Double values - what precision do I use for fprintf?

Double values - what precision do I use for fprintf?

[Shriramana Sharma]

Please observe the following printf output of eighteen double variables:

First I tried using "%20.15f" as the format string:

 268.229220252114942    1.018511211250181
  66.833038547989787   12.450505533056681
  20.512170161382819    0.334923179252419
 259.358845955701327    1.571934717666495
 201.111247720862963    0.139476171219810
 270.658029698352152   -0.612280599380678
 105.175902698424665   -0.076345132989225
 343.809699615507384   -0.219206370786681

Then I used "%30.25f":

 268.2297152740335377529845573    1.0185111507334088098986058
  66.8390907719954157073516399   12.4504269834231084956854829
  20.5123328842112115921736404    0.3349264346316725426966343
 259.3596100022817267927166540    1.5719383906021777708161835
 201.1113154335791932680876926    0.1394751696317115263745734
 270.6577319741974747557833325   -0.6122834912138217511312632
 105.1758654981413201312534511   -0.0763454696609412730712307
 343.8095929658045974974811543   -0.2192182978826520134418843

Ignoring the small differences in the two sets of data (longitude and speed of 
eight celestial bodies computer at two different instants) I wonder - if I 
keep increasing the number of decimal places where will it end?

-- 

Shriramana Sharma  http://samvit.org
Running SUSE Linux 10.0 with KDE 3.5

-- 

Penguin #395953 resides at http://samvit.org
subsisting on SUSE Linux 10.0 with KDE 3.5

Re: Double values - what precision do I use for fprintf?

[Patrick Leslie Polzer]

[-- Attachment #1: Type: text/plain, Size: 631 bytes --]


On Thu, 12 Jan 2006 18:00:19 +0530
Shriramana Sharma <Shriramana Sharma <samjnaa@gmail.com>> wrote:

 | First I tried using "%20.15f" as the format string:
 |
 | [...]
 | 
 | Then I used "%30.25f":
 |
 | [...] 
 | 
 | Ignoring the small differences in the two sets of data (longitude and speed
 | of eight celestial bodies computer at two different instants) I wonder - if
I | keep increasing the number of decimal places where will it end?
At some point you will get only zeroes.  This point is reached when the mantissa
length is exceeded.

Leslie


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Re: Double values - what precision do I use for fprintf?

[Steve Graegert]

On 1/12/06, Shriramana Sharma <samjnaa@gmail.com> wrote:
> Please observe the following printf output of eighteen double variables:
>
> First I tried using "%20.15f" as the format string:
>
>  268.229220252114942    1.018511211250181
>  66.833038547989787   12.450505533056681
>  20.512170161382819    0.334923179252419
>  259.358845955701327    1.571934717666495
>  201.111247720862963    0.139476171219810
>  270.658029698352152   -0.612280599380678
>  105.175902698424665   -0.076345132989225
>  343.809699615507384   -0.219206370786681
>
> Then I used "%30.25f":
>
>  268.2297152740335377529845573    1.0185111507334088098986058
>  66.8390907719954157073516399   12.4504269834231084956854829
>  20.5123328842112115921736404    0.3349264346316725426966343
>  259.3596100022817267927166540    1.5719383906021777708161835
>  201.1113154335791932680876926    0.1394751696317115263745734
>  270.6577319741974747557833325   -0.6122834912138217511312632
>  105.1758654981413201312534511   -0.0763454696609412730712307
>  343.8095929658045974974811543   -0.2192182978826520134418843
>
> Ignoring the small differences in the two sets of data (longitude and speed of
> eight celestial bodies computer at two different instants) I wonder - if I
> keep increasing the number of decimal places where will it end?

Shriramana,

Double precision numbering format is standardized by IEEE 754 with an
8 byte encoding.  1 bit is used for the sign, 11 bits for the exponent
and the remaining 52 bits are used for the precision, which means
precision "ends" at %.52f.

	\Steve

--

Steve Graegert <graegerts@gmail.com>
Software Consultant {C/C++ && Java && .NET}
Office: +49 9131 7123988
Mobile: +49 1520 9289212

Re: Double values - what precision do I use for fprintf?

