP*COS(Z.IM), TEMP*SIN(Z.IM));
+ end function EXP;
+
+ function EXP(Z: in COMPLEX_POLAR ) return COMPLEX_POLAR is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- a) Returns Z on error
+
+ variable ZTEMP : COMPLEX;
+ variable temp: REAL;
+ variable ZOUT : COMPLEX_POLAR;
+ begin
+ -- Check validity of input arguments
+ if ( Z.ARG = -MATH_PI ) then
+ assert FALSE
+ report "Z.ARG = -MATH_PI in EXP(Z)"
+ severity ERROR;
+ return Z;
+ end if;
+
+ -- Get value for special cases
+ if ( Z.MAG = 0.0 and Z.ARG = 0.0 ) then
+ return COMPLEX_POLAR'(1.0, 0.0);
+ end if;
+
+ if ( Z.MAG = MATH_PI and (Z.ARG = MATH_PI_OVER_2 or
+ Z.ARG = -MATH_PI_OVER_2 )) then
+ return COMPLEX_POLAR'(1.0, MATH_PI);
+ end if;
+
+ if ( Z.MAG = MATH_PI_OVER_2 ) then
+ if ( Z.ARG = MATH_PI_OVER_2 ) then
+ return COMPLEX_POLAR'(1.0, MATH_PI_OVER_2);
+ end if;
+
+ if ( Z.ARG = -MATH_PI_OVER_2 ) then
+ return COMPLEX_POLAR'(1.0, -MATH_PI_OVER_2);
+ end if;
+ end if;
+
+ -- Get principal value for general case
+ ZTEMP := POLAR_TO_COMPLEX(Z);
+ ZOUT.MAG := POSITIVE_REAL'(EXP(ZTEMP.RE));
+ ZOUT.ARG := GET_PRINCIPAL_VALUE(ZTEMP.IM);
+
+ return ZOUT;
+ end function EXP;
+
+ function LOG(Z: in COMPLEX ) return COMPLEX is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- a) Returns COMPLEX'(REAL'LOW, 0.0) on error
+
+ variable ZTEMP : COMPLEX_POLAR;
+ variable TEMP : REAL;
+ begin
+ -- Check validity of input arguments
+ if ( Z.RE = 0.0 and Z.IM = 0.0 ) then
+ assert FALSE
+ report "Z.RE = 0.0 and Z.IM = 0.0 in LOG(Z)"
+ severity ERROR;
+ return COMPLEX'(REAL'LOW, 0.0);
+ end if;
+
+ -- Get value for special cases
+ if ( Z.IM = 0.0 ) then
+ if ( Z.RE = -1.0 ) then
+ return COMPLEX'(0.0, MATH_PI);
+ end if;
+ if ( Z.RE = MATH_E ) then
+ return MATH_CBASE_1;
+ end if;
+ if ( Z.RE = 1.0 ) then
+ return MATH_CZERO;
+ end if;
+ end if;
+
+ if ( Z.RE = 0.0 ) then
+ if (Z.IM = 1.0) then
+ return COMPLEX'(0.0, MATH_PI_OVER_2);
+ end if;
+ if (Z.IM = -1.0) then
+ return COMPLEX'(0.0, -MATH_PI_OVER_2);
+ end if;
+ end if;
+
+ -- Get value for general case
+ ZTEMP := COMPLEX_TO_POLAR(Z);
+ TEMP := LOG(ZTEMP.MAG);
+ return COMPLEX'(TEMP, ZTEMP.ARG);
+ end function LOG;
+
+ function LOG2(Z: in COMPLEX ) return COMPLEX is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- a) Returns COMPLEX'(REAL'LOW, 0.0) on error
+
+ variable ZTEMP : COMPLEX_POLAR;
+ variable TEMP : REAL;
+ begin
+
+ -- Check validity of input arguments
+ if ( Z.RE = 0.0 and Z.IM = 0.0 ) then
+ assert FALSE
+ report "Z.RE = 0.0 and Z.IM = 0.0 in LOG2(Z)"
+ severity ERROR;
+ return COMPLEX'(REAL'LOW, 0.0);
+ end if;
+
+ -- Get value for special cases
+ if ( Z.IM = 0.0 ) then
+ if ( Z.RE = 2.0 ) then
+ return MATH_CBASE_1;
+ end if;
+ if ( Z.RE = 1.0 ) then
+ return MATH_CZERO;
+ end if;
+ end if;
+
+ -- Get value for general case
+ ZTEMP := COMPLEX_TO_POLAR(Z);
+ TEMP := MATH_LOG2_OF_E*LOG(ZTEMP.MAG);
+ return COMPLEX'(TEMP, MATH_LOG2_OF_E*ZTEMP.ARG);
+ end function LOG2;
+
+ function LOG10(Z: in COMPLEX ) return COMPLEX is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- a) Returns COMPLEX'(REAL'LOW, 0.0) on error
+
+ variable ZTEMP : COMPLEX_POLAR;
+ variable TEMP : REAL;
+ begin
+ -- Check validity of input arguments
+ if ( Z.RE = 0.0 and Z.IM = 0.0 ) then
+ assert FALSE
+ report "Z.RE = 0.0 and Z.IM = 0.0 in LOG10(Z)"
+ severity ERROR;
+ return COMPLEX'(REAL'LOW, 0.0);
+ end if;
+
