Add ieee 2008 packages.

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diff --git a/libraries/ieee2008/math_complex.vhdl b/libraries/ieee2008/math_complex.vhdl
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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 declaration)
+--             :
+--   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 MATH_COMPLEX is
+  constant CopyRightNotice : STRING
+    := "Copyright 2008 IEEE. All rights reserved.";
+
+  --
+  -- Type Definitions
+  --
+  type COMPLEX is
+  record
+    RE : REAL;                          -- Real part
+    IM : REAL;                          -- Imaginary part
+  end record;
+
+  subtype POSITIVE_REAL is REAL range 0.0 to REAL'high;
+
+  subtype PRINCIPAL_VALUE is REAL range -MATH_PI to MATH_PI;
+
+  type COMPLEX_POLAR is
+  record
+    MAG : POSITIVE_REAL;                -- Magnitude
+    ARG : PRINCIPAL_VALUE;  -- Angle in radians; -MATH_PI is illegal
+  end record;
+
+  --
+  -- Constant Definitions
+  --
+  constant MATH_CBASE_1 : COMPLEX := COMPLEX'(1.0, 0.0);
+  constant MATH_CBASE_J : COMPLEX := COMPLEX'(0.0, 1.0);
+  constant MATH_CZERO   : COMPLEX := COMPLEX'(0.0, 0.0);
+
+
+  --
+  -- Overloaded equality and inequality operators for COMPLEX_POLAR
+  -- (equality and inequality operators for COMPLEX are predefined)
+  --
+
+  function "=" (L : in COMPLEX_POLAR; R : in COMPLEX_POLAR) return BOOLEAN;
+  -- Purpose:
+  --         Returns TRUE if L is equal to R and returns FALSE otherwise
+  -- Special values:
+  --         COMPLEX_POLAR'(0.0, X) = COMPLEX_POLAR'(0.0, Y) returns TRUE
+  --         regardless of the value of X and Y.
+  -- Domain:
+  --         L in COMPLEX_POLAR and L.ARG /= -MATH_PI
+  --         R in COMPLEX_POLAR and R.ARG /= -MATH_PI
+  -- Error conditions:
+  --         Error if L.ARG = -MATH_PI
+  --         Error if R.ARG = -MATH_PI
+  -- Range:
+  --         "="(L,R) is either TRUE or FALSE
+  -- Notes:
+  --         None
+
+  function "/=" (L : in COMPLEX_POLAR; R : in COMPLEX_POLAR) return BOOLEAN;
+  -- Purpose:
+  --         Returns TRUE if L is not equal to R and returns FALSE
+  --         otherwise
+  -- Special values:
+  --         COMPLEX_POLAR'(0.0, X) /= COMPLEX_POLAR'(0.0, Y) returns
+  --         FALSE regardless of the value of X and Y.
+  -- Domain:
+  --         L in COMPLEX_POLAR and L.ARG /= -MATH_PI
+  --         R in COMPLEX_POLAR and R.ARG /= -MATH_PI
+  -- Error conditions:
+  --         Error if L.ARG = -MATH_PI
+  --         Error if R.ARG = -MATH_PI
+  -- Range:
+  --         "/="(L,R) is either TRUE or FALSE
+  -- Notes:
+  --         None
+
+  --
+  -- Function Declarations
+  --
+  function CMPLX(X : in REAL; Y : in REAL := 0.0) return COMPLEX;
+  -- Purpose:
+  --         Returns COMPLEX number X + iY
+  -- Special values:
+  --         None
+  -- Domain:
+  --         X in REAL
+  --         Y in REAL
+  -- Error conditions:
+  --         None
+  -- Range:
+  --         CMPLX(X,Y) is mathematically unbounded
+  -- Notes:
+  --         None
+
+  function GET_PRINCIPAL_VALUE(X : in REAL) return PRINCIPAL_VALUE;
+  -- Purpose:
+  --         Returns principal value of angle X; X in radians
+  -- Special values:
+  --         None
+  -- Domain:
+  --         X in REAL
+  -- Error conditions:
+  --         None
+  -- Range:
+  --         -MATH_PI < GET_PRINCIPAL_VALUE(X) <= MATH_PI
+  -- Notes:
+  --         None
+
+  function COMPLEX_TO_POLAR(Z : in COMPLEX) return COMPLEX_POLAR;
+  -- Purpose:
+  --         Returns principal value COMPLEX_POLAR of Z
+  -- Special values:
+  --         COMPLEX_TO_POLAR(MATH_CZERO) = COMPLEX_POLAR'(0.0, 0.0)
+  --         COMPLEX_TO_POLAR(Z) = COMPLEX_POLAR'(ABS(Z.IM),
+  --                              SIGN(Z.IM)*MATH_PI_OVER_2) if Z.RE = 0.0
+  -- Domain:
+  --         Z in COMPLEX
+  -- Error conditions:
+  --         None
+  -- Range:
+  --         result.MAG >= 0.0
+  --         -MATH_PI < result.ARG <= MATH_PI
+  -- Notes:
+  --         None
+
+  function POLAR_TO_COMPLEX(Z : in COMPLEX_POLAR) return COMPLEX;
+  -- Purpose:
+  --         Returns COMPLEX value of Z
+  -- Special values:
