# math_error

```MATH_ERROR(7)              Linux Programmer's Manual             MATH_ERROR(7)

NAME
math_error - detecting errors from mathematical functions

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

DESCRIPTION
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  feclearex-
cept(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.

Domain error
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 func-
tions return a different value in this case); errno is set to EDOM, and
an "invalid" (FE_INVALID) floating-point exception is raised.

Pole error
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.

Range error
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  func-
tion  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  repre-
sented  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 sig-
nificant bit of the significand).  The representation  of  a  subnormal
number will contain one or more leading zeros in the significand.

NOTES
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).