Defect Report #409

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Submitter: Fred J. Tydeman (USA)
Submission Date: 2012-1-11
Source: WG 14
Reference Document: N1593
Version: 1.1
Date: October 2012
Subject: f(inf) is inf being a range error

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.


Feb 2012 meeting

Committee Discussion

Oct 2012 meeting

Committee Discussion

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, a range error has not happened.

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