[9fans] comparisons with NaN

[9fans] comparisons with NaN

[Richard Miller]

The Plan 9 C compilers do not appear to be compliant with the IEEE floating
point standard when making comparisons with NaN (not a number) values.

The standard says a comparison with one or both operands NaN is "unordered",
ie all relations evaluate to false, except != which is always true.

Testing with this fragment of code:
	double a, b;
	setfcr(0);
	a = 0.0;
	b = sqrt(-1.0);
	if(a <  b) print(" (a < b)");
	if(a <= b) print(" (a <= b)");
	if(a == b) print(" (a == b)");
	if(a != b) print(" (a != b)");
	if(a >= b) print(" (a >= b)");
	if(a >  b) print(" (a > b)");
	if(b <  a) print(" (b < a)");
	if(b <= a) print(" (b <= a)");
	if(b == a) print(" (b == a)");
	if(b != a) print(" (b != a)");
	if(b >= a) print(" (b >= a)");
	if(b >  a) print(" (b > a)");
	print("\n");
on ARM the result is almost completely wrong:
 (a < b) (a <= b) (a != b) (b < a) (b <= a) (b != a)
and on x86 the result is even wronger:
 (a < b) (a <= b) (a == b) (b < a) (b <= a) (b == a)
compared to the IEEE expected result, for example on MacOS:
 (a != b) (b != a)

This was discovered by fgb; I've been looking into the cause -- which is
mainly the assumption, in the compiler and linker, that something like this:
	if (a < b) f();
can safely be transformed to this:
	if (a >= b) goto skip;
	f();
	skip:
Unfortunately if a or b is NaN, the conditional will be false in both cases.

So is this a feature, or a bug that needs fixing?

Re: [9fans] comparisons with NaN

[erik quanstrom]

amd64 does yet something else.

amd64	(a == b) (a >= b) (a > b) (b == a) (b >= a) (b > a)
386	(a < b) (a <= b) (a == b) (b < a) (b <= a) (b == a)
arm	(a < b) (a <= b) (a != b) (b < a) (b <= a) (b != a)
mips	(a < b) (a <= b) (a != b) (b < a) (b <= a) (b != a)

> mainly the assumption, in the compiler and linker, that something like this:
> 	if (a < b) f();
> can safely be transformed to this:
> 	if (a >= b) goto skip;
> 	f();
> 	skip:
> Unfortunately if a or b is NaN, the conditional will be false in both cases.
>
> So is this a feature, or a bug that needs fixing?

how about another option, just a bug.

there are other issues with the floating point, including
the fact that -0.0 is transformed both by the compiler, and
by print(2) to 0.0.  ape's printf prints -0.0 correctly.

at least in terms of passing floating point test suites
(like python's) the NaN issue doesn't come up, but the
-0 issue breaks a number of tests.

- erik

Re: [9fans] comparisons with NaN

[erik quanstrom]

> how about another option, just a bug.

what i mean is, the need for fixing it depends on how much
havoc this issue causes.

- erik

Re: [9fans] comparisons with NaN

[Richard Miller]

> at least in terms of passing floating point test suites
> (like python's) the NaN issue doesn't come up

Actually it was a test suite that revealed the NaN errors.
I wouldn't think it's something anyone needs in normal
day-to-day computation, but sometimes boxes must be ticked.

Re: [9fans] comparisons with NaN

[erik quanstrom]

On Wed Aug 21 12:09:26 EDT 2013, 9fans@hamnavoe.com wrote:
> > at least in terms of passing floating point test suites
> > (like python's) the NaN issue doesn't come up
> 
> Actually it was a test suite that revealed the NaN errors.
> I wouldn't think it's something anyone needs in normal
> day-to-day computation, but sometimes boxes must be ticked.

:-)  it is hard to imagine how this is useful.  it's not like
∑{i→∞}-0 is interesting.  at least ∏{i→∞}-0 has an alternating
sign.  (so does it converge with no limit?)

the difference i have seen is a situation like
	atan2(-0, x)	≡ -π
	atan2(+0, x)	≡ pi, ∀ x<0.

any ideas on how this is useful?

- erik

Re: [9fans] comparisons with NaN

[Bakul Shah]

On Aug 21, 2013, at 9:55 AM, erik quanstrom <quanstro@quanstro.net> wrote:

> On Wed Aug 21 12:09:26 EDT 2013, 9fans@hamnavoe.com wrote:
>>> at least in terms of passing floating point test suites
>>> (like python's) the NaN issue doesn't come up
>> 
>> Actually it was a test suite that revealed the NaN errors.
>> I wouldn't think it's something anyone needs in normal
>> day-to-day computation, but sometimes boxes must be ticked.
> 
> :-)  it is hard to imagine how this is useful.  it's not like
> ∑{i→∞}-0 is interesting.  at least ∏{i→∞}-0 has an alternating
> sign.  (so does it converge with no limit?)
> 
> the difference i have seen is a situation like
> 	atan2(-0, x)	≡ -π
> 	atan2(+0, x)	≡ pi, ∀ x<0.
> 
> any ideas on how this is useful?


See comments by Stephen Canon in
http://stackoverflow.com/questions/1565164/what-is-the-rationale-for-all-comparisons-returning-false-for-ieee754-nan-values

Try this:

#include <u.h>
#include <libc.h>

main(){
        double a, b;
        setfcr(0);
        a = 0.0;
        b = a/a;
        if(a <  b) print(" (a <  b)");
        if(a <= b) print(" (a <= b)");
        if(a == b) print(" (a == b)");
        if(a != b) print(" (a != b)");
        if(a >= b) print(" (a >= b)");
        if(a >  b) print(" (a >  b)");
        if(b <  a) print(" (b <  a)");
        if(b <= a) print(" (b <= a)");
        if(b == a) print(" (b == a)");
        if(b != a) print(" (b != a)");
        if(b >= a) print(" (b >= a)");
        if(b >  a) print(" (b >  a)");
        if(b != b) print(" (b != b)");
        if(b == b) print(" (b == b)");
        print("\n");
	return 0;
}

It falsely reports b == b when b is NaN. 

