Quiet NaN question

[Bonita Montero]

My SSE-FPU generates the following NaNs:

* When I do a any basic dual operation like ADDSD, SUBSD, MULSD or DIVSD
and one of both operands is a NaN, the result has the sign of the NaN
-operand and the lower 51 bits of the mantissa of the result is loa-
ded with the lower 51 bits of the mantissa of the NaN-operand.
* When both operations are NaN, the result is loaded with the sign of
the destination-register and the lower 51 bits of the result-mantissa
is loaded with the lower 51 bits of the destination-register before
the operation. So the associative law doesn't count here and the order
of the operands in a multiplication does count!
* When I do a SQRTSD on a NaN-value, the result has the sign of the
NaN-operand and the lower 51 bits of the result is loaded with the
lower 51 bits of the operand.
* When I do a multiplication of infinity with zero or infinity, I always
get -NaN as a result (binary representation 0xFFF8000000000000u).

Is this behaviour determined anywhere in the IEEE-754-standard?

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[Bonita Montero]

Am 18.06.2016 um 12:15 schrieb Bonita Montero:
> My SSE-FPU generates the following NaNs:
>
> * When I do a any basic dual operation like ADDSD, SUBSD, MULSD or DIVSD
> and one of both operands is a NaN, the result has the sign of the NaN
> -operand and the lower 51 bits of the mantissa of the result is loa-
> ded with the lower 51 bits of the mantissa of the NaN-operand.

And:

* If any operand is a signalling NaN, the result becomes a quiet NaN
if the exception isn't masked.

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[Terje Mathisen]

Yes, a least most of it.

In particular operations on NaN(s) intentionally breaks associativity,
look at comparisons.

Terje

--
- <Terje.Mathisen at tmsw.no>
"almost all programming can be viewed as an exercise in caching"

[Bonita Montero]

Am 19.06.2016 um 00:08 schrieb Terje Mathisen:

> In particular operations on NaN(s) intentionally breaks associativity,
> look at comparisons.

I found a funny thing: When operating on two NaNs with the x87-FPU,
the lower 51 bits of the result is loaded with the larger value of
the lower 51 bits of both operands.

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[Terje Mathisen]

Bonita Montero wrote:
> Am 19.06.2016 um 00:08 schrieb Terje Mathisen:
>
>> In particular operations on NaN(s) intentionally breaks associativity,
>> look at comparisons.
>
> I found a funny thing: When operating on two NaNs with the x87-FPU,
> the lower 51 bits of the result is loaded with the larger value of
> the lower 51 bits of both operands.
>

Not funny:

This is a very natural result of having an internal pathway that sorts
the inputs into larger/smaller (ignoring sign), which is something you
need if you are going to subtract.

It doesn't matter for FMUL or FADD, except when an FADD has inputs with
opposite signs and really was a FSUB.

For FDIV however you need to skip that compare/swap network, but FDIV is
an order of magnitude slower anyway.

[Bruce Evans]

In article <nk78ps$t2a$1...@gioia.aioe.org>,

Terje Mathisen <terje.m...@tmsw.no> wrote:
> Bonita Montero wrote:
> > Am 19.06.2016 um 00:08 schrieb Terje Mathisen:
> >
> >> In particular operations on NaN(s) intentionally breaks associativity,
> >> look at comparisons.
> >
> > I found a funny thing: When operating on two NaNs with the x87-FPU,
> > the lower 51 bits of the result is loaded with the larger value of
> > the lower 51 bits of both operands.

This is with a rounding precision of 53 bits, or perhaps after converting
the value in an x87 register back to a double in memory and loooking at
it in memory. Normally, the rounding precision is 64 bits and it is
the lower 62 or 63 that are compared.

This is also only with quiet NaNs IIRC. The quiet bit gives another
bit to compare, and messes up the comparision if it is not set
consisistently.

> Not funny:
>
> This is a very natural result of having an internal pathway that sorts
> the inputs into larger/smaller (ignoring sign), which is something you
> need if you are going to subtract.
>
> It doesn't matter for FMUL or FADD, except when an FADD has inputs with
> opposite signs and really was a FSUB.
>
> For FDIV however you need to skip that compare/swap network, but FDIV is
> an order of magnitude slower anyway.

This gives predictable results in some cases.

The FreeBSD math library promotes both args to long double for returning
combinations of NaNs to get predictable results in more cases. It
sometimes uses the following as a not very magic C expression for
mixing the NaN x with the NaN y:

(x + (long double)0) + (y + (long double)0)

This adds 0 to ensure that the quiet bit is set consistently, provided
there are no compiler bugs and/or certain #pragmas are set to disallow
certain optimizations). It adds specifically (long double)0 to get
the operands in the x87 on x86 systems (provided the compiler does the
expected thing). This makes the final result depend only on the x87
hardware and not on the types of x and y or compiler optimizations or
bugs.

As was noted in the original posting, x+y is not even commutative for
SSE. It is commutative for x87 since it is basically the bitwise
maximum with some complication for the sign bit. The promotion to
long double is partly to get this commutativity. With commutativity,
there are no compiler bugs from evaluating x+y in the order y+x.
Plain x+y with no compiler bugs would give consistent results if
x, y and the return type are all the same, even if x is signaling
and y is quiet. The magic expression forces x and y to be quiet
before the comparison (although that is not the natural x87 operation)
for the technical reason that it is too difficult to preserve the
non-quietness of x and y unless they have type long double.

This method also works on ia64 and sparc64 systems and was needed to
give consistent results on one or both of those.

Bruce