+  --         None
+  -- Domain:
+  --         Z in COMPLEX_POLAR and Z.ARG /= -MATH_PI
+  -- Error conditions:
+  --         Error if Z.ARG = -MATH_PI
+  -- Range:
+  --         POLAR_TO_COMPLEX(Z) is mathematically unbounded
+  -- Notes:
+  --         None
+
+  function "ABS"(Z : in COMPLEX) return POSITIVE_REAL;
+  -- Purpose:
+  --         Returns absolute value (magnitude) of Z
+  -- Special values:
+  --         None
+  -- Domain:
+  --         Z in COMPLEX
+  -- Error conditions:
+  --         None
+  -- Range:
+  --         ABS(Z) is mathematically unbounded
+  -- Notes:
+  --         ABS(Z) = SQRT(Z.RE*Z.RE + Z.IM*Z.IM)
+
+  function "ABS"(Z : in COMPLEX_POLAR) return POSITIVE_REAL;
+  -- Purpose:
+  --         Returns absolute value (magnitude) of Z
+  -- Special values:
+  --         None
+  -- Domain:
+  --         Z in COMPLEX_POLAR and Z.ARG /= -MATH_PI
+  -- Error conditions:
+  --         Error if Z.ARG = -MATH_PI
+  -- Range:
+  --         ABS(Z) >= 0.0
+  -- Notes:
+  --         ABS(Z) = Z.MAG
+
+  function ARG(Z : in COMPLEX) return PRINCIPAL_VALUE;
+  -- Purpose:
+  --         Returns argument (angle) in radians of the principal
+  --         value of Z
+  -- Special values:
+  --         ARG(Z) = 0.0 if Z.RE >= 0.0 and Z.IM = 0.0
+  --         ARG(Z) = SIGN(Z.IM)*MATH_PI_OVER_2 if Z.RE = 0.0
+  --         ARG(Z) = MATH_PI if Z.RE < 0.0        and Z.IM = 0.0
+  -- Domain:
+  --         Z in COMPLEX
+  -- Error conditions:
+  --         None
+  -- Range:
+  --         -MATH_PI < ARG(Z) <= MATH_PI
+  -- Notes:
+  --         ARG(Z) = ARCTAN(Z.IM, Z.RE)
+
+  function ARG(Z : in COMPLEX_POLAR) return PRINCIPAL_VALUE;
+  -- Purpose:
+  --         Returns argument (angle) in radians of the principal
+  --         value of Z
+  -- Special values:
+  --         None
+  -- Domain:
+  --         Z in COMPLEX_POLAR and Z.ARG /= -MATH_PI
+  -- Error conditions:
+  --         Error if Z.ARG = -MATH_PI
+  -- Range:
+  --         -MATH_PI < ARG(Z) <= MATH_PI
+  -- Notes:
+  --         ARG(Z) = Z.ARG
+
+
+  function "-" (Z : in COMPLEX) return COMPLEX;
+  -- Purpose:
+  --         Returns unary minus of Z
+  -- Special values:
+  --         None
+  -- Domain:
+  --         Z in COMPLEX
+  -- Error conditions:
+  --         None
+  -- Range:
+  --         "-"(Z) is mathematically unbounded
+  -- Notes:
+  --         Returns -x -jy for Z= x + jy
+
+  function "-" (Z : in COMPLEX_POLAR) return COMPLEX_POLAR;
+  -- Purpose:
+  --         Returns principal value of unary minus of Z
+  -- Special values:
+  --         "-"(Z) = COMPLEX_POLAR'(Z.MAG, MATH_PI) if Z.ARG = 0.0
+  -- Domain:
+  --         Z in COMPLEX_POLAR and Z.ARG /= -MATH_PI
+  -- Error conditions:
+  --         Error if Z.ARG = -MATH_PI
+  -- Range:
+  --         result.MAG >= 0.0
+  --         -MATH_PI < result.ARG <= MATH_PI
+  -- Notes:
+  --         Returns COMPLEX_POLAR'(Z.MAG, Z.ARG - SIGN(Z.ARG)*MATH_PI) if
+  --                Z.ARG /= 0.0
+
+  function CONJ (Z : in COMPLEX) return COMPLEX;
+  -- Purpose:
+  --         Returns complex conjugate of Z
+  -- Special values:
+  --         None
+  -- Domain:
+  --         Z in COMPLEX
+  -- Error conditions:
+  --         None
+  -- Range:
+  --         CONJ(Z) is mathematically unbounded
+  -- Notes:
+  --         Returns x -jy for Z= x + jy
+
+  function CONJ (Z : in COMPLEX_POLAR) return COMPLEX_POLAR;
+  -- Purpose:
+  --         Returns principal value of complex conjugate of Z
+  -- Special values:
+  --         CONJ(Z) = COMPLEX_POLAR'(Z.MAG, MATH_PI) if Z.ARG = MATH_PI
+  -- Domain:
+  --         Z in COMPLEX_POLAR and Z.ARG /= -MATH_PI
+  -- Error conditions:
+  --         Error if Z.ARG = -MATH_PI
+  -- Range:
+  --         result.MAG >= 0.0
+  --         -MATH_PI < result.ARG <= MATH_PI
+  -- Notes:
+  --         Returns COMPLEX_POLAR'(Z.MAG, -Z.ARG) if Z.ARG /= MATH_PI
+
+  function SQRT(Z : in COMPLEX) return COMPLEX;
+  -- Purpose:
+  --         Returns square root of Z with positive real part
+  --         or, if the real part is zero, the one with nonnegative
+  --         imaginary part
+  -- Special values:
