----------------------------------------------------------------------
|
----------------------------------------------------------------------
|
---- ----
|
---- ----
|
---- Rand number generator library. ----
|
---- Rand number generator library. ----
|
---- ----
|
---- ----
|
---- This file is part of the Random Number Generator project ----
|
---- This file is part of the Random Number Generator project ----
|
---- http://www.opencores.org/cores/rng_lib/ ----
|
---- http://www.opencores.org/cores/rng_lib/ ----
|
---- ----
|
---- ----
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---- Description ----
|
---- Description ----
|
---- This library has function for generation random numbers with ----
|
---- This library has function for generation random numbers with ----
|
---- the following distributions: ----
|
---- the following distributions: ----
|
---- - Uniform (continous) ----
|
---- - Uniform (continous) ----
|
---- - Exponential (continous) ----
|
---- - Exponential (continous) ----
|
---- - Gaussian (continous) ----
|
---- - Gaussian (continous) ----
|
---- ----
|
---- ----
|
---- Random numbers are produced with a combination of 3 ----
|
---- Random numbers are produced with a combination of 3 ----
|
---- Tausworthe generators which gives very good statistical ----
|
---- Tausworthe generators which gives very good statistical ----
|
---- properties. ----
|
---- properties. ----
|
---- ----
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---- ----
|
---- NOTE! These functions will NOT synthesize. They are for test ----
|
---- NOTE! These functions will NOT synthesize. They are for test ----
|
---- bench use only! ----
|
---- bench use only! ----
|
---- ----
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---- ----
|
---- To Do: ----
|
---- To Do: ----
|
---- - ----
|
---- - ----
|
---- ----
|
---- ----
|
---- Author(s): ----
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---- Author(s): ----
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---- - Geir Drange, gedra@opencores.org ----
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---- - Geir Drange, gedra@opencores.org ----
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---- ----
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---- ----
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----------------------------------------------------------------------
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----------------------------------------------------------------------
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---- ----
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---- ----
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---- Copyright (C) 2004 Authors and OPENCORES.ORG ----
|
---- Copyright (C) 2004 Authors and OPENCORES.ORG ----
|
---- ----
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---- ----
|
---- This source file may be used and distributed without ----
|
---- This source file may be used and distributed without ----
|
---- restriction provided that this copyright statement is not ----
|
---- restriction provided that this copyright statement is not ----
|
---- removed from the file and that any derivative work contains ----
|
---- removed from the file and that any derivative work contains ----
|
---- the original copyright notice and the associated disclaimer. ----
|
---- the original copyright notice and the associated disclaimer. ----
|
---- ----
|
---- ----
|
---- This source file is free software; you can redistribute it ----
|
---- This source file is free software; you can redistribute it ----
|
---- and/or modify it under the terms of the GNU General ----
|
---- and/or modify it under the terms of the GNU General ----
|
---- Public License as published by the Free Software Foundation; ----
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---- Public License as published by the Free Software Foundation; ----
|
---- either version 2.0 of the License, or (at your option) any ----
|
---- either version 2.0 of the License, or (at your option) any ----
|
---- later version. ----
|
---- later version. ----
|
---- ----
|
---- ----
|
---- This source is distributed in the hope that it will be ----
|
---- This source is distributed in the hope that it will be ----
|
---- useful, but WITHOUT ANY WARRANTY; without even the implied ----
|
---- useful, but WITHOUT ANY WARRANTY; without even the implied ----
|
---- warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR ----
|
---- warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR ----
|
---- PURPOSE. See the GNU General Public License for more details.----
|
---- PURPOSE. See the GNU General Public License for more details.----
|
---- ----
|
---- ----
|
---- You should have received a copy of the GNU General ----
|
---- You should have received a copy of the GNU General ----
|
---- Public License along with this source; if not, download it ----
|
---- Public License along with this source; if not, download it ----
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---- from http://www.gnu.org/licenses/gpl.txt ----
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---- from http://www.gnu.org/licenses/gpl.txt ----
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---- ----
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---- ----
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----------------------------------------------------------------------
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----------------------------------------------------------------------
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--
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--
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-- CVS Revision History
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-- CVS Revision History
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--
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--
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-- $Log: not supported by cvs2svn $
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-- $Log: not supported by cvs2svn $
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-- Revision 1.1 2004/09/28 15:12:28 gedra
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-- Revision 1.1 2004/09/28 15:12:28 gedra
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-- Random number library functions.
