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#### 20.8.2 Normalization Functions

The functions described in this section are primarily provided as a way to efficiently perform certain low-level manipulations on floating point numbers that are represented internally using a binary radix; see Floating Point Concepts. These functions are required to have equivalent behavior even if the representation does not use a radix of 2, but of course they are unlikely to be particularly efficient in those cases.

All these functions are declared in math.h.

Function: double frexp (double value, int *exponent)
Function: float frexpf (float value, int *exponent)
Function: long double frexpl (long double value, int *exponent)
Function: _FloatN frexpfN (_FloatN value, int *exponent)
Function: _FloatNx frexpfNx (_FloatNx value, int *exponent)

Preliminary: | MT-Safe | AS-Safe | AC-Safe | See POSIX Safety Concepts.

These functions are used to split the number value into a normalized fraction and an exponent.

If the argument value is not zero, the return value is value times a power of two, and its magnitude is always in the range 1/2 (inclusive) to 1 (exclusive). The corresponding exponent is stored in `*exponent`; the return value multiplied by 2 raised to this exponent equals the original number value.

For example, `frexp (12.8, &exponent)` returns `0.8` and stores `4` in `exponent`.

If value is zero, then the return value is zero and zero is stored in `*exponent`.

Function: double ldexp (double value, int exponent)
Function: float ldexpf (float value, int exponent)
Function: long double ldexpl (long double value, int exponent)
Function: _FloatN ldexpfN (_FloatN value, int exponent)
Function: _FloatNx ldexpfNx (_FloatNx value, int exponent)

Preliminary: | MT-Safe | AS-Safe | AC-Safe | See POSIX Safety Concepts.

These functions return the result of multiplying the floating-point number value by 2 raised to the power exponent. (It can be used to reassemble floating-point numbers that were taken apart by `frexp`.)

For example, `ldexp (0.8, 4)` returns `12.8`.

The following functions, which come from BSD, provide facilities equivalent to those of `ldexp` and `frexp`. See also the ISO C function `logb` which originally also appeared in BSD. The `_FloatN` and `_FloatN` variants of the following functions come from TS 18661-3:2015.

Function: double scalb (double value, double exponent)
Function: float scalbf (float value, float exponent)
Function: long double scalbl (long double value, long double exponent)

Preliminary: | MT-Safe | AS-Safe | AC-Safe | See POSIX Safety Concepts.

The `scalb` function is the BSD name for `ldexp`.

Function: double scalbn (double x, int n)
Function: float scalbnf (float x, int n)
Function: long double scalbnl (long double x, int n)
Function: _FloatN scalbnfN (_FloatN x, int n)
Function: _FloatNx scalbnfNx (_FloatNx x, int n)

Preliminary: | MT-Safe | AS-Safe | AC-Safe | See POSIX Safety Concepts.

`scalbn` is identical to `scalb`, except that the exponent n is an `int` instead of a floating-point number.

Function: double scalbln (double x, long int n)
Function: float scalblnf (float x, long int n)
Function: long double scalblnl (long double x, long int n)
Function: _FloatN scalblnfN (_FloatN x, long int n)
Function: _FloatNx scalblnfNx (_FloatNx x, long int n)

Preliminary: | MT-Safe | AS-Safe | AC-Safe | See POSIX Safety Concepts.

`scalbln` is identical to `scalb`, except that the exponent n is a `long int` instead of a floating-point number.

Function: double significand (double x)
Function: float significandf (float x)
Function: long double significandl (long double x)

Preliminary: | MT-Safe | AS-Safe | AC-Safe | See POSIX Safety Concepts.

`significand` returns the mantissa of x scaled to the range [1, 2). It is equivalent to `scalb (x, (double) -ilogb (x))`.

This function exists mainly for use in certain standardized tests of IEEE 754 conformance.

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