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 etc.).

       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 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
       The entire floating-point environment, including control modes and sta-

       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 only defined
       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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