scalbn, scalbnf, scalbnl, scalbln, scalblnf, scalblnl

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.


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


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

Although scalbn and 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.


#include <stdio.h>
#include <math.h>
#include <float.h>
#include <errno.h>
#include <fenv.h>
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


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

breaks a number into significand and a power of 2
multiplies a number by 2 raised to a power
C++ documentation for scalbn

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