# c Programming/C Reference/math.h/ldexp

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In computing, **ldexp** is a function that multiplies a double precision floating point value by a specified integral power of two, returning the result if it is a valid floating point value for the representation used for double precision floating point values in the execution environment.

## Location[edit]

It is one of the C programming language's math library routines and is declared in the header file math.h.

## Definition[edit]

The function ldexp is defined in the C programming language standard, ISO/IEC 9899 ^{[1]} as follows:

7.12.6.6 The ldexp functions

Synopsis

`#include <math.h>`

`double ldexp(double x, int exp);`

double ldexpf(float x, int exp);`long double ldexpl(long double x, int exp);`

Description

The ldexp functions multiply a floating-point number by an integral power of 2. A range error may occur.

Returns

The`ldexp`

functions return`x`

*2^{exp}

The Open Group Single Unix Specification expands on the interface definition for ldexp in a Unix^{tm} hosted environment.^{[2]}

- The Description section has the following additional information:
- An application wishing to check for error situations should set errno to zero and call feclearexcept(FE_ALL_EXCEPT) before calling these functions. On return, if errno is non-zero or fetestexcept(FE_INVALID | FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW) is non-zero, an error has occurred.

- The "Returns" section is expanded with the following clauses:
- If these functions would cause overflow, a range error must occur and
`ldexp()`

,`ldexpf()`

, and`ldexpl()`

must return ±`HUGE_VAL`

, ±`HUGE_VALF`

, and ±`HUGE_VALL`

(according to the sign of`x`

), respectively. - If the correct value would cause underflow, and is not representable, a range error may occur, and either 0.0 (if supported), or an implementation-defined value must be returned.
- If x is NaN, a NaN must be returned.
- If x is ±0 or ±Inf,
`x`

must be returned. - If exp is 0, x must be returned.
- If the correct value would cause underflow, and is representable, a range error may occur and the correct value must be returned.

- If these functions would cause overflow, a range error must occur and

- It also adds an "Errors section", as follows:
- These functions must fail if:
- Range Error
- The result overflows.
- If the integer expression (math_errhandling & MATH_ERRNO) is non-zero, then errno must be set to [ERANGE]. If the integer expression (math_errhandling & MATH_ERREXCEPT) is non-zero, then the overflow floating-point exception must be raised.

- The result overflows.

- Range Error

- These functions must fail if:

## Implementation[edit]

For binary exponent based floating point representations such as IEEE 754, ldexp can be implemented by simply extracting the exponent from the value of `x`

and adding `exp`

to it and if the result is within the valid exponent values for the representation, replacing `x`

's exponent with the result. If the calculated exponent value is too high the function returns +∞ or -∞ (depending on the sign of `x`

), and if the value is too low, the function returns 0.0.