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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.

double frexp (double value, int *exponent) Function
float frexpf (float value, int *exponent) Function
long double frexpl (long double value, int *exponent) Function
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 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.

double ldexp (double value, int exponent) Function
float ldexpf (float value, int exponent) Function
long double ldexpl (long double value, int exponent) Function
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.

double scalb (double value, int exponent) Function
float scalbf (float value, int exponent) Function
long double scalbl (long double value, int exponent) Function
The scalb function is the BSD name for ldexp.

long long int scalbn (double x, int n) Function
long long int scalbnf (float x, int n) Function
long long int scalbnl (long double x, int n) Function
scalbn is identical to scalb, except that the exponent n is an int instead of a floating-point number.

long long int scalbln (double x, long int n) Function
long long int scalblnf (float x, long int n) Function
long long int scalblnl (long double x, long int n) Function
scalbln is identical to scalb, except that the exponent n is a long int instead of a floating-point number.

long long int significand (double x) Function
long long int significandf (float x) Function
long long int significandl (long double x) Function
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.