math_error - detecting errors from mathematical functions

**#include <math.h>**
**#include <errno.h>**
**#include <fenv.h>**

When an error occurs, most library functions indicate this fact by returning a
special value (e.g., -1 or NULL). Because they typically return a
floating-point number, the mathematical functions declared in

*<math.h>* indicate an error using other mechanisms. There are two
error-reporting mechanisms: the older one sets

*errno*; the newer one
uses the floating-point exception mechanism (the use of

**feclearexcept**(3) and

**fetestexcept**(3), as outlined below)
described in

**fenv**(3).

A portable program that needs to check for an error from a mathematical function
should set

*errno* to zero, and make the following call

feclearexcept(FE_ALL_EXCEPT);

before calling a mathematical function.

Upon return from the mathematical function, if

*errno* is nonzero, or the
following call (see

**fenv**(3)) returns nonzero

fetestexcept(FE_INVALID | FE_DIVBYZERO | FE_OVERFLOW |
FE_UNDERFLOW);

then an error occurred in the mathematical function.

The error conditions that can occur for mathematical functions are described
below.

A

*domain error* occurs when a mathematical function is supplied with an
argument whose value falls outside the domain for which the function is
defined (e.g., giving a negative argument to

**log**(3)). When a domain
error occurs, math functions commonly return a NaN (though some functions
return a different value in this case);

*errno* is set to

**EDOM**,
and an "invalid" (

**FE_INVALID**) floating-point exception is
raised.

A

*pole error* occurs when the mathematical result of a function is an
exact infinity (e.g., the logarithm of 0 is negative infinity). When a pole
error occurs, the function returns the (signed) value

**HUGE_VAL**,

**HUGE_VALF**, or

**HUGE_VALL**, depending on whether the function
result type is

*double*,

*float*, or

*long double*. The sign of
the result is that which is mathematically correct for the function.

*errno* is set to

**ERANGE**, and a "divide-by-zero"
(

**FE_DIVBYZERO**) floating-point exception is raised.

A

*range error* occurs when the magnitude of the function result means that
it cannot be represented in the result type of the function. The return value
of the function depends on whether the range error was an overflow or an
underflow.

A floating result

*overflows* if the result is finite, but is too large to
represented in the result type. When an overflow occurs, the function returns
the value

**HUGE_VAL**,

**HUGE_VALF**, or

**HUGE_VALL**, depending on
whether the function result type is

*double*,

*float*, or

*long
double*.

*errno* is set to

**ERANGE**, and an "overflow"
(

**FE_OVERFLOW**) floating-point exception is raised.

A floating result

*underflows* if the result is too small to be represented
in the result type. If an underflow occurs, a mathematical function typically
returns 0.0 (C99 says a function shall return "an implementation-defined
value whose magnitude is no greater than the smallest normalized positive
number in the specified type").

*errno* may be set to

**ERANGE**,
and an "overflow" (

**FE_UNDERFLOW**) floating-point exception may
be raised.

Some functions deliver a range error if the supplied argument value, or the
correct function result, would be

*subnormal*. A subnormal value is one
that is nonzero, but with a magnitude that is so small that it can't be
presented in normalized form (i.e., with a 1 in the most significant bit of
the significand). The representation of a subnormal number will contain one or
more leading zeros in the significand.

The

*math_errhandling* identifier specified by C99 and POSIX.1 is not
supported by glibc. This identifier is supposed to indicate which of the two
error-notification mechanisms (

*errno*, exceptions retrievable via

**fettestexcept**(3)) is in use. The standards require that at least one be
in use, but permit both to be available. The current (version 2.8) situation
under glibc is messy. Most (but not all) functions raise exceptions on errors.
Some also set

*errno*. A few functions set

*errno*, but don't raise
an exception. A very few functions do neither. See the individual manual pages
for details.

To avoid the complexities of using

*errno* and

**fetestexcept**(3) for
error checking, it is often advised that one should instead check for bad
argument values before each call. For example, the following code ensures that

**log**(3)'s argument is not a NaN and is not zero (a pole error) or less
than zero (a domain error):

double x, r;
if (isnan(x) || islessequal(x, 0)) {
/* Deal with NaN / pole error / domain error */
}
r = log(x);

The discussion on this page does not apply to the complex mathematical functions
(i.e., those declared by

*<complex.h>*), which in general are not
required to return errors by C99 and POSIX.1.

The

**gcc**(1)

*-fno-math-errno* option causes the executable to employ
implementations of some mathematical functions that are faster than the
standard implementations, but do not set

*errno* on error. (The

**gcc**(1)

*-ffast-math* option also enables

*-fno-math-errno*.)
An error can still be tested for using

**fetestexcept**(3).

**gcc**(1),

**errno**(3),

**fenv**(3),

**fpclassify**(3),

**INFINITY**(3),

**isgreater**(3),

**matherr**(3),

**nan**(3)

*info libc*