MATH_ERROR(7)             (2017-09-15)              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
          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 func-
          tions are described below.

        Domain error
          A domain error occurs when a mathematical function is sup-
          plied 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 func-
          tions 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 func-
          tion is an exact infinity (e.g., the logarithm of 0 is

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          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 over-
          flow 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 posi-
          tive 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 argu-
          ment 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 signif-
          icand.

     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 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) sit-
          uation 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

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          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).

     SEE ALSO
          gcc(1), errno(3), fenv(3), fpclassify(3), INFINITY(3),
          isgreater(3), matherr(3), nan(3)

          info libc

     COLOPHON
          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/.

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