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In this article at OpenGenus, we have explored an efficient approximation of Exponential Function that can be computed in O(1) time. This is also known as Schraudolph's method.

**Table of contents**:

- Approximation of Exponential Function
- Java implementation
- C and C++ implementation

## Approximation of Exponential Function

This method was developed by Nicol N. Schraudolph from IDSIA, Lugano, Switzerland in 2007.

We need to compute e^val.

This is an expensive operation and can be approximated efficiently using the following algorithm:

- Get value of exponent val.
- Compute tmp = (1512775 * val) + (1072693248 - 60801);\
- Answer is tmp << 32 (left shifted by 32).

This approach involves:

- 1 multiplication, 1 addition and subtraction
- 1 left shift

This is an efficient in terms of computation.

The Time Complexity of this approach is O(1).

The space complexity is O(1) as well.

## Java implementation

This is the Java implementation of the approach to approximate Exponent function:

```
public static double exp(double val) {
final long tmp = (long) (1512775 * val) + (1072693248 - 60801);
return Double.longBitsToDouble(tmp << 32);
}
```

## C and C++ implementation

In Programming Languages like C and C++, this can be implemented using MACRO and is significantly, faster than other approaches of computing exponent.

In C, this approach is implemented as follows:

```
#include <math.h>
static union
[
double d;
struct
[
#ifdef LITTLE_ENDIAN
int j, i;
#else
int i, j;
#endif
] n;
] eco;
#define EXP_A (1512775)
#define EXP_C 60801
#define EXP(y) (eco.n.i = EXP_A * (y) + (1072693248 - EXP_C), eco.d)
```

With this article at OpenGenus, you must have the complete idea of how to approximate exponential function.