Re: [9fans] comparisons with NaN

[erik quanstrom]

On Wed Aug 21 13:43:54 EDT 2013, bakul@bitblocks.com wrote:
> On Aug 21, 2013, at 9:55 AM, erik quanstrom <quanstro@quanstro.net> wrote:
> 
> > On Wed Aug 21 12:09:26 EDT 2013, 9fans@hamnavoe.com wrote:
> >>> at least in terms of passing floating point test suites
> >>> (like python's) the NaN issue doesn't come up
> >> 
> >> Actually it was a test suite that revealed the NaN errors.
> >> I wouldn't think it's something anyone needs in normal
> >> day-to-day computation, but sometimes boxes must be ticked.
> > 
> > :-)  it is hard to imagine how this is useful.  it's not like
> > ∑{i→∞}-0 is interesting.  at least ∏{i→∞}-0 has an alternating
> > sign.  (so does it converge with no limit?)
> > 
> > the difference i have seen is a situation like
> > 	atan2(-0, x)	≡ -π
> > 	atan2(+0, x)	≡ pi, ∀ x<0.
> > 
> > any ideas on how this is useful?
> 
> 
> See comments by Stephen Canon in
> http://stackoverflow.com/questions/1565164/what-is-the-rationale-for-all-comparisons-returning-false-for-ieee754-nan-values

i think you selected a different antecedent for "this" than
i did.  by "this" i ment to refer to -0.

- erik

Re: [9fans] comparisons with NaN

[Bakul Shah]

> On Wed Aug 21 13:43:54 EDT 2013, bakul@bitblocks.com wrote:
>> On Aug 21, 2013, at 9:55 AM, erik quanstrom <quanstro@quanstro.net> wrote:
>> 
>>> On Wed Aug 21 12:09:26 EDT 2013, 9fans@hamnavoe.com wrote:
>>>> 
>>>> Actually it was a test suite that revealed the NaN errors.
>>>> I wouldn't think it's something anyone needs in normal
>>>> day-to-day computation, but sometimes boxes must be ticked.
>>> 
>>> :-)  it is hard to imagine how this is useful.
>> 
>> See comments by Stephen Canon in
>> http://stackoverflow.com/questions/1565164/what-is-the-rationale-for-all-comparisons-returning-false-for-ieee754-nan-values


That this!

Re: [9fans] comparisons with NaN

[Richard Miller]

> by "this" i ment to refer to -0.

But the subject line says "comparisons with NaN".  Start another
thread about signed zero if you like.  (I'm not facing a test
suite objecting to those at the moment.)

Re: [9fans] comparisons with NaN

[lucio]

> what i mean is, the need for fixing it depends on how much
> havoc this issue causes.

Well, there is also the question of whether anything at all will break
if the bug is fixed.  If not, then the answer is simple.

++L

Re: [9fans] comparisons with NaN

[Charles Forsyth]

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I think that if there is a generally-accepted standard for the behaviour of
a language's handling of floating-point numbers,
it would be reasonable to try to follow the standard, unless it's stupid,
ill-advised, or impossible (or all three).
That reply to the Stack Overflow post -- and this might be the first and
last time I can write this -- was, I thought, concise and compelling.


On 21 August 2013 19:00, Richard Miller <9fans@hamnavoe.com> wrote:

> > by "this" i ment to refer to -0.
>
> But the subject line says "comparisons with NaN".  Start another
> thread about signed zero if you like.  (I'm not facing a test
> suite objecting to those at the moment.)
>
>
>

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Re: [9fans] comparisons with NaN

[erik quanstrom]

On Wed Aug 21 14:23:48 EDT 2013, lucio@proxima.alt.za wrote:
> > what i mean is, the need for fixing it depends on how much
> > havoc this issue causes.
>
> Well, there is also the question of whether anything at all will break
> if the bug is fixed.  If not, then the answer is simple.

fortunately, since plan 9 traps when a computation produces a NaN by default,
and nothing in /sys/src/cmd calls setfcr(2), i think we can exclude this possiblity.

- erik

Re: [9fans] comparisons with NaN

[Richard Miller]

> it would be reasonable to try to follow the standard, unless it's stupid,
> ill-advised, or impossible (or all three).

Not impossible, maybe a bit tricky to stop the linkers from reordering
things.  The cost would be (at least) one extra instruction for each
'if' statement with a floating point inequality and no 'else' clause.

Ron, are you still reading this list?  What do your numerical colleagues
think about NaNs?

Re: [9fans] comparisons with NaN

[Charles Forsyth]

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> it would be reasonable to try to follow the standard, unless it's stupid,
> > ill-advised, or impossible (or all three).
>

I was a little ambiguous. I meant that statement in general, but I in the
particular case of floating-point, being fundamental, probably should work
as now defined,
and I didn't think NaNs satisfied the last bit of being stupid, ill-advised
or impossible.

Looking at the code generated, I'd have thought that it was the use of FCOM
instead of FUCOM that mattered,
not the integer unit comparison that's subsequently used.

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Re: [9fans] comparisons with NaN

[Richard Miller]

On ARM, it turns out that comparisons with NaN can be made to do the
right thing with no code penalty, by a more careful selection of
condition code values in the subsequent conditional branch.  The
meaning of the CC bits in the PSR is subtly different when they've
been copied from the floating point status register.

Suggested patch is 5c-nan-cmp (works on both vfp and emulated arm7500).