math_lib.vhd

任意数据发生器的源代码

----------------------------------------------------------------------
----                                                              ----
---- 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, [e-mail]                           ----
----                                                              ----
----------------------------------------------------------------------
----                                                              ----
---- 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: math_lib.vhd,v $
-- 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;