+  --         SQRT(MATH_CZERO) = MATH_CZERO
+  -- Domain:
+  --         Z in COMPLEX
+  -- Error conditions:
+  --         None
+  -- Range:
+  --         SQRT(Z) is mathematically unbounded
+  -- Notes:
+  --         None
+
+  function SQRT(Z : in COMPLEX_POLAR) return COMPLEX_POLAR;
+  -- Purpose:
+  --         Returns square root of Z with positive real part
+  --         or, if the real part is zero, the one with nonnegative
+  --         imaginary part
+  -- Special values:
+  --         SQRT(Z) = COMPLEX_POLAR'(0.0, 0.0) if Z.MAG = 0.0
+  -- Domain:
+  --         Z in COMPLEX_POLAR and Z.ARG /= -MATH_PI
+  -- Error conditions:
+  --         Error if Z.ARG = -MATH_PI
+  -- Range:
+  --         result.MAG >= 0.0
+  --         -MATH_PI < result.ARG <= MATH_PI
+  -- Notes:
+  --         None
+
+  function EXP(Z : in COMPLEX) return COMPLEX;
+  -- Purpose:
+  --         Returns exponential of Z
+  -- Special values:
+  --         EXP(MATH_CZERO) = MATH_CBASE_1
+  --         EXP(Z) = -MATH_CBASE_1 if Z.RE = 0.0 and ABS(Z.IM) = MATH_PI
+  --         EXP(Z) = SIGN(Z.IM)*MATH_CBASE_J if Z.RE = 0.0 and
+  --                                          ABS(Z.IM) =  MATH_PI_OVER_2
+  -- Domain:
+  --         Z in COMPLEX
+  -- Error conditions:
+  --         None
+  -- Range:
+  --         EXP(Z) is mathematically unbounded
+  -- Notes:
+  --         None
+
+
+
+  function EXP(Z : in COMPLEX_POLAR) return COMPLEX_POLAR;
+  -- Purpose:
+  --         Returns principal value of exponential of Z
+  -- Special values:
+  --         EXP(Z) = COMPLEX_POLAR'(1.0, 0.0) if Z.MAG =0.0 and
+  --                                                        Z.ARG = 0.0
+  --         EXP(Z) = COMPLEX_POLAR'(1.0, MATH_PI) if Z.MAG = MATH_PI and
+  --                                        ABS(Z.ARG) = MATH_PI_OVER_2
+  --         EXP(Z) = COMPLEX_POLAR'(1.0, MATH_PI_OVER_2) if
+  --                                        Z.MAG = MATH_PI_OVER_2 and
+  --                                        Z.ARG = MATH_PI_OVER_2
+  --         EXP(Z) = COMPLEX_POLAR'(1.0, -MATH_PI_OVER_2) if
+  --                                        Z.MAG = MATH_PI_OVER_2 and
+  --                                        Z.ARG = -MATH_PI_OVER_2
+  -- Domain:
+  --         Z in COMPLEX_POLAR and Z.ARG /= -MATH_PI
+  -- Error conditions:
+  --         Error if Z.ARG = -MATH_PI
+  -- Range:
+  --         result.MAG >= 0.0
+  --         -MATH_PI < result.ARG <= MATH_PI
+  -- Notes:
+  --         None
+
+  function LOG(Z : in COMPLEX) return COMPLEX;
+  -- Purpose:
+  --         Returns natural logarithm of Z
+  -- Special values:
+  --         LOG(MATH_CBASE_1) = MATH_CZERO
+  --         LOG(-MATH_CBASE_1) = COMPLEX'(0.0, MATH_PI)
+  --         LOG(MATH_CBASE_J) = COMPLEX'(0.0, MATH_PI_OVER_2)
+  --         LOG(-MATH_CBASE_J) = COMPLEX'(0.0, -MATH_PI_OVER_2)
+  --         LOG(Z) = MATH_CBASE_1 if Z = COMPLEX'(MATH_E, 0.0)
+  -- Domain:
+  --         Z in COMPLEX and ABS(Z) /= 0.0
+  -- Error conditions:
+  --         Error if ABS(Z) = 0.0
+  -- Range:
+  --         LOG(Z) is mathematically unbounded
+  -- Notes:
+  --         None
+
+  function LOG2(Z : in COMPLEX) return COMPLEX;
+  -- Purpose:
+  --         Returns logarithm base 2 of Z
+  -- Special values:
+  --         LOG2(MATH_CBASE_1) = MATH_CZERO
+  --         LOG2(Z) = MATH_CBASE_1 if Z = COMPLEX'(2.0, 0.0)
+  -- Domain:
+  --         Z in COMPLEX and ABS(Z) /= 0.0
+  -- Error conditions:
+  --         Error if ABS(Z) = 0.0
+  -- Range:
+  --         LOG2(Z) is mathematically unbounded
+  -- Notes:
+  --         None
+
+  function LOG10(Z : in COMPLEX) return COMPLEX;
+  -- Purpose:
+  --         Returns logarithm base 10 of Z
+  -- Special values:
+  --         LOG10(MATH_CBASE_1) = MATH_CZERO
+  --         LOG10(Z) = MATH_CBASE_1 if Z = COMPLEX'(10.0, 0.0)
+  -- Domain:
+  --         Z in COMPLEX and ABS(Z) /= 0.0
+  -- Error conditions:
+  --         Error if ABS(Z) = 0.0
+  -- Range:
+  --         LOG10(Z) is mathematically unbounded
+  -- Notes:
+  --         None
+
+  function LOG(Z : in COMPLEX_POLAR) return COMPLEX_POLAR;
+  -- Purpose:
+  --         Returns principal value of natural logarithm of Z
+  -- Special values:
+  --         LOG(Z) = COMPLEX_POLAR'(0.0, 0.0) if Z.MAG = 1.0 and
+  --                                             Z.ARG = 0.0
+  --         LOG(Z) = COMPLEX_POLAR'(MATH_PI, MATH_PI_OVER_2) if
+  --                              Z.MAG = 1.0 and Z.ARG = MATH_PI
+  --         LOG(Z) = COMPLEX_POLAR'(MATH_PI_OVER_2, MATH_PI_OVER_2) if
+  --                              Z.MAG = 1.0 and  Z.ARG = MATH_PI_OVER_2
+  --         LOG(Z) = COMPLEX_POLAR'(MATH_PI_OVER_2, -MATH_PI_OVER_2) if
+  --                              Z.MAG = 1.0 and  Z.ARG = -MATH_PI_OVER_2
+  --         LOG(Z) = COMPLEX_POLAR'(1.0, 0.0) if Z.MAG = MATH_E and
+  --                                             Z.ARG = 0.0
+  -- Domain:
+  --         Z in COMPLEX_POLAR and Z.ARG /= -MATH_PI
+  --         Z.MAG /= 0.0
+  -- Error conditions:
+  --         Error if Z.ARG = -MATH_PI
+  --         Error if Z.MAG = 0.0
+  -- Range:
+  --         result.MAG >= 0.0
+  --         -MATH_PI < result.ARG <= MATH_PI
+  -- Notes:
+  --         None
+
+  function LOG2(Z : in COMPLEX_POLAR) return COMPLEX_POLAR;
+  -- Purpose:
+  --         Returns principal value of logarithm base 2 of Z
+  -- Special values:
+  --         LOG2(Z) = COMPLEX_POLAR'(0.0, 0.0) if Z.MAG = 1.0 and
+  --                                              Z.ARG = 0.0
+  --         LOG2(Z) = COMPLEX_POLAR'(1.0, 0.0) if Z.MAG = 2.0 and
+  --                                             Z.ARG = 0.0
+  -- Domain:
+  --         Z in COMPLEX_POLAR and Z.ARG /= -MATH_PI
+  --         Z.MAG /= 0.0
+  -- Error conditions:
+  --         Error if Z.ARG = -MATH_PI
+  --         Error if Z.MAG = 0.0
+  -- Range:
+  --         result.MAG >= 0.0
+  --         -MATH_PI < result.ARG <= MATH_PI
+  -- Notes:
+  --        None
+
+  function LOG10(Z : in COMPLEX_POLAR) return COMPLEX_POLAR;
+  -- Purpose:
+  --         Returns principal value of logarithm base 10 of Z
+  -- Special values:
+  --         LOG10(Z) = COMPLEX_POLAR'(0.0, 0.0) if Z.MAG = 1.0 and
+  --                                               Z.ARG = 0.0
+  --         LOG10(Z) = COMPLEX_POLAR'(1.0, 0.0) if Z.MAG = 10.0 and
+  --                                               Z.ARG = 0.0
+  -- Domain:
+  --         Z in COMPLEX_POLAR and Z.ARG /= -MATH_PI
+  --         Z.MAG /= 0.0
+  -- Error conditions:
+  --         Error if Z.ARG = -MATH_PI
+  --         Error if Z.MAG = 0.0
+  -- Range:
+  --         result.MAG >= 0.0
+  --         -MATH_PI < result.ARG <= MATH_PI
+  -- Notes:
+  --         None
+
+  function LOG(Z : in COMPLEX; BASE : in REAL) return COMPLEX;
+  -- Purpose:
+  --         Returns logarithm base BASE of Z
+  -- Special values:
+  --         LOG(MATH_CBASE_1, BASE) = MATH_CZERO
+  --         LOG(Z,BASE) = MATH_CBASE_1 if Z = COMPLEX'(BASE, 0.0)
+  -- Domain:
+  --         Z in COMPLEX and ABS(Z) /= 0.0
+  --         BASE > 0.0
+  --         BASE /= 1.0
+  -- Error conditions:
+  --         Error if ABS(Z) = 0.0
+  --         Error if BASE <= 0.0
+  --         Error if BASE = 1.0
+  -- Range:
+  --         LOG(Z,BASE) is mathematically unbounded
+  -- Notes:
+  --         None
+
+  function LOG(Z : in COMPLEX_POLAR; BASE : in REAL) return COMPLEX_POLAR;
+  -- Purpose:
+  --         Returns principal value of logarithm base BASE of Z
+  -- Special values:
+  --         LOG(Z, BASE) = COMPLEX_POLAR'(0.0, 0.0) if Z.MAG = 1.0 and
+  --                                                Z.ARG = 0.0
+  --         LOG(Z, BASE) = COMPLEX_POLAR'(1.0, 0.0) if Z.MAG = BASE and
+  --                                                Z.ARG = 0.0
+  -- Domain:
+  --         Z in COMPLEX_POLAR and Z.ARG /= -MATH_PI
+  --         Z.MAG /= 0.0
+  --         BASE > 0.0
+  --         BASE /= 1.0
+  -- Error conditions:
+  --         Error if Z.ARG = -MATH_PI
+  --         Error if Z.MAG = 0.0
+  --         Error if BASE <= 0.0
+  --         Error if BASE = 1.0
+  -- Range:
+  --         result.MAG >= 0.0
+  --         -MATH_PI < result.ARG <= MATH_PI
+  -- Notes:
+  --         None
+
+  function SIN (Z : in COMPLEX) return COMPLEX;