+ -- Get value for special cases
+ if ( Z.IM = 0.0 ) then
+ if ( Z.RE = 10.0 ) then
+ return MATH_CBASE_1;
+ end if;
+ if ( Z.RE = 1.0 ) then
+ return MATH_CZERO;
+ end if;
+ end if;
+
+ -- Get value for general case
+ ZTEMP := COMPLEX_TO_POLAR(Z);
+ TEMP := MATH_LOG10_OF_E*LOG(ZTEMP.MAG);
+ return COMPLEX'(TEMP, MATH_LOG10_OF_E*ZTEMP.ARG);
+ end function LOG10;
+
+
+ function LOG(Z: in COMPLEX_POLAR ) return COMPLEX_POLAR is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- a) Returns COMPLEX_POLAR(REAL'HIGH, MATH_PI) on error
+
+ variable ZTEMP : COMPLEX;
+ variable ZOUT : COMPLEX_POLAR;
+ begin
+ -- Check validity of input arguments
+ if ( Z.MAG <= 0.0 ) then
+ assert FALSE
+ report "Z.MAG <= 0.0 in LOG(Z)"
+ severity ERROR;
+ return COMPLEX_POLAR'(REAL'HIGH, MATH_PI);
+ end if;
+
+ if ( Z.ARG = -MATH_PI ) then
+ assert FALSE
+ report "Z.ARG = -MATH_PI in LOG(Z)"
+ severity ERROR;
+ return COMPLEX_POLAR'(REAL'HIGH, MATH_PI);
+ end if;
+
+ -- Compute value for special cases
+ if (Z.MAG = 1.0 ) then
+ if ( Z.ARG = 0.0 ) then
+ return COMPLEX_POLAR'(0.0, 0.0);
+ end if;
+
+ if ( Z.ARG = MATH_PI ) then
+ return COMPLEX_POLAR'(MATH_PI, MATH_PI_OVER_2);
+ end if;
+
+ if ( Z.ARG = MATH_PI_OVER_2 ) then
+ return COMPLEX_POLAR'(MATH_PI_OVER_2, MATH_PI_OVER_2);
+ end if;
+
+ if ( Z.ARG = -MATH_PI_OVER_2 ) then
+ return COMPLEX_POLAR'(MATH_PI_OVER_2, -MATH_PI_OVER_2);
+ end if;
+ end if;
+
+ if ( Z.MAG = MATH_E and Z.ARG = 0.0 ) then
+ return COMPLEX_POLAR'(1.0, 0.0);
+ end if;
+
+ -- Compute value for general case
+ ZTEMP.RE := LOG(Z.MAG);
+ ZTEMP.IM := Z.ARG;
+ ZOUT := COMPLEX_TO_POLAR(ZTEMP);
+ return ZOUT;
+ end function LOG;
+
+
+
+ function LOG2(Z: in COMPLEX_POLAR ) return COMPLEX_POLAR is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- a) Returns COMPLEX_POLAR(REAL'HIGH, MATH_PI) on error
+
+ variable ZTEMP : COMPLEX;
+ variable ZOUT : COMPLEX_POLAR;
+ begin
+ -- Check validity of input arguments
+ if ( Z.MAG <= 0.0 ) then
+ assert FALSE
+ report "Z.MAG <= 0.0 in LOG2(Z)"
+ severity ERROR;
+ return COMPLEX_POLAR'(REAL'HIGH, MATH_PI);
+ end if;
+
+ if ( Z.ARG = -MATH_PI ) then
+ assert FALSE
+ report "Z.ARG = -MATH_PI in LOG2(Z)"
+ severity ERROR;
+ return COMPLEX_POLAR'(REAL'HIGH, MATH_PI);
+ end if;
+
+ -- Compute value for special cases
+ if (Z.MAG = 1.0 and Z.ARG = 0.0 ) then
+ return COMPLEX_POLAR'(0.0, 0.0);
+ end if;
+
+ if ( Z.MAG = 2.0 and Z.ARG = 0.0 ) then
+ return COMPLEX_POLAR'(1.0, 0.0);
+ end if;
+
+ -- Compute value for general case
+ ZTEMP.RE := MATH_LOG2_OF_E*LOG(Z.MAG);
+ ZTEMP.IM := MATH_LOG2_OF_E*Z.ARG;
+ ZOUT := COMPLEX_TO_POLAR(ZTEMP);
+ return ZOUT;
+ end function LOG2;
+
+ function LOG10(Z: in COMPLEX_POLAR ) return COMPLEX_POLAR is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- a) Returns COMPLEX_POLAR(REAL'HIGH, MATH_PI) on error
+ variable ZTEMP : COMPLEX;
+ variable ZOUT : COMPLEX_POLAR;
+ begin
+ -- Check validity of input arguments
+ if ( Z.MAG <= 0.0 ) then
+ assert FALSE
+ report "Z.MAG <= 0.0 in LOG10(Z)"
+ severity ERROR;
+ return COMPLEX_POLAR'(REAL'HIGH, MATH_PI);
+ end if;
+
+
+ if ( Z.ARG = -MATH_PI ) then
+ assert FALSE
+ report "Z.ARG = -MATH_PI in LOG10(Z)"
+ severity ERROR;
+ return COMPLEX_POLAR'(REAL'HIGH, MATH_PI);
+ end if;
+
+ -- Compute value for special cases
+ if (Z.MAG = 1.0 and Z.ARG = 0.0 ) then
+ return COMPLEX_POLAR'(0.0, 0.0);
+ end if;
