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------------------------------------------------------------------------
--
-- This source file may be used and distributed without restriction.
-- No declarations or definitions shall be added to this package.
-- This package cannot be sold or distributed for profit.
--
-- ****************************************************************
-- * *
-- * W A R N I N G *
-- * *
-- * This DRAFT version IS NOT endorsed or approved by IEEE *
-- * *
-- ****************************************************************
--
-- Title: PACKAGE MATH_REAL
--
-- Library: This package shall be compiled into a library
-- symbolically named IEEE.
--
-- Purpose: VHDL declarations for mathematical package MATH_REAL
-- which contains common real constants, common real
-- functions, and real trascendental functions.
--
-- Author: IEEE VHDL Math Package Study Group
--
-- Notes:
-- 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.
--
-- 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 Added RANDOM()
-- Version 0.6 Jose A. Torres 4/23/93 Renamed RANDOM as
-- UNIFORM. Modified
-- rights banner.
-- Version 0.7 Jose A. Torres 5/28/93 Rev up for compatibility
-- with package body.
--
-- GHDL history
-- 2005-04-07 Initial version.
-- 2005-09-01 Some PI constants added.
-- 2005-12-20 I. Curtis : significant overhaul to bring closer in line
-- with ieee standard
-------------------------------------------------------------
Library IEEE;
Package MATH_REAL is
-- IAC: should have a string with copyright notice
-- constant CopyRightNotice: STRING
-- := "GPL";
--
-- commonly used constants
--
constant MATH_E : real := 2.71828_18284_59045_23536; -- e
constant MATH_1_OVER_E : real := 0.36787_94411_71442_32160; -- 1/e
constant MATH_PI : real := 3.14159_26535_89793_23846; -- pi
constant MATH_2_PI : real := 2.0 * MATH_PI; -- 2 * pi
constant MATH_1_OVER_PI : real := 0.31830_98861_83790_67154; -- 1/pi
constant MATH_PI_OVER_2 : real := 1.57079_63267_94896_61923; -- pi / 2
constant MATH_PI_OVER_4 : real := 0.78539_81633_97448_30962; -- pi / 4
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 of10
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_SQRT2: real := 1.41421_35623_73095_04880;
-- sqrt of 2
constant MATH_SQRT1_2: real := 0.70710_67811_86547_52440;
-- sqrt of 1/2
constant MATH_SQRT_PI: real := 1.77245_38509_05516_02730;
-- sqrt 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_87685;
-- conversion factor from radian to degree
--
-- function declarations
--
function SIGN (X: real ) return real;
-- returns 1.0 if X > 0.0; 0.0 if X == 0.0; -1.0 if X < 0.0
function CEIL (X : real ) return real;
attribute foreign of ceil : function is "VHPIDIRECT ceil";
-- returns smallest integer value (as real) not less than X
function FLOOR (X : real ) return real;
attribute foreign of floor : function is "VHPIDIRECT floor";
-- returns largest integer value (as real) not greater than X
function ROUND (X : real ) return real;
attribute foreign of round : function is "VHPIDIRECT round";
-- returns integer FLOOR(X + 0.5) if X > 0;
-- return integer CEIL(X - 0.5) if X < 0
-- IAC: we are missing the function TRUNC
-- IAC: we are missing the function MOD
-- IAC: functions FMAX and FMIN should be renamed REALMAX and REALMIN
function FMAX (X, Y : real ) return real;
attribute foreign of fmax : function is "VHPIDIRECT fmax";
-- returns the algebraically larger of X and Y
function FMIN (X, Y : real ) return real;
attribute foreign of fmin : function is "VHPIDIRECT fmin";
-- returns the algebraically smaller of X and Y
procedure UNIFORM (variable Seed1,Seed2:inout integer; variable X:out real);
-- returns a pseudo-random number with uniform distribution in the
-- interval (0.0, 1.0).
-- Before the first call to UNIFORM, the seed values (Seed1, Seed2) must
-- be initialized to values in the range [1, 2147483562] and
-- [1, 2147483398] respectively. The seed values are modified after
-- each call to UNIFORM.
-- This random number generator is portable for 32-bit computers, and
-- it has period ~2.30584*(10**18) for each set of seed values.
--
-- For VHDL-1992, the seeds will be global variables, functions to
-- initialize their values (INIT_SEED) will be provided, and the UNIFORM
-- procedure call will be modified accordingly.
