# ilogb, ilogbf, ilogbl

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< c‎ | numeric‎ | math

Defined in header `<math.h>` |  |
int ilogbf( float arg ); | (1) | (since C99)
int ilogb( double arg ); | (2) | (since C99)
int ilogbl( long double arg ); | (3) | (since C99)
Defined in header `<tgmath.h>` |  |
#define ilogb( arg ) | (4) | (since C99)
Defined in header `<math.h>` |  |
#define FP_ILOGB0 /*implementation-defined*/ | (5) | (since C99)
#define FP_ILOGBNAN /*implementation-defined*/ | (6) | (since C99)

1-3) Extracts the value of the unbiased exponent from the floating-point argument `arg`, and returns it as a signed integer value.
4) Type-generic macros: If `arg` has type long double, `ilogbl` is called. Otherwise, if `arg` has integer type or the type double, `ilogb` is called. Otherwise, `ilogbf` is called.
5) Expands to integer constant expression whose value is either INT_MIN or -INT_MAX.
6) Expands to integer constant expression whose value is either INT_MIN or +INT_MAX.

Formally, the unbiased exponent is the integral part of log
r|arg| as a signed integral value, for non-zero arg, where `r` is FLT_RADIX.

### Parameters

arg | - | floating point value

### Return value

If no errors occur, the unbiased exponent of `arg` is returned as a signed int value.

If `arg` is zero, FP_ILOGB0 is returned.

If `arg` is infinite, INT_MAX is returned.

If `arg` is a NaN, FP_ILOGBNAN is returned.

If the correct result is greater than INT_MAX or smaller than INT_MIN, the return value is unspecified and a domain error or range error may occur

### Error handling

Errors are reported as specified in math_errhandling.

A domain error or range error may occur if `arg` is zero, infinite, or NaN.

If the correct result is greater than INT_MAX or smaller than INT_MIN, a domain error or a range error may occur

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

- If the correct result is greater than INT_MAX or smaller than INT_MIN, FE_INVALID is raised.
- If `arg` is ±0, ±∞, or NaN, FE_INVALID is raised.
- In all other cases, the result is exact (FE_INEXACT is never raised) and the current rounding mode is ignored

### Notes

If `arg` is not zero, infinite, or NaN, the value returned is exactly equivalent to (int)logb(arg).

POSIX requires that a domain error occurs if `arg` is zero, infinite, NaN, or if the correct result is outside of the range of int.

POSIX also requires that, on XSI-conformant systems, the value returned when the correct result is greater than INT_MAX is INT_MAX and the value returned when the correct result is less than INT_MIN is INT_MIN.

The correct result can be represented as int on all known implementations. For overflow to occur, INT_MAX must be less than LDBL_MAX_EXP*log2(FLT_RADIX) or INT_MIN must be greater than LDBL_MIN_EXP-LDBL_MANT_DIG)*log2(FLT_RADIX).

The value of the exponent returned by `ilogb` is always 1 less than the exponent retuned by frexp because of the different normalization requirements: for the exponent `e` returned by `ilogb`, |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

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 = ilogb(f);
        printf("logb()/ilogb() make %f * %d^%d\n", f/scalbn(1.0, i), FLT_RADIX, i);

        // error handling
        feclearexcept(FE_ALL_EXCEPT);
        printf("ilogb(0) = %d\n", ilogb(0));
        if(fetestexcept(FE_INVALID)) puts("    FE_INVALID 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()/ilogb() make 1.92891 * 2^6
    ilogb(0) = -2147483648
        FE_INVALID raised

### References

- C11 standard (ISO/IEC 9899:2011):

  - 7.12/8 Mathematics <math.h> (p: 232)

  - 7.12.6.5 The ilogb functions (p: 244)

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

  - F.10.3.5 The ilogb functions (p: 521)

- C99 standard (ISO/IEC 9899:1999):

  - 7.12/8 Mathematics <math.h> (p: 213)

  - 7.12.6.5 The ilogb functions (p: 224-225)

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

  - F.9.3.5 The ilogb functions (p: 458)

### See also

frexp frexpf frexpl (C99)(C99) | breaks a number into significand and a power of 2 (function)
logb logbf logbl (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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