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Diffstat (limited to 'libraries/ieee/math_complex.vhdl')
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diff --git a/libraries/ieee/math_complex.vhdl b/libraries/ieee/math_complex.vhdl index 278f7413f..af7c3c3fe 100644 --- a/libraries/ieee/math_complex.vhdl +++ b/libraries/ieee/math_complex.vhdl @@ -1,1087 +1,1083 @@ ------------------------------------------------------------------------- +-- ----------------------------------------------------------------- +-- +-- Copyright 2019 IEEE P1076 WG Authors +-- +-- See the LICENSE file distributed with this work for copyright and +-- licensing information and the AUTHORS file. +-- +-- This file to you under the Apache License, Version 2.0 (the "License"). +-- You may obtain a copy of the License at +-- +-- http://www.apache.org/licenses/LICENSE-2.0 +-- +-- Unless required by applicable law or agreed to in writing, software +-- distributed under the License is distributed on an "AS IS" BASIS, +-- WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or +-- implied. See the License for the specific language governing +-- permissions and limitations under the License. -- --- 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 --- ----------------------------------------------------------------------------- +-- 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 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; + constant CopyRightNotice : STRING + := "Copyright IEEE P1076 WG. Licensed Apache 2.0"; + + -- + -- 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; |