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# std::scalbn, std::scalbln

From cppreference.com
< cpp‎ | numeric‎ | math

Defined in header `<cmath>` |  |
float scalbn( float x, int exp ); | (1) | (since C++11)
double scalbn( double x, int exp ); | (2) | (since C++11)
long double scalbn( long double x, int exp ); | (3) | (since C++11)
double scalbn( Integral x, int exp ); | (4) | (since C++11)
float scalbln( float x, long exp ); | (5) | (since C++11)
double scalbln( double x, long exp ); | (6) | (since C++11)
long double scalbln( long double x, long exp ); | (7) | (since C++11)
double scalbln( Integral x, long exp ); | (8) | (since C++11)

1-3,5-7) Multiplies a floating point value `x` by FLT_RADIX raised to power `exp`.
4,8) A set of overloads or a function template accepting an argument of any integral type. Equivalent to (2) or (6) (the argument is cast to double).

### [edit] Parameters

x | - | floating point value
exp | - | integer value

### [edit] Return value

If no errors occur, `x` multiplied by FLT_RADIX to the power of `arg` (x×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.

### [edit] 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 `x` is ±0, it is returned, unmodified
- If `x` is ±∞, it is returned, unmodified
- If `exp` is 0, then `x` is returned, unmodified
- If `x` is NaN, NaN is returned

### [edit] 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 `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`

### [edit] Example

Run this code

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

    #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

### [edit] See also

frexp | decomposes a number into significand and a power of 2 (function) [edit]
ldexp | multiplies a number by 2 raised to a power (function) [edit]
C documentation for scalbn

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