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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 BODY 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.
+--
+-- Source code and algorithms for this package body comes from the
+-- following sources:
+-- IEEE VHDL Math Package Study Group participants,
+-- U. of Mississippi, Mentor Graphics, Synopsys,
+-- Viewlogic/Vantage, Communications of the ACM (June 1988, Vol
+-- 31, Number 6, pp. 747, Pierre L'Ecuyer, Efficient and Portable
+-- Random Number Generators), Handbook of Mathematical Functions
+-- by Milton Abramowitz and Irene A. Stegun (Dover).
+--
+-- History:
+-- Version 0.1 Jose A. Torres 4/23/93 First draft
+-- Version 0.2 Jose A. Torres 5/28/93 Fixed potentially illegal code
+--
+-- GHDL history
+-- 2005-04-07 Initial version.
+-------------------------------------------------------------
+Library IEEE;
+
+Package body MATH_REAL is
+ --
+ -- non-trascendental functions
+ --
+ function SIGN (X: real ) return real is
+ -- returns 1.0 if X > 0.0; 0.0 if X == 0.0; -1.0 if X < 0.0
+ begin
+ assert false severity failure;
+ end SIGN;
+
+ function CEIL (X : real ) return real is
+ begin
+ assert false severity failure;
+ end CEIL;
+
+ function FLOOR (X : real ) return real is
+ begin
+ assert false severity failure;
+ end FLOOR;
+
+ function ROUND (X : real ) return real is
+ begin
+ assert false severity failure;
+ end ROUND;
+
+ function FMAX (X, Y : real ) return real is
+ begin
+ assert false severity failure;
+ end FMAX;
+
+ function FMIN (X, Y : real ) return real is
+ begin
+ assert false severity failure;
+ end FMIN;
+
+ --
+ -- Pseudo-random number generators
+ --
+
+ procedure UNIFORM(variable Seed1,Seed2:inout integer;variable X:out real) is
+ -- 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.
+
+ variable z, k: integer;
+ begin
+ k := Seed1/53668;
+ Seed1 := 40014 * (Seed1 - k * 53668) - k * 12211;
+
+ if Seed1 < 0 then
+ Seed1 := Seed1 + 2147483563;
+ end if;
+
+
+ k := Seed2/52774;
+ Seed2 := 40692 * (Seed2 - k * 52774) - k * 3791;
+
+ if Seed2 < 0 then
+ Seed2 := Seed2 + 2147483399;
+ end if;
+
+ z := Seed1 - Seed2;
+ if z < 1 then
+ z := z + 2147483562;
+ end if;
+
+ X := REAL(Z)*4.656613e-10;
+ end UNIFORM;
+
+
+ function SRAND (seed: in integer ) return integer is
+ begin
+ assert false severity failure;
+ end SRAND;
+
+ function RAND return integer is
+ begin
+ assert false severity failure;
+ end RAND;
+
+ function GET_RAND_MAX return integer is
+ -- The value this function returns should be the same as
+ -- RAND_MAX in /usr/include/stdlib.h
+ begin
+ assert false
+ report "Be sure to update GET_RAND_MAX in mathpack.vhd"
+ severity note;
+ return 2147483647; -- i386 linux
+ end GET_RAND_MAX;
+
+ --
+ -- trascendental and trigonometric functions
+ --
+ function c_sqrt (x : real ) return real;
+ attribute foreign of c_sqrt : function is "VHPIDIRECT sqrt";
+
+ function c_sqrt (x : real ) return real is
+ begin
+ assert false severity failure;
+ end c_sqrt;
+
+ function SQRT (X : real ) return real is
+ begin
+ -- check validity of argument
+ if ( X < 0.0 ) then
+ assert false report "X < 0 in SQRT(X)"
+ severity ERROR;
+ return (0.0);
+ end if;
+ return c_sqrt(X);
+ end SQRT;
+
+ function CBRT (X : real ) return real is
+ begin
+ assert false severity failure;
+ end CBRT;
+
+ function "**" (X : integer; Y : real) return real is
+ -- 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
+ begin
+ -- check validity of argument
+ if ( X = 0 ) and ( Y <= 0.0 ) then
+ assert false report "X = 0 and Y <= 0.0 in X**Y"
+ severity ERROR;
+ return (0.0);
+ end if;
+
+ if ( X < 0 ) and ( Y /= REAL(INTEGER(Y)) ) then
+ assert false
+ report "X < 0 and Y \= integer in X**Y"
+ severity ERROR;
+ return (0.0);
+ end if;
+
+ -- compute the result
+ return EXP (Y * LOG (REAL(X)));
+ end "**";
+
+ function "**" (X : real; Y : real) return real is
+ -- 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
+ begin
+ -- check validity of argument
+ if ( X = 0.0 ) and ( Y <= 0.0 ) then
+ assert false report "X = 0.0 and Y <= 0.0 in X**Y"
+ severity ERROR;
+ return (0.0);
+ end if;
+
+ if ( X < 0.0 ) and ( Y /= REAL(INTEGER(Y)) ) then
+ assert false report "X < 0.0 and Y \= integer in X**Y"
+ severity ERROR;
+ return (0.0);
+ end if;
+
+ -- compute the result
+ return EXP (Y * LOG (X));
+ end "**";
+
+ function EXP (X : real ) return real is
+ begin
+ assert false severity failure;
+ end EXP;
+
+ function c_log (x : real ) return real;
