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From: jichao ? on 12 May 2010 03:07
The probability space is
char prob range
a1 0.001838 [0.998162, 1.0)
a2 0.0975 [0.023162, 0.998162)
a3 0.023162 [0.0, 0.023162)
What I want is the arithmetic code for seq. a2a2a1a3a3.Here is my code to do so,

global low high lowRange highRange
lowRange = [0.998162, 0.023162, 0];
highRange = [1, 0.998162, 0.023162];
low = 0; high = 1;
arithenc(2)
arithenc(2)
arithenc(1)
arithenc(3)
arithenc(3)

function [] =arithenc(i)
global high low lowRange highRange
format long
range = high - low;
nhigh = low + range * highRange(i);
nlow = low + range * lowRange(i);
low = nlow;
high = nhigh;
fprintf('r = %.20f l = %.17f h = %.17f\n', range, low, high);

The result is:
r = 1.00000000000000000000 l = 0.02316200000000000 h = 0.99816199999999999
r = 0.97499999999999998000 l = 0.04574494999999999 h = 0.99636994999999995
r = 0.95062499999999994000 l = 0.99462270124999996 h = 0.99636994999999995
r = 0.00174724874999998560 l = 0.99462270124999996 h = 0.99466317102554747
r = 0.00004046977554750253 l = 0.99462270124999996 h = 0.99462363861094116

But the result like 0.99816199999999999 should be 0.9981612.However,if I do not specify the digits needed after the dot, I would lose some digits.

Could you help me out? Thanks.

PS:The sample data and code derviated directly from Data Compression: The Complete Reference.

jichao.
From: us on 12 May 2010 03:55
"jichao ?"
> fprintf('r = %.20f l = %.17f h = %.17f\n', range, low, high);
>
> The result is:
> r = 1.00000000000000000000 l = 0.02316200000000000 h = 0.99816199999999999
> But the result like 0.99816199999999999 should be 0.9981612.However,if I do not specify the digits needed after the dot, I would lose some digits.
> Could you help me out? Thanks.

well... a FP evergreen...

http://matlabwiki.mathworks.com/MATLAB_FAQ#Why_is_0.3-0.2-0.1_not_equal_to_zero_.28or_similar.29.3F

us
From: jichao ? on 12 May 2010 04:08
"us " <us(a)neurol.unizh.ch> wrote in message <hsdmsq$g3$1(a)fred.mathworks.com>...
> "jichao ?"
> > fprintf('r = %.20f l = %.17f h = %.17f\n', range, low, high);
> >
> > The result is:
> > r = 1.00000000000000000000 l = 0.02316200000000000 h = 0.99816199999999999
> > But the result like 0.99816199999999999 should be 0.9981612.However,if I do not specify the digits needed after the dot, I would lose some digits.
> > Could you help me out? Thanks.
>
> well... a FP evergreen...
>
> http://matlabwiki.mathworks.com/MATLAB_FAQ#Why_is_0.3-0.2-0.1_not_equal_to_zero_.28or_similar.29.3F
>
> us
Thanks.
So do you mean there is no way to get the natural result 0.9981612, and we have to get the natural result by our eyes?

jichao
From: us on 12 May 2010 04:16
"jichao ?" <jcyangzh(a)gmail.com> wrote in message <hsdnl3$iv8$1(a)fred.mathworks.com>...
> "us " <us(a)neurol.unizh.ch> wrote in message <hsdmsq$g3$1(a)fred.mathworks.com>...
> > "jichao ?"
> > > fprintf('r = %.20f l = %.17f h = %.17f\n', range, low, high);
> > >
> > > The result is:
> > > r = 1.00000000000000000000 l = 0.02316200000000000 h = 0.99816199999999999
> > > But the result like 0.99816199999999999 should be 0.9981612.However,if I do not specify the digits needed after the dot, I would lose some digits.
> > > Could you help me out? Thanks.
> >
> > well... a FP evergreen...
> >
> > http://matlabwiki.mathworks.com/MATLAB_FAQ#Why_is_0.3-0.2-0.1_not_equal_to_zero_.28or_similar.29.3F
> >
> > us
> Thanks.
> So do you mean there is no way to get the natural result 0.9981612, and we have to get the natural result by our eyes?
>
> jichao

yes... unless, of course, you come up with your own FPU and FP representation scheme, which would allow you to precisely binarize your particular number...
be aware, though, there will always be another CSSMer, whose pet-number will get lost...

us
From: Steven Lord on 12 May 2010 09:46

"jichao ?" <jcyangzh(a)gmail.com> wrote in message
news:hsdnl3$iv8$1(a)fred.mathworks.com...
> "us " <us(a)neurol.unizh.ch> wrote in message
> <hsdmsq$g3$1(a)fred.mathworks.com>...
>> "jichao ?"
>> > fprintf('r = %.20f l = %.17f h = %.17f\n', range, low, high);
>> >
>> > The result is:
>> > r = 1.00000000000000000000 l = 0.02316200000000000 h =
>> > 0.99816199999999999
>> > But the result like 0.99816199999999999 should be 0.9981612.However,if
>> > I do not specify the digits needed after the dot, I would lose some
>> > digits.
>> > Could you help me out? Thanks.
>>
>> well... a FP evergreen...
>>
>> http://matlabwiki.mathworks.com/MATLAB_FAQ#Why_is_0.3-0.2-0.1_not_equal_to_zero_.28or_similar.29.3F
>>
>> us
> Thanks.
> So do you mean there is no way to get the natural result 0.9981612, and we
> have to get the natural result by our eyes?

Why do you believe that exactly 9981612 ten-millionths is the "natural
result"? How do you know that wherever you obtained your "probability
space" data didn't simply round the data off to an appropriate number of
decimal places, and that the "natural result" shouldn't be exactly
0.99816119999996667987568947284623784627351786157385678326? Or 0.998161 +
(pi-1)/1e7? Either of those would round to 0.9981612.

Binary computers storing numbers in IEEE double precision can only store a
small subset of numbers exactly -- the vast majority of numbers are
approximated, as described in the FAQ entry to which us pointed you.
Roundoff is a fact of life; you need to be aware that it can pop up at the
most inconvenient times, and prepare your code and/or your expectations for
it.

--
Steve Lord
slord(a)mathworks.com
comp.soft-sys.matlab (CSSM) FAQ: http://matlabwiki.mathworks.com/MATLAB_FAQ


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