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Showing content from https://www.open-std.org/jtc1/sc22/wg14/www/docs/n2506.htm below:

Range errors and math functions

Submitter:Fred Tydeman
Submission Date: 2020-03-20
Document: WG14 N2506
Reference Documents:

Summary

The standard has a few incorrect, missing, or ambiguous statements about range errors in some of the math functions.

Does "too large" mean close to +infinity or +/-infinity?

Does "too small" mean close to -infinity or +/-zero?

Implementers have interpreted these terms differently.

Some implementations incorrectly treat f(infinity) as a range error based upon the text: A range error occurs if [the magnitude of] x is too large. While this is covered by 7.12.1#5 about overflows, the CFP group believes it is better to be explicit in each math function where it matters.

Possible Technical Corrigendum:

• Treatment of error conditions

  Change 7.12.1#5

  ... overflows if the magnitude ...

  to:

  ... overflows if the magnitude (absolute value) ...

• Treatment of error conditions

  Change 7.12.1#6

  ... underflows if the magnitude ...

  to:

  ... underflows if the magnitude (absolute value) ...

• The asin functions

  Add to 7.12.4.2#2

  A range error occurs if nonzero x is too close to zero.

• The atan functions

  Add to 7.12.4.3#2

  A range error occurs if nonzero x is too close to zero.

• The atan2 functions

  Add to 7.12.4.4#2

  A range error occurs if x is positive and nonzero y/x is too close to zero.

• The sin functions

  Add to 7.12.4.6#2

  A range error occurs if nonzero x is too close to zero.

• The tan functions

  Add to 7.12.4.7#2

  A range error occurs if nonzero x is too close to zero.

• The asinpi functions

  Change 7.12.4.9#2

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

  to:

  A range error occurs if the magnitude of nonzero x is too small close to zero.

• The atanpi functions

  Change 7.12.4.10#2

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

  to:

  A range error occurs if the magnitude of nonzero x is too small close to zero.

• The atan2pi functions

  Change 7.12.4.11#2

  A range error occurs if x is positive and the magnitude of nonzero y/x is too small.

  to:

  A range error occurs if x is positive and the magnitude of nonzero y/x is too small close to zero.

• The sinpi functions

  Add to 7.12.4.13#2

  A range error occurs if nonzero x is too close to zero.

• The tanpi functions

  Add to 7.12.4.14#2

  A range error occurs if nonzero x is too close to zero.

• The asinh functions

  Add to 7.12.5.2#2

  A range error occurs if nonzero x is too close to zero.

• The atanh functions

  Add to 7.12.5.3#2

  A range error occurs if nonzero x is too close to zero.

• The cosh functions

  Change 7.12.5.4#2 from

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

  to

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

• The sinh functions

  Change 7.12.5.5#2 from

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

  to

  A range error occurs if the magnitude of finite x is too large or if nonzero x is too close to zero.

• The tanh functions

  Add to 7.12.5.6#2

  A range error occurs if nonzero x is too close to zero.

• The exp functions

  Change 7.12.6.1#2 from

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

  to

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

• The exp10 functions

  Change 7.12.6.2#2 from

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

  to

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

• The exp10m1 functions

  Change 7.12.6.3#2 from

  A range error occurs if finite x is too large or if the magnitude of nonzero x is too small.

  to

  A range error occurs if positive finite x is too large or if the magnitude of nonzero x is too small close to zero.

• The exp2 functions

  Change 7.12.6.4#2 from

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

  to

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

• The exp2m1 functions

  Change 7.12.6.5#2 from

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

  to

  A range error occurs if the magnitude of positive finite x is too large or if the magnitude of nonzero x is too small close to zero.

• The expm1 functions

  Change 7.12.6.6#2 from

  A range error occurs if positive x is too large.252)

  to

  A range error occurs if positive finite x is too large or if nonzero x is too close to zero.252)

• The ldexp functions

  Change 7.12.6.9#2 from

  A range error may occur.

  to

  A range error may occur occurs for some finite x, depending on p.

• The log10p1 function

  Change 7.12.6.13#2

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

  to:

  A range error occurs if the magnitude nonzero x is too small close to zero.

• The log1p and logp1 functions

  Add to 7.12.6.14#2

  A range error occurs if nonzero x is too close to zero.

• The log2p1 functions

  Add to 7.12.6.16#2

  A range error occurs if nonzero x is too close to zero.

• The scalbn and scalbln functions

  Change 7.12.6.19#2 from

  A range error may occur.

  to

  A range error may occur occurs for some finite x, depending on n.

• The compoundn functions

  Change 7.12.7.2#2 from

  A range error may occur if n is too large, depending on x.

  to

  A range error may occur occurs if positive finite x n is too large or if x is too near but not equal to -1, depending on n x.

• The hypot functions

  Change 7.12.7.4#2 from

  A range error may occur.

  to

  A range error may occur occurs for some finite arguments.

• The pow functions

  Change 7.12.7.5#2 from

  A range error may occur.

  to

  A range error may occur ocurs if the magnitude of nonzero finite x is too large or too near zero, depending on y.

• The pown functions

  Change 7.12.7.6#2 from

  A range error may occur.

  to

  A range error may occur occurs if the magnitude of nonzero finite x is too large or too near zero, depending on n.

• The powr functions

  Change 7.12.7.7#2 from

  A range error may occur.

  to

  A range error may occur occurs if positive nonzero finite x is too large or too near zero, depending on y.

• The rootn functions

  Change 7.12.7.8#2 from

  A range error may occur if n is -1.

  to

  A range error may occur occurs if n is -1 and the magnitude of nonzero finite x is too large or too near zero .

• The erf functions

  Add to 7.12.8.1#2

  A range error occurs if nonzero x is too close to zero.

• The erfc functions

  Change 7.12.8.2#2

  A range error occurs if positive x is too large.

  to:

  A range error occurs if positive finite x is too large.

• The lgamma functions

  Change 7.12.8.3#2

  A range error occurs if positive x is too large.

  to:

  A range error occurs if positive finite x is too large.

• The tgamma functions

  Change 7.12.8.4#2

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

  to:

  A range error occurs for some negative finite x, and if the magnitude of positive finite x is too large or and may occur if the magnitude of nonzero x is too small close to zero.

• The fmod functions

  Add to 7.12.10.1#2

  A range error occurs if x is finite, both x and y are nonzero, and either is too close to zero.

• The remainder functions

  Add to 7.12.10.2#2

  A range error occurs if x is finite, both x and y are nonzero, and either is too close to zero.

• The fdim functions

  Change 7.12.12.1#2

  A range error may occur.

  to:

  A range error may occur occurs if positive finite x-y is too large or too close to zero.

• The fma functions

  Change 7.12.13.1#2

  A range error may occur.

  to:

  A range error may occur occurs for some finite arguments.

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