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-- Random number library functions.
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--
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--
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--
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--
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--
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--
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|
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library ieee;
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library ieee;
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use ieee.std_logic_1164.all;
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use ieee.std_logic_1164.all;
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use ieee.numeric_std.all;
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use ieee.numeric_std.all;
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use std.textio.all;
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use std.textio.all;
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use work.math_lib.all;
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use work.math_lib.all;
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|
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package rng_lib is
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package rng_lib is
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|
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type distribution is (UNIFORM, GAUSSIAN, EXPONENTIAL);
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type distribution is (UNIFORM, GAUSSIAN, EXPONENTIAL);
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type rand_var is record -- random variable record
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type rand_var is record -- random variable record
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rnd : real; -- random number
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rnd : real; -- random number
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rnd_v : unsigned(31 downto 0); -- random number vector
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rnd_v : unsigned(31 downto 0); -- random number vector
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dist : distribution; -- distribution type
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dist : distribution; -- distribution type
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y, z : real; -- distribution parameters
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y, z : real; -- distribution parameters
|
s1, s2, s3 : unsigned(31 downto 0); -- seeds
|
s1, s2, s3 : unsigned(31 downto 0); -- seeds
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mask1, mask2, mask3 : unsigned(31 downto 0);
|
mask1, mask2, mask3 : unsigned(31 downto 0);
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shft1, shft2, shft3 : natural;
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shft1, shft2, shft3 : natural;
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end record;
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end record;
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|
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function rand (rnd : rand_var) return rand_var;
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function rand (rnd : rand_var) return rand_var;
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function init_uniform(constant a, b, c : natural;
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function init_uniform(constant a, b, c : natural;
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constant lo, hi : real) return rand_var;
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constant lo, hi : real) return rand_var;
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function init_gaussian(constant a, b, c : natural;
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function init_gaussian(constant a, b, c : natural;
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constant mean, stdev : real) return rand_var;
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constant mean, stdev : real) return rand_var;
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function init_exponential(constant a, b, c : natural;
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function init_exponential(constant a, b, c : natural;
|
constant mean : real) return rand_var;
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constant mean : real) return rand_var;
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|
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constant q1 : natural := 13;
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constant q1 : natural := 13;
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constant q2 : natural := 2;
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constant q2 : natural := 2;
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constant q3 : natural := 3;
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constant q3 : natural := 3;
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constant p1 : natural := 12;
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constant p1 : natural := 12;
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constant p2 : natural := 4;
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constant p2 : natural := 4;
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constant p3 : natural := 17;
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constant p3 : natural := 17;
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|
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end rng_lib;
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end rng_lib;
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|
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package body rng_lib is
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package body rng_lib is
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|
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-- Function to convert 32bit unsigned vector to real
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-- Function to convert 32bit unsigned vector to real
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-- Integers only go to 2**31 (VHDL'87), so do it clever
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-- Integers only go to 2**31 (VHDL'87), so do it clever
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function unsigned_2_real (constant a : unsigned(31 downto 0)) return real is
|
function unsigned_2_real (constant a : unsigned(31 downto 0)) return real is
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variable r : real;
|
variable r : real;
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begin
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begin
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r := 2.0*real(to_integer(a(31 downto 1)));
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r := 2.0*real(to_integer(a(31 downto 1)));
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if a(0) = '1' then
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if a(0) = '1' then
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r := r + 1.0;
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r := r + 1.0;
|
end if;
|
end if;
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return(r);
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return(r);
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end unsigned_2_real;
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end unsigned_2_real;
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|
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-- Generate random number using a combination of 3 tausworthe generators
|
-- Generate random number using a combination of 3 tausworthe generators
|
-- Source: Pierre L'Ecuyer, "Maximally Equidistributed Combined Tausworthe
|
-- Source: Pierre L'Ecuyer, "Maximally Equidistributed Combined Tausworthe
|
-- Generators". Mathematics of Computation, vol.65, no.213(1996), pp203--213.
