Add ieee 2008 packages.

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+-- --------------------------------------------------------------------
+--
+-- 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_REAL 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 REAL
+--             :  constants and common REAL elementary mathematical
+--             :  functions.
+--             :
+--   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) $
+-- --------------------------------------------------------------------
+
+package MATH_REAL is
+  constant CopyRightNotice : STRING
+    := "Copyright 2008 IEEE. All rights reserved.";
+
+  --
+  -- Constant Definitions
+  --
+  constant MATH_E             : REAL := 2.71828_18284_59045_23536;
+                                        -- Value of e
+  constant MATH_1_OVER_E      : REAL := 0.36787_94411_71442_32160;
+                                        -- Value of 1/e
+  constant MATH_PI            : REAL := 3.14159_26535_89793_23846;
+                                        -- Value of pi
+  constant MATH_2_PI          : REAL := 6.28318_53071_79586_47693;
+                                        -- Value of 2*pi
+  constant MATH_1_OVER_PI     : REAL := 0.31830_98861_83790_67154;
+                                        -- Value of 1/pi
+  constant MATH_PI_OVER_2     : REAL := 1.57079_63267_94896_61923;
+                                        -- Value of pi/2
+  constant MATH_PI_OVER_3     : REAL := 1.04719_75511_96597_74615;
+                                        -- Value of pi/3
+  constant MATH_PI_OVER_4     : REAL := 0.78539_81633_97448_30962;
+                                        -- Value of pi/4
+  constant MATH_3_PI_OVER_2   : REAL := 4.71238_89803_84689_85769;
+                                        -- Value 3*pi/2
+  constant MATH_LOG_OF_2      : REAL := 0.69314_71805_59945_30942;
+                                        -- Natural log of 2
+  constant MATH_LOG_OF_10     : REAL := 2.30258_50929_94045_68402;
+                                        -- Natural log of 10
+  constant MATH_LOG2_OF_E     : REAL := 1.44269_50408_88963_4074;
+                                        -- Log base 2 of e
+  constant MATH_LOG10_OF_E    : REAL := 0.43429_44819_03251_82765;
+                                        -- Log base 10 of e
+  constant MATH_SQRT_2        : REAL := 1.41421_35623_73095_04880;
+                                        -- square root of 2
+  constant MATH_1_OVER_SQRT_2 : REAL := 0.70710_67811_86547_52440;
+                                        -- square root of 1/2
+  constant MATH_SQRT_PI       : REAL := 1.77245_38509_05516_02730;
+                                        -- square root of pi
+  constant MATH_DEG_TO_RAD    : REAL := 0.01745_32925_19943_29577;
+  -- Conversion factor from degree to radian
+  constant MATH_RAD_TO_DEG    : REAL := 57.29577_95130_82320_87680;
+  -- Conversion factor from radian to degree
+
+  --
+  -- Function Declarations
+  --
+  function SIGN (X : in REAL) return REAL;
+  -- Purpose:
+  --         Returns 1.0 if X > 0.0; 0.0 if X = 0.0; -1.0 if X < 0.0
+  -- Special values:
+  --         None
+  -- Domain:
+  --         X in REAL
+  -- Error conditions:
+  --         None
+  -- Range:
+  --         ABS(SIGN(X)) <= 1.0
+  -- Notes:
+  --         None
+
+  function CEIL (X : in REAL) return REAL;
+  -- Purpose:
+  --         Returns smallest INTEGER value (as REAL) not less than X
+  -- Special values:
+  --         None
+  -- Domain:
+  --         X in REAL
+  -- Error conditions:
+  --         None
+  -- Range:
+  --         CEIL(X) is mathematically unbounded
