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

< cpp‎ | numeric‎ | math
Common mathematical functions
Basic operations
Exponential functions
Power functions
Trigonometric and hyperbolic functions
Error and gamma functions
Nearest integer floating point operations
Floating point manipulation functions
Macro constants
Defined in header <cmath>
float       scalbn ( float x, int exp );
float       scalbnf( 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 );
long double scalbnl( long double x, int exp );
(3) (since C++11)
double      scalbn ( IntegralType x, int exp );
(4) (since C++11)
float       scalbln ( float x, long exp );
float       scalblnf( 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 );
long double scalblnl( long double x, long exp );
(7) (since C++11)
double      scalbln ( IntegralType 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).


x - floating point value
exp - integer value

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.

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


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


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

decomposes a number into significand and a power of 2
multiplies a number by 2 raised to a power