Say you have 100000000 32-bit floating point values in an array, and each of these floats has a value between 0.0 and 1.0. If you tried to sum them all up like this

result = 0.0;
for (i = 0; i < 100000000; i++) {
    result += array[i];
}

you'd run into problems as result gets much larger than 1.0.

So what are some of the ways to more accurately perform the summation?

algorithm floating-point numerical
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