+  -- Notes:
+  --         a) Implementations have to support at least the domain
+  --                ABS(X) < REAL(INTEGER'HIGH)
+
+  function FLOOR (X : in REAL) return REAL;
+  -- Purpose:
+  --         Returns largest INTEGER value (as REAL) not greater than X
+  -- Special values:
+  --         FLOOR(0.0) = 0.0
+  -- Domain:
+  --         X in REAL
+  -- Error conditions:
+  --         None
+  -- Range:
+  --         FLOOR(X) is mathematically unbounded
+  -- Notes:
+  --         a) Implementations have to support at least the domain
+  --                ABS(X) < REAL(INTEGER'HIGH)
+
+  function ROUND (X : in REAL) return REAL;
+  -- Purpose:
+  --         Rounds X to the nearest integer value (as real). If X is
+  --         halfway between two integers, rounding is away from 0.0
+  -- Special values:
+  --         ROUND(0.0) = 0.0
+  -- Domain:
+  --         X in REAL
+  -- Error conditions:
+  --         None
+  -- Range:
+  --         ROUND(X) is mathematically unbounded
+  -- Notes:
+  --         a) Implementations have to support at least the domain
+  --                ABS(X) < REAL(INTEGER'HIGH)
+
+  function TRUNC (X : in REAL) return REAL;
+  -- Purpose:
+  --         Truncates X towards 0.0 and returns truncated value
+  -- Special values:
+  --         TRUNC(0.0) = 0.0
+  -- Domain:
+  --         X in REAL
+  -- Error conditions:
+  --         None
+  -- Range:
+  --         TRUNC(X) is mathematically unbounded
+  -- Notes:
+  --         a) Implementations have to support at least the domain
+  --                ABS(X) < REAL(INTEGER'HIGH)
+
+  function "MOD" (X, Y : in REAL) return REAL;
+  -- Purpose:
+  --         Returns floating point modulus of X/Y, with the same sign as
+  --         Y, and absolute value less than the absolute value of Y, and
+  --         for some INTEGER value N the result satisfies the relation
+  --         X = Y*N + MOD(X,Y)
+  -- Special values:
+  --         None
+  -- Domain:
+  --         X in REAL; Y in REAL and Y /= 0.0
+  -- Error conditions:
+  --         Error if Y = 0.0
+  -- Range:
+  --         ABS(MOD(X,Y)) < ABS(Y)
+  -- Notes:
+  --         None
+
+  function REALMAX (X, Y : in REAL) return REAL;
+  -- Purpose:
+  --         Returns the algebraically larger of X and Y
+  -- Special values:
+  --         REALMAX(X,Y) = X when X = Y
+  -- Domain:
+  --         X in REAL; Y in REAL
+  -- Error conditions:
+  --         None
+  -- Range:
+  --         REALMAX(X,Y) is mathematically unbounded
+  -- Notes:
+  --         None
+
+  function REALMIN (X, Y : in REAL) return REAL;
+  -- Purpose:
+  --         Returns the algebraically smaller of X and Y
+  -- Special values:
+  --         REALMIN(X,Y) = X when X = Y
+  -- Domain:
+  --         X in REAL; Y in REAL
+  -- Error conditions:
+  --         None
+  -- Range:
+  --         REALMIN(X,Y) is mathematically unbounded
+  -- Notes:
+  --         None
+
+  procedure UNIFORM(variable SEED1, SEED2 : inout POSITIVE; variable X : out REAL);
+  -- Purpose:
+  --         Returns, in X, a pseudo-random number with uniform
+  --         distribution in the open interval (0.0, 1.0).
+  -- Special values:
+  --         None
+  -- Domain:
+  --         1 <= SEED1 <= 2147483562; 1 <= SEED2 <= 2147483398
+  -- Error conditions:
+  --         Error if SEED1 or SEED2 outside of valid domain
+  -- Range:
+  --         0.0 < X < 1.0
+  -- Notes:
+  --         a) The semantics for this function are described by the
+  --            algorithm published by Pierre L'Ecuyer in "Communications
+  --            of the ACM," vol. 31, no. 6, June 1988, pp. 742-774.