+ attribute foreign of c_log : function is "VHPIDIRECT log";
+
+ function c_log (x : real ) return real is
+ begin
+ assert false severity failure;
+ end c_log;
+
+ function LOG (X : real ) return real is
+ -- returns natural logarithm of X; X > 0
+ --
+ -- This function computes the exponential using the following series:
+ -- log(x) = 2[ (x-1)/(x+1) + (((x-1)/(x+1))**3)/3.0 + ...] ; x > 0
+ --
+ begin
+ -- check validity of argument
+ if ( x <= 0.0 ) then
+ assert false report "X <= 0 in LOG(X)"
+ severity ERROR;
+ return(REAL'LOW);
+ end if;
+ return c_log(x);
+ end LOG;
+
+ function LOG (BASE: positive; X : real) return real is
+ -- returns logarithm base BASE of X; X > 0
+ begin
+ -- check validity of argument
+ if ( BASE <= 0 ) or ( x <= 0.0 ) then
+ assert false report "BASE <= 0 or X <= 0.0 in LOG(BASE, X)"
+ severity ERROR;
+ return(REAL'LOW);
+ end if;
+ -- compute the value
+ return (LOG(X)/LOG(REAL(BASE)));
+ end LOG;
+
+ function SIN (X : real ) return real is
+ begin
+ assert false severity failure;
+ end SIN;
+
+
+ function COS (x : REAL) return REAL is
+ begin
+ assert false severity failure;
+ end COS;
+
+ function TAN (x : REAL) return REAL is
+ begin
+ assert false severity failure;
+ end TAN;
+
+ function c_asin (x : real ) return real;
+ attribute foreign of c_asin : function is "VHPIDIRECT asin";
+
+ function c_asin (x : real ) return real is
+ begin
+ assert false severity failure;
+ end c_asin;
+
+ function ASIN (x : real ) return real is
+ -- returns -PI/2 < asin X < PI/2; | X | <= 1
+ begin
+ if abs x > 1.0 then
+ assert false
+ report "Out of range parameter passed to ASIN"
+ severity ERROR;
+ return x;
+ else
+ return c_asin(x);
+ end if;
+ end ASIN;
+
+ function c_acos (x : real ) return real;
+ attribute foreign of c_acos : function is "VHPIDIRECT acos";
+
+ function c_acos (x : real ) return real is
+ begin
+ assert false severity failure;
+ end c_acos;
+
+ function ACOS (x : REAL) return REAL is
+ -- returns 0 < acos X < PI; | X | <= 1
+ begin
+ if abs x > 1.0 then
+ assert false
+ report "Out of range parameter passed to ACOS"
+ severity ERROR;
+ return x;
+ else
+ return c_acos(x);
+ end if;
+ end ACOS;
+
+ function ATAN (x : REAL) return REAL is
+ -- returns -PI/2 < atan X < PI/2
+ begin
+ assert false severity failure;
+ end ATAN;
+
+ function c_atan2 (x : real; y : real) return real;
+ attribute foreign of c_atan2 : function is "VHPIDIRECT atan2";
+
+ function c_atan2 (x : real; y: real) return real is
+ begin
+ assert false severity failure;
+ end c_atan2;
+
+ function ATAN2 (x : REAL; y : REAL) return REAL is
+ -- returns atan (X/Y); -PI < atan2(X,Y) < PI; Y /= 0.0
+ begin
+ if y = 0.0 and x = 0.0 then
+ assert false
+ report "atan2(0.0, 0.0) is undetermined, returned 0,0"
+ severity NOTE;
+ return 0.0;
+ else
+ return c_atan2(x,y);
+ end if;
+ end ATAN2;
+
+
+ function SINH (X : real) return real is
+ -- hyperbolic sine; returns (e**X - e**(-X))/2
+ begin
+ assert false severity failure;
+ end SINH;
+
+ function COSH (X : real) return real is
+ -- hyperbolic cosine; returns (e**X + e**(-X))/2
+ begin
+ assert false severity failure;
+ end COSH;
+
+ function TANH (X : real) return real is
+ -- hyperbolic tangent; -- returns (e**X - e**(-X))/(e**X + e**(-X))
+ begin
+ assert false severity failure;
+ end TANH;
+
+ function ASINH (X : real) return real is
+ -- returns ln( X + sqrt( X**2 + 1))
+ begin
+ assert false severity failure;
+ end ASINH;
+
+ function c_acosh (x : real ) return real;
+ attribute foreign of c_acosh : function is "VHPIDIRECT acosh";
+
+ function c_acosh (x : real ) return real is
+ begin
+ assert false severity failure;
+ end c_acosh;
+
+ function ACOSH (X : real) return real is
+ -- returns ln( X + sqrt( X**2 - 1)); X >= 1
+ begin
+ if abs x >= 1.0 then
+ assert false report "Out of range parameter passed to ACOSH"
+ severity ERROR;
+ return x;
+ end if;
+ return c_acosh(x);
+ end ACOSH;
+
+ function c_atanh (x : real ) return real;
+ attribute foreign of c_atanh : function is "VHPIDIRECT atanh";
+
+ function c_atanh (x : real ) return real is
+ begin
+ assert false severity failure;
+ end c_atanh;
+
+ function ATANH (X : real) return real is
+ -- returns (ln( (1 + X)/(1 - X)))/2 ; | X | < 1
+ begin
+ if abs x < 1.0 then
+ assert false report "Out of range parameter passed to ATANH"
+ severity ERROR;
+ return x;
+ end if;
+ return c_atanh(x);
+ end ATANH;
+
+end MATH_REAL;
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