The idea is to be able to compute 1.0 - h * z + (z * r - x * y) in high precision. If h * z is slightly less than 1.0, then w = 1.0 - h * z can lose a lot of b

The idea is to be able to compute 1.0 - h * z + (z * r - x * y) in high precision. If h * z is slightly less than 1.0, then w = 1.0 - h * z can lose a lot of bits of precision. To recover the bits that were dropped in subtracting h * z from 1.0, we compute which bits of h * z were used (the high bits) and then subtract those bits from h * z to get only the low bits. We find the bits that were used by simply undoing the operation: 1.0 - w is mathematically the same as h * z, but is not the same as implemented due to limited precision. So (1.0 - w) - h * z is the extra bits that were dropped from the computation of w. Add that to the final term z * r - x * y before that result is added to w, and we have a more precise computation of w + z * r - x * y.