+
+ if ( Z.MAG = 10.0 and Z.ARG = 0.0 ) then
+ return COMPLEX_POLAR'(1.0, 0.0);
+ end if;
+
+ -- Compute value for general case
+ ZTEMP.RE := MATH_LOG10_OF_E*LOG(Z.MAG);
+ ZTEMP.IM := MATH_LOG10_OF_E*Z.ARG;
+ ZOUT := COMPLEX_TO_POLAR(ZTEMP);
+ return ZOUT;
+ end function LOG10;
+
+ function LOG(Z: in COMPLEX; BASE: in REAL ) return COMPLEX is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- a) Returns COMPLEX'(REAL'LOW, 0.0) on error
+
+ variable ZTEMP : COMPLEX_POLAR;
+ variable TEMPRE : REAL;
+ variable TEMPIM : REAL;
+ begin
+ -- Check validity of input arguments
+ if ( Z.RE = 0.0 and Z.IM = 0.0 ) then
+ assert FALSE
+ report "Z.RE = 0.0 and Z.IM = 0.0 in LOG(Z,BASE)"
+ severity ERROR;
+ return COMPLEX'(REAL'LOW, 0.0);
+ end if;
+
+ if ( BASE <= 0.0 or BASE = 1.0 ) then
+ assert FALSE
+ report "BASE <= 0.0 or BASE = 1.0 in LOG(Z,BASE)"
+ severity ERROR;
+ return COMPLEX'(REAL'LOW, 0.0);
+ end if;
+
+ -- Get value for special cases
+ if ( Z.IM = 0.0 ) then
+ if ( Z.RE = BASE ) then
+ return MATH_CBASE_1;
+ end if;
+ if ( Z.RE = 1.0 ) then
+ return MATH_CZERO;
+ end if;
+ end if;
+
+ -- Get value for general case
+ ZTEMP := COMPLEX_TO_POLAR(Z);
+ TEMPRE := LOG(ZTEMP.MAG, BASE);
+ TEMPIM := ZTEMP.ARG/LOG(BASE);
+ return COMPLEX'(TEMPRE, TEMPIM);
+ end function LOG;
+
+ function LOG(Z: in COMPLEX_POLAR; BASE: in REAL ) return COMPLEX_POLAR is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- a) Returns COMPLEX_POLAR(REAL'HIGH, MATH_PI) on error
+
+ variable ZTEMP : COMPLEX;
+ variable ZOUT : COMPLEX_POLAR;
+ begin
+ -- Check validity of input arguments
+ if ( Z.MAG <= 0.0 ) then
+ assert FALSE
+ report "Z.MAG <= 0.0 in LOG(Z,BASE)"
+ severity ERROR;
+ return COMPLEX_POLAR'(REAL'HIGH, MATH_PI);
+ end if;
+
+ if ( BASE <= 0.0 or BASE = 1.0 ) then
+ assert FALSE
+ report "BASE <= 0.0 or BASE = 1.0 in LOG(Z,BASE)"
+ severity ERROR;
+ return COMPLEX_POLAR'(REAL'HIGH, MATH_PI);
+ end if;
+
+ if ( Z.ARG = -MATH_PI ) then
+ assert FALSE
+ report "Z.ARG = -MATH_PI in LOG(Z,BASE)"
+ severity ERROR;
+ return COMPLEX_POLAR'(REAL'HIGH, MATH_PI);
+ end if;
+
+ -- Compute value for special cases
+ if (Z.MAG = 1.0 and Z.ARG = 0.0 ) then
+ return COMPLEX_POLAR'(0.0, 0.0);
+ end if;
+
+ if ( Z.MAG = BASE and Z.ARG = 0.0 ) then
+ return COMPLEX_POLAR'(1.0, 0.0);
+ end if;
+
+ -- Compute value for general case
+ ZTEMP.RE := LOG(Z.MAG, BASE);
+ ZTEMP.IM := Z.ARG/LOG(BASE);
+ ZOUT := COMPLEX_TO_POLAR(ZTEMP);
+ return ZOUT;
+ end function LOG;
+
+
+ function SIN(Z: in COMPLEX ) return COMPLEX is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- None
+ begin
+ -- Get value for special cases
+ if ( Z.IM = 0.0 ) then
+ if ( Z.RE = 0.0 or Z.RE = MATH_PI) then
+ return MATH_CZERO;
+ end if;
+ end if;
+
+ -- Get value for general case
+ return COMPLEX'(SIN(Z.RE)*COSH(Z.IM), COS(Z.RE)*SINH(Z.IM));
+ end function SIN;
+
+ function SIN(Z: in COMPLEX_POLAR ) return COMPLEX_POLAR is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- a) Returns COMPLEX_POLAR(0.0, 0.0) on error
+
+ variable Z1, Z2 : COMPLEX;
+ variable ZOUT : COMPLEX_POLAR;
+ begin
+ -- Check validity of input arguments
+ if ( Z.ARG = -MATH_PI ) then
+ assert FALSE
+ report "Z.ARG = -MATH_PI in SIN(Z)"
+ severity ERROR;
+ return COMPLEX_POLAR'(0.0, 0.0);
+ end if;
+
+ -- Compute value for special cases
+ if ( Z.MAG = 0.0 and Z.ARG = 0.0 ) then
+ return COMPLEX_POLAR'(0.0, 0.0);
