Issue 0409: f(inf) is inf being a range error

This issue has been automatically converted from the original issue lists and some formatting may not have been preserved.

Authors: WG 14, Fred J. Tydeman (USA)
Date: 2012-01-11
Reference document: N1593
Submitted against: C11 / C17
Status: Closed
Converted from: n2396.htm

Summary

Several of the functions in <math.h> that compute infinity for f(infinity) have the phrase (or something similar):

A range error occurs if the magnitude of x is too large.

Since infinity is 'too large', one might conclude that f(infinity) is a range error for those functions.

However, 7.12.1#5 has:

A floating result overflows if the magnitude of the mathematical result is finite but so large that the mathematical result cannot be represented without extraordinary roundoff error ...

The key word being 'finite'. So, one could conclude f(infinity) being infinity is not overflow (and therefore, not a range error).

To me, this appears to be a contradiction. I have encountered both kinds of implementations; some treat this case as a range error, and others that do not.

For both LIA and IEEE-754, f(infinity) being infinity is not considered an error.

Suggested Change

1. 7.12.5.4 The cosh functions

   Change to: A range error occurs if the magnitude of finite x is too large.

2. 7.12.5.5 The sinh functions

   Change to: A range error occurs if the magnitude of finite x is too large.

3. 7.12.6.1 The exp functions

   Change to: A range error occurs if the magnitude of finite x is too large.

4. 7.12.6.2 The exp2 functions

   Change to: A range error occurs if the magnitude of finite x is too large.

5. 7.12.6.3 The expm1 functions

   Change to: A range error occurs if the magnitude of finite x is too large.

6. 7.12.6.6 The ldexp functions

   Change to: A range error may occur for finite arguments.

7. 7.12.6.13 The scalbn and scalbln functions

   Change to: A range error may occur for finite arguments.

8. 7.12.7.3 The hypot functions

   Change to: A range error may occur for finite arguments.

9. 7.12.7.4 The pow functions

   Change to: A range error may occur for finite arguments.

10. 7.12.8.2 The erfc functions

    Change to: A range error occurs if finite x is too large.

11. 7.12.8.3 The lgamma functions

    Change to: A range error occurs if finite x is too large.

12. 7.12.8.4 The tgamma functions

    Change to: A range error occurs if the magnitude of finite x is too large and may occur if the magnitude of x is too small.

13. 7.12.12.1 The fdim functions

    Change to: A range error may occur for finite arguments.

14. 7.12.13.1 The fma functions

    Change to: A range error may occur for finite arguments.

Comment from WG14 on 2016-10-21:

Feb 2012 meeting

Committee Discussion

• The committee rejected the Suggested Change in the main body of this defect report.

• The committee considered the following, but rejected it (as just being a restatement of 7.12.1 paragraphs 4 and 5).

  If the result overflows, a range error shall occur.

• A question arose as to why these range error cases are listed in the individual functions (instead of just being covered by the blanket 7.12.1 paragraphs 4, 5, and 6)

  7.12.1 paragraph 1 has the answer:

  The behavior of each of the functions in <math.h> is specified for all representable values of its input arguments, except where stated otherwise.

• Several other approaches were discussed, without any consensus reached

  1. Add a footnote to 7.12.1 paragraph 5, first sentence:

     In an implementation that supports infinities, a range error may happen for functions that map an infinity argument into an exact infinity or exact zero result.

  2. Add to end of 7.12.1 paragraph 4:

     Recommended practice

     In an implementation that supports infinities, a range error should not happen for functions that map an infinity argument into an exact infinity or exact zero result.

  3. Add to 7.12.1 paragraph 4:

     An implementation may define additional range errors, provided that such errors are consistent with the mathematical definition of the function.

Oct 2012 meeting

Committee Discussion

• Fred wrote a paper N1629 discussing "Fixing a contradiction" and "Taking care of infinity".
• The definition of range error, however, in 7.12.1 paragraph 4 indicates infinity is excluded (since it has a representation), and as such no change is required.

Oct 2015 meeting

Committee Discussion

Fred presented another paper N1979 noting an error in the October 2012 committee response, and after discussion, the proposed clarification was adopted, and is as follows

Proposed Committee Response

The definition of range error in 7.12.1 paragraph 4 excludes infinity.

For example, exp(+infinity) is +infinity. Since the input +infinity is representable, then the output +infinity is representable in an object of the specified type. By, 7.12.1 paragraph 4, a range error has not happened. Also, by 7.12.1 paragraph 5, since the result is not finite, overflow has not happened.