Fw: [PATCH 0/3] libm: Clean up gamma functions
Brian Inglis
Brian.Inglis@SystematicSw.ab.ca
Fri Aug 28 03:51:05 GMT 2020
On 2020-08-27 21:13, Keith Packard wrote:
> Brian Inglis writes:
>
>> Last C17 public FDIS N2176 is available via:
>>
>> https://web.archive.org/web/20181230041359if_/http://www.open-std.org/jtc1/sc22/wg14/www/abq/c17_updated_proposed_fdis.pdf
>>
>> see 7.12.8.3 lgamma and 7.12.8.4 tgamma on pp181-182, 7.26 tgmath #5 lgamma,
>> tgamma pp272-273, 7.31.1 complex clgamma, ctgamma p332, F10.5.3 lgamma and
>> F.10.5.4 tgamma.
>
> Thanks for the link -- the difference for lgamma is that in C99:
>
> A range error occurs if x is too large. A range error may occur
> if x is a negative integer or zero.
>
> While in C17:
>
> A range error occurs if positive x is too large. A pole error
> may occur if x is a negative integer or zero.
>
> Frustratingly, tgamma still returns different errors. In C99:
>
> A domain error or range error may occur if x is a negative
> integer or zero. A range error may occur if the magnitude of x
> is too large or too small.
>
> While in C17:
>
> A domain error or pole error may occur if x is a negative
> integer or zero. A range error occurs if the magnitude of x is
> too large and may occur if the magnitude of x is too small.
>
> C17 appears to have added this new 'pole' error, which seems to match
> what the IEEE 754 calls a 'divideByZero exception'. Let's see if my
> understanding of the various errors is correct:
>
> IEEE C17 POSIX errno Exception
> divideByZero Pole Pole ERANGE FE_DIVBYZERO
> invalid Domain Domain EDOM FE_INVALID
> overflow Range Range ERANGE FE_OVERFLOW
>
> POSIX is more specific than C17, but it does appear to have been updated
> to follow that spec, including the term 'Pole Error' which wasn't in
> C99.
>
> As my tests all refer to the POSIX spec (which defines the
> errno/exception values), I think they're correct. Here's the set of
> values I'm testing for both tgamma and lgamma (I'm not testing gamma
> currently; we need to sort out what it should be doing first):
>
> Value tgamma lgamma
> POSIX result errno exception POSIX result errno exception
>
> +0 Pole +INFINITY ERANGE FE_DIVBYZERO Pole +INFINITY ERANGE FE_DIVBYZERO
> -0 Pole -INFINITY ERANGE FE_DIVBYZERO Pole +INFINITY ERANGE FE_DIVBYZERO
> -1 Domain NAN EDOM FE_INVALID Pole +INFINITY ERANGE FE_DIVBYZERO
> +3e38f Range +INFINITY ERANGE FE_OVERFLOW Range +INFINITY ERANGE FE_OVERFLOW
> +1.7e308 Range +INFINITY ERANGE FE_OVERFLOW Range +INFINITY ERANGE FE_OVERFLOW
> -3e38f Domain NAN EDOM FE_INVALID Pole +INFINITY ERANGE FE_DIVBYZERO
> -1.7e308 Domain NAN EDOM FE_INVALID Pole +INFINITY ERANGE FE_DIVBYZERO
> +inf None +INFINITY 0 0 None +INFINITY 0 0
> -inf Domain NAN EDOM FE_INVALID None +INFINITY 0 0
>
> I have rationalized the differences in this way:
>
> Domain error means there is no defined limit for the function
> approaching the parameter. Pole error means that there *is* a
> defined limit in this case.
>
> For non-positive inputs, the limit of the value of the tgamma
> function depends on whether that limit is approached from above
> or below.
>
> For zero, we can separate out 'approach from below' and
> 'approach from above' with the sign -- -0 might well be the
> result of an underflow from below, hence returning the value of
> the function as approached from below makes "sense", in this
> case -INFINITY. Similarly, +0 might well be underflow from
> above, so the function can return +INFINITY. In both cases, as
> the limit is well defined, this represents a Pole error rather
> than a Domain error, hence the differences in errno and exceptions.
>
> For negative integers, as the limit depends on whether the value
> is approached from below or above and we have no way of
> distinguishing these two cases from the input, the limit is not
> well defined, so we have a Domain error and return
> NAN/EDOM/FE_INVALID.
>
> For the lgamma function, the limit for non-positive integers is
> always +INFINITY because it returns ln(|Γ(x)|). This makes it
> well defined and hence a Pole error rather than a Domain error
>
> Huge negative values (-1e308) are negative integers, and hence
> treated that way, generating a Domain error for tgamma and Range
> error for lgamma
>
> +INFINITY input and +INFINITY output generate *no* error
> presumably because there's an assumption that the computation
> which resulted in +INFINITY being provided to these functions
> already raised a FE_OVERFLOW exception, and perhaps an ERANGE
> errno.
>
> Please review the table above to see if you agree about what errno and
> exception values each of the provided inputs should generate. I'd really
> like to know if you can suggest additional test cases to use to validate
> the correctness of these functions.
I don't get so don't do maths above my comfort level: but it is possible that
ORs in the specs could mean that some important implementations (e.g BSD and
glibc) may differ in errors reported depending on which, possibly different,
exceptional input values are passed. You could check the BSD and glibc specs and
tests for these functions to see what the expected outputs are for what inputs,
what exceptional values generate which errno values, and whether all
possibilities are allowed by all the specs. POSIX always defers to C where the
latter defines library implementations, but as long as they do not contradict
normative content, POSIX may add additional conditions or requirements.
--
Take care. Thanks, Brian Inglis, Calgary, Alberta, Canada
This email may be disturbing to some readers as it contains
too much technical detail. Reader discretion is advised.
[Data in IEC units and prefixes, physical quantities in SI.]
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