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Conference hydra::amiga_v1

Title:	AMIGA NOTES
Notice:	Join us in the NEW conference - HYDRA::AMIGA_V2
Moderator:	HYDRA::MOORE

Created:	Sat Apr 26 1986
Last Modified:	Wed Feb 05 1992
Last Successful Update:	Fri Jun 06 1997
Number of topics:	5378
Total number of notes:	38326

2049.0. "help with Manx floating, please..." by JFRSON::OSBORNE (Blade Walker) Wed Dec 28 1988 09:19

I'm having a problem with the floating point numerics in the Manx C
compiler, and since I'm not familiar with floating point, I think I 
need some help with the routines.

The problem is that I convert a string, "84500" for example, to either
float or double, using atof. I then want to display it as a two-decimal
string, so I sprintf with a conversion control string "%10.2f". The
result is "84499.99". If I look at the double before conversion, it
is (in hex) A5 0A 00 51. The first three bytes convert to 84500 * 2^7.

I need better precision than this, in the output string. Should I use
a different floating-point library, or what?

Thanks 
John O.

T.R	Title	User	Personal Name	Date	Lines
2049.1	Is this an answer ?...	CHEOPE::ZABOT	Marco Zabot-Adv.Tech.mgr-Turin ACT	`Wed Dec 28 1988 10:56`	37
	I will try to discuss here the `precision' problem. So if you are interested only in a direct answer to your question , I doubt you can find it here. As you know a floating point number is made of two parts: a mantissa and an exponent. The mantissa in the set of 'significative' digits that represent the number. Depending on the BASE chosen ( 2, 10,..) there are numbers ( called `rational') that can be exactly represented only by a fraction. E.g. 1/3. You may not represent this number in any other way, unless you choose a base that make it `integer' ( 3 in this case, or any power of 3 . Then (1/3)decimal = (0.1)base 3). Some numbers may be easily represented in Base 10 and cannot be represented in base 2 (eg. 0.1 decimal ). A system is `precise' if the representation of the number is close to the real value up to the very last digit. So it is `accurate' depending on the number of digits that are present in the mantissa. Consequently: 85.000 = all the numbers between 84.4995 and 85.0005 84.499 = all the numbers between 84.4985 and 84.4995 if you introduce a rounding factor of .5 on the last (not shown) digit. But if you truncate the number ( which normally happens) then 84.499 = all the numbers between 84.499+delta to 85.000 (delta small at will). In numeric computation you have to chose. Either you keep track of how accurate and precise your computation is, by extending the number of digits ( using single or double precision on different operation ) , or you transform everything into `integer' and work that way.In this case you must compute the exponent by itself. The last method is a lot faster in computing and easy to implement. For a good discussion of it, please refer to Leo Brodie's book " Introduction to Forth" in which he discusses whether it is necessary to introduce floating point in Forth or not. Summing up: any conversion may lose a bit of information, hence do as few conversions as you can !!
2049.2	using double IEEE floating	JFRSON::OSBORNE	Blade Walker	`Wed Jan 11 1989 08:14`	11
	Thanks Marco, I tried integer computation, but still didn't get the level of precision I needed. After organizing the upgrade documentation to the Manx C compiler, I found that compiling with "+fi" option and linking in the mt.lib provides IEEE double floating precision (8 bytes), about 16 signifigant digits. It may be slow, but this is a calculator simulation, so it's fine for this purpose. Thanks again, John O.