[Nate Jenkins]

>> Please observe the following printf output of eighteen double variables:
>>
>> First I tried using "%20.15f" as the format string:
>>
>>  268.229220252114942    1.018511211250181
>>  66.833038547989787   12.450505533056681
>>  20.512170161382819    0.334923179252419
>>  259.358845955701327    1.571934717666495
>>  201.111247720862963    0.139476171219810
>>  270.658029698352152   -0.612280599380678
>>  105.175902698424665   -0.076345132989225
>>  343.809699615507384   -0.219206370786681
>>
>> Then I used "%30.25f":
>>
>>  268.2297152740335377529845573    1.0185111507334088098986058
>>  66.8390907719954157073516399   12.4504269834231084956854829
>>  20.5123328842112115921736404    0.3349264346316725426966343
>>  259.3596100022817267927166540    1.5719383906021777708161835
>>  201.1113154335791932680876926    0.1394751696317115263745734
>>  270.6577319741974747557833325   -0.6122834912138217511312632
>>  105.1758654981413201312534511   -0.0763454696609412730712307
>>  343.8095929658045974974811543   -0.2192182978826520134418843
>>
>> Ignoring the small differences in the two sets of data (longitude and 
>> speed of
>> eight celestial bodies computer at two different instants) I wonder - if 
>> I
>> keep increasing the number of decimal places where will it end?
>
> Shriramana,
>
> Double precision numbering format is standardized by IEEE 754 with an
> 8 byte encoding.  1 bit is used for the sign, 11 bits for the exponent
> and the remaining 52 bits are used for the precision, which means
> precision "ends" at %.52f.
>
> \Steve
>

If it is a 64-bit-floating-point data type, then isn't one supposed to use 
the "long" modifier, i.e. "%.52f" -> "%.52lf"?  Or is that not portable?

I am not concerned so much about being portable.  However, I have always 
followed the idea that "%f" is for 4 Byte floats and "%lf" is for 8 Byte 
floats or doubles...

Is that compiler specific or ????

~ Nate


"Do or do not or delegate to somebody else.  There is no try."

Re: Double values - what precision do I use for fprintf?

[Scott]

On Thu, Jan 12, 2006 at 07:51:08PM +0100, Steve Graegert wrote:
> 
> Double precision numbering format is standardized by IEEE 754 with an
> 8 byte encoding.  1 bit is used for the sign, 11 bits for the exponent
> and the remaining 52 bits are used for the precision, which means
> precision "ends" at %.52f.
> 
> 	\Steve
> 
> Steve Graegert <graegerts@gmail.com>

Ummm, I'm no expert and in fact completely out of my element here, but
how would 52 bits yield 52 decimal numerals following the decimal
point? Wouldn't it be true that 52 bits could represent at most an
integer of 2^52 (4503599627370496)? So I am at a loss as to how such a
format could accurately represent more than 16 significant decimal
digits....

Scott Swanson

Re: Double values - what precision do I use for fprintf?

[Mihai Dontu]

Nate Jenkins wrote:
>>> Please observe the following printf output of eighteen double variables:
>>>
>>> First I tried using "%20.15f" as the format string:
>>>
>>>  268.229220252114942    1.018511211250181
>>>  66.833038547989787   12.450505533056681
>>>  20.512170161382819    0.334923179252419
>>>  259.358845955701327    1.571934717666495
>>>  201.111247720862963    0.139476171219810
>>>  270.658029698352152   -0.612280599380678
>>>  105.175902698424665   -0.076345132989225
>>>  343.809699615507384   -0.219206370786681
>>>
>>> Then I used "%30.25f":
>>>
>>>  268.2297152740335377529845573    1.0185111507334088098986058
>>>  66.8390907719954157073516399   12.4504269834231084956854829
>>>  20.5123328842112115921736404    0.3349264346316725426966343
>>>  259.3596100022817267927166540    1.5719383906021777708161835
>>>  201.1113154335791932680876926    0.1394751696317115263745734
>>>  270.6577319741974747557833325   -0.6122834912138217511312632
>>>  105.1758654981413201312534511   -0.0763454696609412730712307
>>>  343.8095929658045974974811543   -0.2192182978826520134418843
>>>
>>> Ignoring the small differences in the two sets of data (longitude and 
>>> speed of
>>> eight celestial bodies computer at two different instants) I wonder - 
>>> if I
>>> keep increasing the number of decimal places where will it end?
>>
>>
>> Shriramana,
>>
>> Double precision numbering format is standardized by IEEE 754 with an
>> 8 byte encoding.  1 bit is used for the sign, 11 bits for the exponent
>> and the remaining 52 bits are used for the precision, which means
>> precision "ends" at %.52f.
>>
>> \Steve
>>
> 
> If it is a 64-bit-floating-point data type, then isn't one supposed to 
> use the "long" modifier, i.e. "%.52f" -> "%.52lf"?  Or is that not 
> portable?
> 
> I am not concerned so much about being portable.  However, I have always 
> followed the idea that "%f" is for 4 Byte floats and "%lf" is for 8 Byte 
> floats or doubles...
> 
> Is that compiler specific or ????
> 
> ~ Nate
> 
> 
> "Do or do not or delegate to somebody else.  There is no try."
> 
> 
> -
> To unsubscribe from this list: send the line "unsubscribe 
> linux-c-programming" in
> the body of a message to majordomo@vger.kernel.org
> More majordomo info at  http://vger.kernel.org/majordomo-info.html
> 
>
According to man 3 printf, we have:
"
l      (ell) A following integer conversion corresponds to a long int or unsigned long int argument, or a following  n
        conversion corresponds to a pointer to a long int argument, or a following c conversion corresponds to a wint_t
        argument, or a following s conversion corresponds to a pointer to wchar_t argument.

