Help me understand a particular floating point error.

[kiseitai2]

Hello awesome people of bytes.com. After a year working on a thesis project, I stumbled upon an interesting phenomenon. When I set a float variable to 10060.000000, it never changed after going through some floating point arithmetic that involved a small number (10060f - 0.00027333f = 10060f?). Changing this variable to about 1000 or less gave the right result. Finally, changing this float variable to double fixed this problem (10060d - 0.00027333f = <10060d, which is correct). Is there a theoretical basis as to why the float-only arithmetic operation failed compared to the double - float one? I thought that 32 bits floats had enough decimals to handle most of the result of 10060 - 0.00027333. At the time of this issue, I was testing my code on Win Vista 32bits. I have not tested the Mac and Linux versions to see if they have the same issue. Thanks for your time!

[weaknessforcats]

Floats contain only 6 or 7 significant figures. More than that gets rounded to 6 or 7 significant figures.

A double will have 15-16 significant figures.

All calculations involving float will convert the float to a double, do the calculation as a double and then convert the result back to a float with possible loss of data.

All calculations should be using double only. A float is an obsolete data type left over from the olden days of computers with tiny memories.

[Banfa]

If you repeated have to add (or subtract) a very small floating point value from a large floating point value then you quickly get inaccuracies due to rounding errors. There is a method called, the Kahan summation algorithm, that improves the accuracy of this sort of operation by correcting the sum as it goes along for low order bits dropped when you add a small floating point number to a large one..

[kiseitai2]

Thanks for your responses. For some reason I confused the exponent range with the number of significant digits, so I thought floats had more significant spaces than they actually do. The reason why I was using floats is because I like to keep memory usage as low as I can for as long as I can. Thus, I tend to use the smallest possible type whenever possible. Thanks again for correcting me!

[donbock]

You might find this article helpful: What Every Computer Scientist Should Know About Floating-Point Arithmetic.