Re: floating point, how many significant figures?

From:

SG <s.gesemann@gmail.com>

Newsgroups:

comp.lang.c++.moderated

Date:

Fri, 25 Jun 2010 07:11:03 CST

Message-ID:

<383c0a12-e6f6-45c4-8291-6e669bfec4f0@r27g2000yqb.googlegroups.com>

On 25 Jun., 02:49, Andrew wrote:

[Subject: floating point, how many significant figures?]
I always thought the answer was 15, assuming IEEE (seems fairly safe
to assume that these days for all but some esoteric embedded
environments).

It may be safe to assume. Just for the record: C and C++ guarantee
floats to have a precision of about 6 significant decimal digits and
double and long double to have about 10.

Then I came across a C++ program that requires 16. And
with Visual Studio it seems to work. Then I recompiled it with GCC and
spotted several differences. All the program did was to read in a file
with several numbers and output those numbers again in a different
way. But the program held the numbers as double rather than string.
Here are some examples of the differences I found:

VS GCC
-937566.2364699869 -937566.2364699868
-939498.8118815000 -939498.8118814999
928148.9855319375 928148.9855319374
543195.7159558449 543195.7159558448

Checking aginst the original input file, VS is the one that gets it
right. Can anyone comment on why the difference with GCC please?

                 937566.2364699869 =
   11100100111001011110.001111001000100101001100000011000 01110...

The closest representable number with an IEEE-754 64bit float is

   11100100111001011110.001111001000100101001100000011000 =
                 937566.2364699868 485...

The closest representable 16-digit decimal number is

                 937566.2364699868

So, your program you compiled with GCC did a good job. The four
closest double values to your decimal string are

                 937566.2364699867 321...
                 937566.2364699868 485...
                 937566.2364699869 649...
                 937566.2364699870 813...

It seems, the program you used to create your input file did a bad
job, because neither of these numbers should be approximated with the
string "937566.2364699869".

If you're interested in a lossless double->string->double roundtrip
you should use 17 decimal digits and high quality conversions.

Cheers!
SG

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