|
-- Generators". Mathematics of Computation, vol.65, no.213(1996), pp203--213.
|
function rng (rnd : rand_var) return rand_var is
|
function rng (rnd : rand_var) return rand_var is
|
variable new_rnd : rand_var;
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variable new_rnd : rand_var;
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variable b : unsigned(31 downto 0);
|
variable b : unsigned(31 downto 0);
|
begin
|
begin
|
new_rnd := rnd;
|
new_rnd := rnd;
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b := ((new_rnd.s1 sll q1) xor new_rnd.s1) srl new_rnd.shft1;
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b := ((new_rnd.s1 sll q1) xor new_rnd.s1) srl new_rnd.shft1;
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new_rnd.s1 := ((new_rnd.s1 and new_rnd.mask1) sll p1) xor b;
|
new_rnd.s1 := ((new_rnd.s1 and new_rnd.mask1) sll p1) xor b;
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b := ((new_rnd.s2 sll q2) xor new_rnd.s2) srl new_rnd.shft2;
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b := ((new_rnd.s2 sll q2) xor new_rnd.s2) srl new_rnd.shft2;
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new_rnd.s2 := ((new_rnd.s2 and new_rnd.mask2) sll p2) xor b;
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new_rnd.s2 := ((new_rnd.s2 and new_rnd.mask2) sll p2) xor b;
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b := ((new_rnd.s3 sll q3) xor new_rnd.s3) srl new_rnd.shft3;
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b := ((new_rnd.s3 sll q3) xor new_rnd.s3) srl new_rnd.shft3;
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new_rnd.s3 := ((new_rnd.s3 and new_rnd.mask3) sll p3) xor b;
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new_rnd.s3 := ((new_rnd.s3 and new_rnd.mask3) sll p3) xor b;
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new_rnd.rnd_v := new_rnd.s1 xor new_rnd.s2 xor new_rnd.s3;
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new_rnd.rnd_v := new_rnd.s1 xor new_rnd.s2 xor new_rnd.s3;
|
-- normalize to range [0,1)
|
-- normalize to range [0,1)
|
new_rnd.rnd := unsigned_2_real(new_rnd.rnd_v) / 65536.0;
|
new_rnd.rnd := unsigned_2_real(new_rnd.rnd_v) / 65536.0;
|
new_rnd.rnd := new_rnd.rnd / 65536.0;
|
new_rnd.rnd := new_rnd.rnd / 65536.0;
|
return (new_rnd);
|
return (new_rnd);
|
end rng;
|
end rng;
|
|
|
-- rand function generates a random variable with different distributions
|
-- rand function generates a random variable with different distributions
|
function rand (rnd : rand_var) return rand_var is
|
function rand (rnd : rand_var) return rand_var is
|
variable rnd_out : rand_var;
|
variable rnd_out : rand_var;
|
variable x, y, z : real;
|
variable x, y, z : real;
|
variable t : real := 0.0;
|
variable t : real := 0.0;
|
begin
|
begin
|
case rnd.dist is
|
case rnd.dist is
|
-- Uniform distribution
|
-- Uniform distribution
|
when UNIFORM =>
|
when UNIFORM =>
|
rnd_out := rng(rnd);
|
rnd_out := rng(rnd);
|
rnd_out.rnd := rnd.y + (rnd_out.rnd * (rnd.z - rnd.y));
|
rnd_out.rnd := rnd.y + (rnd_out.rnd * (rnd.z - rnd.y));
|
-- Gaussian distribution
|
-- Gaussian distribution
|
when GAUSSIAN => -- Box-Mueller method
|
when GAUSSIAN => -- Box-Mueller method
|
z := 2.0;
|
z := 2.0;
|
rnd_out := rnd;
|
rnd_out := rnd;
|
while z > 1.0 or z = 0.0 loop
|
while z > 1.0 or z = 0.0 loop
|
-- choose x,y in uniform square (-1,-1) to (+1,+1)
|
-- choose x,y in uniform square (-1,-1) to (+1,+1)
|
rnd_out := rng(rnd_out);
|
rnd_out := rng(rnd_out);
|
x := -1.0 + 2.0 * rnd_out.rnd;
|