+  --            The algorithm is based on the combination of two
+  --            multiplicative linear congruential generators for 32-bit
+  --            platforms.
+  --
+  --         b) Before the first call to UNIFORM, the seed values
+  --            (SEED1, SEED2) have to be initialized to values in the range
+  --            [1, 2147483562] and [1, 2147483398] respectively.  The
+  --            seed values are modified after each call to UNIFORM.
+  --
+  --         c) This random number generator is portable for 32-bit
+  --            computers, and it has a period of ~2.30584*(10**18) for each
+  --            set of seed values.
+  --
+  --         d) For information on spectral tests for the algorithm, refer
+  --            to the L'Ecuyer article.
+
+  function SQRT (X : in REAL) return REAL;
+  -- Purpose:
+  --         Returns square root of X
+  -- Special values:
+  --         SQRT(0.0) = 0.0
+  --         SQRT(1.0) = 1.0
+  -- Domain:
+  --         X >= 0.0
+  -- Error conditions:
+  --         Error if X < 0.0
+  -- Range:
+  --         SQRT(X) >= 0.0
+  -- Notes:
+  --         a) The upper bound of the reachable range of SQRT is
+  --            approximately given by:
+  --                SQRT(X) <= SQRT(REAL'HIGH)
+
+  function CBRT (X : in REAL) return REAL;
+  -- Purpose:
+  --         Returns cube root of X
+  -- Special values:
+  --         CBRT(0.0) = 0.0
+  --         CBRT(1.0) = 1.0
+  --         CBRT(-1.0) = -1.0
+  -- Domain:
+  --         X in REAL
+  -- Error conditions:
+  --         None
+  -- Range:
+  --         CBRT(X) is mathematically unbounded
+  -- Notes:
+  --         a) The reachable range of CBRT is approximately given by:
+  --                ABS(CBRT(X)) <= CBRT(REAL'HIGH)
+
+  function "**" (X : in INTEGER; Y : in REAL) return REAL;
+  -- Purpose:
+  --         Returns Y power of X ==>  X**Y
+  -- Special values:
+  --         X**0.0 = 1.0; X /= 0
+  --         0**Y = 0.0; Y > 0.0
+  --         X**1.0 = REAL(X); X >= 0
+  --         1**Y = 1.0
+  -- Domain:
+  --         X > 0
+  --         X = 0 for Y > 0.0
+  --         X < 0 for Y = 0.0
+  -- Error conditions:
+  --         Error if X < 0 and Y /= 0.0
+  --         Error if X = 0 and Y <= 0.0
+  -- Range:
+  --         X**Y >= 0.0
+  -- Notes:
+  --         a) The upper bound of the reachable range for "**" is
+  --            approximately given by:
+  --                X**Y <= REAL'HIGH
+
+  function "**" (X : in REAL; Y : in REAL) return REAL;
+  -- Purpose:
+  --         Returns Y power of X ==>  X**Y
+  -- Special values:
+  --         X**0.0 = 1.0; X /= 0.0
+  --         0.0**Y = 0.0; Y > 0.0
+  --         X**1.0 = X; X >= 0.0
+  --         1.0**Y = 1.0
+  -- Domain:
+  --         X > 0.0
+  --         X = 0.0 for Y > 0.0
+  --         X < 0.0 for Y = 0.0
+  -- Error conditions:
+  --         Error if X < 0.0 and Y /= 0.0
+  --         Error if X = 0.0 and Y <= 0.0
+  -- Range:
+  --         X**Y >= 0.0
+  -- Notes:
+  --         a) The upper bound of the reachable range for "**" is
+  --            approximately given by:
+  --                X**Y <= REAL'HIGH
+
+  function EXP (X : in REAL) return REAL;
+  -- Purpose:
+  --         Returns e**X; where e = MATH_E
+  -- Special values:
+  --         EXP(0.0) = 1.0
+  --         EXP(1.0) = MATH_E
+  --         EXP(-1.0) = MATH_1_OVER_E
