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:
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:
>>> `0.1`
James
On Thursday 05 May 2005 10:37 am, so sayeth 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:
mrstephengross wrote: > 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:
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.
Beware that this is probably only relevant if you have your numbers as strings, not as floats:
py> 0.103 0.10299999999999999
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.
>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.
>I'd give you an example, but this sounds kinda like a homework
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.
mrstephengross wrote: >>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.
How about:
py> def digits(f): ... return len(str(f).split('.')[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...
On 5 May 2005 10:37:00 -0700, mrstephengross <mrstephengr...@hotmail.com> wrote:
> 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:
On 2005-05-05, mrstephengross <mrstephengr...@hotmail.com> wrote:
>>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,
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.
> so string processing won't work.
That's the only way to answer the question you asked.
>>I'd give you an example, but this sounds kinda like a homework >> 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.
-- Grant Edwards grante Yow! Hmmm... A hash-singer at and a cross-eyed guy were visi.com SLEEPING on a deserted island, when...
>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.
mrstephengross wrote: > 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.
""" 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. """
"mrstephengross" wrote: > >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.
if they're not strings, your question is meaningless. as others have pointed out, the exact internal representation for 0.103 is more like 0.10299999999999999433786257441170164383947849273681640625 which has a lot more than 3 digits...
> >I'd give you an example, but this sounds kinda like a homework > assignment.
> The task may sound like it comes from class, but I can assure you that > I am indeed a professional developer.
well professional or not, you clearly need to refresh your floating point skills. I suggest reading the following documents before proceeding:
On Thu, 05 May 2005 18:42:17 +0000, Charles Krug wrote: > On 5 May 2005 10:37:00 -0700, mrstephengross <mrstephengr...@hotmail.com> > wrote: >> 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:
>> Thanks in advance! >> --Steve (mrstephengr...@hotmail.com)
> 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.
You beat me to it.
Step one for mrstephengross is to *rigorously* define what he means by "significant digits", then go from there. Since I think he mentioned something about predicting how much space it will take to print out, my suggestion is to run through whatever printing routines there are and get a string out, the measure the string, as anything else will likely be wrong. If that's not possible with the formatting library, you've already lost; you'll have to completely correctly re-implement the formatting library, and not only is that a major PITA, you almost never get it bug-for-bug right...
Jeremy Bowers wrote: > Step one for mrstephengross is to *rigorously* define what he means by > "significant digits", then go from there. Since I think he mentioned > something about predicting how much space it will take to print out, my > suggestion is to run through whatever printing routines there are and get > a string out, the measure the string, as anything else will likely be > wrong. If that's not possible with the formatting library, you've already > lost; you'll have to completely correctly re-implement the formatting > library, and not only is that a major PITA, you almost never get it > bug-for-bug right...
Especially since all of his examples have the same number of significant digits (3), as the term is usually meant. Zeroes to the right are significant, not zeroes to the left.
-- Erik Max Francis && m...@alcyone.com && http://www.alcyone.com/max/ San Jose, CA, USA && 37 20 N 121 53 W && AIM erikmaxfrancis What is it that shapes a species? -- Louis Wu
On 2005-05-05, Erik Max Francis <m...@alcyone.com> wrote:
> Especially since all of his examples have the same number of > significant digits (3), as the term is usually meant. Zeroes > to the right are significant, not zeroes to the left.
And only the person who performed the measurement knows how many of the zeros to the right are significant.
-- Grant Edwards grante Yow! They don't hire at PERSONAL PINHEADS, visi.com Mr. Toad!
On 2005-05-05, Jeremy Bowers <j...@jerf.org> wrote:
> Since I think he mentioned something about predicting how much > space it will take to print out, my suggestion is to run > through whatever printing routines there are and get a string > out,
A step which will require him to tell the printing routine how many digits he wants printed.
-- Grant Edwards grante Yow! FUN is never having at to say you're SUSHI!! visi.com
On 2005-05-05, mrstephengross <mrstephengr...@hotmail.com> wrote:
>>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.
No, it isn't. The question is equally meaningless in any language.
-- Grant Edwards grante Yow! WHO sees a BEACH at BUNNY sobbing on a SHAG visi.com RUG?!
On Fri, 06 May 2005 02:44:43 +0000, Grant Edwards wrote: > On 2005-05-05, Jeremy Bowers <j...@jerf.org> wrote:
>> Since I think he mentioned something about predicting how much space it >> will take to print out, my suggestion is to run through whatever >> printing routines there are and get a string out,
> A step which will require him to tell the printing routine how many digits > he wants printed.
Not necessarily; consider the str() of a float in Python, especially given the "significant digits" aspect (it may be ill-defined, but I can think of several well-defined ways to mean that, where str() embodies one of them). The easiest way to tell how long the number will be when str prints it out is to simply ask it.
In C++, this may be harder, as your output software may insist on rendering everything directly, with no way to reach in and tell what it did. Imagine the standard IOStreams, without the ability to stream into a string. Now it's a lot harder to tell. So if you've got something "smart" like the default str() in Python, you may not be able to tell in advance what it is going to do, short of trying to manually reverse engineer it. I've tried that a few times, and in each instance, I can get 95-99%... but I never quite make it to 100%, usually because I find a bug somewhere and can't figure out how to characterize and replicate it.
(The biggest of these so far was when I tried to reconstruct Tk's wrapping in a text widget, so I could tell how many screen lines the given piece of text I produced would consume, whereupon I discovered Tk didn't correctly wrap all Unicode characters... it correctly (as far as I could see) reported their widths, but happily let the characters run right off the right edge of the widget under certain circumstances I could never characterize without putting in even more effort than I cared to. The bugs aren't always *important*, one can imagine the opposite problem of wrapping a little too quickly, and it could be years before anyone notices if it's just a few pixels off in the right direction, but it'll still screw you up if you try to replicate it.)
Jeremy Bowers wrote: > Not necessarily; consider the str() of a float in Python, especially given > the "significant digits" aspect (it may be ill-defined, but I can think of > several well-defined ways to mean that, where str() embodies one of them). > The easiest way to tell how long the number will be when str prints it out > is to simply ask it.
Grant's point was that as significance is used in scientific studies, there's no way to answer the question without having the number in advance. If I say that the length of something is 1100 m, you don't know whether I mean 1.1 x 10^3 m, 1.10 x 10^3 m, 1.100 x 10^3 m, etc. These all have different significances. The figure 1100 m can't tell you how many significance figures are involved without further information.
In particular, the example he gave involved changing significance depending on the number of zeroes _before_ the other digits, not after them, which is now how significance works. So obviously when he says "significant digits" he doesn't mean the same thing that's used by scientists, so the question can't really be answered.
If he simply wanted to get the number of digits involved, then that's fine, but that's not what significance is.
-- Erik Max Francis && m...@alcyone.com && http://www.alcyone.com/max/ San Jose, CA, USA && 37 20 N 121 53 W && AIM erikmaxfrancis Eternity is very long, especially near the end. -- Woody Allen
> > >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.
> if they're not strings, your question is meaningless. as others have > pointed out, the exact internal representation for 0.103 is more like > 0.10299999999999999433786257441170164383947849273681640625 > which has a lot more than 3 digits...
On Thu, 05 May 2005 20:08:46 -0700, Erik Max Francis wrote: > Grant's point was that as significance is used in scientific studies, > there's no way to answer the question without having the number in > advance.
My point was that the original poster never defined "significance" in that manner, and in the manner in which he seemed to be using the term, my comments made sense. Which is why the first thing I said was he needs to rigorously define what he means, and everything after that was predicated on the assumption he seemed to be looking at consumed screen space.
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