How to detect a double's significant digits

[mrstephengross]

Hi all... How can I find out the number of significant digits (to the
right of the decimal place, that is) in a double? At least, I *think*
that's what I'm asking for. For instance:

0.103 --> 3
0.0103 --> 4
0.00103 --> 5
0.000103 --> 6
0.0000103 --> 7

Thanks in advance!
--Steve (mrstephengross @hotmail.com)

[James Stroud]

Re: How to detect a double's significant digits

Significant digits are an accounting concept. As such, it is up to the
accountant to keep track of these as only she knows the precision of her
measurements.

Koan for the day:

What are the significant digits of 0.1?

Hint:
[color=blue][color=green][color=darkred]
>>> `0.1`[/color][/color][/color]

James


On Thursday 05 May 2005 10:37 am, so sayeth mrstephengross:[color=blue]
> Hi all... How can I find out the number of significant digits (to the
> right of the decimal place, that is) in a double? At least, I *think*
> that's what I'm asking for. For instance:
>
> 0.103 --> 3
> 0.0103 --> 4
> 0.00103 --> 5
> 0.000103 --> 6
> 0.0000103 --> 7
>
> Thanks in advance!
> --Steve (mrstephengross @hotmail.com)[/color]

--
James Stroud, Ph.D.
UCLA-DOE Institute for Genomics and Proteomics
Box 951570
Los Angeles, CA 90095

http://www.jamesstroud.com/

[mrstephengross]

Re: How to detect a double's significant digits

So how can I get the kind of information I want then?

For example:

0.103 --> 3
0.0103 --> 4
0.00103 --> 5
0.000103 --> 6
0.0000103 --> 7

Any ideas?
--Steve

[phil]

Re: How to detect a double's significant digits

fl = 1.0002
x = str(fl)
pos = x.find('.')
print len( x[pos+1:] )[color=blue][color=green][color=darkred]
>>> 4[/color][/color][/color]

mrstephengross wrote:
[color=blue]
> Hi all... How can I find out the number of significant digits (to the
> right of the decimal place, that is) in a double? At least, I *think*
> that's what I'm asking for. For instance:
>
> 0.103 --> 3
> 0.0103 --> 4
> 0.00103 --> 5
> 0.000103 --> 6
> 0.0000103 --> 7
>
> Thanks in advance!
> --Steve (mrstephengross @hotmail.com)
>
>[/color]

[mrstephengross]

Re: How to detect a double's significant digits

Ok, that won't work. First of all, str() is not a function. If I want
to convert the float into a string, the conversion function will have
to use some kind of numeric precision, which will screw things up.
Consider this:

float f = 1.004;
ostringstream s;
s << f;
cout << s.str();

The above code may produce "1.004", or "1.0040", or "1.00400",
depending on the stream's precision setting. I need a way to detect the
number of digits to the right of decimal point *prior* to doing any
kind of string conversion.

--Steve

[Steven Bethard]

Re: How to detect a double's significant digits

mrstephengross wrote:[color=blue]
> So how can I get the kind of information I want then?
>
> For example:
>
> 0.103 --> 3
> 0.0103 --> 4
> 0.00103 --> 5
> 0.000103 --> 6
> 0.0000103 --> 7[/color]

Beware that this is probably only relevant if you have your numbers as
strings, not as floats:

py> 0.103
0.1029999999999 9999

But, assuming you have your numbers as strings, I would suggest looking
at str.split() and len(). I'd give you an example, but this sounds
kinda like a homework assignment.

STeVe

[Steven Bethard]

Re: How to detect a double's significant digits

mrstephengross wrote:[color=blue]
> First of all, str() is not a function.[/color]

Yes it is.
[color=blue]
> float f = 1.004;
> ostringstream s;
> s << f;
> cout << s.str();[/color]

This doesn't look like Python to me. Are you sure you're on the right
newsgroup?

STeVe

[mrstephengross]

Re: How to detect a double's significant digits

>But, assuming you have your numbers as strings, I would suggest
looking
at str.split() and len().

Well, the numbers are in fact stored as numbers, so string processing
won't work.
[color=blue]
>I'd give you an example, but this sounds kinda like a homework[/color]
assignment.

The task may sound like it comes from class, but I can assure you that
I am indeed a professional developer. I'm doing some rather intricate
text processing / rendering stuff these days, and C++ is unfortunately
none too handy for that sort of thing. Unfortunately, I have to use it
for the task.

Thanks,
--Steve

[Steven Bethard]

Re: How to detect a double's significant digits

mrstephengross wrote:[color=blue]
> Well, the numbers are in fact stored as numbers, so string processing
> won't work.[/color]

What kind of numbers? Python floats?

