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/trunk/bench/vhdl/math_lib.vhd
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----------------------------------------------------------------------
---- ----
---- Math function library. ----
---- ----
---- This file is part of the Random Number Generator project ----
---- http://www.opencores.org/cores/rng_lib/ ----
---- ----
---- Description ----
---- These math function are copied from the draft version of the ----
---- IEEE MATH_REAL package. ----
---- ----
---- To Do: ----
---- - ----
---- ----
---- Author(s): ----
---- - Geir Drange, gedra@opencores.org ----
---- ----
----------------------------------------------------------------------
---- ----
---- Copyright (C) 2004 Authors and OPENCORES.ORG ----
---- ----
---- This source file may be used and distributed without ----
---- restriction provided that this copyright statement is not ----
---- removed from the file and that any derivative work contains ----
---- the original copyright notice and the associated disclaimer. ----
---- ----
---- This source file is free software; you can redistribute it ----
---- and/or modify it under the terms of the GNU General ----
---- Public License as published by the Free Software Foundation; ----
---- either version 2.0 of the License, or (at your option) any ----
---- later version. ----
---- ----
---- This source is distributed in the hope that it will be ----
---- useful, but WITHOUT ANY WARRANTY; without even the implied ----
---- warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR ----
---- PURPOSE. See the GNU General Public License for more details.----
---- ----
---- You should have received a copy of the GNU General ----
---- Public License along with this source; if not, download it ----
---- from http://www.gnu.org/licenses/gpl.txt ----
---- ----
----------------------------------------------------------------------
--
-- CVS Revision History
--
-- $Log: not supported by cvs2svn $
--
--
library ieee;
use ieee.std_logic_1164.all;
use ieee.numeric_std.all;
 
package math_lib is
 
function sqrt(x: real) return real; -- returns square root
function ln(x: real ) return real; -- natural logarithm
function log(x: real) return real; -- base 10 logarithm
function exp(x: real ) return real; -- exponential function
-- Some mathematical constants
constant MATH_E: real := 2.71828_18284_59045_23536;
end math_lib;
 
package body math_lib is
 
-- Square root calculation
function sqrt (x : real ) return real is
-- returns square root of X; X >= 0
--
-- Computes square root using the Newton-Raphson approximation:
-- F(n+1) = 0.5*[F(n) + x/F(n)];
--
constant inival: real := 1.5;
constant eps : real := 0.000001;
constant relative_err : real := eps*X;
variable oldval : real;
variable newval : real;
 
begin
-- check validity of argument
if x < 0.0 then
report "x < 0 in sqrt(x)"
severity failure;
return (0.0);
end if;
-- get the square root for special cases
if x = 0.0 then
return 0.0;
else
if x = 1.0 then
return 1.0; -- return exact value
end if;
end if;
-- get the square root for general cases
oldval := inival;
newval := (X/oldval + oldval)/2.0;
while ( abs(newval -oldval) > relative_err ) loop
oldval := newval;
newval := (X/oldval + oldval)/2.0;
end loop;
return newval;
end sqrt;
 
-- Natural logarithm calculation
function ln (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
--
constant eps : real := 0.000001; -- precision criteria
 
variable xlocal: real ; -- following variables are
variable oldval: real ; -- used to evaluate the series
variable xlocalsqr: real ;
variable factor : real ;
variable count: integer ;
variable newval: real ;
begin
-- check validity of argument
if x <= 0.0 then
report "x <= 0 in ln(x)"
severity failure;
return(real'LOW);
end if;
 
-- compute value for special cases
if x = 1.0 then
return 0.0;
else
if x = MATH_E then
return 1.0;
end if;
end if;
 
-- compute value for general cases
xlocal := (x - 1.0)/(x + 1.0);
oldval := xlocal;
xlocalsqr := xlocal*xlocal;
factor := xlocal*xlocalsqr;
count := 3;
newval := oldval + (factor/real(count));
while ( abs(newval - oldval) > eps ) loop
oldval := newval;
count := count +2;
factor := factor * xlocalsqr;
newval := oldval + factor/real(count);
end loop;
newval := newval * 2.0;
return newval;
end ln;
 
-- Base 10 logarithm calculation
function log (x: real) return real is
-- returns logarithm base 10 of x; x > 0
begin
-- check validity of argument
if x <= 0.0 then
assert false report "x <= 0.0 in log(x)"
severity ERROR;
return(real'LOW);
end if;
 
-- compute the value
return (ln(x)/2.30258509299);
end log;
 
-- Calculate e**x
function exp (x: real ) return real is
-- returns e**X; where e = MATH_E
--
-- This function computes the exponential using the following series:
-- exp(x) = 1 + x + x**2/2! + x**3/3! + ... ; x > 0
--
constant eps : real := 0.000001; -- precision criteria
variable reciprocal: boolean := x < 0.0;-- check sign of argument
variable xlocal : real := abs(x); -- use positive value
variable oldval: real ; -- following variables are
variable num: real ; -- used for series evaluation
variable count: integer ;
variable denom: real ;
variable newval: real ;
begin
-- compute value for special cases
if x = 0.0 then
return 1.0;
else
if x = 1.0 then
return MATH_E;
end if;
end if;
 
-- compute value for general cases
oldval := 1.0;
num := xlocal;
count := 1;
denom := 1.0;
newval:= oldval + num/denom;
while ( abs(newval - oldval) > eps ) loop
oldval := newval;
num := num*xlocal;
count := count +1;
denom := denom*(real(count));
newval := oldval + num/denom;
end loop;
if reciprocal then
newval := 1.0/newval;
end if;
return newval;
end exp;
 
end math_lib;

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