From 8c778be42999972dcda1aac95999e0eb1a5e3e9c Mon Sep 17 00:00:00 2001 From: Tristan Gingold Date: Sat, 4 Jan 2014 11:25:55 +0100 Subject: Add ieee 2008 packages. --- libraries/ieee2008/math_complex.vhdl | 1080 ++++++++++++++++++++++++++++++++++ 1 file changed, 1080 insertions(+) create mode 100644 libraries/ieee2008/math_complex.vhdl (limited to 'libraries/ieee2008/math_complex.vhdl') diff --git a/libraries/ieee2008/math_complex.vhdl b/libraries/ieee2008/math_complex.vhdl new file mode 100644 index 000000000..9d4cdcad3 --- /dev/null +++ b/libraries/ieee2008/math_complex.vhdl @@ -0,0 +1,1080 @@ +-- -------------------------------------------------------------------- +-- +-- Copyright © 2008 by IEEE. All rights reserved. +-- +-- This source file is an essential part of IEEE Std 1076-2008, +-- IEEE Standard VHDL Language Reference Manual. This source file may not be +-- copied, sold, or included with software that is sold without written +-- permission from the IEEE Standards Department. This source file may be +-- copied for individual use between licensed users. This source file is +-- provided on an AS IS basis. The IEEE disclaims ANY WARRANTY EXPRESS OR +-- IMPLIED INCLUDING ANY WARRANTY OF MERCHANTABILITY AND FITNESS FOR USE +-- FOR A PARTICULAR PURPOSE. The user of the source file shall indemnify +-- and hold IEEE harmless from any damages or liability arising out of the +-- use thereof. +-- +-- Title : Standard VHDL Mathematical Packages +-- : (MATH_COMPLEX package declaration) +-- : +-- Library : This package shall be compiled into a library +-- : symbolically named IEEE. +-- : +-- Developers: IEEE DASC VHDL Mathematical Packages Working Group +-- : +-- Purpose : This package defines a standard for designers to use in +-- : describing VHDL models that make use of common COMPLEX +-- : constants and common COMPLEX mathematical functions and +-- : operators. +-- : +-- Limitation: The values generated by the functions in this package +-- : may vary from platform to platform, and the precision +-- : of results is only guaranteed to be the minimum required +-- : by IEEE Std 1076-2008. +-- : +-- Note : This package may be modified to include additional data +-- : required by tools, but it must in no way change the +-- : external interfaces or simulation behavior of the +-- : description. It is permissible to add comments and/or +-- : attributes to the package declarations, but not to change +-- : or delete any original lines of the package declaration. +-- : The package body may be changed only in accordance with +-- : the terms of Clause 16 of this standard. +-- : +-- -------------------------------------------------------------------- +-- $Revision: 1220 $ +-- $Date: 2008-04-10 17:16:09 +0930 (Thu, 10 Apr 2008) $ +-- -------------------------------------------------------------------- + +use WORK.MATH_REAL.all; +package MATH_COMPLEX is + constant CopyRightNotice : STRING + := "Copyright 2008 IEEE. All rights reserved."; + + -- + -- Type Definitions + -- + type COMPLEX is + record + RE : REAL; -- Real part + IM : REAL; -- Imaginary part + end record; + + subtype POSITIVE_REAL is REAL range 0.0 to REAL'high; + + subtype PRINCIPAL_VALUE is REAL range -MATH_PI to MATH_PI; + + type COMPLEX_POLAR is + record + MAG : POSITIVE_REAL; -- Magnitude + ARG : PRINCIPAL_VALUE; -- Angle in radians; -MATH_PI is illegal + end record; + + -- + -- Constant Definitions + -- + constant MATH_CBASE_1 : COMPLEX := COMPLEX'(1.0, 0.0); + constant MATH_CBASE_J : COMPLEX := COMPLEX'(0.0, 1.0); + constant MATH_CZERO : COMPLEX := COMPLEX'(0.0, 0.0); + + + -- + -- Overloaded equality and inequality operators for