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Showing content from http://en.cppreference.com/w/c/numeric/math/logb.html below:

logb, logbf, logbl - cppreference.com

float       logbf( float arg );

double      logb( double arg );

long double logbl( long double arg );

#define logb( arg )

1-3) Extracts the value of the unbiased radix-independent exponent from the floating-point argument arg, and returns it as a floating-point value.

4) Type-generic macros: If arg has type long double, logbl is called. Otherwise, if arg has integer type or the type double, logb is called. Otherwise, logbf is called.

Formally, the unbiased exponent is the signed integral part of logr|arg| (returned by this function as a floating-point value), for non-zero arg, where r is FLT_RADIX. If arg is subnormal, it is treated as though it was normalized.

If no errors occur, the unbiased exponent of arg is returned as a signed floating-point value.

If a domain error occurs, an implementation-defined value is returned.

If a pole error occurs, -HUGE_VAL, -HUGE_VALF, or -HUGE_VALL is returned.

Errors are reported as specified in math_errhandling.

Domain or range error may occur if arg is zero.

If the implementation supports IEEE floating-point arithmetic (IEC 60559),

• If arg is ±0, -∞ is returned and FE_DIVBYZERO is raised.
• If arg is ±∞, +∞ is returned.
• If arg is NaN, NaN is returned.
• In all other cases, the result is exact (FE_INEXACT is never raised) and the current rounding mode is ignored.

POSIX requires that a pole error occurs if arg is ±0.

The value of the exponent returned by logb is always 1 less than the exponent returned by frexp because of the different normalization requirements: for the exponent e returned by logb, |arg*r-e
| is between 1 and r (typically between 1 and 2), but for the exponent e returned by frexp, |arg*2-e
| is between 0.5 and 1.

Compares different floating-point decomposition functions.

#include <fenv.h>
#include <float.h>
#include <math.h>
#include <stdio.h>
// #pragma STDC FENV_ACCESS ON
 
int main(void)
{
    double f = 123.45;
    printf("Given the number %.2f or %a in hex,\n", f, f);
 
    double f3;
    double f2 = modf(f, &f3);
    printf("modf() makes %.0f + %.2f\n", f3, f2);
 
    int i;
    f2 = frexp(f, &i);
    printf("frexp() makes %f * 2^%d\n", f2, i);
 
    i = logb(f);
    printf("logb()/logb() make %f * %d^%d\n", f/scalbn(1.0, i), FLT_RADIX, i);
 
    // error handling
    feclearexcept(FE_ALL_EXCEPT);
    printf("logb(0) = %f\n", logb(0));
    if (fetestexcept(FE_DIVBYZERO))
        puts("    FE_DIVBYZERO raised");
}

Possible output:

Given the number 123.45 or 0x1.edccccccccccdp+6 in hex,
modf() makes 123 + 0.45
frexp() makes 0.964453 * 2^7
logb()/logb() make 1.928906 * 2^6
logb(0) = -Inf
    FE_DIVBYZERO raised

• C23 standard (ISO/IEC 9899:2024):

• 7.12.6.11 The logb functions (p: TBD)

• 7.25 Type-generic math <tgmath.h> (p: TBD)

• F.10.3.11 The logb functions (p: TBD)

• C17 standard (ISO/IEC 9899:2018):

• 7.12.6.11 The logb functions (p: 179-180)

• 7.25 Type-generic math <tgmath.h> (p: 373-375)

• F.10.3.11 The logb functions (p: 381)

• C11 standard (ISO/IEC 9899:2011):

• 7.12.6.11 The logb functions (p: 246)

• 7.25 Type-generic math <tgmath.h> (p: 373-375)

• F.10.3.11 The logb functions (p: 522)

• C99 standard (ISO/IEC 9899:1999):

• 7.12.6.11 The logb functions (p: 227)

• 7.22 Type-generic math <tgmath.h> (p: 335-337)

• F.9.3.11 The logb functions (p: 459)

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