+  --         EXP(X) = 0.0 for X <= -LOG(REAL'HIGH)
+  -- Domain:
+  --         X in REAL such that EXP(X) <= REAL'HIGH
+  -- Error conditions:
+  --         Error if X > LOG(REAL'HIGH)
+  -- Range:
+  --         EXP(X) >= 0.0
+  -- Notes:
+  --         a) The usable domain of EXP is approximately given by:
+  --                X <= LOG(REAL'HIGH)
+
+  function LOG (X : in REAL) return REAL;
+  -- Purpose:
+  --         Returns natural logarithm of X
+  -- Special values:
+  --         LOG(1.0) = 0.0
+  --         LOG(MATH_E) = 1.0
+  -- Domain:
+  --         X > 0.0
+  -- Error conditions:
+  --         Error if X <= 0.0
+  -- Range:
+  --         LOG(X) is mathematically unbounded
+  -- Notes:
+  --         a) The reachable range of LOG is approximately given by:
+  --                LOG(0+) <= LOG(X) <= LOG(REAL'HIGH)
+
+  function LOG2 (X : in REAL) return REAL;
+  -- Purpose:
+  --         Returns logarithm base 2 of X
+  -- Special values:
+  --         LOG2(1.0) = 0.0
+  --         LOG2(2.0) = 1.0
+  -- Domain:
+  --         X > 0.0
+  -- Error conditions:
+  --         Error if X <= 0.0
+  -- Range:
+  --         LOG2(X) is mathematically unbounded
+  -- Notes:
+  --         a) The reachable range of LOG2 is approximately given by:
+  --                LOG2(0+) <= LOG2(X) <= LOG2(REAL'HIGH)
+
+  function LOG10 (X : in REAL) return REAL;
+  -- Purpose:
+  --         Returns logarithm base 10 of X
+  -- Special values:
+  --         LOG10(1.0) = 0.0
+  --         LOG10(10.0) = 1.0
+  -- Domain:
+  --         X > 0.0
+  -- Error conditions:
+  --         Error if X <= 0.0
+  -- Range:
+  --         LOG10(X) is mathematically unbounded
+  -- Notes:
+  --         a) The reachable range of LOG10 is approximately given by:
+  --                LOG10(0+) <= LOG10(X) <= LOG10(REAL'HIGH)
+
+  function LOG (X : in REAL; BASE : in REAL) return REAL;
+  -- Purpose:
+  --         Returns logarithm base BASE of X
+  -- Special values:
+  --         LOG(1.0, BASE) = 0.0
+  --         LOG(BASE, BASE) = 1.0
+  -- Domain:
+  --         X > 0.0
+  --         BASE > 0.0
+  --         BASE /= 1.0
+  -- Error conditions:
+  --         Error if X <= 0.0
+  --         Error if BASE <= 0.0
+  --         Error if BASE = 1.0
+  -- Range:
+  --         LOG(X, BASE) is mathematically unbounded
+  -- Notes:
+  --         a) When BASE > 1.0, the reachable range of LOG is
+  --            approximately given by:
+  --                LOG(0+, BASE) <= LOG(X, BASE) <= LOG(REAL'HIGH, BASE)
+  --         b) When 0.0 < BASE < 1.0, the reachable range of LOG is
+  --            approximately given by:
+  --                LOG(REAL'HIGH, BASE) <= LOG(X, BASE) <= LOG(0+, BASE)
+
+  function SIN (X : in REAL) return REAL;
+  -- Purpose:
+  --         Returns sine of X; X in radians
+  -- Special values:
+  --         SIN(X) = 0.0 for X = k*MATH_PI, where k is an INTEGER
+  --         SIN(X) = 1.0 for X = (4*k+1)*MATH_PI_OVER_2, where k is an
+  --                                                           INTEGER
+  --         SIN(X) = -1.0 for X = (4*k+3)*MATH_PI_OVER_2, where k is an
+  --                                                           INTEGER
+  -- Domain:
+  --         X in REAL
+  -- Error conditions:
+  --         None
+  -- Range:
+  --         ABS(SIN(X)) <= 1.0
+  -- Notes:
+  --         a) For larger values of ABS(X), degraded accuracy is allowed.