ll     (ell-ell).  A following integer conversion corresponds to a long long int or unsigned long long  int  argument,
        or a following n conversion corresponds to a pointer to a long long int argument.
"
But there are OS-es that do not recognize the ll.
Today I had a small problem displaying the fields of a "struct stat" variable. It was all messed up, until
i saw that dev_t is declared as "unsigned long long". So I did
printf( "%llu %u %u %u", st.st_dev, st.st_inode, st.st_size, st.st_atime );

M.D.


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Re: Double values - what precision do I use for fprintf?

[Scott]

On Thu, Jan 12, 2006 at 02:57:29PM -0700, Scott wrote:
> On Thu, Jan 12, 2006 at 07:51:08PM +0100, Steve Graegert wrote:
> > 
> > Double precision numbering format is standardized by IEEE 754 with an
> > 8 byte encoding.  1 bit is used for the sign, 11 bits for the exponent
> > and the remaining 52 bits are used for the precision, which means
> > precision "ends" at %.52f.
> > 
> > 	\Steve
> > 
> > Steve Graegert <graegerts@gmail.com>
> 
> Ummm, I'm no expert and in fact completely out of my element here, but
> how would 52 bits yield 52 decimal numerals following the decimal
> point? Wouldn't it be true that 52 bits could represent at most an
> integer of 2^52 (4503599627370496)? So I am at a loss as to how such a
> format could accurately represent more than 16 significant decimal
> digits....

As usual, brain engages immediately *after* pressing 'send'. Wouldn't
it be more accurate to say that the format can represent:

(2^52)*(2^11) =
323170060713110073007148766886699519604441026697154840321303454275246\
551388678908931972014115229134636887179609218980194941195591504909210\
950881523864482831206308773673009960917501977503896521067960576383840\
675682767922186426197561618380943384761704705816458520363050428875758\
915410658086075523991239303855219143333896683424206849747865645694948\
561760353263220580778056593310261927084603141502585928641771167259436\
037184618573575983511523016459044036976132332872312271256847108202097\
251571017269313234696785425806566979350459972683529986382155251663894\
37335543602135433229604645318478604952148193555853611059596230656

Which is just slightly more than 52 decimal places....

Or am I way off base here...?

Scott Swanson

Re: Double values - what precision do I use for fprintf?

[Steve Graegert]

On 1/12/06, Scott <drmemory@3rivers.net> wrote:
> On Thu, Jan 12, 2006 at 07:51:08PM +0100, Steve Graegert wrote:
> >
> > Double precision numbering format is standardized by IEEE 754 with an
> > 8 byte encoding.  1 bit is used for the sign, 11 bits for the exponent
> > and the remaining 52 bits are used for the precision, which means
> > precision "ends" at %.52f.
> >
> >       \Steve
> >
> > Steve Graegert <graegerts@gmail.com>
>
> Ummm, I'm no expert and in fact completely out of my element here, but
> how would 52 bits yield 52 decimal numerals following the decimal
> point? Wouldn't it be true that 52 bits could represent at most an
> integer of 2^52 (4503599627370496)? So I am at a loss as to how such a
> format could accurately represent more than 16 significant decimal
> digits....

You're perfectly right, but that's not what I meant.  I just jumped on
the printf analogy to make clear that it does not _print_ any numbers
(except zero) beyond %.52f.  From this POV printf precision "ends"
there, although we know that such numbers are not accurately displayed
beyond 16 significant digits.

