# scalbn, scalbnf, scalbnl, scalbln, scalblnf, scalblnl

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< c‎ | numeric‎ | math

Defined in header `<math.h>` |  |
float scalbnf( float arg, int exp ); | (1) | (since C99)
double scalbn( double arg, int exp ); | (2) | (since C99)
long double scalbnl( long double arg, int exp ); | (3) | (since C99)
Defined in header `<tgmath.h>` |  |
#define scalbn( arg, exp ) | (4) | (since C99)
Defined in header `<math.h>` |  |
float scalblnf( float arg, long exp ); | (5) | (since C99)
double scalbln( double arg, long exp ); | (6) | (since C99)
long double scalblnl( long double arg, long exp ); | (7) | (since C99)
Defined in header `<tgmath.h>` |  |
#define scalbln( arg, exp ) | (8) | (since C99)

1-3,5-7) Multiplies a floating point value `arg` by FLT_RADIX raised to power `exp`.
4,8) Type-generic macros: If `arg` has type long double, `scalbnl` or `scalblnl` is called. Otherwise, if `arg` has integer type or the type double, `scalbn` or `scalbln` is called. Otherwise, `scalbnf` or `scalblnf` is called, respectively.

### Parameters

arg | - | floating point value
exp | - | integer value

### Return value

If no errors occur, `arg` multiplied by FLT_RADIX to the power of `exp` (arg×FLT_RADIXexp
) is returned.

If a range error due to overflow occurs, `±HUGE_VAL`, `±HUGE_VALF`, or `±HUGE_VALL` is returned.

If a range error due to underflow occurs, the correct result (after rounding) is returned.

### Error handling

Errors are reported as specified in math_errhandling.

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

- Unless a range error occurs, FE_INEXACT is never raised (the result is exact)
- Unless a range error occurs, the current rounding mode is ignored
- If `arg` is ±0, it is returned, unmodified
- If `arg` is ±∞, it is returned, unmodified
- If `exp` is 0, then `arg` is returned, unmodified
- If `arg` is NaN, NaN is returned

### Notes

On binary systems (where FLT_RADIX is `2`), `scalbn` is equivalent to ldexp.

Although `std::scalbn` and `std::scalbln` are specified to perform the operation efficiently, on many implementations they are less efficient than multiplication or division by a power of two using arithmetic operators.

The `scalbln` function is provided because the factor required to scale from the smallest positive floating-point value to the largest finite one may be greater than 32767, the standard-guaranteed INT_MAX. In particular, for the 80-bit `long double`, the factor is 32828.

The GNU implementation does not set `errno` regardless of `math_errhandling`.

### Example

Run this code

    #include <stdio.h>
    #include <math.h>
    #include <float.h>
    #include <errno.h>
    #include <fenv.h>
    #pragma STDC FENV_ACCESS ON
    int main(void)
    {
        printf("scalbn(7, -4) = %f\n", scalbn(7, -4));
        printf("scalbn(1, -1074) = %g (minimum positive subnormal double)\n",
                scalbn(1, -1074));
        printf("scalbn(nextafter(1,0), 1024) = %g (largest finite double)\n",
                scalbn(nextafter(1,0), 1024));
        // special values
        printf("scalbn(-0, 10) = %f\n", scalbn(-0.0, 10));
        printf("scalbn(-Inf, -1) = %f\n", scalbn(-INFINITY, -1));
        //error handling
        errno = 0; feclearexcept(FE_ALL_EXCEPT);
        printf("scalbn(1, 1024) = %f\n", scalbn(1, 1024));
        if(errno == ERANGE) perror("    errno == ERANGE");
        if(fetestexcept(FE_OVERFLOW)) puts("    FE_OVERFLOW raised");
    }

Possible output:

    scalbn(7, -4) = 0.437500
    scalbn(1, -1074) = 4.94066e-324 (minimum positive subnormal double)
    scalbn(nextafter(1,0), 1024) = 1.79769e+308 (largest finite double)
    scalbn(-0, 10) = -0.000000
    scalbn(-Inf, -1) = -inf
    scalbn(1, 1024) = inf
        errno == ERANGE: Numerical result out of range
        FE_OVERFLOW raised

### References

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

  - 7.12.6.13 The scalbn functions (p: 247)

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

  - F.10.3.13 The scalbn functions (p: 523)

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

  - 7.12.6.13 The scalbn functions (p: 228)

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

  - F.9.3.13 The scalbn functions (p: 460)

### See also

frexp frexpf frexpl (C99)(C99) | breaks a number into significand and a power of 2 (function)
ldexp ldexpf ldexpl (C99)(C99) | multiplies a number by 2 raised to a power (function)
C++ documentation for scalbn

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