recognition and optimization of prefix computation or variants in C/C++ compilers

Hi,

Does the current C/C++ compilers in industry recognize idioms of the
form of prefix computation and transform them? For instance, given

for (i = 0; i < n; i++)
for (j = 0; j < i; j++)
result[i] = result[i] + a[j];


transform this to

result [0] = a[0];
for (i = 1; i < n; i++)
result[i] = result[i-1] + a[i];

If so, under what class of optimizations do they do this?

In the general case, a similar prefix pattern can be identified and
seen in certain search/traversal algorithms also. Do the existing
compilers handle any of those as well?