x := -1.0 + 2.0 * rnd_out.rnd;
|
rnd_out := rng(rnd_out);
|
rnd_out := rng(rnd_out);
|
y := -1.0 + 2.0 * rnd_out.rnd;
|
y := -1.0 + 2.0 * rnd_out.rnd;
|
z := (x * x) + (y * y);
|
z := (x * x) + (y * y);
|
end loop;
|
end loop;
|
-- Box-Mueller transform
|
-- Box-Mueller transform
|
rnd_out.rnd := rnd_out.y + rnd_out.z * y * sqrt(-2.0 * log(z)/z);
|
rnd_out.rnd := rnd_out.y + rnd_out.z * y * sqrt(-2.0 * ln(z)/z);
|
-- Exponential distribution
|
-- Exponential distribution
|
when EXPONENTIAL =>
|
when EXPONENTIAL =>
|
rnd_out := rng(rnd);
|
rnd_out := rng(rnd);
|
rnd_out.rnd := -rnd_out.y * log(1.0 - rnd_out.rnd);
|
rnd_out.rnd := -rnd_out.y * log(1.0 - rnd_out.rnd);
|
when others =>
|
when others =>
|
report "rand() function encountered an error!"
|
report "rand() function encountered an error!"
|
severity failure;
|
severity failure;
|
end case;
|
end case;
|
return (rnd_out);
|
return (rnd_out);
|
end rand;
|
end rand;
|
|
|
-- Initialize seeds, used by all init_ functions
|
-- Initialize seeds, used by all init_ functions
|
function gen_seed (constant a, b, c : natural) return rand_var is
|
function gen_seed (constant a, b, c : natural) return rand_var is
|
variable seeded : rand_var;
|
variable seeded : rand_var;
|
variable x : unsigned(31 downto 0) := "11111111111111111111111111111111";
|
variable x : unsigned(31 downto 0) := "11111111111111111111111111111111";
|
constant k1 : natural := 31;
|
constant k1 : natural := 31;
|
constant k2 : natural := 29;
|
constant k2 : natural := 29;
|
constant k3 : natural := 28;
|
constant k3 : natural := 28;
|
begin
|
begin
|
seeded.shft1 := k1-p1;
|
seeded.shft1 := k1-p1;
|
seeded.shft2 := k2-p2;
|
seeded.shft2 := k2-p2;
|
seeded.shft3 := k3-p3;
|
seeded.shft3 := k3-p3;
|
seeded.mask1 := x sll (32-k1);
|
seeded.mask1 := x sll (32-k1);
|
seeded.mask2 := x sll (32-k2);
|
seeded.mask2 := x sll (32-k2);
|
seeded.mask3 := x sll (32-k3);
|
seeded.mask3 := x sll (32-k3);
|
seeded.s1 := to_unsigned(390451501, 32);
|
seeded.s1 := to_unsigned(390451501, 32);
|
seeded.s2 := to_unsigned(613566701, 32);
|
seeded.s2 := to_unsigned(613566701, 32);
|
seeded.s3 := to_unsigned(858993401, 32);
|
seeded.s3 := to_unsigned(858993401, 32);
|
if to_unsigned(a, 32) > (to_unsigned(1, 32) sll (32-k1)) then
|
if to_unsigned(a, 32) > (to_unsigned(1, 32) sll (32-k1)) then
|
seeded.s1 := to_unsigned(a, 32);
|
seeded.s1 := to_unsigned(a, 32);
|
end if;
|
end if;
|
if to_unsigned(b, 32) > (to_unsigned(1, 32) sll (32-k2)) then
|
if to_unsigned(b, 32) > (to_unsigned(1, 32) sll (32-k2)) then
|
seeded.s2 := to_unsigned(b, 32);
|
seeded.s2 := to_unsigned(b, 32);
|
end if;
|
end if;
|
if to_unsigned(c, 32) > (to_unsigned(1, 32) sll (32-k3)) then
|
if to_unsigned(c, 32) > (to_unsigned(1, 32) sll (32-k3)) then
|
seeded.s3 := to_unsigned(c, 32);
|
seeded.s3 := to_unsigned(c, 32);
|
end if;
|
end if;
|
return(seeded);
|
return(seeded);
|
end gen_seed;
|
end gen_seed;
|
|
|
-- Uniform distribution random variable initialization
|
-- Uniform distribution random variable initialization
|
-- a,b,c are seeds
|
-- a,b,c are seeds
|
-- lo,hi is the range for the uniform distribution
|
-- lo,hi is the range for the uniform distribution
|
function init_uniform(constant a, b, c : natural;
|
function init_uniform(constant a, b, c : natural;
|
constant lo, hi : real) return rand_var is
|
constant lo, hi : real) return rand_var is
|
variable rnd, rout : rand_var;
|
variable rnd, rout : rand_var;
|
begin
|
begin
|
if lo >= hi then
|
if lo >= hi then
|
report "Uniform parameter error: 'hi' must be > 'lo'!"
