Scalbn

Defined in header <cmath>.

Description

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). ​Additional Overloads are provided for all integer types, which are treated as double.

Declarations

C++23

int exponent

// 1)
constexpr /* floating-point-type */
            scalbn ( /* floating-point-type */ num, int exp );
// 2)
constexpr float scalbnf( float num, int exp );
// 3)
constexpr long double scalbnl( long double num, int exp );

long exponent

// 4)
constexpr /* floating-point-type */
            scalbln ( /* floating-point-type */ num, long exp );
// 5)
constexpr float scalblnf( float num, long exp );
// 6)
constexpr long double scalblnl( long double num, long exp );

Additional Overloads

// 7)
template< class Integer >
constexpr double scalbn( Integer num, int exp );
// 8)
template< class Integer >
constexpr double scalbln( Integer num, long exp );

C++11

int exponent

// 1)
float scalbn ( float num, int exp );
// 2)
double scalbn ( double num, int exp );
// 3)
long double scalbn ( long double num, int exp );
// 4)
float scalbnf( float num, int exp );
// 5)
long double scalbnl( long double num, int exp );

long exponent

// 6)
float scalbln ( float num, long exp );
// 7)
double scalbln ( double num, long exp );
// 8)
long double scalbln ( long double num, long exp );
// 9)
float scalblnf( float num, long exp );
// 10)
long double scalblnl( long double num, long exp );

Additional Overloads

// 11)
template< class Integer >
constexpr double scalbn( Integer num, int exp );
// 12)
template< class Integer >
constexpr double scalbln( Integer num, long exp );

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_RADIX^exp) 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 Additional Overloads. 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)

Examples

#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 Result

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