-- IAC: functions SRAND, RAND and GET_RAND_MAX should not be visible
function SRAND (seed: in integer ) return integer;
attribute foreign of srand : function is "VHPIDIRECT srand";
--
-- sets value of seed for sequence of
-- pseudo-random numbers.
-- It uses the foreign native C function srand().
function RAND return integer;
attribute foreign of rand : function is "VHPIDIRECT rand";
--
-- returns an integer pseudo-random number with uniform distribution.
-- It uses the foreign native C function rand().
-- Seed for the sequence is initialized with the
-- SRAND() function and value of the seed is changed every
-- time SRAND() is called, but it is not visible.
-- The range of generated values is platform dependent.
function GET_RAND_MAX return integer;
--
-- returns the upper bound of the range of the
-- pseudo-random numbers generated by RAND().
-- The support for this function is platform dependent, and
-- it uses foreign native C functions or constants.
-- It may not be available in some platforms.
-- Note: the value of (RAND() / GET_RAND_MAX()) is a
-- pseudo-random number distributed between 0 & 1.
function SQRT (X : real ) return real;
-- returns square root of X; X >= 0
function CBRT (X : real ) return real;
attribute foreign of cbrt : function is "VHPIDIRECT cbrt";
-- returns cube root of X
function "**" (X : integer; Y : real) return real;
-- returns Y power of X ==> X**Y;
-- error if X = 0 and Y <= 0.0
-- error if X < 0 and Y does not have an integer value
function "**" (X : real; Y : real) return real;
-- returns Y power of X ==> X**Y;
-- error if X = 0.0 and Y <= 0.0
-- error if X < 0.0 and Y does not have an integer value
function EXP (X : real ) return real;
attribute foreign of exp : function is "VHPIDIRECT exp";
-- returns e**X; where e = MATH_E
function LOG (X : real ) return real;
-- returns natural logarithm of X; X > 0
function LOG (X: in real; BASE: in real) return real;
-- returns logarithm base BASE of X; X > 0
function LOG2 (X : in real ) return real;
-- returns logarithm base 2 of X; X > 0
function LOG10 (X : in real ) return real;
-- returns logarithm base 10 of X; X > 0
function SIN (X : real ) return real;
attribute foreign of sin : function is "VHPIDIRECT sin";
-- returns sin X; X in radians
function COS ( X : real ) return real;
attribute foreign of cos : function is "VHPIDIRECT cos";
-- returns cos X; X in radians
function TAN (X : real ) return real;
attribute foreign of tan : function is "VHPIDIRECT tan";
-- returns tan X; X in radians
-- X /= ((2k+1) * PI/2), where k is an integer
-- IAC: function should be called ARCSIN
function ASIN (X : real ) return real;
-- returns -PI/2 < asin X < PI/2; | X | <= 1
-- IAC: function should be called ARCCOS
function ACOS (X : real ) return real;
-- returns 0 < acos X < PI; | X | <= 1
-- IAC: function should be called ARCTAN
function ATAN (X : real) return real;
attribute foreign of atan : function is "VHPIDIRECT atan";
-- returns -PI/2 < atan X < PI/2
-- IAC: function ATAN2 should not exist
function ATAN2 (X : real; Y : real) return real;
-- returns atan (X/Y); -PI < atan2(X,Y) < PI; Y /= 0.0
function SINH (X : real) return real;
attribute foreign of sinh : function is "VHPIDIRECT sinh";
-- hyperbolic sine; returns (e**X - e**(-X))/2
function COSH (X : real) return real;
attribute foreign of cosh : function is "VHPIDIRECT cosh";
-- hyperbolic cosine; returns (e**X + e**(-X))/2
function TANH (X : real) return real;
attribute foreign of tanh : function is "VHPIDIRECT tanh";
-- hyperbolic tangent; -- returns (e**X - e**(-X))/(e**X + e**(-X))
-- IAC: function should be called ARCSINH
function ASINH (X : real) return real;
attribute foreign of asinh : function is "VHPIDIRECT asinh";
-- returns ln( X + sqrt( X**2 + 1))
-- IAC: function should be called ARCCOSH
function ACOSH (X : real) return real;
-- returns ln( X + sqrt( X**2 - 1)); X >= 1
-- IAC: function should be called ARCTANH
function ATANH (X : real) return real;
-- returns (ln( (1 + X)/(1 - X)))/2 ; | X | < 1
end MATH_REAL;
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