|Re: [hatari-devel] Use correct white noise|
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On Thursday 30 August 2012 12:02, Nicolas Pomarède wrote:
> Le 14/07/2012 22:01, David Savinkoff a crit :
> > Hi,
> > This patch uses the correct LFSR for the YM2149. The previous must
> > have had a typo. currentNoise ^=YM2149_RndCompute() is corrected.
> > BTW the noise doesn't sound different.
> > The code is also optimized in Galois form.
> > see: (also note 17 stage table at end)
> > http://www.newwaveinstruments.com/resources/articles/m_sequence_linear_fe
> > David
> sorry for the late reply, been quite busy lately. I will modifiy Hatari
> with your patch as soon as I can (I have some changes to finish/push
> Regarding the fact that it doesn't really change the perceived result, I
> also noticed that some times ago while trying different random methods
> (the one you sent is similar to the one used in MAME for example). Even
> using the rand() function gives similar result.
> In the end as this is white noise, the only thing that really matters is
> the period in reg6 and the frequency at which we compute a new value ;
> as long as the pseudo-random function is close enough to randomness,
> result is not really discernible.
I saw your message about 20 minutes after you posted it, but
couldn't reply because talking is more natural than typing.
Sometimes I can have a conversation, but all that I can type
is an ACK (acknowledge). :)
I did some research and found:
Only one reference to the pseudo-random noise in the YM2149.
Someone associated with MAME originally claimed the LFSR is
17 bits with taps at bits 17 and 15... MAME was later changed
to a LFSR with taps at bits 17 and 14. I found an open source
VHDL project that uses taps at bits 17 and 15 (so does Hatari),
the VHDL code should be Corrected And Optimized. See
No data or proof exists that the YM2149 is even a 17 bit LFSR.
If the YM2149 is a 17 bit LFSR, it probably has taps at bits
17 and 14 because this was a popular LFSR from the 1970's
(National Semiconductor MM5837 / AMI S2688).
*taps at bits 17 and 15 are '6-sigma erroneous', which exceeds
the 2^17 possible possibilities. ;)
Synthesizer musicians of 70's and 80's did not like the sound
of this digital noise source and preferred an analog noise
It is possible to determine the LFSR in the YM2149.
One must make a good recording of YM2149 white noise as
a mono .WAV file (data).
Then one must determine 1's and 0's by inspection, and type
at least twice as many bits as the length of the LFSR into
the python code below (34 minimum for 17 bit LFSR - try 64 bits).
I modified the code by adding data comments at the end.
*** Open Challenge:
Determine the Characteristic Polynomial and provide your data,
method and apparatus.
The answer is Not at the back of the book, so you will have to
try several different data strings to be certain of your answer.
If this experiment is independently verified by a few different
sources, it can be made official by consensus.
Note that a 17 bit LFSR with taps at 17 and 14 will have the
characteristic polynomial (x^17 + x^3 + 1).
x^17 + x^3 + 1 = x^17 + x^3 + x^0
tap at 17-0 = 17
tap at 17-3 = 14
**** Python Code ****
Copyright (C) 2012 Bo Zhu http://about.bozhu.me
Permission is hereby granted, free of charge, to any person obtaining a
copy of this software and associated documentation files (the "Software"),
to deal in the Software without restriction, including without limitation
the rights to use, copy, modify, merge, publish, distribute, sublicense,
and/or sell copies of the Software, and to permit persons to whom the
Software is furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
DEALINGS IN THE SOFTWARE.
N = len(sequence)
s = sequence[:]
for k in range(N):
if s[k] == 1:
f = set([k + 1, 0]) # use a set to denote polynomial
l = k + 1
g = set()
a = k
b = 0
for n in range(k + 1, N):
d = 0
for ele in f:
d ^= s[ele + n - l]
if d == 0:
b += 1
if 2 * l > n:
f ^= set([a - b + ele for ele in g])
b += 1
temp = f.copy()
f = set([b - a + ele for ele in f]) ^ g
l = n + 1 - l
g = temp
a = b
b = n - l + 1
# output the polynomial
result = ''
lis = sorted(polynomial, reverse=True)
for i in lis:
if i == 0:
result += '1'
result += 'x^%s' % str(i)
if i != lis[-1]:
result += ' + '
return (print_poly(f), l)
if __name__ == '__main__':
seq = (0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0)
# seq = (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1)
# seq = (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1)
(poly, span) = Berlekamp_Massey_algorithm(seq)
print 'The input sequence is %s.' % str(seq)
print 'Its characteristic polynomial is (%s),' % poly,
print 'and linear span is %d.' % span