3 ms·

It has been long known that one cannot rely on floating point for precise calculations, e.g. monetary values. One should use integers instead or some kind of ot

It has been long known that one cannot rely on floating point for precise calculations, e.g. monetary values. One should use integers instead or some kind of other precise representation. But it does surprise me that even on the same CPU architecture you cannot expect every machine to produce the same results.

profquail 17y ago
I concentrated in optimization and numerical analysis for my undergrad degree in Math, and I'm still surprised on a regular basis how many programmers out there don't know about the inaccuracies and errors that come out of floating-point representations.
- pmorici 17y ago
  Are you really that surprised. Crappy programmers abound and many introductory programming classes have students write programs to calculate monetary things using floating point so it's no small wonder many people think it's ok.
- jwr 17y ago
  My thoughts exactly. Tom Christiansen brings these things up as if they were a huge surprise, but they aren't, or at least shouldn't be. To put it another way, it isn't Apple doing something wrong. If your code depends on rounding errors in FP representations, your code is buggy. That's also why good numerical algorithms are hard to design. You need to worry about losing precision. As a simple example, if you calculate (a-b)c and a is almost equal to b, you're much better off doing ac-b*c. These tricks are important.
- brettnak 17y ago
  As did, I. I am a professional programmer now and didn't go through the CS school ( To all sophomores out there: We do exist. ) Do they really not teach this sort of thing in a formal CS school?
  - wtallis 17y ago
    Most CS undergraduate programs in the US suck enough these days that numerical analysis isn't taught at the undergrad level. For example, at my school, undergraduates get to choose between the automata/grammars/computability class and a "numerical methods" class that is really watered down. There is a two-semester undergraduate numerical analysis class, but as I recall it can't count toward your degree except as a general elective. To get numerical analysis to count as a CS elective, you have to take the graduate level class.
barrkel 17y ago
For the same CPU architecture, compiler and FPU control word, you should expect the same results. For example, on x86, many C / C++ compilers interpret long double as a 64-bit float while others interpret it as 80-bit extended precision. And extended precision TBYTE (in Intel syntax) does actually take up 10 bytes. There's a speed loss for not aligning, but no correctness loss. In a possibly related note, however, Apple has bizarre and unnecessarily strict alignment policies for Mac OS on x86: http://blogs.embarcadero.com/eboling/2009/05/20/5607 http://blogs.embarcadero.com/eboling/2009/05/20/5607
- tentonova2 17y ago
  For the same CPU architecture, compiler and FPU control word, you should expect the same results. That's a stretch. Just because it's called "GCC" doesn't mean it behaves exactly the same on every platform, even if the CPU architecture is the same. Apple makes extensive modifications, has their own ABI (see below), etc. In a possibly related note, however, Apple has bizarre and unnecessarily strict alignment policies for Mac OS on x86: It's not "bizarre and unnecessarily strict" if you want to be able to rely on SSE2+. Apple had the advantage of being able to define their ABI without regard to most legacy concerns, and so they did. The reason that it's strictly enforced everywhere is that since Apple's compilers use SSE2+ they must be able to assume that, at function entry, the stack is properly (16 byte) aligned. I understand your pain -- I've had to update a JIT implementation to deal with this, along with quite a bit of assembly that assumed 4 byte alignment, but Apple's reasoning makes sense. See also: http://stackoverflow.com/questions/612443/why-does-the-mac-abi-require-16-byte-stack-alignment-for-x86-32/898760#898760 http://stackoverflow.com/questions/612443/why-does-the-mac-a...
  - barrkel 17y ago
    The stack is not actually aligned on function entry, because the return address is on top, so more alignment will be needed to avoid SSE2 locals being misaligned. It's not so hard for the callee side of the ABI to make sure the stack is aligned if it's going to use SSE2 and friends; it's rather more onerous to require every call site to make the alignments for the benefit of the callee.

profquail 17y ago

I concentrated in optimization and numerical analysis for my undergrad degree in Math, and I'm still surprised on a regular basis how many programmers out there don't know about the inaccuracies and errors that come out of floating-point representations.

pmorici 17y ago
Are you really that surprised. Crappy programmers abound and many introductory programming classes have students write programs to calculate monetary things using floating point so it's no small wonder many people think it's ok.
jwr 17y ago
My thoughts exactly. Tom Christiansen brings these things up as if they were a huge surprise, but they aren't, or at least shouldn't be. To put it another way, it isn't Apple doing something wrong. If your code depends on rounding errors in FP representations, your code is buggy. That's also why good numerical algorithms are hard to design. You need to worry about losing precision. As a simple example, if you calculate (a-b)c and a is almost equal to b, you're much better off doing ac-b*c. These tricks are important.
brettnak 17y ago
As did, I. I am a professional programmer now and didn't go through the CS school ( To all sophomores out there: We do exist. ) Do they really not teach this sort of thing in a formal CS school?
- wtallis 17y ago
  Most CS undergraduate programs in the US suck enough these days that numerical analysis isn't taught at the undergrad level. For example, at my school, undergraduates get to choose between the automata/grammars/computability class and a "numerical methods" class that is really watered down. There is a two-semester undergraduate numerical analysis class, but as I recall it can't count toward your degree except as a general elective. To get numerical analysis to count as a CS elective, you have to take the graduate level class.

barrkel 17y ago

For the same CPU architecture, compiler and FPU control word, you should expect the same results. For example, on x86, many C / C++ compilers interpret long double as a 64-bit float while others interpret it as 80-bit extended precision. And extended precision TBYTE (in Intel syntax) does actually take up 10 bytes. There's a speed loss for not aligning, but no correctness loss. In a possibly related note, however, Apple has bizarre and unnecessarily strict alignment policies for Mac OS on x86: http://blogs.embarcadero.com/eboling/2009/05/20/5607 http://blogs.embarcadero.com/eboling/2009/05/20/5607

tentonova2 17y ago
For the same CPU architecture, compiler and FPU control word, you should expect the same results. That's a stretch. Just because it's called "GCC" doesn't mean it behaves exactly the same on every platform, even if the CPU architecture is the same. Apple makes extensive modifications, has their own ABI (see below), etc. In a possibly related note, however, Apple has bizarre and unnecessarily strict alignment policies for Mac OS on x86: It's not "bizarre and unnecessarily strict" if you want to be able to rely on SSE2+. Apple had the advantage of being able to define their ABI without regard to most legacy concerns, and so they did. The reason that it's strictly enforced everywhere is that since Apple's compilers use SSE2+ they must be able to assume that, at function entry, the stack is properly (16 byte) aligned. I understand your pain -- I've had to update a JIT implementation to deal with this, along with quite a bit of assembly that assumed 4 byte alignment, but Apple's reasoning makes sense. See also: http://stackoverflow.com/questions/612443/why-does-the-mac-abi-require-16-byte-stack-alignment-for-x86-32/898760#898760 http://stackoverflow.com/questions/612443/why-does-the-mac-a...
- barrkel 17y ago
  The stack is not actually aligned on function entry, because the return address is on top, so more alignment will be needed to avoid SSE2 locals being misaligned. It's not so hard for the callee side of the ABI to make sure the stack is aligned if it's going to use SSE2 and friends; it's rather more onerous to require every call site to make the alignments for the benefit of the callee.