[Cfp-interest 2042] Re: Subnormals

[Fred J. Tydeman]

On Sun, 27 Jun 2021 16:15:29 -0700 Jim Thomas wrote:
>
>Some general comments 
>
>It's common for CPUs to have behavior-changing controls that can be changed at execution time. Implementations 
>should generally be able to define characteristics of their floating-point arithmetic based on a default configuration of such 
>controls. For example, an implementation on a 754 CPU with trap enablement modes should be able to conform to Annex 
>F, even though a user might enable traps thereby causing non-conforming behavior. Also, C doesn't provide a way for a 
>user to change the behaviors related to subnormals and underflow. A program that does so is going outside the C 
>standard. I think we should avoid "changeable at runtime".

I removed that from the proposal.

>IEC 60559 is a well-defined floating-point standard. We don't have a viable more general standard (LIA?) that covers 
>arithmetics that don't conform to IEC 60559. There are limitless possibilities. I don't think C should try to characterize 
>non-standard behaviors just because they appear in an implementation. It might be different if a behavior is widely 
>adopted in a uniform way. Are we trying codify some such existing practice?

ARM chips, as far as I know, are in most cell phones.  So, they are widely adopted.
But, I do not know what state the FPU control bits are in.  I have made that part optional.

>What is the purpose of the macro? Presumably, it is intended to tell a program something useful about the arithmetic. 
>Considering the scope of possibilities for how subnormals might be treated, how can this macro provide information that 
>code might be based on? Are there examples of real code that uses it? If so, how do they use it?

Again, I made the other *_HAS_SUBNORM values be optional.
While the user is only asking about *_HAS_SUBNORM == 0,
I have looked at the more general case that I have encountered in my FPU testing.

>"Flush to zero" is not defined and is used only once in C, in a footnote. A related problem is that the operations that flush 
>results to zero would need to be identified (or characterized). For example, would negate (-), fabs, and copysign be 
>expected to flush to zero? How about conversion to same or wider format?

I would expect all FP operations to be consistent on flushing; either all or none.
I believe that adding flushed subnormals shall be treated as zeros defines
their behaviour.

>Some specific comments (in brackets) 
>
>So, if subnormal operands are treated as zero, then subnormal numbers could be considered as non-canonical 
>encodings of zero.
>
>[Comment: The words here confuse the distinction between the representation and the value. Consider changing the 
>sentence above to:  if subnormal representations are treated as zero values, then they can be regarded as 
>non-canonical zero representations.]

Changed.

>That would mean (independent of flushing subnormal results):
>
>...    
>
>         nextdown(minimum normal) is true zero. [Comment: Why "true" zero? Does true zero mean canonical zero? 
>Functions for such implementations are not required to produce canonical results.]

Yes, changed. 5.2.4.2.2#6 has:

  Typically, floating-point operations deliver results with canonical representations. 
  IEC 60559 operations deliver results with canonical representations, unless specified otherwise.

>        signbit(-subnormal) is same as signbit(1.e0 * -subnormal); [Comment: Why?] which could be positive (zero). 
>[Comment: I don't think we've said anything about how implementations that treat subnormal representations as zero 
>values must treat the sign bit of such representations.]

I expect a bare operand and an operand in an expression to be treated the same.
I added some washy words about the sign.

>However, if subnormal operands are NOT treated as zero, that would mean (independent of flushing subnormal results):
>
>...
>        iscanonical(subnormal) is true (non-zero). [Comment: Depends on whether the representation of the subnormal 
>is canonical.]

Agreed.  But since subnormals have the minimum exponent, can one value
have more than one representation?

Attached is an updated version.


---
Fred J. Tydeman        Tydeman Consulting
tydeman at tybor.com      Testing, numerics, programming
+1 (702) 608-6093      Vice-chair of PL22.11 (ANSI "C")
Sample C99+FPCE tests: http://www.tybor.com
Savers sleep well, investors eat well, spenders work forever.

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