5 ms·

Safer to assume that floats are never deterministic.

by TylerE 3y ago

jacobolus 3y ago
Floats follow a clear specification which determines precisely how basic arithmetic should work. They should work the same on all popular modern platforms. (Whether specific software libraries are the same is a separate question.)
- zokier 3y ago
  But transcendentals like sine are not part of the strictly defined basic arithmetic; they are intentionally defined with relaxed behavior.
  - gpderetta 3y ago
    Even there many standard libraries provide very good precision at least within sane domain.
    - TylerE 3y ago
      Yeah, that’s kind of my point. 99% consistent isn’t.
  - jacobolus 3y ago
    If you implement sine in software using the same sequence of basic arithmetic instructions, the result should be the same across platforms. If you make two different implementations using different arithmetic, then of course you can't rely on them being the same.
    - zokier 3y ago
      Point being that IEEE 754 defines two sets of operations, the required operations (section 5) that should be produce correctly rounded results to the last digit, and recommend operations (section 9) with relaxed requirements. And sine belongs to the latter section, so IEEE 754 does not mandate reproducible results for sine.
      - jacobolus 3y ago
        My understanding is that most software always uses some software implementation of sine, rather than calling a hardware instruction. Which is definitely what you should do if you care about getting the exact same results across platforms.
        dzaima 3y ago
        Software implementations can and do differ (even dynamically) based on the hardware though - e.g. glibc's sin(x) function, what C code will end up using (if not other languages relying on the C stdlib), uses FMA instructions on my CPU, and thus the exact same binary on the exact same OS with the exact same glibc should behave differently on a very old CPU without FMA where it should have a different implementation (as generally things using FMA cannot be exactly ported to hardware without it without a gigantic drop in performance which'd be extremely unacceptable).
        jacobolus 3y ago
        Yeah, the lack of FMA in some contexts is a serious bummer. It would be great if every popular CPU platform would figure out a way to get FMA implemented, and if programming languages would figure out better ways to help programmers use it explicitly without making their code too ugly.
        adgjlsfhk1 3y ago
        at this point, Intel, AMD, Arm, and RiscV all do and have for a while. The only one that is at all relevant that doesn't is Apple m-series under rosetta.
aardvark179 3y ago
Floats are well defined, and it is perfectly possible to reason about how algorithms based on them should behave. Few languages specify the accuracy of things like trig functions, so relying on them can be tricky, and JavaScript is particularly bad in that respect.
saagarjha 3y ago
This is not always a safe assumption (in certain scenarios floating point results being nondeterministic has the possibility to introduce bugs and security issues) and is also a kind of sad way to look at the world. The response to "I don't understand how this works" should not be to adopt an incorrect viewpoint, but to know the limitations of your understanding.
- otabdeveloper4 3y ago
  Irrational numbers cannot have an exact representation in digital bits. (Computers use rational numbers with modular arithmetic under the hood.)
  - saagarjha 3y ago
    Yes I am aware of this fact
- TylerE 3y ago
  It’s not that I don’t understand, it’s that I do. Floats are inherently lossy representations. Yes, this means the more operations you perform on a float input, the fuzzier the value is.You ignore that harsh reality at your peril. If you find engineering rigor sad, I don’t know what to tell you.
  - saagarjha 3y ago
    "Floats are not deterministic" is not engineering rigor, it's just wrong. They are specified precisely by IEEE-754 in how they must behave and which operations are allowed to produce which results.
    - TylerE 3y ago
      IEEE 754 conforming floats conform to IEEE-754. If they actually conform. Low end devices with shitty software implementations often get the hard edge cases wrong.
mhh__ 3y ago
They're always deterministic in some sense (and as long as your OS respects the rounding mode after a context switch properly). This might sound pedantic but it determines how we think about floats — the behaviour is specified quite exactly.
- TylerE 3y ago
  What I mean is that the same code running on different hardware/os may not always give the same answer. It’ll be close, but you can’t always expect bit for bit identical.
- ducttapecrown 3y ago
  They're always deterministic, just as long as physics is.
- kens 3y ago
  Curiously, early Intel 386 processors had a bug where 32-bit multiplies were genuinely nondeterministic: some answers would depend on the voltage, frequency, temperature, and manufacturing conditions. The problem was essentially analog, a layout issue, where the signal didn't always have enough margin. (This is unrelated to the famous Pentium FDIV bug.) Until Intel got the problem fixed, they would stamp bad chips with "16 BIT S/W ONLY", while good chips were labeled "ΣΣ".
contravariant 3y ago
I don't think that's safe at all. Catastrophic cancellation would be quite a lot less catastrophic if rounding errors were random but accurate on average.
throwway120385 3y ago
It depends. If you're constrained to one chip and one platform you can characterize or you can estimate the characteristics of a float that matter in your application. In some applications like embedded that's actually totally fine, and modern embedded chips can often do floating point as fast or faster than they can emulate fixed point to work around floating point's drawbacks. On one project I worked on they originally wrote everything fixed point out of fear that floating point would introduce some deleterious effect. But in the end they rewrote parts of the project using floating point to no ill effect and great performance improvement. And there were features of the product that they had to strike because the rewrite needed to support them couldn't touch certain sensitive areas of the code that had been tested extensively in the 2 or 3 years of development. It would have been much better to evaluate the assumption that floats are bad early on in the project and make the decision based on real information. The heuristic they were applying ended up costing part of the product that was strategically important.
- Jyaif 3y ago
  > constrained to one chip and one platform and constrained to one compiler at a precise version, and one set of compiler options
charlieyu1 3y ago
But why? We all know 0.1+0.2 won’t give 0.3 with floats but at least we should expect deterministic result for same numbers and same operations and same order, no?