+  -- Purpose:
+  --         Returns sine of Z
+  -- Special values:
+  --         SIN(MATH_CZERO) = MATH_CZERO
+  --         SIN(Z) = MATH_CZERO if Z = COMPLEX'(MATH_PI, 0.0)
+  -- Domain:
+  --         Z in COMPLEX
+  -- Error conditions:
+  --         None
+  -- Range:
+  --         ABS(SIN(Z)) <= SQRT(SIN(Z.RE)*SIN(Z.RE) +
+  --                                         SINH(Z.IM)*SINH(Z.IM))
+  -- Notes:
+  --         None
+
+  function SIN (Z : in COMPLEX_POLAR) return COMPLEX_POLAR;
+  -- Purpose:
+  --         Returns principal value of sine of Z
+  -- Special values:
+  --         SIN(Z) = COMPLEX_POLAR'(0.0, 0.0) if Z.MAG = 0.0 and
+  --                                            Z.ARG = 0.0
+  --         SIN(Z) = COMPLEX_POLAR'(0.0, 0.0) if Z.MAG = MATH_PI and
+  --                                            Z.ARG = 0.0
+  -- Domain:
+  --         Z in COMPLEX_POLAR and Z.ARG /= -MATH_PI
+  -- Error conditions:
+  --         Error if Z.ARG = -MATH_PI
+  -- Range:
+  --         result.MAG >= 0.0
+  --         -MATH_PI < result.ARG <= MATH_PI
+  -- Notes:
+  --         None
+
+  function COS (Z : in COMPLEX) return COMPLEX;
+  -- Purpose:
+  --         Returns cosine of Z
+  -- Special values:
+  --         COS(Z) = MATH_CZERO if Z = COMPLEX'(MATH_PI_OVER_2, 0.0)
+  --         COS(Z) = MATH_CZERO if Z = COMPLEX'(-MATH_PI_OVER_2, 0.0)
+  -- Domain:
+  --         Z in COMPLEX
+  -- Error conditions:
+  --         None
+  -- Range:
+  --         ABS(COS(Z)) <= SQRT(COS(Z.RE)*COS(Z.RE) +
+  --                                         SINH(Z.IM)*SINH(Z.IM))
+  -- Notes:
+  --         None
+
+
+  function COS (Z : in COMPLEX_POLAR) return COMPLEX_POLAR;
+  -- Purpose:
+  --         Returns principal value of cosine of Z
+  -- Special values:
+  --         COS(Z) = COMPLEX_POLAR'(0.0, 0.0) if Z.MAG = MATH_PI_OVER_2
+  --                                               and Z.ARG = 0.0
+  --         COS(Z) = COMPLEX_POLAR'(0.0, 0.0) if Z.MAG = MATH_PI_OVER_2
+  --                                               and Z.ARG = MATH_PI
+  -- Domain:
+  --         Z in COMPLEX_POLAR and Z.ARG /= -MATH_PI
+  -- Error conditions:
+  --         Error if Z.ARG = -MATH_PI
+  -- Range:
+  --         result.MAG >= 0.0
+  --         -MATH_PI < result.ARG <= MATH_PI
+  -- Notes:
+  --         None
+
+  function SINH (Z : in COMPLEX) return COMPLEX;
+  -- Purpose:
+  --         Returns hyperbolic sine of Z
+  -- Special values:
+  --         SINH(MATH_CZERO) = MATH_CZERO
+  --         SINH(Z) = MATH_CZERO if Z.RE = 0.0 and Z.IM = MATH_PI
+  --         SINH(Z) = MATH_CBASE_J if Z.RE = 0.0 and
+  --                                               Z.IM = MATH_PI_OVER_2
+  --         SINH(Z) = -MATH_CBASE_J if Z.RE = 0.0 and
+  --                                               Z.IM = -MATH_PI_OVER_2
+  -- Domain:
+  --         Z in COMPLEX
+  -- Error conditions:
+  --         None
+  -- Range:
+  --         ABS(SINH(Z)) <= SQRT(SINH(Z.RE)*SINH(Z.RE) +
+  --                                         SIN(Z.IM)*SIN(Z.IM))
+  -- Notes:
+  --         None
+
+  function SINH (Z : in COMPLEX_POLAR) return COMPLEX_POLAR;
+  -- Purpose:
+  --         Returns principal value of hyperbolic sine of Z
+  -- Special values:
+  --         SINH(Z) = COMPLEX_POLAR'(0.0, 0.0) if Z.MAG = 0.0 and
+  --                                            Z.ARG = 0.0
+  --         SINH(Z) = COMPLEX_POLAR'(0.0, 0.0) if Z.MAG = MATH_PI and
+  --                                            Z.ARG = MATH_PI_OVER_2
+  --         SINH(Z) = COMPLEX_POLAR'(1.0, MATH_PI_OVER_2) if Z.MAG =
+  --                         MATH_PI_OVER_2 and Z.ARG = MATH_PI_OVER_2
+  --         SINH(Z) = COMPLEX_POLAR'(1.0, -MATH_PI_OVER_2) if Z.MAG =
+  --                         MATH_PI_OVER_2 and Z.ARG = -MATH_PI_OVER_2
+  -- Domain:
+  --         Z in COMPLEX_POLAR and Z.ARG /= -MATH_PI
+  -- Error conditions:
+  --         Error if Z.ARG = -MATH_PI
+  -- Range:
+  --         result.MAG >= 0.0
+  --         -MATH_PI < result.ARG <= MATH_PI
+  -- Notes:
+  --         None
+
+  function COSH (Z : in COMPLEX) return COMPLEX;
+  -- Purpose:
