Subversion Repositories rng_lib

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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                           ----

----                                                              ----

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----                                                              ----

---- 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                     ----

----                                                              ----

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--

-- CVS Revision History

--

-- $Log: not supported by cvs2svn $

-- Revision 1.1  2004/09/28 15:02:56  gedra

-- Math functions library.

--

--

--

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;