Exact sums are not correctly rounded to even #5
Description
Consider exactly representable f32 numbers 4194304.0 and 4194304.5. Their sum is 8388608.5, which is not exactly representable as an f32, so it needs to be rounded to the nearest even mantissa, which is 8388608. However accurate doesn't do this correctly:
let a: f32 = 4194304.0;
let b: f32 = 4194304.5;
println!("a = {:.1}", a);
println!("b = {:.1}", b);
println!("a + b = {:.1}", a + b);
use accurate::traits::SumAccumulator;
let s1 = accurate::sum::OnlineExactSum::zero().absorb([a, b]).sum();
let s2 = accurate::sum::i_fast_sum_in_place(&mut [a, b]);
println!("OnlineExactSum: {:.1}", s1);
println!("i_fast_sum: {:.1}", s2);The above prints:
a = 4194304.0
b = 4194304.5
a + b = 8388608.0
OnlineExactSum: 8388609.0
i_fast_sum: 8388609.0