# logb, logbf, logbl

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< c‎ | numeric‎ | math

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(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

- 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)

### See also

frexp frexpf frexpl (C99)(C99) | breaks a number into significand and a power of 2 (function)
ilogb ilogbf ilogbl (C99)(C99)(C99) | extracts exponent of the given number (function)
scalbn scalbnf scalbnl scalbln scalblnf scalblnl (C99)(C99)(C99)(C99)(C99)(C99) | computes efficiently a number times FLT_RADIX raised to a power (function)

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