+
+  function COS (X : in REAL) return REAL;
+  -- Purpose:
+  --         Returns cosine of X; X in radians
+  -- Special values:
+  --         COS(X) = 0.0 for X = (2*k+1)*MATH_PI_OVER_2, where k is an
+  --                                                            INTEGER
+  --         COS(X) = 1.0 for X = (2*k)*MATH_PI, where k is an INTEGER
+  --         COS(X) = -1.0 for X = (2*k+1)*MATH_PI, where k is an INTEGER
+  -- Domain:
+  --         X in REAL
+  -- Error conditions:
+  --         None
+  -- Range:
+  --         ABS(COS(X)) <= 1.0
+  -- Notes:
+  --         a) For larger values of ABS(X), degraded accuracy is allowed.
+
+  function TAN (X : in REAL) return REAL;
+  -- Purpose:
+  --         Returns tangent of X; X in radians
+  -- Special values:
+  --         TAN(X) = 0.0 for X = k*MATH_PI, where k is an INTEGER
+  -- Domain:
+  --         X in REAL and
+  --         X /= (2*k+1)*MATH_PI_OVER_2, where k is an INTEGER
+  -- Error conditions:
+  --         Error if X = ((2*k+1) * MATH_PI_OVER_2), where k is an
+  --                                                           INTEGER
+  -- Range:
+  --         TAN(X) is mathematically unbounded
+  -- Notes:
+  --         a) For larger values of ABS(X), degraded accuracy is allowed.
+
+  function ARCSIN (X : in REAL) return REAL;
+  -- Purpose:
+  --         Returns inverse sine of X
+  -- Special values:
+  --         ARCSIN(0.0) = 0.0
+  --         ARCSIN(1.0) = MATH_PI_OVER_2
+  --         ARCSIN(-1.0) = -MATH_PI_OVER_2
+  -- Domain:
+  --         ABS(X) <= 1.0
+  -- Error conditions:
+  --         Error if ABS(X) > 1.0
+  -- Range:
+  --         ABS(ARCSIN(X) <= MATH_PI_OVER_2
+  -- Notes:
+  --         None
+
+  function ARCCOS (X : in REAL) return REAL;
+  -- Purpose:
+  --         Returns inverse cosine of X
+  -- Special values:
+  --         ARCCOS(1.0) = 0.0
+  --         ARCCOS(0.0) = MATH_PI_OVER_2
+  --         ARCCOS(-1.0) = MATH_PI
+  -- Domain:
+  --         ABS(X) <= 1.0
+  -- Error conditions:
+  --         Error if ABS(X) > 1.0
+  -- Range:
+  --         0.0 <= ARCCOS(X) <= MATH_PI
+  -- Notes:
+  --         None
+
+  function ARCTAN (Y : in REAL) return REAL;
+  -- Purpose:
+  --         Returns the value of the angle in radians of the point
+  --        (1.0, Y), which is in rectangular coordinates
+  -- Special values:
+  --         ARCTAN(0.0) = 0.0
+  -- Domain:
+  --         Y in REAL
+  -- Error conditions:
+  --         None
+  -- Range:
+  --         ABS(ARCTAN(Y)) <= MATH_PI_OVER_2
+  -- Notes:
+  --         None
+
+  function ARCTAN (Y : in REAL; X : in REAL) return REAL;
+  -- Purpose:
+  --         Returns the principal value of the angle in radians of
+  --         the point (X, Y), which is in rectangular coordinates
+  -- Special values:
+  --         ARCTAN(0.0, X) = 0.0 if X > 0.0
+  --         ARCTAN(0.0, X) = MATH_PI if X < 0.0
+  --         ARCTAN(Y, 0.0) = MATH_PI_OVER_2 if Y > 0.0
