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logb, logbf, logbl

Defined in header `<math.h>`
float logbf( float arg );	(1)	(since C99)
double logb( double arg );	(2)	(since C99)
long double logbl( long double arg );	(3)	(since C99)
Defined in header `<tgmath.h>`
#define logb( arg )	(4)	(since C99)

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 log
r|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.

Parameters

arg

floating point value

Return value

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.

Error handling

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

Notes

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 retuned 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.

Example

Compares different floating-point decomposition functions.

#include <stdio.h>
#include <math.h>
#include <float.h>
#include <fenv.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

References

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)

frexpfrexpffrexpl (C99)(C99)	breaks a number into significand and a power of `2` (function)
ilogbilogbfilogbl (C99)(C99)(C99)	extracts exponent of the given number (function)
scalbnscalbnfscalbnlscalblnscalblnfscalblnl (C99)(C99)(C99)(C99)(C99)(C99)	computes efficiently a number times `FLT_RADIX` raised to a power (function)
C++ documentation for `logb`