ilogb, ilogbf, ilogbl

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ilogbllogb
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FP_ILOGB0FP_ILOGBNAN
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FP_LLOGB0FP_LLOGBNAN
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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),

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

(C99)(C99)
 breaks a number into significand and a power of 2
(function)
(C99)(C99)(C99)
 extracts exponent of the given number
(function)
(C99)(C99)(C99)(C99)(C99)(C99)
 computes efficiently a number times FLT_RADIX raised to a power
(function)
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