Safer to assume that floats are never deterministic.

by TylerE 3y ago

Safer to assume that floats are never deterministic.

Floats follow a clear specification which determines precisely how basic arithmetic should work. They should work the same on all popular modern platforms. (Whether specific software libraries are the same is a separate question.)

zokier 3y ago
But transcendentals like sine are not part of the strictly defined basic arithmetic; they are intentionally defined with relaxed behavior.
- gpderetta 3y ago
  Even there many standard libraries provide very good precision at least within sane domain.
  - TylerE 3y ago
    Yeah, that’s kind of my point. 99% consistent isn’t.
- jacobolus 3y ago
  If you implement sine in software using the same sequence of basic arithmetic instructions, the result should be the same across platforms. If you make two different implementations using different arithmetic, then of course you can't rely on them being the same.
  - zokier 3y ago
    Point being that IEEE 754 defines two sets of operations, the required operations (section 5) that should be produce correctly rounded results to the last digit, and recommend operations (section 9) with relaxed requirements. And sine belongs to the latter section, so IEEE 754 does not mandate reproducible results for sine.
    - jacobolus 3y ago
      My understanding is that most software always uses some software implementation of sine, rather than calling a hardware instruction. Which is definitely what you should do if you care about getting the exact same results across platforms.
      - dzaima 3y ago
        Software implementations can and do differ (even dynamically) based on the hardware though - e.g. glibc's sin(x) function, what C code will end up using (if not other languages relying on the C stdlib), uses FMA instructions on my CPU, and thus the exact same binary on the exact same OS with the exact same glibc should behave differently on a very old CPU without FMA where it should have a different implementation (as generally things using FMA cannot be exactly ported to hardware without it without a gigantic drop in performance which'd be extremely unacceptable).
        jacobolus 3y ago
        Yeah, the lack of FMA in some contexts is a serious bummer. It would be great if every popular CPU platform would figure out a way to get FMA implemented, and if programming languages would figure out better ways to help programmers use it explicitly without making their code too ugly.
        adgjlsfhk1 3y ago
        at this point, Intel, AMD, Arm, and RiscV all do and have for a while. The only one that is at all relevant that doesn't is Apple m-series under rosetta.

aardvark179 3y ago

Floats are well defined, and it is perfectly possible to reason about how algorithms based on them should behave. Few languages specify the accuracy of things like trig functions, so relying on them can be tricky, and JavaScript is particularly bad in that respect.

saagarjha 3y ago

This is not always a safe assumption (in certain scenarios floating point results being nondeterministic has the possibility to introduce bugs and security issues) and is also a kind of sad way to look at the world. The response to "I don't understand how this works" should not be to adopt an incorrect viewpoint, but to know the limitations of your understanding.

otabdeveloper4 3y ago
Irrational numbers cannot have an exact representation in digital bits. (Computers use rational numbers with modular arithmetic under the hood.)
- saagarjha 3y ago
  Yes I am aware of this fact
TylerE 3y ago
It’s not that I don’t understand, it’s that I do. Floats are inherently lossy representations. Yes, this means the more operations you perform on a float input, the fuzzier the value is.You ignore that harsh reality at your peril. If you find engineering rigor sad, I don’t know what to tell you.
- saagarjha 3y ago
  "Floats are not deterministic" is not engineering rigor, it's just wrong. They are specified precisely by IEEE-754 in how they must behave and which operations are allowed to produce which results.
  - TylerE 3y ago
    IEEE 754 conforming floats conform to IEEE-754. If they actually conform. Low end devices with shitty software implementations often get the hard edge cases wrong.

mhh__ 3y ago

They're always deterministic in some sense (and as long as your OS respects the rounding mode after a context switch properly). This might sound pedantic but it determines how we think about floats — the behaviour is specified quite exactly.

TylerE 3y ago
What I mean is that the same code running on different hardware/os may not always give the same answer. It’ll be close, but you can’t always expect bit for bit identical.
ducttapecrown 3y ago
They're always deterministic, just as long as physics is.
kens 3y ago
Curiously, early Intel 386 processors had a bug where 32-bit multiplies were genuinely nondeterministic: some answers would depend on the voltage, frequency, temperature, and manufacturing conditions. The problem was essentially analog, a layout issue, where the signal didn't always have enough margin. (This is unrelated to the famous Pentium FDIV bug.) Until Intel got the problem fixed, they would stamp bad chips with "16 BIT S/W ONLY", while good chips were labeled "ΣΣ".

contravariant 3y ago

I don't think that's safe at all. Catastrophic cancellation would be quite a lot less catastrophic if rounding errors were random but accurate on average.

throwway120385 3y ago

It depends. If you're constrained to one chip and one platform you can characterize or you can estimate the characteristics of a float that matter in your application. In some applications like embedded that's actually totally fine, and modern embedded chips can often do floating point as fast or faster than they can emulate fixed point to work around floating point's drawbacks. On one project I worked on they originally wrote everything fixed point out of fear that floating point would introduce some deleterious effect. But in the end they rewrote parts of the project using floating point to no ill effect and great performance improvement. And there were features of the product that they had to strike because the rewrite needed to support them couldn't touch certain sensitive areas of the code that had been tested extensively in the 2 or 3 years of development. It would have been much better to evaluate the assumption that floats are bad early on in the project and make the decision based on real information. The heuristic they were applying ended up costing part of the product that was strategically important.

Jyaif 3y ago
> constrained to one chip and one platform and constrained to one compiler at a precise version, and one set of compiler options

charlieyu1 3y ago

But why? We all know 0.1+0.2 won’t give 0.3 with floats but at least we should expect deterministic result for same numbers and same operations and same order, no?