+ end if;
+
+ if ( Z.MAG = MATH_PI and Z.ARG = 0.0 ) then
+ return COMPLEX_POLAR'(0.0, 0.0);
+ end if;
+
+ -- Compute value for general case
+ Z1 := POLAR_TO_COMPLEX(Z);
+ Z2 := COMPLEX'(SIN(Z1.RE)*COSH(Z1.IM), COS(Z1.RE)*SINH(Z1.IM));
+ ZOUT := COMPLEX_TO_POLAR(Z2);
+ return ZOUT;
+ end function SIN;
+
+ function COS(Z: in COMPLEX ) return COMPLEX is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- None
+ begin
+
+
+ -- Get value for special cases
+ if ( Z.IM = 0.0 ) then
+ if ( Z.RE = MATH_PI_OVER_2 or Z.RE = -MATH_PI_OVER_2) then
+ return MATH_CZERO;
+ end if;
+ end if;
+
+ -- Get value for general case
+ return COMPLEX'(COS(Z.RE)*COSH(Z.IM), -SIN(Z.RE)*SINH(Z.IM));
+ end function COS;
+
+ function COS(Z: in COMPLEX_POLAR ) return COMPLEX_POLAR is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- a) Returns COMPLEX_POLAR(0.0, 0.0) on error
+
+ variable Z1, Z2 : COMPLEX;
+ variable ZOUT : COMPLEX_POLAR;
+ begin
+ -- Check validity of input arguments
+ if ( Z.ARG = -MATH_PI ) then
+ assert FALSE
+ report "Z.ARG = -MATH_PI in COS(Z)"
+ severity ERROR;
+ return COMPLEX_POLAR'(0.0, 0.0);
+ end if;
+
+ -- Compute value for special cases
+ if ( Z.MAG = MATH_PI_OVER_2 and Z.ARG = 0.0 ) then
+ return COMPLEX_POLAR'(0.0, 0.0);
+ end if;
+
+ if ( Z.MAG = MATH_PI_OVER_2 and Z.ARG = MATH_PI ) then
+ return COMPLEX_POLAR'(0.0, 0.0);
+ end if;
+
+ -- Compute value for general case
+ Z1 := POLAR_TO_COMPLEX(Z);
+ Z2 := COMPLEX'(COS(Z1.RE)*COSH(Z1.IM), -SIN(Z1.RE)*SINH(Z1.IM));
+ ZOUT := COMPLEX_TO_POLAR(Z2);
+ return ZOUT;
+ end function COS;
+
+ function SINH(Z: in COMPLEX ) return COMPLEX is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- None
+ begin
+ -- Get value for special cases
+ if ( Z.RE = 0.0 ) then
+ if ( Z.IM = 0.0 or Z.IM = MATH_PI ) then
+ return MATH_CZERO;
+ end if;
+
+
+
+ if ( Z.IM = MATH_PI_OVER_2 ) then
+ return MATH_CBASE_J;
+ end if;
+
+ if ( Z.IM = -MATH_PI_OVER_2 ) then
+ return -MATH_CBASE_J;
+ end if;
+ end if;
+
+ -- Get value for general case
+ return COMPLEX'(SINH(Z.RE)*COS(Z.IM), COSH(Z.RE)*SIN(Z.IM));
+ end function SINH;
+
+ function SINH(Z: in COMPLEX_POLAR ) return COMPLEX_POLAR is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- a) Returns COMPLEX_POLAR(0.0, 0.0) on error
+
+ variable Z1, Z2 : COMPLEX;
+ variable ZOUT : COMPLEX_POLAR;
+ begin
+ -- Check validity of input arguments
+ if ( Z.ARG = -MATH_PI ) then
+ assert FALSE
+ report "Z.ARG = -MATH_PI in SINH(Z)"
+ severity ERROR;
+ return COMPLEX_POLAR'(0.0, 0.0);
+ end if;
+
+ -- Compute value for special cases
+ if ( Z.MAG = 0.0 and Z.ARG = 0.0 ) then
+ return COMPLEX_POLAR'(0.0, 0.0);
+ end if;
+
+ if ( Z.MAG = MATH_PI and Z.ARG = MATH_PI_OVER_2 ) then
+ return COMPLEX_POLAR'(0.0, 0.0);
+ end if;
+
+ if ( Z.MAG = MATH_PI_OVER_2 and Z.ARG = MATH_PI_OVER_2 ) then
+ return COMPLEX_POLAR'(1.0, MATH_PI_OVER_2);
+ end if;
+
+ if ( Z.MAG = MATH_PI_OVER_2 and Z.ARG = -MATH_PI_OVER_2 ) then
+ return COMPLEX_POLAR'(1.0, -MATH_PI_OVER_2);
+ end if;
+
+ -- Compute value for general case
+ Z1 := POLAR_TO_COMPLEX(Z);
+ Z2 := COMPLEX'(SINH(Z1.RE)*COS(Z1.IM), COSH(Z1.RE)*SIN(Z1.IM));
+ ZOUT := COMPLEX_TO_POLAR(Z2);
+ return ZOUT;
+ end function SINH;
+
+
+ function COSH(Z: in COMPLEX ) return COMPLEX is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- None
+ begin
+ -- Get value for special cases
+ if ( Z.RE = 0.0 ) then
