Exceptions¶

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 (perhaps the code address where it occurred).

Each of the macros FE_DIVBYZERO, FE_INEXACT, FE_INVALID, FE_OVERFLOW, FE_UNDERFLOW is defined when the implementation supports handling of the corresponding exception, and if so then defines the corresponding bit(s), so that one can call exception handling functions, for example, using the integer argument FE_OVERFLOW|FE_UNDERFLOW. Other exceptions may be supported. The macro FE_ALL_EXCEPT is the bitwise OR of all bits corresponding to supported exceptions.

The feclearexcept() function clears the supported exceptions represented by the bits in its argument.

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 represented by the bits in excepts.

The fesetexceptflag() function sets the complete status for the exceptions represented by excepts to the value *flagp. This value must have been obtained by an earlier call of fegetexceptflag() with a last argument 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 operations 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 current 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 values:

-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 status flags, can be handled as one opaque object, of type fenv_t. The default environment is denoted by FE_DFL_ENV (of type const fenv_t *). This is the environment setup at program start and it is defined by ISO C to have round to nearest, all exceptions cleared and a nonstop (continue on exceptions) mode.

The fegetenv() function saves the current floating-point environment in the object *envp.

The feholdexcept() function does the same, then clears all exception flags, and sets a nonstop (continue on exceptions) mode, if available. 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 represented 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.

glibc notes¶

If possible, the GNU C Library defines a macro FE_NOMASK_ENV which represents 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 glibc 2.2, glibc supports the functions feenableexcept() 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 exceptions.