logb, logbf, logbl

 

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Numerics

Common mathematical functions

Floating-point environment

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Type-generic math

 

Common mathematical functions

Functions
Basic operations
abslabsllabsimaxabs (C99) fabs divldivlldivimaxdiv (C99) fmod	remainder (C99) remquo (C99) fma (C99) fmax (C99) fmin (C99) fdim (C99) nannanfnanl (C99)(C99)(C99)
Exponential functions
exp exp2 (C99) expm1 (C99)	log log10 log1p (C99) log2 (C99)
Power functions
sqrt cbrt (C99)	hypot (C99) pow
Trigonometric and hyperbolic functions
sin cos tan asin acos atan atan2	sinh cosh tanh asinh (C99) acosh (C99) atanh (C99)
Error and gamma functions
erf (C99) erfc (C99)	lgamma (C99) tgamma (C99)
Nearest integer floating point operations
ceil floor roundlroundllround (C99)(C99)(C99)	trunc (C99) nearbyint (C99) rintlrintllrint (C99)(C99)(C99)
Floating point manipulation functions
ldexp scalbnscalbln (C99)(C99) ilogb (C99) logb (C99)	frexp modf nextafternexttoward (C99)(C99) copysign (C99)
Classification
fpclassify (C99)
isfinite (C99)
isinf (C99)
isnan (C99)
isnormal (C99)
signbit (C99)
Macro constants
HUGE_VALFHUGE_VALHUGE_VALL (C99)(C99)	FP_NORMALFP_SUBNORMALFP_ZEROFP_INFINITEFP_NAN (C99)(C99)(C99)(C99)(C99)

 

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

Run this code

#include <stdio.h>
#include <math.h>
#include <float.h>
#include <fenv.h>
 
#pragma STDC FENV_ACCESS ON
int main()
{
    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

See also

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