+ if ( Z.IM = 0.0 ) then
+ return MATH_CBASE_1;
+ end if;
+
+ if ( Z.IM = MATH_PI ) then
+ return -MATH_CBASE_1;
+ end if;
+
+ if ( Z.IM = MATH_PI_OVER_2 or Z.IM = -MATH_PI_OVER_2 ) then
+ return MATH_CZERO;
+ end if;
+ end if;
+
+ -- Get value for general case
+ return COMPLEX'(COSH(Z.RE)*COS(Z.IM), SINH(Z.RE)*SIN(Z.IM));
+ end function COSH;
+
+ function COSH(Z: in COMPLEX_POLAR ) return COMPLEX_POLAR is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- a) Returns COMPLEX_POLAR(0.0, 0.0) on error
+
+ variable Z1, Z2 : COMPLEX;
+ variable ZOUT : COMPLEX_POLAR;
+ begin
+ -- Check validity of input arguments
+ if ( Z.ARG = -MATH_PI ) then
+ assert FALSE
+ report "Z.ARG = -MATH_PI in COSH(Z)"
+ severity ERROR;
+ return COMPLEX_POLAR'(0.0, 0.0);
+ end if;
+
+ -- Compute value for special cases
+ if ( Z.MAG = 0.0 and Z.ARG = 0.0 ) then
+ return COMPLEX_POLAR'(1.0, 0.0);
+ end if;
+
+ if ( Z.MAG = MATH_PI and Z.ARG = MATH_PI_OVER_2 ) then
+ return COMPLEX_POLAR'(1.0, MATH_PI);
+ end if;
+
+ if ( Z.MAG = MATH_PI_OVER_2 and Z.ARG = MATH_PI_OVER_2 ) then
+ return COMPLEX_POLAR'(0.0, 0.0);
+ end if;
+
+ if ( Z.MAG = MATH_PI_OVER_2 and Z.ARG = -MATH_PI_OVER_2 ) then
+ return COMPLEX_POLAR'(0.0, 0.0);
+ end if;
+
+ -- Compute value for general case
+ Z1 := POLAR_TO_COMPLEX(Z);
+ Z2 := COMPLEX'(COSH(Z1.RE)*COS(Z1.IM), SINH(Z1.RE)*SIN(Z1.IM));
+ ZOUT := COMPLEX_TO_POLAR(Z2);
+ return ZOUT;
+ end function COSH;
+
+
+ --
+ -- Arithmetic Operators
+ --
+ function "+" ( L: in COMPLEX; R: in COMPLEX ) return COMPLEX is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- None
+ begin
+ return COMPLEX'(L.RE + R.RE, L.IM + R.IM);
+ end function "+";
+
+ function "+" ( L: in REAL; R: in COMPLEX ) return COMPLEX is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- None
+ begin
+ return COMPLEX'(L + R.RE, R.IM);
+ end function "+";
+
+ function "+" ( L: in COMPLEX; R: in REAL ) return COMPLEX is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- None
+ begin
+ return COMPLEX'(L.RE + R, L.IM);
+ end function "+";
+
+ function "+" (L: in COMPLEX_POLAR; R: in COMPLEX_POLAR)
+ return COMPLEX_POLAR is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- a) Returns COMPLEX_POLAR'(0.0, 0.0) on error
+ --
+ variable ZL, ZR : COMPLEX;
+ variable ZOUT : COMPLEX_POLAR;
+ begin
+ -- Check validity of input arguments
+ if ( L.ARG = -MATH_PI ) then
+ assert FALSE
+ report "L.ARG = -MATH_PI in +(L,R)"
+ severity ERROR;
+ return COMPLEX_POLAR'(0.0, 0.0);
+ end if;
+
+
+ if ( R.ARG = -MATH_PI ) then
+ assert FALSE
+ report "R.ARG = -MATH_PI in +(L,R)"
+ severity ERROR;
+ return COMPLEX_POLAR'(0.0, 0.0);
+ end if;
+
+ -- Get principal value
+ ZL := POLAR_TO_COMPLEX( L );
+ ZR := POLAR_TO_COMPLEX( R );
+ ZOUT := COMPLEX_TO_POLAR(COMPLEX'(ZL.RE + ZR.RE, ZL.IM +ZR.IM));
+ return ZOUT;
+ end function "+";
+
+ function "+" ( L: in REAL; R: in COMPLEX_POLAR) return COMPLEX_POLAR is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- a) Returns COMPLEX_POLAR'(0.0, 0.0) on error
+ variable ZR : COMPLEX;
+ variable ZOUT : COMPLEX_POLAR;
+ begin
+ -- Check validity of input arguments
+ if ( R.ARG = -MATH_PI ) then
+ assert FALSE
+ report "R.ARG = -MATH_PI in +(L,R)"
+ severity ERROR;
+ return COMPLEX_POLAR'(0.0, 0.0);
+ end if;
+
+ -- Get principal value
+ ZR := POLAR_TO_COMPLEX( R );
+ ZOUT := COMPLEX_TO_POLAR(COMPLEX'(L + ZR.RE, ZR.IM));
