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diff --git a/libraries/ieee/math_complex.vhdl b/libraries/ieee/math_complex.vhdl index 2f9376bfb..278f7413f 100644 --- a/libraries/ieee/math_complex.vhdl +++ b/libraries/ieee/math_complex.vhdl @@ -1,126 +1,1087 @@ ---------------------------------------------------------------- +------------------------------------------------------------------------ -- --- This source file may be used and distributed without restriction. --- No declarations or definitions shall be included in this package. --- This package cannot be sold or distributed for profit. +-- Copyright 1996 by IEEE. All rights reserved. -- --- **************************************************************** --- * * --- * W A R N I N G * --- * * --- * This DRAFT version IS NOT endorsed or approved by IEEE * --- * * --- **************************************************************** +-- 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: PACKAGE MATH_COMPLEX +-- Title: Standard VHDL Mathematical Packages (IEEE Std 1076.2-1996, +-- MATH_COMPLEX) -- --- Purpose: VHDL declarations for mathematical package MATH_COMPLEX --- which contains common complex constants and basic complex --- functions and operations. +-- Library: This package shall be compiled into a library +-- symbolically named IEEE. -- --- Author: IEEE VHDL Math Package Study Group +-- Developers: IEEE DASC VHDL Mathematical Packages Working Group -- --- Notes: --- The package body uses package IEEE.MATH_REAL +-- 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. -- --- The package body shall be considered the formal definition of --- the semantics of this package. Tool developers may choose to implement --- the package body in the most efficient manner available to them. +-- 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. -- --- History: --- Version 0.1 (Strawman) Jose A. Torres 6/22/92 --- Version 0.2 Jose A. Torres 1/15/93 --- Version 0.3 Jose A. Torres 4/13/93 --- Version 0.4 Jose A. Torres 4/19/93 --- Version 0.5 Jose A. Torres 4/20/93 --- Version 0.6 Jose A. Torres 4/23/93 Added unary minus --- and CONJ for polar --- Version 0.7 Jose A. Torres 5/28/93 Rev up for compatibility --- with package body. -------------------------------------------------------------- -Library IEEE; - -Package MATH_COMPLEX is - - - type COMPLEX is record RE, IM: real; end record; - type COMPLEX_VECTOR is array (integer range <>) of COMPLEX; - type COMPLEX_POLAR is record MAG: real; ARG: real; end record; - - constant CBASE_1: complex := COMPLEX'(1.0, 0.0); - constant CBASE_j: complex := COMPLEX'(0.0, 1.0); - constant CZERO: complex := COMPLEX'(0.0, 0.0); - - function CABS(Z: in complex ) return real; - -- returns absolute value (magnitude) of Z - - function CARG(Z: in complex ) return real; - -- returns argument (angle) in radians of a complex number - - function CMPLX(X: in real; Y: in real:= 0.0 ) return complex; - -- returns complex number X + iY - - function "-" (Z: in complex ) return complex; - -- unary minus - - function "-" (Z: in complex_polar ) return complex_polar; - -- unary minus - - function CONJ (Z: in complex) return complex; - -- returns complex conjugate - - function CONJ (Z: in complex_polar) return complex_polar; - -- returns complex conjugate - - function CSQRT(Z: in complex ) return complex_vector; - -- returns square root of Z; 2 values - - function CEXP(Z: in complex ) return complex; - -- returns e**Z - - function COMPLEX_TO_POLAR(Z: in complex ) return complex_polar; - -- converts complex to complex_polar - - function POLAR_TO_COMPLEX(Z: in complex_polar ) return complex; - -- converts complex_polar to complex - - - -- arithmetic operators - - function "+" ( L: in complex; R: in complex ) return complex; - function "+" ( L: in complex_polar; R: in complex_polar) return complex; - function "+" ( L: in complex_polar; R: in complex ) return complex; - function "+" ( L: in complex; R: in complex_polar) return complex; - function "+" ( L: in real; R: in complex ) return complex; - function "+" ( L: in complex; R: in real ) return complex; - function "+" ( L: in real; R: in complex_polar) return complex; - function "+" ( L: in complex_polar; R: in real) return complex; - - function "-" ( L: in complex; R: in complex ) return complex; - function "-" ( L: in complex_polar; R: in complex_polar) return complex; - function "-" ( L: in complex_polar; R: in complex ) return complex; - function "-" ( L: in complex; R: in complex_polar) return complex; - function "-" ( L: in real; R: in complex ) return complex; - function "-" ( L: in complex; R: in real ) return complex; - function "-" ( L: in real; R: in complex_polar) return complex; - function "-" ( L: in complex_polar; R: in real) return complex; - - function "*" ( L: in complex; R: in complex ) return complex; - function "*" ( L: in complex_polar; R: in complex_polar) return complex; - function "*" ( L: in complex_polar; R: in complex ) return complex; - function "*" ( L: in complex; R: in complex_polar) return complex; - function "*" ( L: in real; R: in complex ) return complex; - function "*" ( L: in complex; R: in real ) return complex; - function "*" ( L: in real; R: in complex_polar) return complex; - function "*" ( L: in complex_polar; R: in real) return complex; - - - function "/" ( L: in complex; R: in complex ) return complex; - function "/" ( L: in complex_polar; R: in complex_polar) return complex; - function "/" ( L: in complex_polar; R: in complex ) return complex; - function "/" ( L: in complex; R: in complex_polar) return complex; - function "/" ( L: in real; R: in complex ) return complex; - function "/" ( L: in complex; R: in real ) return complex; - function "/" ( L: in real; R: in complex_polar) return complex; - function "/" ( L: in complex_polar; R: in real) return complex; +-- 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; |