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

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< cpp‎ | numeric‎ | math

Defined in header `<cmath>` |  |
int exponent |  |
| (1) |
float scalbn ( float num, int exp ); double scalbn ( double num, int exp ); long double scalbn ( long double num, int exp ); |  | (since C++11) (until C++23)
constexpr /* floating-point-type */ scalbn ( /* floating-point-type */ num, int exp ); |  | (since C++23)
float scalbnf( float num, int exp ); | (2) | (since C++11) (constexpr since C++23)
long double scalbnl( long double num, int exp ); | (3) | (since C++11) (constexpr since C++23)
long exponent |  |
| (4) |
float scalbln ( float num, long exp ); double scalbln ( double num, long exp ); long double scalbln ( long double num, long exp ); |  | (since C++11) (until C++23)
constexpr /* floating-point-type */ scalbln ( /* floating-point-type */ num, long exp ); |  | (since C++23)
float scalblnf( float num, long exp ); | (5) | (since C++11) (constexpr since C++23)
long double scalblnl( long double num, long exp ); | (6) | (since C++11) (constexpr since C++23)
Additional overloads |  |
Defined in header `<cmath>` |  |
template< class Integer > double scalbn( Integer num, int exp ); | (A) | (since C++11) (constexpr since C++23)
template< class Integer > double scalbln( Integer num, long exp ); | (B) | (since C++11) (constexpr since C++23)

1-6) Multiplies a floating point value num by FLT_RADIX raised to power exp. The library provides overloads of `std::scalbn` and `std::scalbln` for all cv-unqualified floating-point types as the type of the parameter num. (since C++23)
A,B) Additional overloads are provided for all integer types, which are treated as double.

### Parameters

num | - | floating-point or integer value
exp | - | integer value

### Return value

If no errors occur, num multiplied by FLT_RADIX to the power of exp (num×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 num is ±0, it is returned, unmodified
- If num is ±∞, it is returned, unmodified
- If exp is 0, then num is returned, unmodified
- If num is NaN, NaN is returned

### Notes

On binary systems (where FLT_RADIX is 2), `std::scalbn` is equivalent to std::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 function name stands for "new scalb", where `scalb` was an older non-standard function whose second argument had floating-point type.

The `std::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`.

The additional overloads are not required to be provided exactly as (A,B). They only need to be sufficient to ensure that for their argument num of integer type:

- std::scalbn(num, exp) has the same effect as std::scalbn(static_cast<double>(num), exp).
- std::scalbln(num, exp) has the same effect as std::scalbln(static_cast<double>(num), exp).

### Example

Run this code

    #include <cerrno>
    #include <cfenv>
    #include <cmath>
    #include <cstring>
    #include <iostream>

    // #pragma STDC FENV_ACCESS ON

    int main()
    {
        std::cout << "scalbn(7, -4) = " << std::scalbn(7, -4) << '\n'
                  << "scalbn(1, -1074) = " << std::scalbn(1, -1074)
                  << " (minimum positive subnormal double)\n"
                  << "scalbn(nextafter(1,0), 1024) = "
                  << std::scalbn(std::nextafter(1,0), 1024)
                  << " (largest finite double)\n";

        // special values
        std::cout << "scalbn(-0, 10) = " << std::scalbn(-0.0, 10) << '\n'
                  << "scalbn(-Inf, -1) = " << std::scalbn(-INFINITY, -1) << '\n';

        // error handling
        errno = 0;
        std::feclearexcept(FE_ALL_EXCEPT);

        std::cout << "scalbn(1, 1024) = " << std::scalbn(1, 1024) << '\n';

        if (errno == ERANGE)
            std::cout << "    errno == ERANGE: " << std::strerror(errno) << '\n';
        if (std::fetestexcept(FE_OVERFLOW))
            std::cout << "    FE_OVERFLOW raised\n";
    }

Possible output:

    scalbn(7, -4) = 0.4375
    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
    scalbn(-Inf, -1) = -inf
    scalbn(1, 1024) = inf
        errno == ERANGE: Numerical result out of range
        FE_OVERFLOW raised

### See also

frexp frexpf frexpl (C++11)(C++11) | decomposes a number into significand and a power of 2 (function)
ldexp ldexpf ldexpl (C++11)(C++11) | multiplies a number by 2 raised to a power (function)

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