+ return ZOUT;
+ end function "+";
+
+ function "+" ( L: in COMPLEX_POLAR; R: in REAL) return COMPLEX_POLAR is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- a) Returns COMPLEX_POLAR'(0.0, 0.0) on error
+ --
+ variable ZL : COMPLEX;
+ variable ZOUT : COMPLEX_POLAR;
+ begin
+ -- Check validity of input arguments
+ if ( L.ARG = -MATH_PI ) then
+ assert FALSE
+ report "L.ARG = -MATH_PI in +(L,R)"
+ severity ERROR;
+ return COMPLEX_POLAR'(0.0, 0.0);
+ end if;
+
+ -- Get principal value
+ ZL := POLAR_TO_COMPLEX( L );
+ ZOUT := COMPLEX_TO_POLAR(COMPLEX'(ZL.RE + R, ZL.IM));
+ return ZOUT;
+ end function "+";
+
+ function "-" ( L: in COMPLEX; R: in COMPLEX ) return COMPLEX is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- None
+ begin
+ return COMPLEX'(L.RE - R.RE, L.IM - R.IM);
+ end function "-";
+
+ function "-" ( L: in REAL; R: in COMPLEX ) return COMPLEX is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- None
+ begin
+ return COMPLEX'(L - R.RE, -1.0 * R.IM);
+ end function "-";
+
+ function "-" ( L: in COMPLEX; R: in REAL ) return COMPLEX is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- None
+ begin
+ return COMPLEX'(L.RE - R, L.IM);
+ end function "-";
+
+ function "-" ( L: in COMPLEX_POLAR; R: in COMPLEX_POLAR)
+ return COMPLEX_POLAR is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- a) Returns COMPLEX_POLAR'(0.0, 0.0) on error
+ --
+ variable ZL, ZR : COMPLEX;
+ variable ZOUT : COMPLEX_POLAR;
+ begin
+ -- Check validity of input arguments
+ if ( L.ARG = -MATH_PI ) then
+ assert FALSE
+ report "L.ARG = -MATH_PI in -(L,R)"
+ severity ERROR;
+ return COMPLEX_POLAR'(0.0, 0.0);
+ end if;
+
+ if ( R.ARG = -MATH_PI ) then
+ assert FALSE
+ report "R.ARG = -MATH_PI in -(L,R)"
+ severity ERROR;
+ return COMPLEX_POLAR'(0.0, 0.0);
+ end if;
+ -- Get principal value
+ ZL := POLAR_TO_COMPLEX( L );
+ ZR := POLAR_TO_COMPLEX( R );
+ ZOUT := COMPLEX_TO_POLAR(COMPLEX'(ZL.RE - ZR.RE, ZL.IM -ZR.IM));
+ return ZOUT;
+ end function "-";
+
+ function "-" ( L: in REAL; R: in COMPLEX_POLAR) return COMPLEX_POLAR is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- a) Returns COMPLEX_POLAR'(0.0, 0.0) on error
+ --
+ variable ZR : COMPLEX;
+ variable ZOUT : COMPLEX_POLAR;
+ begin
+ -- Check validity of input arguments
+ if ( R.ARG = -MATH_PI ) then
+ assert FALSE
+ report "R.ARG = -MATH_PI in -(L,R)"
+ severity ERROR;
+ return COMPLEX_POLAR'(0.0, 0.0);
+ end if;
+
+ -- Get principal value
+ ZR := POLAR_TO_COMPLEX( R );
+ ZOUT := COMPLEX_TO_POLAR(COMPLEX'(L - ZR.RE, -1.0*ZR.IM));
+ return ZOUT;
+ end function "-";
+
+ function "-" ( L: in COMPLEX_POLAR; R: in REAL) return COMPLEX_POLAR is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- a) Returns COMPLEX_POLAR'(0.0, 0.0) on error
+ --
+ variable ZL : COMPLEX;
+ variable ZOUT : COMPLEX_POLAR;
+ begin
+ -- Check validity of input arguments
+ if ( L.ARG = -MATH_PI ) then
+ assert FALSE
+ report "L.ARG = -MATH_PI in -(L,R)"
+ severity ERROR;
+ return COMPLEX_POLAR'(0.0, 0.0);
+ end if;
+
+ -- Get principal value
+ ZL := POLAR_TO_COMPLEX( L );
+ ZOUT := COMPLEX_TO_POLAR(COMPLEX'(ZL.RE - R, ZL.IM));
+ return ZOUT;
+ end function "-";
+
+
+ function "*" ( L: in COMPLEX; R: in COMPLEX ) return COMPLEX is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- None
+ begin
+ return COMPLEX'(L.RE * R.RE - L.IM * R.IM, L.RE * R.IM + L.IM * R.RE);