+  --         ARCTAN(Y, 0.0) = -MATH_PI_OVER_2 if Y < 0.0
+  -- Domain:
+  --         Y in REAL
+  --         X in REAL, X /= 0.0 when Y = 0.0
+  -- Error conditions:
+  --         Error if X = 0.0 and Y = 0.0
+  -- Range:
+  --         -MATH_PI < ARCTAN(Y,X) <= MATH_PI
+  -- Notes:
+  --         None
+
+  function SINH (X : in REAL) return REAL;
+  -- Purpose:
+  --         Returns hyperbolic sine of X
+  -- Special values:
+  --         SINH(0.0) = 0.0
+  -- Domain:
+  --         X in REAL
+  -- Error conditions:
+  --         None
+  -- Range:
+  --         SINH(X) is mathematically unbounded
+  -- Notes:
+  --         a) The usable domain of SINH is approximately given by:
+  --                ABS(X) <= LOG(REAL'HIGH)
+
+
+  function COSH (X : in REAL) return REAL;
+  -- Purpose:
+  --         Returns hyperbolic cosine of X
+  -- Special values:
+  --         COSH(0.0) = 1.0
+  -- Domain:
+  --         X in REAL
+  -- Error conditions:
+  --         None
+  -- Range:
+  --         COSH(X) >= 1.0
+  -- Notes:
+  --         a) The usable domain of COSH is approximately given by:
+  --                ABS(X) <= LOG(REAL'HIGH)
+
+  function TANH (X : in REAL) return REAL;
+  -- Purpose:
+  --         Returns hyperbolic tangent of X
+  -- Special values:
+  --         TANH(0.0) = 0.0
+  -- Domain:
+  --         X in REAL
+  -- Error conditions:
+  --         None
+  -- Range:
+  --         ABS(TANH(X)) <= 1.0
+  -- Notes:
+  --         None
+
+  function ARCSINH (X : in REAL) return REAL;
+  -- Purpose:
+  --         Returns inverse hyperbolic sine of X
+  -- Special values:
+  --         ARCSINH(0.0) = 0.0
+  -- Domain:
+  --         X in REAL
+  -- Error conditions:
+  --         None
+  -- Range:
+  --         ARCSINH(X) is mathematically unbounded
+  -- Notes:
+  --         a) The reachable range of ARCSINH is approximately given by:
+  --                ABS(ARCSINH(X)) <= LOG(REAL'HIGH)
+
+  function ARCCOSH (X : in REAL) return REAL;
+  -- Purpose:
+  --         Returns inverse hyperbolic cosine of X
+  -- Special values:
+  --         ARCCOSH(1.0) = 0.0
+  -- Domain:
+  --         X >= 1.0
+  -- Error conditions:
+  --         Error if X < 1.0
+  -- Range:
+  --         ARCCOSH(X) >= 0.0
+  -- Notes:
+  --         a) The upper bound of the reachable range of ARCCOSH is
+  --            approximately given by:   ARCCOSH(X) <= LOG(REAL'HIGH)
+
+  function ARCTANH (X : in REAL) return REAL;
+  -- Purpose:
+  --         Returns inverse hyperbolic tangent of X
+  -- Special values:
+  --         ARCTANH(0.0) = 0.0
+  -- Domain:
+  --         ABS(X) < 1.0
+  -- Error conditions:
+  --         Error if ABS(X) >= 1.0
+  -- Range:
+  --         ARCTANH(X) is mathematically unbounded
+  -- Notes:
+  --         a) The reachable range of ARCTANH is approximately given by:
+  --                ABS(ARCTANH(X)) < LOG(REAL'HIGH)
+
+end package MATH_REAL;