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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 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.

   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  functions 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  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.

NOTES

       The  math_errhandling  identifier  specified  by  C99 and POSIX.1-2001 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.1-2001.

       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).

SEE ALSO

       gcc(1), errno(3), fenv(3), fpclassify(3), INFINITY(3), isgreater(3), matherr(3), nan(3)
       info libc

COLOPHON

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