Defect Report #296

Submitter: Fred Tydeman (USA)
Submission Date: 2004-02-10
Source: WG 14
Reference Document: N1053
Version: 1.2
Date: 2006-04-04
Subject: Is exp(INFINITY) overflow? A range error? A divide-by-zero exception? INFINITY without any errors?

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 log(0.0)), then the function returns the value of the macro HUGE_VAL, HUGE_VALF, or ...; if the integer expression math_errhandling & MATH_ERREXCEPT is nonzero, the "divide-by-zero" floating-point exception is raised if the mathematical result is an exact infinity ...

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 log(0.0)), then the function returns the value of the macro HUGE_VAL, HUGE_VALF, or ...

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).

Committee Discussion (for history only)

The following table tries to list all math functions that have an infinity for an input or an infinity for an output, as specified by Annex F.

Inf -> Inf

acosh(+INF)
asinh
cosh
sinh
exp(+INF)
exp2(+INF)
expm1(+INF)
frexp
ldexp
log(+INF)
log10(+INF)
log1p(+INF)
log2(+INF)
logb
modf
scalb
cbrt
fabs
hypot
pow(x,-INF), |x| < 1
pow(x,+INF), |x| > 1
pow(-INF,y), y > 0
pow(+INF,y), y > 0
sqrt(+INF)
lgamma
tgamma(+INF)
ceil
floor
nearbyint
rint
round
trunc
copysign(INF,y), y is anything
nextafter(INF,INF)
nexttoward(INF,INF)
fdim(INF,-INF)
fmax(+INF,any)
fmin(-INF,any)
fma(INF,INF,INF), x*y has same sign of z


Inf -> NaN + FE_INVALID

acos
asin
cos
sin
tan
acosh(-INF)
atanh
log(-INF)
log10(-INF)
log1p(-INF)
log2(-INF)
sqrt(-INF)
tgamma(-INF)
lrint
llrint
lround
llround
fmod(INF,any)
remainder(INF,any)
remquo(INF,any)
fma(INF,INF,INF), x*y has opposite sign of z
fma(0,INF,z), z not a NaN
fma(x,INF,-INF), x has same sign as INF


Inf -> finite

atan
atan2
tanh
exp(-INF)
exp2(-INF)
expm1(-INF)
pow(0,+INF)
pow(-1,INF)
pow(+1,INF)
pow(INF,0)
pow(x,-INF), |x| > 1
pow(x,+INF), |x| < 1
pow(-INF,y), y < 0
pow(+INF,y), y < 0
erf
erfc
fmod(x,INF), x not infinite
remainder(x,INF), x finite
remquo(x,INF), x finite
copysign(x,INF), x finite
fdim(INF,INF)
fmax(-INF,y), y finite
fmin(+INF,y), y finite


finite -> Inf + FE_DIVBYZERO

atanh(+/-1)
log(+/-0)
log10(+/-0)
log1p(-1)
log2(+/-0)
logb(+/-0)
pow(0,y), y an odd integer < 0
pow(0,y), y < 0 and not an odd integer [and finite]
lgamma(x), x is negative integer or zero
tgamma(+/-0)


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 log(0.0)), then the function returns the value of the macro HUGE_VAL, HUGE_VALF, or ...

Rationale Change

Add the following to 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).