COMPLEX_POLAR + -- (equality and inequality operators for COMPLEX are predefined) + -- + + function "=" (L : in COMPLEX_POLAR; R : in COMPLEX_POLAR) return BOOLEAN; + -- Purpose: + -- Returns TRUE if L is equal to R and returns FALSE otherwise + -- Special values: + -- COMPLEX_POLAR'(0.0, X) = COMPLEX_POLAR'(0.0, Y) returns TRUE + -- regardless of the value of X and Y. + -- Domain: + -- L in COMPLEX_POLAR and L.ARG /= -MATH_PI + -- R in COMPLEX_POLAR and R.ARG /= -MATH_PI + -- Error conditions: + -- Error if L.ARG = -MATH_PI + -- Error if R.ARG = -MATH_PI + -- Range: + -- "="(L,R) is either TRUE or FALSE + -- Notes: + -- None + + function "/=" (L : in COMPLEX_POLAR; R : in COMPLEX_POLAR) return BOOLEAN; + -- Purpose: + -- Returns TRUE if L is not equal to R and returns FALSE + -- otherwise + -- Special values: + -- COMPLEX_POLAR'(0.0, X) /= COMPLEX_POLAR'(0.0, Y) returns + -- FALSE regardless of the value of X and Y. + -- Domain: + -- L in COMPLEX_POLAR and L.ARG /= -MATH_PI + -- R in COMPLEX_POLAR and R.ARG /= -MATH_PI + -- Error conditions: + -- Error if L.ARG = -MATH_PI + -- Error if R.ARG = -MATH_PI + -- Range: + -- "/="(L,R) is either TRUE or FALSE + -- Notes: + -- None + + -- + -- Function Declarations + -- + function CMPLX(X : in REAL; Y : in REAL := 0.0) return COMPLEX; + -- Purpose: + -- Returns COMPLEX number X + iY + -- Special values: + -- None + -- Domain: + -- X in REAL + -- Y in REAL + -- Error conditions: + -- None + -- Range: + -- CMPLX(X,Y) is mathematically unbounded + -- Notes: + -- None + + function GET_PRINCIPAL_VALUE(X : in REAL) return PRINCIPAL_VALUE; + -- Purpose: + -- Returns principal value of angle X; X in radians + -- Special values: + -- None + -- Domain: + -- X in REAL + -- Error conditions: + -- None + -- Range: + -- -MATH_PI < GET_PRINCIPAL_VALUE(X) <= MATH_PI + -- Notes: + -- None + + function COMPLEX_TO_POLAR(Z : in COMPLEX) return COMPLEX_POLAR; + -- Purpose: + -- Returns principal value COMPLEX_POLAR of Z + -- Special values: + -- COMPLEX_TO_POLAR(MATH_CZERO) = COMPLEX_POLAR'(0.0, 0.0) + -- COMPLEX_TO_POLAR(Z) = COMPLEX_POLAR'(ABS(Z.IM), + -- SIGN(Z.IM)*MATH_PI_OVER_2) if Z.RE = 0.0 + -- Domain: + -- Z in COMPLEX + -- Error conditions: + -- None + -- Range: + -- result.MAG >= 0.0 + -- -MATH_PI < result.ARG <= MATH_PI + -- Notes: + -- None + + function POLAR_TO_COMPLEX(Z : in COMPLEX_POLAR) return COMPLEX; + -- Purpose: + -- Returns COMPLEX value of Z + -- Special values: + -- None + -- Domain: + -- Z in COMPLEX_POLAR and Z.ARG /= -MATH_PI + -- Error conditions: + -- Error if Z.ARG = -MATH_PI + -- Range: + -- POLAR_TO_COMPLEX(Z) is mathematically unbounded + -- Notes: + -- None + + function "ABS"(Z : in COMPLEX) return POSITIVE_REAL; + -- Purpose: + -- Returns absolute value (magnitude) of Z + -- Special values: + -- None + -- Domain: + -- Z in COMPLEX + -- Error conditions: + -- None + -- Range: + -- ABS(Z) is mathematically unbounded + -- Notes: + -- ABS(Z) = SQRT(Z.RE*Z.RE + Z.IM*Z.IM) + + function "ABS"(Z : in COMPLEX_POLAR) return POSITIVE_REAL; + -- Purpose: + -- Returns absolute value (magnitude) of Z + -- Special values: + -- None + -- Domain: + -- Z in COMPLEX_POLAR and Z.ARG /= -MATH_PI + -- Error conditions: + -- Error if Z.ARG = -MATH_PI + -- Range: + -- ABS(Z) >= 0.0 + -- Notes: + -- ABS(Z) = Z.MAG + + function ARG(Z : in COMPLEX) return PRINCIPAL_VALUE; + -- Purpose: + -- Returns argument (angle) in radians of the principal + -- value of Z + -- Special values: + -- ARG(Z) = 0.0 if Z.RE >= 0.0 and Z.IM = 0.0 + -- ARG(Z) = SIGN(Z.IM)*MATH_PI_OVER_2 if Z.RE = 0.0 + -- ARG(Z) = MATH_PI if Z.RE < 0.0 and Z.IM = 0.0 + -- Domain: + -- Z in COMPLEX + -- Error conditions: + -- None + -- Range: + -- -MATH_PI < ARG(Z) <= MATH_PI + -- Notes: + -- ARG(Z) = ARCTAN(Z.IM, Z.RE) + + function ARG(Z : in COMPLEX_POLAR) return PRINCIPAL_VALUE; + -- Purpose: + -- Returns argument (angle) in radians of the principal + -- value of Z + -- Special values: + -- None + -- Domain: + -- Z in COMPLEX_POLAR and Z.ARG /= -MATH_PI + -- Error conditions: + -- Error if Z.ARG = -MATH_PI + -- Range: + -- -MATH_PI < ARG(Z) <= MATH_PI + -- Notes: + -- ARG(Z) = Z.ARG + + + function "-" (Z : in COMPLEX) return COMPLEX; + -- Purpose: + -- Returns unary minus of Z + -- Special values: + -- None + -- Domain: + -- Z in COMPLEX + -- Error conditions: + -- None + -- Range: + -- "-"(Z) is mathematically unbounded + -- Notes: + -- Returns -x -jy for Z= x + jy + + function "-" (Z : in COMPLEX_POLAR) return COMPLEX_POLAR; + -- Purpose: + -- Returns principal value of unary minus of Z + -- Special values: + -- "-"(Z) = COMPLEX_POLAR'(Z.MAG, MATH_PI) if Z.ARG = 0.0 + -- Domain: + -- Z in COMPLEX_POLAR and Z.ARG /= -MATH_PI + -- Error conditions: + -- Error if Z.ARG = -MATH_PI + -- Range: + -- result.MAG >= 0.0 + -- -MATH_PI < result.ARG <= MATH_PI + -- Notes: + -- Returns COMPLEX_POLAR'(Z.MAG, Z.ARG - SIGN(Z.ARG)*MATH_PI) if + -- Z.ARG /= 0.0 + + function CONJ (Z : in COMPLEX) return COMPLEX; + -- Purpose: + -- Returns complex conjugate of Z + -- Special values: + -- None + -- Domain: + -- Z in COMPLEX + -- Error conditions: + -- None + -- Range: + -- CONJ(Z) is mathematically unbounded + -- Notes: + -- Returns x -jy for Z= x + jy + + function CONJ (Z : in COMPLEX_POLAR) return COMPLEX_POLAR; + -- Purpose: + -- Returns principal value of complex conjugate of Z + -- Special values: + -- CONJ(Z) = COMPLEX_POLAR'(Z.MAG, MATH_PI) if Z.ARG = MATH_PI + -- Domain: + -- Z in COMPLEX_POLAR and Z.ARG /= -MATH_PI + -- Error conditions: + -- Error if Z.ARG = -MATH_PI + -- Range: + -- result.MAG >= 0.0 + -- -MATH_PI < result.ARG <= MATH_PI + -- Notes: + -- Returns COMPLEX_POLAR'(Z.MAG, -Z.ARG) if Z.ARG /= MATH_PI + + function SQRT(Z : in COMPLEX) return COMPLEX; + -- Purpose: + -- Returns square root of Z with positive real part + -- or, if the real part is zero, the one with nonnegative + -- imaginary part + -- Special values: + -- SQRT(MATH_CZERO) = MATH_CZERO + -- Domain: + -- Z in COMPLEX + -- Error conditions: + -- None + -- Range: + -- SQRT(Z) is mathematically unbounded + -- Notes: + -- None + + function SQRT(Z : in COMPLEX_POLAR) return COMPLEX_POLAR; + -- Purpose: + -- Returns square root of Z with positive real part + -- or, if the real part is zero, the one with nonnegative + -- imaginary part + -- Special values: + -- SQRT(Z) = COMPLEX_POLAR'(0.0, 0.0) if Z.MAG = 0.0 + -- Domain: + -- Z in COMPLEX_POLAR and Z.ARG /= -MATH_PI + -- Error conditions: + -- Error if Z.ARG = -MATH_PI + -- Range: + -- result.MAG >= 0.0 + -- -MATH_PI < result.ARG <= MATH_PI + -- Notes: + -- None + + function EXP(Z : in COMPLEX) return COMPLEX; + -- Purpose: + -- Returns exponential of Z + -- Special values: + -- EXP(MATH_CZERO) = MATH_CBASE_1 + -- EXP(Z) = -MATH_CBASE_1 if Z.RE = 0.0 and ABS(Z.IM) = MATH_PI + -- EXP(Z) = SIGN(Z.IM)*MATH_CBASE_J if Z.RE = 0.0 and + -- ABS(Z.IM) = MATH_PI_OVER_2 + -- Domain: + -- Z in COMPLEX + -- Error conditions: + -- None + -- Range: + -- EXP(Z) is mathematically unbounded + -- Notes: + -- None + + + + function EXP(Z : in COMPLEX_POLAR) return COMPLEX_POLAR; + -- Purpose: + -- Returns principal value of exponential of Z + -- Special values: + -- EXP(Z) = COMPLEX_POLAR'(1.0, 0.0) if Z.MAG =0.0 and + -- Z.ARG = 0.0 + -- EXP(Z) = COMPLEX_POLAR'(1.0, MATH_PI) if Z.MAG = MATH_PI