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Many of the math functions are defined only over a subset of the real or
complex numbers. Even if they are mathematically defined, their result
may be larger or smaller than the range representable by their return
type without loss of accuracy. These are known as *domain errors*,
*overflows*, and
*underflows*, respectively. Math functions do several things when
one of these errors occurs. In this manual we will refer to the
complete response as *signalling* a domain error, overflow, or
underflow.

When a math function suffers a domain error, it raises the invalid
exception and returns NaN. It also sets `errno` to `EDOM`

;
this is for compatibility with old systems that do not support IEEE 754 exception handling. Likewise, when overflow occurs, math
functions raise the overflow exception and, in the default rounding
mode, return *∞* or *-∞* as appropriate
(in other rounding modes, the largest finite value of the appropriate
sign is returned when appropriate for that rounding mode). They also
set `errno` to `ERANGE`

if returning *∞* or
*-∞*; `errno` may or may not be set to
`ERANGE`

when a finite value is returned on overflow. When
underflow occurs, the underflow exception is raised, and zero
(appropriately signed) or a subnormal value, as appropriate for the
mathematical result of the function and the rounding mode, is
returned. `errno` may be set to `ERANGE`

, but this is not
guaranteed; it is intended that the GNU C Library should set it when the
underflow is to an appropriately signed zero, but not necessarily for
other underflows.

When a math function has an argument that is a signaling NaN,
the GNU C Library does not consider this a domain error, so `errno`

is
unchanged, but the invalid exception is still raised (except for a few
functions that are specified to handle signaling NaNs differently).

Some of the math functions are defined mathematically to result in a
complex value over parts of their domains. The most familiar example of
this is taking the square root of a negative number. The complex math
functions, such as `csqrt`

, will return the appropriate complex value
in this case. The real-valued functions, such as `sqrt`

, will
signal a domain error.

Some older hardware does not support infinities. On that hardware,
overflows instead return a particular very large number (usually the
largest representable number). `math.h` defines macros you can use
to test for overflow on both old and new hardware.

- Macro:
*double***HUGE_VAL** - Macro:
*float***HUGE_VALF** - Macro:
*long double***HUGE_VALL** An expression representing a particular very large number. On machines that use IEEE 754 floating point format,

`HUGE_VAL`

is infinity. On other machines, it’s typically the largest positive number that can be represented.Mathematical functions return the appropriately typed version of

`HUGE_VAL`

or`-HUGE_VAL`

when the result is too large to be represented.

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