texcept,  fegetenv,  fegetround,  feholdexcept,  fesetround,  fesetenv,
       feupdateenv,  feenableexcept,  fedisableexcept, fegetexcept - floating-
       point rounding and exception handling

       #include <fenv.h>

       int feclearexcept(int excepts);
       int fegetexceptflag(fexcept_t *flagp, int excepts);
       int feraiseexcept(int excepts);
       int fesetexceptflag(const fexcept_t *flagp, int excepts);
       int fetestexcept(int excepts);

       int fegetround(void);
       int fesetround(int rounding_mode);

       int fegetenv(fenv_t *envp);
       int feholdexcept(fenv_t *envp);
       int fesetenv(const fenv_t *envp);
       int feupdateenv(const fenv_t *envp);

       Link with -lm.

       These eleven functions were defined in C99, and describe  the  handling
       of  floating-point  rounding  and  exceptions  (overflow,  zero-divide,

       The divide-by-zero exception occurs when an operation on finite numbers
       produces infinity as exact answer.

       The  overflow exception occurs when a result has to be represented as a
       floating-point number, but has (much) larger absolute  value  than  the
       largest (finite) floating-point number that is representable.

       The underflow exception occurs when a result has to be represented as a
       floating-point number, but has smaller absolute value than the smallest
       positive normalized floating-point number (and would lose much accuracy
       when represented as a denormalized number).

       The inexact exception occurs when the rounded result of an operation is
       not  equal  to  the  infinite  precision result.  It may occur whenever
       overflow or underflow occurs.

       The invalid exception occurs when there is no well-defined  result  for
       an operation, as for 0/0 or infinity - infinity or sqrt(-1).

   Exception handling
       Exceptions  are  represented  in  two  ways: as a single bit (exception
       present/absent), and these  bits  correspond  in  some  implementation-
       defined  way  with  bit  positions in an integer, and also as an opaque
       structure that may contain more information about the  exception  (per-
       haps the code address where it occurred).
       The fegetexceptflag() function stores a representation of the state  of
       the  exception  flags represented by the argument excepts in the opaque
       object *flagp.

       The feraiseexcept() function raises  the  supported  exceptions  repre-
       sented by the bits in excepts.

       The  fesetexceptflag() function sets the complete status for the excep-
       tions represented by excepts to the value *flagp.  This value must have
       been obtained by an earlier call of fegetexceptflag() with a last argu-
       ment that contained all bits in excepts.

       The fetestexcept() function returns a word in which the  bits  are  set
       that  were  set in the argument excepts and for which the corresponding
       exception is currently set.

   Rounding mode
       The rounding mode determines how the result  of  floating-point  opera-
       tions  is  treated when the result cannot be exactly represented in the
       significand.  Various rounding modes may be provided: round to  nearest
       (the  default), round up (toward positive infinity), round down (toward
       negative infinity), and round toward zero.

       Each  of  the  macros   FE_TONEAREST,   FE_UPWARD,   FE_DOWNWARD,   and
       FE_TOWARDZERO  is  defined when the implementation supports getting and
       setting the corresponding rounding direction.

       The fegetround() function returns the macro corresponding to  the  cur-
       rent rounding mode.

       The  fesetround()  function  sets the rounding mode as specified by its
       argument and returns zero when it was successful.

       C99 and POSIX.1-2008 specify  an  identifier,  FLT_ROUNDS,  defined  in
       <float.h>, which indicates the implementation-defined rounding behavior
       for floating-point addition.  This identifier has one of the  following

       -1     The rounding mode is not determinable.

       0      Rounding is toward 0.

       1      Rounding is toward nearest number.

       2      Rounding is toward positive infinity.

       3      Rounding is toward negative infinity.

       Other values represent machine-dependent, nonstandard rounding modes.

       The value of FLT_ROUNDS should reflect the current rounding mode as set
       by fesetround() (but see BUGS).

   Floating-point environment
       It returns zero when successful.

       The fesetenv() function restores the  floating-point  environment  from
       the  object *envp.  This object must be known to be valid, for example,
       the result of a call  to  fegetenv()  or  feholdexcept()  or  equal  to
       FE_DFL_ENV.  This call does not raise exceptions.

       The feupdateenv() function installs the floating-point environment rep-
       resented by the object *envp, except that currently  raised  exceptions
       are  not  cleared.   After calling this function, the raised exceptions
       will be a bitwise OR of those previously set with those in  *envp.   As
       before, the object *envp must be known to be valid.

       These  functions  return  zero  on  success  and  nonzero  if  an error

       These functions first appeared in glibc in version 2.1.

       IEC 60559 (IEC 559:1989), ANSI/IEEE 854, C99, POSIX.1-2001.

   Glibc notes
       If possible, the GNU C Library defines a macro FE_NOMASK_ENV which rep-
       resents  an  environment  where every exception raised causes a trap to
       occur.  You can test for this macro using #ifdef.  It is  defined  only
       if  _GNU_SOURCE  is defined.  The C99 standard does not define a way to
       set individual bits in the floating-point mask, for example, to trap on
       specific  flags.  Since version 2.2, glibc supports the functions feen-
       ableexcept() and fedisableexcept()  to  set  individual  floating-point
       traps, and fegetexcept() to query the state.

       #define _GNU_SOURCE         /* See feature_test_macros(7) */
       #include <fenv.h>

       int feenableexcept(int excepts);
       int fedisableexcept(int excepts);
       int fegetexcept(void);

       The  feenableexcept()  and fedisableexcept() functions enable (disable)
       traps for each of the exceptions represented by excepts and return  the
       previous  set  of enabled exceptions when successful, and -1 otherwise.
       The fegetexcept() function returns the set  of  all  currently  enabled

       C99  specifies  that  the value of FLT_ROUNDS should reflect changes to
       the current rounding mode, as set  by  fesetround().   Currently,  this
       does not occur: FLT_ROUNDS always has the value 1.

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