CppCon 2015: John Farrier “Demystifying Floating Point"

[@skilz8098]

The comment about stack overflow is fairly on point.

[@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.

[@justcurious1940]

u are totally correct but i just wanna say that we only have 254 groups for normal values and 1 group for NANs and 1 group for subnormals

[@hanyouchu4661]

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.

[@alexloktionoff6833]

oh yea, don't forget to put f or d suffixes to all constants in the code to avoid double rounding!

[@richardcavell]

Kudos for the Guru Meditation at 6:15

[@soulstudiosmusic]

Perplexing subject for a good talk.

[@alexloktionoff6833]

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?

[@ehsanamini8501]

@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?

[@ehsanamini8501]

Oh I get it now. 1 represents a negative number, 0 a positive number.

[@Silvertestrun]

Thank you!

[@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.

[@soulstudiosmusic]

+sandeep jana See section where he mentions the three different types of floating point numbers available in VS.

[@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.

[@alexloktionoff6833]

but not all h/w follows bit exact rounding. +/-.5ulp what we can rely...

[@georganatoly6646]

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

[@CharIie83]

great talk

[@RajeshKumar28sep]

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

[@acmdz]

Oh, that's really helpful!

[@victornoagbodji]

great talk : )

[@Courserasrikanthdrk]

ok,,,,,,,,,,,,,the talk has expressed very important maths topics :----------------------------------------------------------------------)

[@MaherBaba]

you see everything don't you

[@MaherBaba]

what u mean?

[@dascandy]

Your 64-bit floats occupy 65 bits.

[@pranavjain3905]

the exponent register should have 11 exponent bits

[@Xeverous]

-ffast-math not mentioned?

[@andik70]

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?

[@richardcavell]

Theoretically, that’s what happens. Think conceptually.

[@UpstreamNL]

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