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Examples of floating point problems

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Re: Examples of floating point problems

#71

Post by pwpwp »

WalterBright wrote: post #65

> NaN/infinity values can propagate and cause chaos NaN is the most misunderstood feature of IEEE floating point. Most people react to a NaN like they'd react to the dentist telling them they need a root canal. But NaN is actually a very valuable and useful tool! NaN is just a value that represents an invalid floating point value. The result of any operation on a NaN is a NaN. This means that NaNs propagate from the…

I don't find this convincing.

> What do you return for an index into the array?

An option/maybe type would solve this much better.

> Yes, I know, it can be clumsy to trace it back to its source

An exception would be much better, alerting you to the exact spot where the problem occurred.

Re: Examples of floating point problems

#72

Post by jordigh »

WalterBright wrote: post #65

> NaN/infinity values can propagate and cause chaos NaN is the most misunderstood feature of IEEE floating point. Most people react to a NaN like they'd react to the dentist telling them they need a root canal. But NaN is actually a very valuable and useful tool! NaN is just a value that represents an invalid floating point value. The result of any operation on a NaN is a NaN. This means that NaNs propagate from the…

> What's the result of 1.0/0.0? It's not a number, so it's a NaN

It's not often that I get to correct Mr D himself, but 1.0/0.0 is...

Re: Examples of floating point problems

#73

Post by WalterBright »

jordigh wrote: post #72
WalterBright wrote: post #65

> NaN/infinity values can propagate and cause chaos NaN is the most misunderstood feature of IEEE floating point. Most people react to a NaN like they'd react to the dentist telling them they need a root canal. But NaN is actually a very valuable and useful tool! NaN is just a value that represents an invalid floating point value. The result of any operation on a NaN is a NaN. This means that NaNs propagate from the…

> What's the result of 1.0/0.0? It's not a number, so it's a NaN It's not often that I get to correct Mr D himself, but 1.0/0.0 is...

You're right. I'll fix it.

Re: Examples of floating point problems

#74

Post by WalterBright »

pwpwp wrote: post #71
WalterBright wrote: post #65

> NaN/infinity values can propagate and cause chaos NaN is the most misunderstood feature of IEEE floating point. Most people react to a NaN like they'd react to the dentist telling them they need a root canal. But NaN is actually a very valuable and useful tool! NaN is just a value that represents an invalid floating point value. The result of any operation on a NaN is a NaN. This means that NaNs propagate from the…

I don't find this convincing. > What do you return for an index into the array? An option/maybe type would solve this much better. > Yes, I know, it can be clumsy to trace it back to its source An exception would be much better, alerting you to the exact spot where the problem occurred.

> An option/maybe type would solve this much better.

NaN's are already an option type, although implemented in hardware. The checking comes for free.

> An exception would be much better

You can configure the FPU to cause an Invalid Operation Exception, but I personally don't find that attractive.

Re: Examples of floating point problems

#75

Post by jordigh »

pwpwp wrote: post #71
WalterBright wrote: post #65

> NaN/infinity values can propagate and cause chaos NaN is the most misunderstood feature of IEEE floating point. Most people react to a NaN like they'd react to the dentist telling them they need a root canal. But NaN is actually a very valuable and useful tool! NaN is just a value that represents an invalid floating point value. The result of any operation on a NaN is a NaN. This means that NaNs propagate from the…

I don't find this convincing. > What do you return for an index into the array? An option/maybe type would solve this much better. > Yes, I know, it can be clumsy to trace it back to its source An exception would be much better, alerting you to the exact spot where the problem occurred.

Exceptions are actually part of floats, they're called "signalling nans".

So technically Python is correct when it decided that 0.0/0.0 should raise an exception instead of just quietly returning NaN. Raising an exception is a standards-conforming option.

https://stackoverflow.com/questions/18118408/what-is-the-dif...

Re: Examples of floating point problems

#77

Post by owisd »

My 'favourite' is that the quadratic formula -b±sqrt(b²-4ac)/2a falls apart when you solve for the positive solution using floating point for cases where ε=b²/4ac is small, the workaround being to use the binomial expansion -b/2a*(0.5ε-0.125ε²+O(ε³))

Re: Examples of floating point problems

#78

Post by pwpwp »

WalterBright wrote: post #74
pwpwp wrote: post #71

Earlier quoted context omitted.

I don't find this convincing. > What do you return for an index into the array? An option/maybe type would solve this much better. > Yes, I know, it can be clumsy to trace it back to its source An exception would be much better, alerting you to the exact spot where the problem occurred.

> An option/maybe type would solve this much better. NaN's are already an option type, although implemented in hardware. The checking comes for free. > An exception would be much better You can configure the FPU to cause an Invalid Operation Exception, but I personally don't find that attractive.

Good points!

Re: Examples of floating point problems

#79

Post by Lind5 »

AI already has led to a rethinking of computer architectures, in which the conventional von Neumann structure is replaced by near-compute and at-memory floorplans. But novel layouts aren’t enough to achieve the power reductions and speed increases required for deep learning networks. The industry also is updating the standards for floating-point (FP) arithmetic. https://semiengineering.com/will-floating-point-8-solve-ai-m...

Re: Examples of floating point problems

#80

Post by ratorx »

WalterBright wrote: post #74
pwpwp wrote: post #71

Earlier quoted context omitted.

I don't find this convincing. > What do you return for an index into the array? An option/maybe type would solve this much better. > Yes, I know, it can be clumsy to trace it back to its source An exception would be much better, alerting you to the exact spot where the problem occurred.

> An option/maybe type would solve this much better. NaN's are already an option type, although implemented in hardware. The checking comes for free. > An exception would be much better You can configure the FPU to cause an Invalid Operation Exception, but I personally don't find that attractive.

The missing bit is language tooling. The regular floating point API exposed by most languages don’t force handling of NaNs.

The benefit of the option type is not necessarily just the extra value, but also the fact that the API that forces you to handle the None value. It’s the difference between null and Option.

Even if the API was better, I think there’s value in expressing it as Option which compiles down to using NaNs for the extra value to keep it similar to other Option specialisations and not have to remember about this special primitive type that has option built in.

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