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For the probably simplest solution to the given problem if summing doubles there is a hardware in every x86 CPU which allows the biggest number during the computation to be 1.18e4932 (using 80 bits internally, 15 from that for the exponent, vs. only 11 in the 64-bit double). By just activating it the sum can be done very fast, and no need for any modification: first sum, then divide, convert to double at the end.

You should not use SSE for that however, but the old x87 "FPU" instructions.

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And if you have to use Microsoft or Intel C compiler for 64-bits Windows, you have to use assembly to reach that functionality which is still in the CPU. With the open source compilers it's better. You can write C code that works with both GCC and clang.