$1.$ Write a C implementation of Kahan$$s summation algorithm. Your task is to write a function that

takes an array of double precision floating point numbers and returns its sum. The prototype of your

function should be:

$1$ double kahan$\_$sum$($double$*$ a$,$ int length$)$;

For comparison also write a function that implements the naive sum of all the elements of the array in

order $($i$.$e$.$ a$[0]+$ a$[1]+...+$ a$[$length $-1]).$ The prototype of this function should be:

$1$ double naive$\_$sum$($double$*$ a$,$ int length$)$;

Test your functions with the following code:

$1$ double table$[10000]$;

$2$ table$[0]=1\mathrm{.}0$;

$3$ for $($int i $=1$; i $<10000$; i$++)\{$

$4$ table$[$i$]=1$e$-16$;

$5\}$

$6$ printf$("$naive $=\%1\mathrm{.}14$e

$",$ naive$\_$sum$($table$,10000))$;

$7$ printf$("$kahan $=\%1\mathrm{.}14$e

$",$ kahan$\_$sum$($table$,10000))$;

$8$ return$(0)$;

$9\}$