Float rounding errors in simple program

[Halide]

First post in a while --hey!

OK, I'm using a float variable, and a resultant value is 10.825. Using setprecision(2) with std::cout yields 10.82 instead of 10.83. I realize that a small precision error would actually cause the value of 10.825 to be 10.8249999... which is revealed using setprecision(10). So, what gives? How should I store a correctly rounded dollar value?

[Flangazor]

Since C++ truncates basic values instead of rounding, you can round to whichever precision you like by adding 5*10^-x where x is the precision.

0.2 rounded (0.2 + 0.5) becomes 0.
0.5 rounded (0.5 + 0.5) becomes 1.
0.02 becomes 0.0.
0.06 becomes 0.11 -> 0.1.

etc.

gl hf

[Halide]

But, if you add 0.05 to a 2 precision float, it could possibly cause rounding errors as well.

Suppose you have 10.8249999 -- which is supposed to be 10.825. By adding 0.05, you increase the value to 10.8749999, which still rounds to 10.87 instead of 10.88...

[Flangazor]

Not at all.

10.8249999 + 0.0005 = 10.825499 which truncates to 10.825

10.874999 + 0.0005 = 10.875499 which truncates to 10.875

This is correct behaviour because 10.874999 SHOULD round to 10.87 and should NOT round to 10.88.

gl hf

[Halide]

I think I'm not being clear...

First of all, I did some calculations, and I get the value of 10.825...in reality it's not -- it's offset to 10.824999...you see what I'm saying?

It should NOT round down because the value SHOULD be 10.825

btw, I'm using Dev-C++ on Win XP, if this matters...

[jamessan]

It's not going to matter which compiler you use. This is a limitation of trying to express floating point numbers in binary.

Interesting link regarding floating point approximations (http://www.unna.org/unna/apple/documentation/developer/QAs-2.x/html/floatpnt.htm)

[Halide]

Ah...nice link.

so, I could just store it as an integer, and divide by 100 :) That is prettier than adding 0.001 to the float! :D thx