CppCon 2015: John Farrier “Demystifying Floating Point'

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Every day we develop software that relies on math while we often overlook the importance of understanding the implications of using our IEEE floats. From the often cited “floating point error” to unstable algorithms, this talk will explain the importance of floats, understanding their storage, the impact of the IEEE floats on math, and designing algorithms better. Finally, the talk will conclude with a quick case study of storing time for games and simulations.
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John Farrier is a software engineer, researcher, and musician. He designs software architectures for military modeling and simulation activities. His projects support efforts across the U.S. Department of Defense ranging from lab-based experimental software to fielded software on live fire test ranges.
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[dascandy]

There are the same amount of numbers between 0.5 and 0.25, between 0.25 and 0.125, between 0.125 and 0.0625, ... so if you count the number of floats between 0 and 1, that's a lot more than between 1 and 2. In fact, there are 255 "groups" of numbers, each from N to N*2, each having 8388608 numbers.

[skilz]

The comment about stack overflow is fairly on point.

[hanyouchu]

The difference between float and double for the Kahan version of triangle area is due to input conversion from decimal to binary. If you cast the float input to double, the results are almost identical.

[alexloktionoff]

Can anybody provide a link to those 50 equations /*test-cases???*/ that must fork same on all IEEE754 machines?

[enhex]

Why 0.0 to 0.1 have more precision?
Is it because every floating point number is unique, and there's a lot of overlaps up to 2^23?

[ehsanamini]

@4:31 and @8:10 why does -1^0 compute to zero? Shouldn't it be 1? Is it a typo or am I missing something?

[janasandeep]

At 11:08 (slide 24), the binary representation of 1.0e-37 shown here is different from what I got using visual studio: EA1C0802 (little endian). Why so? The latter does not seem to be a denormalized number.

[georganatoly]

Very good talk. It wouldn't have occurred to me to group like exponentiation.

[Calm_Energy]

Units in last place = ulps. This is a measurement I've never seen before. Some compilers can control how rounding works via options.

[RajeshKumarsep]

5:22, for 64 bits its should be 11 bit of exp

[Courserasrikanthdrk]

talk has expressed very important maths topics

[andik]

16:56 'on the CPU math is done exactly and then rounded to give it back to you'  did you really say that? Do you really mean that?

[UpstreamNL]

Confusing talk. This guy is all over the place. Every slide in no way connects to the previous slide.