+  --         Returns hyperbolic cosine of Z
+  -- Special values:
+  --         COSH(MATH_CZERO) = MATH_CBASE_1
+  --         COSH(Z) = -MATH_CBASE_1 if Z.RE = 0.0 and Z.IM = MATH_PI
+  --         COSH(Z) = MATH_CZERO if Z.RE = 0.0 and Z.IM = MATH_PI_OVER_2
+  --         COSH(Z) = MATH_CZERO if Z.RE = 0.0 and Z.IM = -MATH_PI_OVER_2
+  -- Domain:
+  --         Z in COMPLEX
+  -- Error conditions:
+  --         None
+  -- Range:
+  --         ABS(COSH(Z)) <= SQRT(SINH(Z.RE)*SINH(Z.RE) +
+  --                                         COS(Z.IM)*COS(Z.IM))
+  -- Notes:
+  --         None
+
+
+  function COSH (Z : in COMPLEX_POLAR) return COMPLEX_POLAR;
+  -- Purpose:
+  --         Returns principal value of hyperbolic cosine of Z
+  -- Special values:
+  --         COSH(Z) = COMPLEX_POLAR'(1.0, 0.0) if Z.MAG = 0.0 and
+  --                                            Z.ARG = 0.0
+  --         COSH(Z) = COMPLEX_POLAR'(1.0, MATH_PI) if Z.MAG = MATH_PI and
+  --                                            Z.ARG = MATH_PI_OVER_2
+  --         COSH(Z) = COMPLEX_POLAR'(0.0, 0.0) if Z.MAG =
+  --                        MATH_PI_OVER_2 and Z.ARG = MATH_PI_OVER_2
+  --         COSH(Z) = COMPLEX_POLAR'(0.0, 0.0) if Z.MAG =
+  --                        MATH_PI_OVER_2 and Z.ARG = -MATH_PI_OVER_2
+  -- Domain:
+  --         Z in COMPLEX_POLAR and Z.ARG /= -MATH_PI
+  -- Error conditions:
+  --         Error if Z.ARG = -MATH_PI
+  -- Range:
+  --         result.MAG >= 0.0
+  --         -MATH_PI < result.ARG <= MATH_PI
+  -- Notes:
+  --         None
+
+  --
+  -- Arithmetic Operators
+  --
+
+  function "+" (L : in COMPLEX; R : in COMPLEX) return COMPLEX;
+  -- Purpose:
+  --         Returns arithmetic addition of L and R
+  -- Special values:
+  --         None
+  -- Domain:
+  --         L in COMPLEX
+  --         R in COMPLEX
+  -- Error conditions:
+  --         None
+  -- Range:
+  --         "+"(Z) is mathematically unbounded
+  -- Notes:
+  --         None
+
+  function "+" (L : in REAL; R : in COMPLEX) return COMPLEX;
+  -- Purpose:
+  --         Returns arithmetic addition of L and R
+  -- Special values:
+  --         None
+  -- Domain:
+  --         L in REAL
+  --         R in COMPLEX
+  -- Error conditions:
+  --         None
+  -- Range:
+  --         "+"(Z) is mathematically unbounded
+  -- Notes:
+  --         None
+
+  function "+" (L : in COMPLEX; R : in REAL) return COMPLEX;
+  -- Purpose:
+  --         Returns arithmetic addition of L and R
+  -- Special values:
+  --         None
+  -- Domain:
+  --         L in COMPLEX
+  --         R in REAL
+  -- Error conditions:
+  --         None
+  -- Range:
+  --         "+"(Z) is mathematically unbounded
+  -- Notes:
+  --         None
+
+  function "+" (L : in COMPLEX_POLAR; R : in COMPLEX_POLAR)
+    return COMPLEX_POLAR;
+  -- Purpose:
+  --         Returns arithmetic addition of L and R
+  -- Special values:
+  --         None
+  -- Domain:
+  --         L in COMPLEX_POLAR and L.ARG /= -MATH_PI
+  --         R in COMPLEX_POLAR and R.ARG /= -MATH_PI
+  -- Error conditions:
+  --         Error if L.ARG = -MATH_PI
+  --         Error if R.ARG = -MATH_PI
+  -- Range:
+  --         result.MAG >= 0.0
+  --         -MATH_PI < result.ARG <= MATH_PI
+  -- Notes:
+  --         None
+
+
+  function "+" (L : in REAL; R : in COMPLEX_POLAR) return COMPLEX_POLAR;
+  -- Purpose:
+  --         Returns arithmetic addition of L and R
+  -- Special values:
+  --         None
+  -- Domain:
+  --         L in REAL
+  --         R in COMPLEX_POLAR and R.ARG /= -MATH_PI
+  -- Error conditions:
+  --         Error if R.ARG = -MATH_PI
+  -- Range:
+  --         result.MAG >= 0.0
+  --         -MATH_PI < result.ARG <= MATH_PI
+  -- Notes:
+  --         None
+
+  function "+" (L : in COMPLEX_POLAR; R : in REAL) return COMPLEX_POLAR;
+  -- Purpose:
+  --         Returns arithmetic addition of L and R
+  -- Special values:
+  --         None
+  -- Domain:
+  --         L in COMPLEX_POLAR and L.ARG /= -MATH_PI
+  --         R in REAL
+  -- Error conditions:
+  --         Error if L.ARG = -MATH_PI
+  -- Range:
+  --         result.MAG >= 0.0
