------------------------------------------------------------------------
--
-- 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;