**Submitter:** Fred Tydeman (USA)

**Submission Date:** 2004-02-10

**Source:** WG 14

**Reference Document:**comp.std.c 2004-1-20:
<math.h>, infinity and range errors

**Version:** 1.0

**Date:** 2004-02-10

**Subject:** Is ` exp(INFINITY)` overflow? A
range error? A divide-by-zero exception?

**Summary**

I believe that there are some words missing from 7.12.1
Treatment of error conditions. Currently, the words allow
` exp(INFINITY)` to be considered an overflow of
the divide-by-zero type. This is wrong. An infinite result
from infinite operands is not an error; it is an exact
unexceptional operation.

**Details from C99+TC1**

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 in an object of the specified type. If a floating result overflows and default rounding is in effect, or if the mathematical result is an exact infinity (for example), then the function returns the value of the macrolog(0.0),HUGE_VAL, or ...; if the integer expressionHUGE_VALFis nonzero, the "divide-by-zero" floating-point exception is raised if the mathematical result is an exact infinity ...math_errhandling & MATH_ERREXCEPT

In addition, IEEE-754 has in 6.1 Infinity Arithmetic:

Arithmetic on INFINITY is always exact and therefor shall signal no exceptions, except for the invalid operations specified for INFINITY in 7.1.

The invalid operations on INFINITY in IEEE-754 are: INF-INF, 0*INF, INF/INF, INF REM y, sqrt(-INF).

**Suggested Technical Corrigendum**

Add ", from finite arguments," as indicated below to paragraph 4 in 7.12.1 Treatment of error conditions.

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 in an object of the specified type. If a floating result overflows and default rounding is in effect, or if the mathematical result is an exact infinity, from finite arguments, (for example), then the function returns the value of the macrolog(0.0),HUGE_VAL, or ...HUGE_VALF

In addition, add the following to the Rationale in 7.12.1:

Operations on INFINITY are either invalid or exact. Some examples of invalid operations are: INF-INF, INF*0, INF/INF, sqrt(-INF), cexp(r+I*INF). Some examples of exact operations, which also are unexceptional, are INF+x, INF*x, INF/x, sqrt(+INF), exp(INF).