path: root/libraries/ieee/math_complex.vhdl

------------------------------------------------------------------------
--
-- Copyright 1996 by IEEE. All rights reserved.
--
-- This source file is an essential part of IEEE Std 1076.2-1996, IEEE Standard 
-- VHDL Mathematical Packages. 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 used to implement this standard 
-- and may be distributed in compiled form in any manner so long as the 
-- compiled form does not allow direct decompilation of the original source file.
-- 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 (IEEE Std 1076.2-1996,
--              MATH_COMPLEX)
--
-- 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-
--              1993.
--
-- Notes:
--              No declarations or definitions shall be included in, or
--              excluded from, this package.
--              The "package declaration" defines the types, subtypes, and
--              declarations of MATH_COMPLEX.
--              The standard mathematical definition and conventional meaning
--              of the mathematical functions that are part of this standard
--              represent the formal semantics of the implementation of the
--              MATH_COMPLEX package declaration.  The purpose of the
--              MATH_COMPLEX package body is to provide a guideline for
--              implementations to verify their implementation of MATH_COMPLEX.
--              Tool developers may choose to implement the package body in
--              the most efficient manner available to them.
--
-- -----------------------------------------------------------------------------
-- Version    : 1.5
-- Date       : 24 July 1996
-- -----------------------------------------------------------------------------

use WORK.MATH_REAL.all;
package MATH_COMPLEX is
    constant CopyRightNotice: STRING
      := "Copyright 1996 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  MATH_COMPLEX;