The Compiler Will Not Reassociate

This double-precision sum runs at 3.01 cycles per element, matching the 3-cycle FP add latency:

double s = 0.0;
for (long i = 0; i < n; i++)
    s = s + d[i];

You rewrite it by hand with four accumulators and get 1.01, the best this part can do for scalar FP addition. A reviewer objects:

Delete the hand-rolled version. -O3 unrolls loops; the compiler will do this transformation itself and the original is readable.

You check the assembly at -O3 and the compiler did unroll the loop, but kept one accumulator and the CPE is still 3.01. Why?

The compiler cannot prove the array does not alias the accumulator, so it must reload after every store.

Floating-point addition is not associative, so splitting the sum into four partial sums can change the result; the compiler is not allowed to do it unless you pass a flag such as -ffast-math that waives IEEE semantics.

-O3 unrolls only loops whose trip count is a compile-time constant, and this one is not.

Four accumulators exceed the number of available architectural registers, so the compiler spills them and gains nothing.