+  --         -MATH_PI < result.ARG <= MATH_PI
+  -- Notes:
+  --         None
+
+  function "-" (L : in COMPLEX; R : in COMPLEX) return COMPLEX;
+  -- Purpose:
+  --         Returns arithmetic subtraction of L minus R
+  -- Special values:
+  --         None
+  -- Domain:
+  --         L in COMPLEX
+  --         R in COMPLEX
+  -- Error conditions:
+  --         None
+  -- Range:
+  --         "-"(Z) is mathematically unbounded
+  -- Notes:
+  --         None
+
+  function "-" (L : in REAL; R : in COMPLEX) return COMPLEX;
+  -- Purpose:
+  --         Returns arithmetic subtraction of L minus R
+  -- Special values:
+  --         None
+  -- Domain:
+  --         L in REAL
+  --         R in COMPLEX
+  -- Error conditions:
+  --         None
+  -- Range:
+  --         "-"(Z) is mathematically unbounded
+  -- Notes:
+  --         None
+
+  function "-" (L : in COMPLEX; R : in REAL) return COMPLEX;
+  -- Purpose:
+  --         Returns arithmetic subtraction of L minus R
+  -- Special values:
+  --         None
+  -- Domain:
+  --         L in COMPLEX
+  --         R in REAL
+  -- Error conditions:
+  --         None
+  -- Range:
+  --         "-"(Z) is mathematically unbounded
+  -- Notes:
+  --         None
+
+  function "-" (L : in COMPLEX_POLAR; R : in COMPLEX_POLAR)
+    return COMPLEX_POLAR;
+  -- Purpose:
+  --         Returns arithmetic subtraction of L minus R
+  -- Special values:
+  --         None
+  -- Domain:
+  --         L in COMPLEX_POLAR and L.ARG /= -MATH_PI
+  --         R in COMPLEX_POLAR and R.ARG /= -MATH_PI
+  -- Error conditions:
+  --         Error if L.ARG = -MATH_PI
+  --         Error if R.ARG = -MATH_PI
+  -- Range:
+  --         result.MAG >= 0.0
+  --         -MATH_PI < result.ARG <= MATH_PI
+  -- Notes:
+  --         None
+
+  function "-" (L : in REAL; R : in COMPLEX_POLAR) return COMPLEX_POLAR;
+  -- Purpose:
+  --         Returns arithmetic subtraction of L minus R
+  -- Special values:
+  --         None
+  -- Domain:
+  --         L in REAL
+  --         R in COMPLEX_POLAR and R.ARG /= -MATH_PI
+  -- Error conditions:
+  --         Error if R.ARG = -MATH_PI
+  -- Range:
+  --         result.MAG >= 0.0
+  --         -MATH_PI < result.ARG <= MATH_PI
+  -- Notes:
+  --         None
+
+
+  function "-" (L : in COMPLEX_POLAR; R : in REAL) return COMPLEX_POLAR;
+  -- Purpose:
+  --         Returns arithmetic subtraction of L minus R
+  -- Special values:
+  --         None
+  -- Domain:
+  --         L in COMPLEX_POLAR and L.ARG /= -MATH_PI
+  --         R in REAL
+  -- Error conditions:
+  --         Error if L.ARG = -MATH_PI
+  -- Range:
+  --         result.MAG >= 0.0
+  --         -MATH_PI < result.ARG <= MATH_PI
+  -- Notes:
+  --         None
+
+  function "*" (L : in COMPLEX; R : in COMPLEX) return COMPLEX;
+  -- Purpose:
+  --         Returns arithmetic multiplication of L and R
+  -- Special values:
+  --         None
+  -- Domain:
+  --         L in COMPLEX
+  --         R in COMPLEX
+  -- Error conditions:
+  --         None
+  -- Range:
+  --         "*"(Z) is mathematically unbounded
+  -- Notes:
+  --         None
+
+  function "*" (L : in REAL; R : in COMPLEX) return COMPLEX;
+  -- Purpose:
+  --         Returns arithmetic multiplication of L and R
+  -- Special values:
+  --         None
+  -- Domain:
+  --         L in REAL
+  --         R in COMPLEX
+  -- Error conditions:
+  --         None
+  -- Range:
+  --         "*"(Z) is mathematically unbounded
+  -- Notes:
+  --         None
+
+  function "*" (L : in COMPLEX; R : in REAL) return COMPLEX;
+  -- Purpose:
+  --         Returns arithmetic multiplication of L and R
+  -- Special values:
+  --         None
+  -- Domain:
+  --         L in COMPLEX
+  --         R in REAL
+  -- Error conditions:
+  --         None
+
+  -- Range:
+  --         "*"(Z) is mathematically unbounded
+  -- Notes:
+  --         None
+
+  function "*" (L : in COMPLEX_POLAR; R : in COMPLEX_POLAR)
+    return COMPLEX_POLAR;
+  -- Purpose:
+  --         Returns arithmetic multiplication of L and R
+  -- Special values:
+  --         None
+  -- Domain:
+  --         L in COMPLEX_POLAR and L.ARG /= -MATH_PI