+ end function "*";
+
+
+ function "*" ( L: in REAL; R: in COMPLEX ) return COMPLEX is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- None
+ begin
+ return COMPLEX'(L * R.RE, L * R.IM);
+ end function "*";
+
+ function "*" ( L: in COMPLEX; R: in REAL ) return COMPLEX is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- None
+ begin
+ return COMPLEX'(L.RE * R, L.IM * R);
+ end function "*";
+
+ function "*" ( L: in COMPLEX_POLAR; R: in COMPLEX_POLAR)
+ return COMPLEX_POLAR is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- a) Returns COMPLEX_POLAR'(0.0, 0.0) on error
+ --
+ variable ZOUT : COMPLEX_POLAR;
+ begin
+ -- Check validity of input arguments
+ if ( L.ARG = -MATH_PI ) then
+ assert FALSE
+ report "L.ARG = -MATH_PI in *(L,R)"
+ severity ERROR;
+ return COMPLEX_POLAR'(0.0, 0.0);
+ end if;
+
+ if ( R.ARG = -MATH_PI ) then
+ assert FALSE
+ report "R.ARG = -MATH_PI in *(L,R)"
+ severity ERROR;
+ return COMPLEX_POLAR'(0.0, 0.0);
+ end if;
+
+ -- Get principal value
+ ZOUT.MAG := L.MAG * R.MAG;
+ ZOUT.ARG := GET_PRINCIPAL_VALUE(L.ARG + R.ARG);
+
+ return ZOUT;
+ end function "*";
+
+ function "*" ( L: in REAL; R: in COMPLEX_POLAR) return COMPLEX_POLAR is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- a) Returns COMPLEX_POLAR'(0.0, 0.0) on error
+ --
+ variable ZL : COMPLEX_POLAR;
+ variable ZOUT : COMPLEX_POLAR;
+ begin
+ -- Check validity of input arguments
+ if ( R.ARG = -MATH_PI ) then
+ assert FALSE
+ report "R.ARG = -MATH_PI in *(L,R)"
+ severity ERROR;
+ return COMPLEX_POLAR'(0.0, 0.0);
+ end if;
+
+ -- Get principal value
+ ZL.MAG := POSITIVE_REAL'(ABS(L));
+ if ( L < 0.0 ) then
+ ZL.ARG := MATH_PI;
+ else
+ ZL.ARG := 0.0;
+ end if;
+
+ ZOUT.MAG := ZL.MAG * R.MAG;
+ ZOUT.ARG := GET_PRINCIPAL_VALUE(ZL.ARG + R.ARG);
+
+ return ZOUT;
+ end function "*";
+
+ function "*" ( L: in COMPLEX_POLAR; R: in REAL) return COMPLEX_POLAR is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- a) Returns COMPLEX_POLAR'(0.0, 0.0) on error
+ --
+ variable ZR : COMPLEX_POLAR;
+ variable ZOUT : COMPLEX_POLAR;
+ begin
+ -- Check validity of input arguments
+ if ( L.ARG = -MATH_PI ) then
+ assert FALSE
+ report "L.ARG = -MATH_PI in *(L,R)"
+ severity ERROR;
+ return COMPLEX_POLAR'(0.0, 0.0);
+ end if;
+
+ -- Get principal value
+ ZR.MAG := POSITIVE_REAL'(ABS(R));
+ if ( R < 0.0 ) then
+ ZR.ARG := MATH_PI;
+ else
+ ZR.ARG := 0.0;
+ end if;
+
+ ZOUT.MAG := L.MAG * ZR.MAG;
+ ZOUT.ARG := GET_PRINCIPAL_VALUE(L.ARG + ZR.ARG);
+
+ return ZOUT;
+ end function "*";
+
+ function "/" ( L: in COMPLEX; R: in COMPLEX ) return COMPLEX is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- a) Returns COMPLEX'(REAL'HIGH, 0.0) on error
+ --
+ variable TEMP : REAL := R.RE*R.RE + R.IM*R.IM;
+ begin
+ -- Check validity of input arguments
+ if (TEMP = 0.0) then
+ assert FALSE
+ report "Attempt to divide COMPLEX by (0.0, 0.0)"
+ severity ERROR;
+ return COMPLEX'(REAL'HIGH, 0.0);
+ end if;
+
+ -- Get value
+ return COMPLEX'( (L.RE * R.RE + L.IM * R.IM) / TEMP,
+ (L.IM * R.RE - L.RE * R.IM) / TEMP);
+ end function "/";
+
+ function "/" ( L: in REAL; R: in COMPLEX ) return COMPLEX is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- a) Returns COMPLEX'(REAL'HIGH, 0.0) on error
+ --
+ variable TEMP : REAL := R.RE*R.RE + R.IM*R.IM;
+ begin
+ -- Check validity of input arguments
+ if (TEMP = 0.0) then
+ assert FALSE
