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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 non-zero, or
       the following call (see fenv(3)) returns non-zero

           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  non-zero,  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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