+  --         R in COMPLEX_POLAR and R.ARG /= -MATH_PI
+  -- Error conditions:
+  --         Error if L.ARG = -MATH_PI
+  --         Error if R.ARG = -MATH_PI
+  -- Range:
+  --         result.MAG >= 0.0
+  --         -MATH_PI < result.ARG <= MATH_PI
+  -- Notes:
+  --         None
+
+  function "*" (L : in REAL; R : in COMPLEX_POLAR) return COMPLEX_POLAR;
+  -- Purpose:
+  --         Returns arithmetic multiplication of L and R
+  -- Special values:
+  --         None
+  -- Domain:
+  --         L in REAL
+  --         R in COMPLEX_POLAR and R.ARG /= -MATH_PI
+  -- Error conditions:
+  --         Error if R.ARG = -MATH_PI
+  -- Range:
+  --         result.MAG >= 0.0
+  --         -MATH_PI < result.ARG <= MATH_PI
+  -- Notes:
+  --         None
+
+  function "*" (L : in COMPLEX_POLAR; R : in REAL) return COMPLEX_POLAR;
+  -- Purpose:
+  --         Returns arithmetic multiplication of L and R
+  -- Special values:
+  --         None
+  -- Domain:
+  --         L in COMPLEX_POLAR and L.ARG /= -MATH_PI
+  --         R in REAL
+  -- Error conditions:
+  --         Error if L.ARG = -MATH_PI
+  -- Range:
+  --         result.MAG >= 0.0
+  --         -MATH_PI < result.ARG <= MATH_PI
+  -- Notes:
+  --         None
+
+
+  function "/" (L : in COMPLEX; R : in COMPLEX) return COMPLEX;
+  -- Purpose:
+  --         Returns arithmetic division of L by R
+  -- Special values:
+  --         None
+  -- Domain:
+  --         L in COMPLEX
+  --         R in COMPLEX and R /= MATH_CZERO
+  -- Error conditions:
+  --         Error if R = MATH_CZERO
+  -- Range:
+  --         "/"(Z) is mathematically unbounded
+  -- Notes:
+  --         None
+
+  function "/" (L : in REAL; R : in COMPLEX) return COMPLEX;
+  -- Purpose:
+  --         Returns arithmetic division of L by R
+  -- Special values:
+  --         None
+  -- Domain:
+  --         L in REAL
+  --         R in COMPLEX and R /= MATH_CZERO
+  -- Error conditions:
+  --         Error if R = MATH_CZERO
+  -- Range:
+  --         "/"(Z) is mathematically unbounded
+  -- Notes:
+  --         None
+
+  function "/" (L : in COMPLEX; R : in REAL) return COMPLEX;
+  -- Purpose:
+  --         Returns arithmetic division of L by R
+  -- Special values:
+  --         None
+  -- Domain:
+  --         L in COMPLEX
+  --         R in REAL and R /= 0.0
+  -- Error conditions:
+  --         Error if R = 0.0
+  -- Range:
+  --         "/"(Z) is mathematically unbounded
+  -- Notes:
+  --         None
+
+  function "/" (L : in COMPLEX_POLAR; R : in COMPLEX_POLAR)
+    return COMPLEX_POLAR;
+  -- Purpose:
+  --         Returns arithmetic division of L by R
+  -- Special values:
+  --         None
+  -- Domain:
+  --         L in COMPLEX_POLAR and L.ARG /= -MATH_PI
+  --         R in COMPLEX_POLAR and R.ARG /= -MATH_PI
+  --         R.MAG > 0.0
+  -- Error conditions:
+  --         Error if R.MAG <= 0.0
+  --         Error if L.ARG = -MATH_PI
+  --         Error if R.ARG = -MATH_PI
+  -- Range:
+  --         result.MAG >= 0.0
+  --         -MATH_PI < result.ARG <= MATH_PI
+  -- Notes:
+  --         None
+
+  function "/" (L : in REAL; R : in COMPLEX_POLAR) return COMPLEX_POLAR;
+  -- Purpose:
+  --         Returns arithmetic division of L by R
+  -- Special values:
+  --         None
+  -- Domain:
+  --         L in REAL
+  --         R in COMPLEX_POLAR and R.ARG /= -MATH_PI
+  --         R.MAG > 0.0
+  -- Error conditions:
+  --         Error if R.MAG <= 0.0
+  --         Error if R.ARG = -MATH_PI
+  -- Range:
+  --         result.MAG >= 0.0
+  --         -MATH_PI < result.ARG <= MATH_PI
+  -- Notes:
+  --         None
+
+  function "/" (L : in COMPLEX_POLAR; R : in REAL) return COMPLEX_POLAR;
+  -- Purpose:
+  --         Returns arithmetic division of L by R
+  -- Special values:
+  --         None
+  -- Domain:
+  --         L in COMPLEX_POLAR and L.ARG /= -MATH_PI
+  --         R /= 0.0
+  -- Error conditions:
+  --         Error if L.ARG = -MATH_PI
+  --         Error if R = 0.0
+  -- Range:
+  --         result.MAG >= 0.0
+  --         -MATH_PI < result.ARG <= MATH_PI
+  -- Notes:
+  --         None
+end package MATH_COMPLEX;