math_error - detecting errors from mathematical functions

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 "underflow"
(**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 fetestexcept(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).

This page is part of release 5.10 of the Linux `man-pages`

project. A description of the project, information about reporting bugs,
and the latest version of this page, can be found at
https://www.kernel.org/doc/man-pages/.