[Cfp-interest 1965] Q(NAN) and Q(0*inf)

[Fred J. Tydeman]

On Thu, 25 Mar 2021 08:45:23 -0600 Rajan Bhakta wrote:
>
>      Fred: Send the IEEE 754 errata note that is currently not reflected
>in the errata list to the CFP group.

Attached.


---
Fred J. Tydeman        Tydeman Consulting
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+1 (702) 608-6093      Vice-chair of PL22.11 (ANSI "C")
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   Submitter:CFP group
   Submission Date: 2021-01-24
   Document: WG14 N2642
   Title: N2642: Quantum exponent of NaN
   Reference Documents: N2596, IEEE 754-2019

   Summary: Q(x) is used to denote the quantum exponent of decimal
   floating-point x. Q(infinity) is defined as infinity. Some math
   functions make reference to Q(NAN). However, Q(NAN) is not defined in
   either C23 or IEEE 754-2019.

   5.2.4.2.3 paragraph 9 says the preferred quantum exponent is specified
   by IEEE 754-2019.

   The table of Preferred quantum exponents in paragraph 10 of 5.2.4.2.3
   makes reference to Q(x) and preferred quantum exponent of the result.

   There are five cases where a NaN operand does not produce a NaN result
   for math functions. While the result's value is defined, the quantum
   exponent of that result is not well defined -- mainly because Q(NAN)
   is not defined.
     * compoundn(NAN,0) -- F.10.4.2 says value is 1. The table in
       5.2.4.2.3 says its quantum exponent is floor(0*min(0,Q(NAN))).
     * hypot(+/-INFINITY,NAN) -- F.10.4.4 says value is +INFINITY. The
       table in 5.2.4.2.3 says its quantum exponent is
       min(Q(+/-INFINITY),Q(NAN)).
     * pow(1,NAN) -- F.10.4.5 says value is 1. The table in 5.2.4.2.3
       says its quantum exponent is floor(NAN*Q(1)).
     * pow(NAN,0) -- F.10.4.5 says value is 1. The table in 5.2.4.2.3
       says its quantum exponent is floor(0*Q(NAN)).
     * pown(NAN,0) -- F.10.4.6 says value is 1. The table in 5.2.4.2.3
       says its quantum exponent is floor(0*Q(NAN)).

   There are many cases where an infinity operand does not produce an
   infinity result for math functions. While the result's value is
   defined, the quantum exponent of that result is sometimes not well
   defined -- mainly because zero*infinity is not defined.
     * pow(1,infinity) -- F.10.4.5 says value is 1. The table in
       5.2.4.2.3 says its quantum exponent is floor(infinity*Q(1)) --
       which could be infinity*zero.
     * pow(infinity,0) -- F.10.4.5 says value is 1. The table in
       5.2.4.2.3 says its quantum exponent is floor(0*Q(infinity)) --
       which is zero*infinity.
     * pown(infinity,0) -- F.10.4.6 says value is 1. The table in
       5.2.4.2.3 says its quantum exponent is floor(0*Q(infinity)) --
       which is zero*infinity.

   These appear to be defects in IEEE 754-2019.

   Suggested changes to C23: Change 5.2.4.2.3, paragraph 10 from:

     The following table shows, for each operation delivering a result
     in decimal floating-point format, how the preferred quantum
     exponents of the operands, Q(x), Q(y), etc., determine the
     preferred quantum exponent of the operation result.

   to

     The following table shows, for each operation delivering a result
     in decimal floating-point format, how the preferred quantum
     exponents of the operands, Q(x), Q(y), etc., determine the
     preferred quantum exponent of the operation result[DEL: . :DEL]
     [INS: , provided the table formula is defined for the arguments.
     Cases where the formula is undefined (because of infinities and
     NaNs) are covered by the observation that an infinite result always
     has a quantum exponent of infinity (so its preferred quantum
     exponent is immaterial), and the additional rule: :INS]

     [INS: A finite result from a NaN or infinity operand has a
     preferred quantum exponent of 0. :INS]