Notes

. In single-precision, there are fewer bits available to represent smaller numbers accurately. When adding small numbers together, the loss of precision becomes more pronounced, leading to larger relative errors.
. forward:-
When you add smaller numbers together in a forward sequence, such as starting with
i is small and increases, you're dealing with decreasing magnitudes.
As the numbers get smaller, their contribution to the sum becomes less significant relative to the total sum.
n single-precision arithmetic, the smaller numbers lose precision more quickly as they are added together. Their bits become less meaningful due to the limited precision, leading to a larger relative error.
backward :-
When adding larger numbers together in a backward sequence, such as starting with :
i is large and decreases, you're dealing with increasing magnitudes.
The larger numbers retain more precision as they are added together in a backward sequence. The initial numbers dominate the sum, and their contributions have a relatively larger impact on the result.
While rounding errors still occur, they tend to accumulate less significantly compared to the forward summation because the larger numbers maintain their precision better.