January 27, 2009
Walter Bright wrote:
> Don wrote:
>> Walter Bright wrote:
>>> Don wrote:
>>>> tango.math doesn't use the C library at all, except when inline asm is unavailable. Of they differ from the C functions, in that none of them set errno!
>>>> One really annoying issue still remains, though -- the floating point flags in the CPU. They are entirely deterministic, but are they considered to be part of the return value of the function? Or would we allow them to be ignored?
>>>> A compiler could check the exception flags before allowing memoisation. But one could also do the same thing for 'errno'.
>>>>
>>>> Likewise, floating point rounding modes. Essentially, the floating point   status register is a hidden global variable, read from# and written to during every floating point operation.
>>>>
>>>> # - only the rounding mode and truncation affect the return value. We could deal with it by regarding that as a whole-program setting. But (depending on the CPU), the old exception flags generally get ORed with the new exception flags.
>>>
>>> Those are good points. I don't know what the answer is. My inclination is to say if your program relies on changing the rounding mode or fiddles with the exception flags, it's undefined behavior.
>>
>> One form of error analysis is to run the program with different rounding modes, and compare the results.
>>
>> You can also use rounding modes to implement interval arithmetic, but this would normally be restricted to low-level functions. The rounding mode would not escape from those functions.
>>
>> I normally use the exception flags for debugging.
>>
>>>> Also, you can set the flags to allow any floating point function to throw a hardware exception. It's difficult for any function using floating point to claim to be nothrow under ANY circumstances; but that's a horrible limitation.
>>>
>>> I would say that is not supported by D. I've never heard of a use for them.
>>
>> What happens if a nothrow function throws an exception? IMHO a satisfactory response would be to abort the program with an error message/ drop you into a debugger -- anyway, that's the only thing I use when running with FP exceptions enabled.
> 
> I'd be ok with saying throwing fp exceptions is a non-recoverable error, like a seg fault or stack overflow, and is acceptable in a nothrow function.

There are some important uses for catching fp exceptions, including one which in the revised IEEE standard: the product of an array of doubles.
eg real.max * real.max * real.min * real.min == 1.0, but you get overflows during the calculation.

What you do is enable floating point overflow and underflow as an exception, and set up an exception handler inside that function; the handler is essentially an inner function. Then you have a seperate counter for how many times it has overflowed.
The thing to note about this is that although FP exceptions are used, they never leave the function which created them, so there's no stack unwinding, no destructors are called, etc.

All functionality would be preserved if it is a non-recoverable error to transmit an fp exception across a function boundary (but possible to catch the fp exception in the function which generated it).

But possibly such situations are so small in number that they can all be put in the standard library.

>> I guess it's reasonable to argue that using the floating-point flags is sufficiently hard-core that pure and nothrow should pretend that they don't exist.
>>
>> Still, some functions (especially correctly-rounded floating-point i/o) go to a lot of trouble to support them.  I have a suspicion that it's not worth the effort.
> 
> So we have two options. One is to say that floating point arithmetic cannot be made pure. The other is to ignore the problem (saying it's undefined behavior).

It might not be a difficulty to ignore the problem. The flags are getting very hard to use these days, since the x87 flags are different from the SSE flags.

I would recommend stating that when calling a pure function, the state of the FPU flags is implementation-dependent. Even better would be if we can state that the built-in math functions will respect the flags, despite being pure. They are very unlikely to be memoized since they are so simple.
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