	\Steve

--

Steve Graegert <graegerts@gmail.com>
Software Consultant {C/C++ && Java && .NET}
Office: +49 9131 7123988
Mobile: +49 1520 9289212

Re: Double values - what precision do I use for fprintf?

[Glynn Clements]

Nate Jenkins wrote:

> If it is a 64-bit-floating-point data type, then isn't one supposed to use 
> the "long" modifier, i.e. "%.52f" -> "%.52lf"?  Or is that not portable?

You cannot pass a float to printf(); a float will automatically be cast to
double.

More generally, a float argument will be cast to double if the
function doesn't have a prototype, or if the prototype doesn't specify
a type for the argument (i.e. for a variadic function). Similarly,
char and short values are automatically converted to int in such
circumstances.

-- 
Glynn Clements <glynn@gclements.plus.com>

Re: Double values - what precision do I use for fprintf?

[Nate Jenkins]

>
> Nate Jenkins wrote:
>
>> If it is a 64-bit-floating-point data type, then isn't one supposed to 
>> use
>> the "long" modifier, i.e. "%.52f" -> "%.52lf"?  Or is that not portable?
>
> You cannot pass a float to printf(); a float will automatically be cast to
> double.
>
> More generally, a float argument will be cast to double if the
> function doesn't have a prototype, or if the prototype doesn't specify
> a type for the argument (i.e. for a variadic function). Similarly,
> char and short values are automatically converted to int in such
> circumstances.
>
> -- 
> Glynn Clements <glynn@gclements.plus.com>
>

So for a short example:
(this should compile but with a few casting warnings)

<.......code.......>

float fNum = 3.1415926535897932384626433832795; // will get truncated
double dNum = fNum; // will get some extra garbage trailing
char cNum = '*'; // 42 in ASCII
short sNum = cNum;
int nNum = cNum;


//////////// floating point number types ////////////

printf("%f \n", fNum);
// IIRC,  7 digits --> "3.141593

printf("%f \n", dNum);
// IIRC, 15 digits --> "3.14159200000261"
// or something like that due to extra garbage
// trailing without formatting?

printf("%lf \n", dNum);
// same --> "3.14159200000261"  Should not work but it does?


//////////// integer number types ////////////

printf("%c \n", cNum);
printf("%c \n", (char)(sNum));
printf("%c \n", (char)(nNum));
// so all of these would show --> "*" ?

printf("%hi \n", cNum);
printf("%hi \n", sNum);
printf("%hi \n", (short)(nNum));
// so all of these would show --> "42" ?

printf("%d \n", cNum);
printf("%d \n", sNum);
printf("%d \n", nNum);
// so all of these would show --> "42" ?

<......./code.......>



Are my comment assumptions wrong?  I have been using "%lf" for years... 
Could the old compiler I use be made to consider "%lf" the same as "%f" ?

Nate

Re: Double values - what precision do I use for fprintf?

[Glynn Clements]

Nate Jenkins wrote:

> >> If it is a 64-bit-floating-point data type, then isn't one supposed to 
> >> use
> >> the "long" modifier, i.e. "%.52f" -> "%.52lf"?  Or is that not portable?
> >
> > You cannot pass a float to printf(); a float will automatically be cast to
> > double.
> >
> > More generally, a float argument will be cast to double if the
> > function doesn't have a prototype, or if the prototype doesn't specify
> > a type for the argument (i.e. for a variadic function). Similarly,
> > char and short values are automatically converted to int in such
> > circumstances.
> 
> So for a short example:
> (this should compile but with a few casting warnings)

Regarding the lack of trailing garbage: the default precision for "%f"
is 6 decimal places, i.e. "%.6f". If you use e.g. "%.50f", you will
get:

	3.14159274101257324218750000000000000000000000000000 

in all three cases. Everything after the 6th decimal place is garbage
due to the value having been truncated to float precision in the first
place. It doesn't matter whether the conversion from float to double
is done by copying fNum to dNum or by passing fNum to printf().

> Are my comment assumptions wrong?  I have been using "%lf" for years... 
> Could the old compiler I use be made to consider "%lf" the same as "%f" ?

Technically, "%lf" is undefined for printf() etc (although it is
meaningful for sscanf() etc). In practice, most implementations simply
ignore the "l", so "%lf" and "%f" are equivalent.

-- 
Glynn Clements <glynn@gclements.plus.com>