+ report "Attempt to divide COMPLEX by (0.0, 0.0)"
+ severity ERROR;
+ return COMPLEX'(REAL'HIGH, 0.0);
+ end if;
+
+ -- Get value
+ TEMP := L / TEMP;
+ return COMPLEX'( TEMP * R.RE, -TEMP * R.IM );
+ end function "/";
+
+ function "/" ( L: in COMPLEX; R: in REAL ) return COMPLEX is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- a) Returns COMPLEX'(REAL'HIGH, 0.0) on error
+ begin
+ -- Check validity of input arguments
+ if (R = 0.0) then
+ assert FALSE
+ report "Attempt to divide COMPLEX by 0.0"
+ severity ERROR;
+ return COMPLEX'(REAL'HIGH, 0.0);
+ end if;
+
+ -- Get value
+ return COMPLEX'(L.RE / R, L.IM / R);
+ end function "/";
+
+
+ function "/" ( L: in COMPLEX_POLAR; R: in COMPLEX_POLAR)
+ return COMPLEX_POLAR is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- a) Returns COMPLEX_POLAR'(REAL'HIGH, 0.0) on error
+ --
+ variable ZOUT : COMPLEX_POLAR;
+ begin
+ -- Check validity of input arguments
+ if (R.MAG = 0.0) then
+ assert FALSE
+ report "Attempt to divide COMPLEX_POLAR by (0.0, 0.0)"
+ severity ERROR;
+ return COMPLEX_POLAR'(REAL'HIGH, 0.0);
+ end if;
+
+ if ( L.ARG = -MATH_PI ) then
+ assert FALSE
+ report "L.ARG = -MATH_PI in /(L,R)"
+ severity ERROR;
+ return COMPLEX_POLAR'(REAL'HIGH, 0.0);
+ end if;
+
+ if ( R.ARG = -MATH_PI ) then
+ assert FALSE
+ report "R.ARG = -MATH_PI in /(L,R)"
+ severity ERROR;
+ return COMPLEX_POLAR'(0.0, 0.0);
+ end if;
+
+ -- Get principal value
+ ZOUT.MAG := L.MAG/R.MAG;
+ ZOUT.ARG := GET_PRINCIPAL_VALUE(L.ARG - R.ARG);
+
+ return ZOUT;
+ end function "/";
+
+ function "/" ( L: in COMPLEX_POLAR; R: in REAL) return COMPLEX_POLAR is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- a) Returns COMPLEX_POLAR'(REAL'HIGH, 0.0) on error
+ --
+ variable ZR : COMPLEX_POLAR;
+ variable ZOUT : COMPLEX_POLAR;
+ begin
+ -- Check validity of input arguments
+ if (R = 0.0) then
+ assert FALSE
+ report "Attempt to divide COMPLEX_POLAR by 0.0"
+ severity ERROR;
+ return COMPLEX_POLAR'(REAL'HIGH, 0.0);
+ end if;
+
+ if ( L.ARG = -MATH_PI ) then
+ assert FALSE
+ report "L.ARG = -MATH_PI in /(L,R)"
+ severity ERROR;
+ return COMPLEX_POLAR'(REAL'HIGH, 0.0);
+ end if;
+
+ -- Get principal value
+ ZR.MAG := POSITIVE_REAL'(ABS(R));
+ if R < 0.0 then
+ ZR.ARG := MATH_PI;
+ else
+ ZR.ARG := 0.0;
+ end if;
+
+ ZOUT.MAG := L.MAG/ZR.MAG;
+ ZOUT.ARG := GET_PRINCIPAL_VALUE(L.ARG - ZR.ARG);
+
+ return ZOUT;
+ end function "/";
+
+ function "/" ( L: in REAL; R: in COMPLEX_POLAR) return COMPLEX_POLAR is
+ -- Description:
+ -- See function declaration in IEEE Std 1076.2-1996
+ -- Notes:
+ -- a) Returns COMPLEX_POLAR'(REAL'HIGH, 0.0) on error
+ --
+ variable ZL : COMPLEX_POLAR;
+ variable ZOUT : COMPLEX_POLAR;
+ begin
+ -- Check validity of input arguments
+ if (R.MAG = 0.0) then
+ assert FALSE
+ report "Attempt to divide COMPLEX_POLAR by (0.0, 0.0)"
+ severity ERROR;
+ return COMPLEX_POLAR'(REAL'HIGH, 0.0);
+ end if;
+
+ if ( R.ARG = -MATH_PI ) then
+ assert FALSE
+ report "R.ARG = -MATH_P in /(L,R)"
+ severity ERROR;
+ return COMPLEX_POLAR'(0.0, 0.0);
+ end if;
+
+ -- Get principal value
+ ZL.MAG := POSITIVE_REAL'(ABS(L));
+ if L < 0.0 then
+ ZL.ARG := MATH_PI;
+ else
+ ZL.ARG := 0.0;
+ end if;
+
+ ZOUT.MAG := ZL.MAG/R.MAG;
+ ZOUT.ARG := GET_PRINCIPAL_VALUE(ZL.ARG - R.ARG);
+
+ return ZOUT;
+ end function "/";
+
+end package body MATH_COMPLEX;
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