Stable LogSumExp

Compute $\log {\sum }_i{e}^{x_i}\backslash log\backslash sum\_i\; e^\{x\_i\}$ for a vector x without overflow, even when entries are as large as $10001000$.

Implement solve(x).

Returns. Return a Python float.

Examples

Example 1

Input:

solve([1000.0, 1001.0])

Output:

1001.313262

Example 2

Input:

solve([0.0, 0.0])

Output:

0.693147

Example 3

Input:

solve([-1000.0, -1000.0])

Output:

-999.306853