# ldexp

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

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

## Definition

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`×2exp

The Open Group Single Unix Specification expands on the interface definition for ldexp in a Unixtm 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 shall occur and `ldexp()`, `ldexpf()`, and `ldexpl()` shall 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 shall be returned.
If x is NaN, a NaN shall be returned.
If x is ±0 or ±Inf, `x` shall be returned.
If exp is 0, x shall be returned.
If the correct value would cause underflow, and is representable, a range error may occur and the correct value shall be returned.
It also adds an "Errors section", as follows:
These functions shall fail if:
Range Error
The result overflows.
If the integer expression (math_errhandling & MATH_ERRNO) is non-zero, then errno shall be set to [ERANGE]. If the integer expression (math_errhandling & MATH_ERREXCEPT) is non-zero, then the overflow floating-point exception shall be raised.

## Implementation

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.