and + -- ABS(Z.ARG) = MATH_PI_OVER_2 + -- EXP(Z) = COMPLEX_POLAR'(1.0, MATH_PI_OVER_2) if + -- Z.MAG = MATH_PI_OVER_2 and + -- Z.ARG = MATH_PI_OVER_2 + -- EXP(Z) = COMPLEX_POLAR'(1.0, -MATH_PI_OVER_2) if + -- Z.MAG = MATH_PI_OVER_2 and + -- Z.ARG = -MATH_PI_OVER_2 + -- Domain: + -- Z in COMPLEX_POLAR and Z.ARG /= -MATH_PI + -- Error conditions: + -- Error if Z.ARG = -MATH_PI + -- Range: + -- result.MAG >= 0.0 + -- -MATH_PI < result.ARG <= MATH_PI + -- Notes: + -- None + + function LOG(Z : in COMPLEX) return COMPLEX; + -- Purpose: + -- Returns natural logarithm of Z + -- Special values: + -- LOG(MATH_CBASE_1) = MATH_CZERO + -- LOG(-MATH_CBASE_1) = COMPLEX'(0.0, MATH_PI) + -- LOG(MATH_CBASE_J) = COMPLEX'(0.0, MATH_PI_OVER_2) + -- LOG(-MATH_CBASE_J) = COMPLEX'(0.0, -MATH_PI_OVER_2) + -- LOG(Z) = MATH_CBASE_1 if Z = COMPLEX'(MATH_E, 0.0) + -- Domain: + -- Z in COMPLEX and ABS(Z) /= 0.0 + -- Error conditions: + -- Error if ABS(Z) = 0.0 + -- Range: + -- LOG(Z) is mathematically unbounded + -- Notes: + -- None + + function LOG2(Z : in COMPLEX) return COMPLEX; + -- Purpose: + -- Returns logarithm base 2 of Z + -- Special values: + -- LOG2(MATH_CBASE_1) = MATH_CZERO + -- LOG2(Z) = MATH_CBASE_1 if Z = COMPLEX'(2.0, 0.0) + -- Domain: + -- Z in COMPLEX and ABS(Z) /= 0.0 + -- Error conditions: + -- Error if ABS(Z) = 0.0 + -- Range: + -- LOG2(Z) is mathematically unbounded + -- Notes: + -- None + + function LOG10(Z : in COMPLEX) return COMPLEX; + -- Purpose: + -- Returns logarithm base 10 of Z + -- Special values: + -- LOG10(MATH_CBASE_1) = MATH_CZERO + -- LOG10(Z) = MATH_CBASE_1 if Z = COMPLEX'(10.0, 0.0) + -- Domain: + -- Z in COMPLEX and ABS(Z) /= 0.0 + -- Error conditions: + -- Error if ABS(Z) = 0.0 + -- Range: + -- LOG10(Z) is mathematically unbounded + -- Notes: + -- None + + function LOG(Z : in COMPLEX_POLAR) return COMPLEX_POLAR; + -- Purpose: + -- Returns principal value of natural logarithm of Z + -- Special values: + -- LOG(Z) = COMPLEX_POLAR'(0.0, 0.0) if Z.MAG = 1.0 and + -- Z.ARG = 0.0 + -- LOG(Z) = COMPLEX_POLAR'(MATH_PI, MATH_PI_OVER_2) if + -- Z.MAG = 1.0 and Z.ARG = MATH_PI + -- LOG(Z) = COMPLEX_POLAR'(MATH_PI_OVER_2, MATH_PI_OVER_2) if + -- Z.MAG = 1.0 and Z.ARG = MATH_PI_OVER_2 + -- LOG(Z) = COMPLEX_POLAR'(MATH_PI_OVER_2, -MATH_PI_OVER_2) if + -- Z.MAG = 1.0 and Z.ARG = -MATH_PI_OVER_2 + -- LOG(Z) = COMPLEX_POLAR'(1.0, 0.0) if Z.MAG = MATH_E and + -- Z.ARG = 0.0 + -- Domain: + -- Z in COMPLEX_POLAR and Z.ARG /= -MATH_PI + -- Z.MAG /= 0.0 + -- Error conditions: + -- Error if Z.ARG = -MATH_PI + -- Error if Z.MAG = 0.0 + -- Range: + -- result.MAG >= 0.0 + -- -MATH_PI < result.ARG <= MATH_PI + -- Notes: + -- None + + function LOG2(Z : in COMPLEX_POLAR) return COMPLEX_POLAR; + -- Purpose: + -- Returns principal value of logarithm base 2 of Z + -- Special values: + -- LOG2(Z) = COMPLEX_POLAR'(0.0, 0.0) if Z.MAG = 1.0 and + -- Z.ARG = 0.0 + -- LOG2(Z) = COMPLEX_POLAR'(1.0, 0.0) if Z.MAG = 2.0 and + -- Z.ARG = 0.0 + -- Domain: + -- Z in COMPLEX_POLAR and Z.ARG /= -MATH_PI + -- Z.MAG /= 0.0 + -- Error conditions: + -- Error if Z.ARG = -MATH_PI + -- Error if Z.MAG = 0.0 + -- Range: + -- result.MAG >= 0.0 + -- -MATH_PI < result.ARG <= MATH_PI + -- Notes: + -- None + + function LOG10(Z : in COMPLEX_POLAR) return COMPLEX_POLAR; + -- Purpose: + -- Returns principal value of logarithm base 10 of Z + -- Special values: + -- LOG10(Z) = COMPLEX_POLAR'(0.0, 0.0) if Z.MAG = 1.0 and + -- Z.ARG = 0.0 + -- LOG10(Z) = COMPLEX_POLAR'(1.0, 0.0) if Z.MAG = 10.0 and + -- Z.ARG = 0.0 + -- Domain: + -- Z in COMPLEX_POLAR and Z.ARG /= -MATH_PI + -- Z.MAG /= 0.0 + -- Error conditions: + -- Error if Z.ARG = -MATH_PI + -- Error if Z.MAG = 0.0 + -- Range: + -- result.MAG >= 0.0 + -- -MATH_PI < result.ARG <= MATH_PI + -- Notes: + -- None + + function LOG(Z : in COMPLEX; BASE : in REAL) return COMPLEX; + -- Purpose: + -- Returns logarithm base BASE of Z + -- Special values: + -- LOG(MATH_CBASE_1, BASE) = MATH_CZERO + -- LOG(Z,BASE) = MATH_CBASE_1 if Z = COMPLEX'(BASE, 0.0) + -- Domain: + -- Z in COMPLEX and ABS(Z) /= 0.0 + -- BASE > 0.0 + -- BASE /= 1.0 + -- Error conditions: + -- Error if ABS(Z) = 0.0 + -- Error if BASE <= 0.0 + -- Error if BASE = 1.0 + -- Range: + -- LOG(Z,BASE) is mathematically unbounded + -- Notes: + -- None + + function LOG(Z : in COMPLEX_POLAR; BASE : in REAL) return COMPLEX_POLAR; + -- Purpose: + -- Returns principal value of logarithm base BASE of Z + -- Special values: + -- LOG(Z, BASE) = COMPLEX_POLAR'(0.0, 0.0) if Z.MAG = 1.0 and + -- Z.ARG = 0.0 + -- LOG(Z, BASE) = COMPLEX_POLAR'(1.0, 0.0) if Z.MAG = BASE and + -- Z.ARG = 0.0 + -- Domain: + -- Z in COMPLEX_POLAR and Z.ARG /= -MATH_PI + -- Z.MAG /= 0.0 + -- BASE > 0.0 + -- BASE /= 1.0 + -- Error conditions: + -- Error if Z.ARG = -MATH_PI + -- Error if Z.MAG = 0.0 + -- Error if BASE <= 0.0 + -- Error if BASE = 1.0 + -- Range: + -- result.MAG >= 0.0 + -- -MATH_PI < result.ARG <= MATH_PI + -- Notes: + -- None + + function SIN (Z : in COMPLEX) return COMPLEX; + -- Purpose: + -- Returns sine of Z + -- Special values: + -- SIN(MATH_CZERO) = MATH_CZERO + -- SIN(Z) = MATH_CZERO if Z = COMPLEX'(MATH_PI, 0.0) + -- Domain: + -- Z in COMPLEX + -- Error conditions: + -- None + -- Range: + -- ABS(SIN(Z)) <= SQRT(SIN(Z.RE)*SIN(Z.RE) + + -- SINH(Z.IM)*SINH(Z.IM)) + -- Notes: + -- None + + function SIN (Z : in COMPLEX_POLAR) return COMPLEX_POLAR; + -- Purpose: + -- Returns principal value of sine of Z + -- Special values: + -- SIN(Z) = COMPLEX_POLAR'(0.0, 0.0) if Z.MAG = 0.0 and + -- Z.ARG = 0.0 + -- SIN(Z) = COMPLEX_POLAR'(0.0, 0.0) if Z.MAG = MATH_PI and + -- Z.ARG = 0.0 + -- Domain: + -- Z in COMPLEX_POLAR and Z.ARG /= -MATH_PI + -- Error conditions: + -- Error if Z.ARG = -MATH_PI + -- Range: + -- result.MAG >= 0.0 + -- -MATH_PI < result.ARG <= MATH_PI + -- Notes: + -- None + + function COS (Z : in COMPLEX) return COMPLEX; + -- Purpose: + -- Returns cosine of Z + -- Special values: + -- COS(Z) = MATH_CZERO if Z = COMPLEX'(MATH_PI_OVER_2, 0.0) + -- COS(Z) = MATH_CZERO if Z = COMPLEX'(-MATH_PI_OVER_2, 0.0) + -- Domain: + -- Z in COMPLEX + -- Error conditions: + -- None + -- Range: + -- ABS(COS(Z)) <= SQRT(COS(Z.RE)*COS(Z.RE) + + -- SINH(Z.IM)*SINH(Z.IM)) + -- Notes: + -- None + + + function COS (Z : in COMPLEX_POLAR) return COMPLEX_POLAR; + -- Purpose: + -- Returns principal value of cosine of Z + -- Special values: + -- COS(Z) = COMPLEX_POLAR'(0.0, 0.0) if Z.MAG = MATH_PI_OVER_2 + -- and Z.ARG = 0.0 + -- COS(Z) = COMPLEX_POLAR'(0.0, 0.0) if Z.MAG = MATH_PI_OVER_2 + -- and Z.ARG = MATH_PI + -- Domain: + -- Z in COMPLEX_POLAR and Z.ARG /= -MATH_PI + -- Error conditions: + -- Error if Z.ARG = -MATH_PI + -- Range: + -- result.MAG >= 0.0 + -- -MATH_PI < result.ARG <= MATH_PI + -- Notes: + -- None + + function SINH (Z : in COMPLEX) return COMPLEX; + -- Purpose: + -- Returns hyperbolic sine of Z + -- Special values: + -- SINH(MATH_CZERO) = MATH_CZERO + -- SINH(Z) = MATH_CZERO if Z.RE = 0.0 and Z.IM = MATH_PI + -- SINH(Z) = MATH_CBASE_J if Z.RE = 0.0 and + -- Z.IM = MATH_PI_OVER_2 + -- SINH(Z) = -MATH_CBASE_J if Z.RE = 0.0 and + -- Z.IM = -MATH_PI_OVER_2 + -- Domain: + -- Z in COMPLEX + -- Error conditions: + -- None + -- Range: + -- ABS(SINH(Z)) <= SQRT(SINH(Z.RE)*SINH(Z.RE) + + -- SIN(Z.IM)*SIN(Z.IM)) + -- Notes: + -- None + + function SINH (Z : in COMPLEX_POLAR) return COMPLEX_POLAR; + -- Purpose: + -- Returns principal value of hyperbolic sine of Z + -- Special values: + -- SINH(Z) = COMPLEX_POLAR'(0.0, 0.0) if Z.MAG = 0.0 and + -- Z.ARG = 0.0 + -- SINH(Z) = COMPLEX_POLAR'(0.0, 0.0) if Z.MAG = MATH_PI and + -- Z.ARG = MATH_PI_OVER_2 + -- SINH(Z) = COMPLEX_POLAR'(1.0, MATH_PI_OVER_2) if Z.MAG = + -- MATH_PI_OVER_2 and Z.ARG = MATH_PI_OVER_2 + -- SINH(Z) = COMPLEX_POLAR'(1.0, -MATH_PI_OVER_2) if Z.MAG = + -- MATH_PI_OVER_2 and Z.ARG = -MATH_PI_OVER_2 + -- Domain: + -- Z in COMPLEX_POLAR and Z.ARG /= -MATH_PI + -- Error conditions: + -- Error if Z.ARG = -MATH_PI + -- Range: + -- result.MAG >= 0.0 + -- -MATH_PI < result.ARG <= MATH_PI + -- Notes: + -- None + + function COSH (Z : in COMPLEX) return COMPLEX; + -- Purpose: + -- Returns hyperbolic cosine of Z + -- Special values: + -- COSH(MATH_CZERO) = MATH_CBASE_1 + -- COSH(Z) = -MATH_CBASE_1 if Z.RE = 0.0 and Z.IM = MATH_PI + -- COSH(Z) = MATH_CZERO if Z.RE = 0.0 and Z.IM = MATH_PI_OVER_2 + -- COSH(Z) = MATH_CZERO if Z.RE = 0.0 and Z.IM = -MATH_PI_OVER_2 + -- Domain: + -- Z in COMPLEX + -- Error conditions: + -- None + -- Range: + -- ABS(COSH(Z)) <= SQRT(SINH(Z.RE)*SINH(Z.RE) + + -- COS(Z.IM)*COS(Z.IM)) + -- Notes: + -- None + + + function COSH (Z : in COMPLEX_POLAR) return COMPLEX_POLAR; + -- Purpose: + -- Returns principal value of hyperbolic cosine of Z + -- Special values: + -- COSH(Z) = COMPLEX_POLAR'(1.0, 0.0) if Z.MAG = 0.0 and + -- Z.ARG = 0.0 + -- COSH(Z) = COMPLEX_POLAR'(1.0, MATH_PI) if Z.MAG = MATH_PI and + -- Z.ARG = MATH_PI_OVER_2 + -- COSH(Z) = COMPLEX_POLAR'(0.0, 0.0) if Z.MAG = + -- MATH_PI_OVER_2 and Z.ARG = MATH_PI_OVER_2 + -- COSH(Z) = COMPLEX_POLAR'(0.0, 0.0) if Z.MAG = + -- MATH_PI_OVER_2 and Z.ARG = -MATH_PI_OVER_2 + -- Domain: + -- Z in COMPLEX_POLAR and Z.ARG /= -MATH_PI + -- Error conditions: + -- Error if Z.ARG = -MATH_PI + -- Range: + -- result.MAG >= 0.0 + -- -MATH_PI < result.ARG <= MATH_PI + -- Notes: + -- None + + -- + -- Arithmetic Operators + -- + + function "+" (L : in COMPLEX; R : in COMPLEX) return COMPLEX; + -- Purpose: + -- Returns arithmetic addition of L and R + -- Special values: + -- None + -- Domain: + -- L in COMPLEX + -- R in COMPLEX + -- Error conditions: + -- None + -- Range: + -- "+"(Z) is mathematically unbounded + -- Notes: + -- None + + function "+" (L : in REAL; R : in COMPLEX) return COMPLEX; + -- Purpose: + -- Returns arithmetic addition of L and R + -- Special values: + -- None + -- Domain: + -- L in REAL + -- R in COMPLEX + -- Error conditions: + -- None + -- Range: + -- "+"(Z) is mathematically unbounded + -- Notes: + -- None + + function "+" (L : in COMPLEX; R : in REAL) return COMPLEX; + -- Purpose: + -- Returns arithmetic addition of L and R + -- Special values: + -- None + -- Domain: + -- L in COMPLEX + -- R in REAL + -- Error conditions: + -- None + -- Range: + -- "+"(Z) is mathematically unbounded + -- Notes: + -- None + + function "+" (L : in COMPLEX_POLAR; R : in COMPLEX_POLAR) + return COMPLEX_POLAR; + -- Purpose: + -- Returns arithmetic addition of L and R + -- Special values: + -- None + -- Domain: + -- L in COMPLEX_POLAR and L.ARG /= -MATH_PI + -- R in COMPLEX_POLAR and R.ARG /= -MATH_PI + -- Error conditions: + -- Error if L.ARG = -MATH_PI + -- Error if R.ARG = -MATH_PI + -- Range: + -- result.MAG >= 0.0 + -- -MATH_PI < result.ARG <= MATH_PI + -- Notes: + -- None + + + function "+" (L : in REAL; R : in COMPLEX_POLAR) return COMPLEX_POLAR; + -- Purpose: + -- Returns arithmetic addition of L and R + -- Special values: + -- None + -- Domain: + -- L in REAL + -- R in COMPLEX_POLAR and R.ARG /= -MATH_PI + -- Error