|
report "Uniform parameter error: 'hi' must be > 'lo'!"
|
severity failure;
|
severity failure;
|
end if;
|
end if;
|
rnd := gen_seed(a, b, c);
|
rnd := gen_seed(a, b, c);
|
rnd.dist := UNIFORM;
|
rnd.dist := UNIFORM;
|
rnd.y := lo;
|
rnd.y := lo;
|
rnd.z := hi;
|
rnd.z := hi;
|
rout := rand(rnd);
|
rout := rand(rnd);
|
return(rout);
|
return(rout);
|
end init_uniform;
|
end init_uniform;
|
|
|
-- Gaussian distribution random variable initialization
|
-- Gaussian distribution random variable initialization
|
-- a,b,c are seeds
|
-- a,b,c are seeds
|
-- mean,stdev is mean and standard deviation
|
-- mean,stdev is mean and standard deviation
|
function init_gaussian(constant a, b, c : natural;
|
function init_gaussian(constant a, b, c : natural;
|
constant mean, stdev : real) return rand_var is
|
constant mean, stdev : real) return rand_var is
|
variable rnd, rout : rand_var;
|
variable rnd, rout : rand_var;
|
begin
|
begin
|
if stdev = 0.0 then
|
if stdev = 0.0 then
|
report "Gaussian parameter error: 'stdev' must be non-zero!"
|
report "Gaussian parameter error: 'stdev' must be non-zero!"
|
severity failure;
|
severity failure;
|
end if;
|
end if;
|
rnd := gen_seed(a, b, c);
|
rnd := gen_seed(a, b, c);
|
rnd.dist := GAUSSIAN;
|
rnd.dist := GAUSSIAN;
|
rnd.y := mean;
|
rnd.y := mean;
|
rnd.z := stdev;
|
rnd.z := stdev;
|
rout := rand(rnd);
|
rout := rand(rnd);
|
return(rout);
|
return(rout);
|
end init_gaussian;
|
end init_gaussian;
|
|
|
-- Exponential distribution random variable initialization
|
-- Exponential distribution random variable initialization
|
-- a,b,c are seeds
|
-- a,b,c are seeds
|
-- mean: mean value
|
-- mean: mean value
|
function init_exponential(constant a, b, c : natural;
|
function init_exponential(constant a, b, c : natural;
|
constant mean : real) return rand_var is
|
constant mean : real) return rand_var is
|
variable rnd, rout : rand_var;
|
variable rnd, rout : rand_var;
|
begin
|
begin
|
if mean <= 0.0 then
|
if mean <= 0.0 then
|
report "Exponential parameter error: 'mean' must be > 0!"
|
report "Exponential parameter error: 'mean' must be > 0!"
|
severity failure;
|
severity failure;
|
end if;
|
end if;
|
rnd := gen_seed(a, b, c);
|
rnd := gen_seed(a, b, c);
|
rnd.dist := EXPONENTIAL;
|
rnd.dist := EXPONENTIAL;
|
rnd.y := mean;
|
rnd.y := mean;
|
rout := rand(rnd);
|
rout := rand(rnd);
|
return(rout);
|
return(rout);
|
end init_exponential;
|
end init_exponential;
|
|
|
end rng_lib;
|
end rng_lib;
|
|
|