STeVe

[Steven Bethard]

Re: How to detect a double's significant digits

mrstephengross wrote:[color=blue][color=green]
>>But, assuming you have your numbers as strings, I would suggest[/color]
>
> looking
> at str.split() and len().
>
> Well, the numbers are in fact stored as numbers, so string processing
> won't work.[/color]

How about:

py> def digits(f):
.... return len(str(f).spli t('.')[1].rstrip('0'))
....
py> for f in [0.103, 0.1030, 0.0103, 0.010300]:
.... print f, digits(f)
....
0.103 3
0.103 3
0.0103 4
0.0103 4

I believe the rstrip is unnecessary because I think str() will never
produce additional following zeros, but you can guarantee it by calling
rstrip if you want.

Note that, for example, 0.103 and 0.1030 are identical as far as Python
is concerned, so I hope you're not hoping to show a difference between
these two...

STeVe

[Charles Krug]

Re: How to detect a double's significant digits

On 5 May 2005 10:37:00 -0700, mrstephengross <mrstephengross @hotmail.com> wrote:[color=blue]
> Hi all... How can I find out the number of significant digits (to the
> right of the decimal place, that is) in a double? At least, I *think*
> that's what I'm asking for. For instance:
>
> 0.103 --> 3
> 0.0103 --> 4
> 0.00103 --> 5
> 0.000103 --> 6
> 0.0000103 --> 7
>
> Thanks in advance!
> --Steve (mrstephengross @hotmail.com)
>[/color]

I would say that each of these examples has three signficant figures.
Each of them can be expressed as:

1.03e+n

For any integer n.

The fact that you've only shown the cases where n \in {-1, -2, -3, -4,
-5 . . } doesn't change the generality of the answer.

[Grant Edwards]

Re: How to detect a double's significant digits

On 2005-05-05, mrstephengross <mrstephengross @hotmail.com> wrote:[color=blue][color=green]
>>But, assuming you have your numbers as strings, I would suggest[/color]
> looking
> at str.split() and len().
>
> Well, the numbers are in fact stored as numbers,[/color]

Then your question is in fact meaningless. The related
question that can be answered is "where is the least
significant '1' bit in the IEEE representation" . If that's
useful information, the struct module will help you find it.
[color=blue]
> so string processing won't work.[/color]

That's the only way to answer the question you asked.
[color=blue][color=green]
>>I'd give you an example, but this sounds kinda like a homework
>> assignment.[/color]
>
> The task may sound like it comes from class, but I can assure
> you that I am indeed a professional developer. I'm doing some
> rather intricate text processing / rendering stuff these days,
> and C++ is unfortunately none too handy for that sort of
> thing. Unfortunately, I have to use it for the task.[/color]

--
Grant Edwards grante Yow! Hmmm... A hash-singer
at and a cross-eyed guy were
visi.com SLEEPING on a deserted
island, when...

[mrstephengross]

Re: How to detect a double's significant digits

>This doesn't look like Python to me. Are you sure you're on the right
newsgroup?

Er, ok, I'm an idiot. This was all supposed to be on comp.lang.c++, but
obviously I posted on the wrong one. Sorry for all the hassle. In
python, this stuff is a heck of a lot easier.

--Steve

[phil]

Re: How to detect a double's significant digits

Bollocks, works here.

That looks like Java!!! Aaaihh!

mrstephengross wrote:
[color=blue]
> Ok, that won't work. First of all, str() is not a function. If I want
> to convert the float into a string, the conversion function will have
> to use some kind of numeric precision, which will screw things up.
> Consider this:
>
> float f = 1.004;
> ostringstream s;
> s << f;
> cout << s.str();
>
> The above code may produce "1.004", or "1.0040", or "1.00400",
> depending on the stream's precision setting. I need a way to detect the
> number of digits to the right of decimal point *prior* to doing any
> kind of string conversion.
>
> --Steve
>
>[/color]

[Peter Otten]

Re: How to detect a double's significant digits

mrstephengross wrote:
[color=blue]
> This was all supposed to be on comp.lang.c++, but[/color]

You may still want to read the following thread on Python-Dev:

http://mail.python.org/pipermail/python-dev/2004-March/043703.html

A link mentioned by Andrew Koenig may be helpful:

http://www.netlib.org/fp/

"""
file g_fmt.c
by David Gay
for ANSI C or C++ source for function g_fmt(char *, double):
, with help from dtoa, g_fmt(buf, x) sets buf to the shortest
, decimal string that correctly rounds to x and returns buf.
"""

Peter