conditions: + -- Error if R.ARG = -MATH_PI + -- Range: + -- result.MAG >= 0.0 + -- -MATH_PI < result.ARG <= MATH_PI + -- Notes: + -- None + + function "+" (L : in COMPLEX_POLAR; R : in REAL) return COMPLEX_POLAR; + -- Purpose: + -- Returns arithmetic addition of L and R + -- Special values: + -- None + -- Domain: + -- L in COMPLEX_POLAR and L.ARG /= -MATH_PI + -- R in REAL + -- Error conditions: + -- Error if L.ARG = -MATH_PI + -- Range: + -- result.MAG >= 0.0 + -- -MATH_PI < result.ARG <= MATH_PI + -- Notes: + -- None + + function "-" (L : in COMPLEX; R : in COMPLEX) return COMPLEX; + -- Purpose: + -- Returns arithmetic subtraction of L minus R + -- Special values: + -- None + -- Domain: + -- L in COMPLEX + -- R in COMPLEX + -- Error conditions: + -- None + -- Range: + -- "-"(Z) is mathematically unbounded + -- Notes: + -- None + + function "-" (L : in REAL; R : in COMPLEX) return COMPLEX; + -- Purpose: + -- Returns arithmetic subtraction of L minus R + -- Special values: + -- None + -- Domain: + -- L in REAL + -- R in COMPLEX + -- Error conditions: + -- None + -- Range: + -- "-"(Z) is mathematically unbounded + -- Notes: + -- None + + function "-" (L : in COMPLEX; R : in REAL) return COMPLEX; + -- Purpose: + -- Returns arithmetic subtraction of L minus R + -- Special values: + -- None + -- Domain: + -- L in COMPLEX + -- R in REAL + -- Error conditions: + -- None + -- Range: + -- "-"(Z) is mathematically unbounded + -- Notes: + -- None + + function "-" (L : in COMPLEX_POLAR; R : in COMPLEX_POLAR) + return COMPLEX_POLAR; + -- Purpose: + -- Returns arithmetic subtraction of L minus R + -- Special values: + -- None + -- Domain: + -- L in COMPLEX_POLAR and L.ARG /= -MATH_PI + -- R in COMPLEX_POLAR and R.ARG /= -MATH_PI + -- Error conditions: + -- Error if L.ARG = -MATH_PI + -- Error if R.ARG = -MATH_PI + -- Range: + -- result.MAG >= 0.0 + -- -MATH_PI < result.ARG <= MATH_PI + -- Notes: + -- None + + function "-" (L : in REAL; R : in COMPLEX_POLAR) return COMPLEX_POLAR; + -- Purpose: + -- Returns arithmetic subtraction of L minus R + -- Special values: + -- None + -- Domain: + -- L in REAL + -- R in COMPLEX_POLAR and R.ARG /= -MATH_PI + -- Error conditions: + -- Error if R.ARG = -MATH_PI + -- Range: + -- result.MAG >= 0.0 + -- -MATH_PI < result.ARG <= MATH_PI + -- Notes: + -- None + + + function "-" (L : in COMPLEX_POLAR; R : in REAL) return COMPLEX_POLAR; + -- Purpose: + -- Returns arithmetic subtraction of L minus R + -- Special values: + -- None + -- Domain: + -- L in COMPLEX_POLAR and L.ARG /= -MATH_PI + -- R in REAL + -- Error conditions: + -- Error if L.ARG = -MATH_PI + -- Range: + -- result.MAG >= 0.0 + -- -MATH_PI < result.ARG <= MATH_PI + -- Notes: + -- None + + function "*" (L : in COMPLEX; R : in COMPLEX) return COMPLEX; + -- Purpose: + -- Returns arithmetic multiplication of L and R + -- Special values: + -- None + -- Domain: + -- L in COMPLEX + -- R in COMPLEX + -- Error conditions: + -- None + -- Range: + -- "*"(Z) is mathematically unbounded + -- Notes: + -- None + + function "*" (L : in REAL; R : in COMPLEX) return COMPLEX; + -- Purpose: + -- Returns arithmetic multiplication of L and R + -- Special values: + -- None + -- Domain: + -- L in REAL + -- R in COMPLEX + -- Error conditions: + -- None + -- Range: + -- "*"(Z) is mathematically unbounded + -- Notes: + -- None + + function "*" (L : in COMPLEX; R : in REAL) return COMPLEX; + -- Purpose: + -- Returns arithmetic multiplication of L and R + -- Special values: + -- None + -- Domain: + -- L in COMPLEX + -- R in REAL + -- Error conditions: + -- None + + -- Range: + -- "*"(Z) is mathematically unbounded + -- Notes: + -- None + + function "*" (L : in COMPLEX_POLAR; R : in COMPLEX_POLAR) + return COMPLEX_POLAR; + -- Purpose: + -- Returns arithmetic multiplication of L and R + -- Special values: + -- None + -- Domain: + -- L in COMPLEX_POLAR and L.ARG /= -MATH_PI + -- R in COMPLEX_POLAR and R.ARG /= -MATH_PI + -- Error conditions: + -- Error if L.ARG = -MATH_PI + -- Error if R.ARG = -MATH_PI + -- Range: + -- result.MAG >= 0.0 + -- -MATH_PI < result.ARG <= MATH_PI + -- Notes: + -- None + + function "*" (L : in REAL; R : in COMPLEX_POLAR) return COMPLEX_POLAR; + -- Purpose: + -- Returns arithmetic multiplication of L and R + -- Special values: + -- None + -- Domain: + -- L in REAL + -- R in COMPLEX_POLAR and R.ARG /= -MATH_PI + -- Error conditions: + -- Error if R.ARG = -MATH_PI + -- Range: + -- result.MAG >= 0.0 + -- -MATH_PI < result.ARG <= MATH_PI + -- Notes: + -- None + + function "*" (L : in COMPLEX_POLAR; R : in REAL) return COMPLEX_POLAR; + -- Purpose: + -- Returns arithmetic multiplication of L and R + -- Special values: + -- None + -- Domain: + -- L in COMPLEX_POLAR and L.ARG /= -MATH_PI + -- R in REAL + -- Error conditions: + -- Error if L.ARG = -MATH_PI + -- Range: + -- result.MAG >= 0.0 + -- -MATH_PI < result.ARG <= MATH_PI + -- Notes: + -- None + + + function "/" (L : in COMPLEX; R : in COMPLEX) return COMPLEX; + -- Purpose: + -- Returns arithmetic division of L by R + -- Special values: + -- None + -- Domain: + -- L in COMPLEX + -- R in COMPLEX and R /= MATH_CZERO + -- Error conditions: + -- Error if R = MATH_CZERO + -- Range: + -- "/"(Z) is mathematically unbounded + -- Notes: + -- None + + function "/" (L : in REAL; R : in COMPLEX) return COMPLEX; + -- Purpose: + -- Returns arithmetic division of L by R + -- Special values: + -- None + -- Domain: + -- L in REAL + -- R in COMPLEX and R /= MATH_CZERO + -- Error conditions: + -- Error if R = MATH_CZERO + -- Range: + -- "/"(Z) is mathematically unbounded + -- Notes: + -- None + + function "/" (L : in COMPLEX; R : in REAL) return COMPLEX; + -- Purpose: + -- Returns arithmetic division of L by R + -- Special values: + -- None + -- Domain: + -- L in COMPLEX + -- R in REAL and R /= 0.0 + -- Error conditions: + -- Error if R = 0.0 + -- Range: + -- "/"(Z) is mathematically unbounded + -- Notes: + -- None + + function "/" (L : in COMPLEX_POLAR; R : in COMPLEX_POLAR) + return COMPLEX_POLAR; + -- Purpose: + -- Returns arithmetic division of L by R + -- Special values: + -- None + -- Domain: + -- L in COMPLEX_POLAR and L.ARG /= -MATH_PI + -- R in COMPLEX_POLAR and R.ARG /= -MATH_PI + -- R.MAG > 0.0 + -- Error conditions: + -- Error if R.MAG <= 0.0 + -- Error if L.ARG = -MATH_PI + -- Error if R.ARG = -MATH_PI + -- Range: + -- result.MAG >= 0.0 + -- -MATH_PI < result.ARG <= MATH_PI + -- Notes: + -- None + + function "/" (L : in REAL; R : in COMPLEX_POLAR) return COMPLEX_POLAR; + -- Purpose: + -- Returns arithmetic division of L by R + -- Special values: + -- None + -- Domain: + -- L in REAL + -- R in COMPLEX_POLAR and R.ARG /= -MATH_PI + -- R.MAG > 0.0 + -- Error conditions: + -- Error if R.MAG <= 0.0 + -- Error if R.ARG = -MATH_PI + -- Range: + -- result.MAG >= 0.0 + -- -MATH_PI < result.ARG <= MATH_PI + -- Notes: + -- None + + function "/" (L : in COMPLEX_POLAR; R : in REAL) return COMPLEX_POLAR; + -- Purpose: + -- Returns arithmetic division of L by R + -- Special values: + -- None + -- Domain: + -- L in COMPLEX_POLAR and L.ARG /= -MATH_PI + -- R /= 0.0 + -- Error conditions: + -- Error if L.ARG = -MATH_PI + -- Error if R = 0.0 + -- Range: + -- result.MAG >= 0.0 + -- -MATH_PI < result.ARG <= MATH_PI + -- Notes: + -- None +end package MATH_COMPLEX; -- cgit v1.2.3