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20.8.5 Setting and modifying single bits of FP values

There are some operations that are too complicated or expensive to perform by hand on floating-point numbers. ISO C99 defines functions to do these operations, which mostly involve changing single bits.

Function: double copysign (double x, double y)
Function: float copysignf (float x, float y)
Function: long double copysignl (long double x, long double y)
These functions return x but with the sign of y. They work even if x or y are NaN or zero. Both of these can carry a sign (although not all implementations support it) and this is one of the few operations that can tell the difference.

`copysign` never raises an exception.

This function is defined in IEC 559 (and the appendix with recommended functions in IEEE 754/IEEE 854).

Function: int signbit (float-type x)
`signbit` is a generic macro which can work on all floating-point types. It returns a nonzero value if the value of x has its sign bit set.

This is not the same as `x < 0.0`, because IEEE 754 floating point allows zero to be signed. The comparison `-0.0 < 0.0` is false, but `signbit (-0.0)` will return a nonzero value.

Function: double nextafter (double x, double y)
Function: float nextafterf (float x, float y)
Function: long double nextafterl (long double x, long double y)
The `nextafter` function returns the next representable neighbor of x in the direction towards y. The size of the step between x and the result depends on the type of the result. If x = y the function simply returns y. If either value is `NaN`, `NaN` is returned. Otherwise a value corresponding to the value of the least significant bit in the mantissa is added or subtracted, depending on the direction. `nextafter` will signal overflow or underflow if the result goes outside of the range of normalized numbers.

This function is defined in IEC 559 (and the appendix with recommended functions in IEEE 754/IEEE 854).

Function: double nexttoward (double x, long double y)
Function: float nexttowardf (float x, long double y)
Function: long double nexttowardl (long double x, long double y)
These functions are identical to the corresponding versions of `nextafter` except that their second argument is a ```long double```.

Function: double nan (const char *tagp)
Function: float nanf (const char *tagp)
Function: long double nanl (const char *tagp)
The `nan` function returns a representation of NaN, provided that NaN is supported by the target platform. `nan ("n-char-sequence")` is equivalent to `strtod ("NAN(n-char-sequence)")`.

The argument tagp is used in an unspecified manner. On IEEE 754 systems, there are many representations of NaN, and tagp selects one. On other systems it may do nothing.

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