A (quite) accurate ln1+x function, or "how close can you get" part II

[Albert Chan]

(01-31-2019 07:04 PM)Albert Chan Wrote:  Excess ULP error is due to correction *lowering* decimal exponent.

To avoid excess ULP error, we like correction same sign as X

Y = 1+X, rounded-toward 1.0

log1p(X) ~ LN(Y) - (Y-1-X)/Y

Previous example, log1p(X = -0.00099950016) :
Y = round-toward-1 of 1+X = 0.9990004999 (10 digits)

log1p(X) ~ LN(Y) - (Y-1-X)/Y
= -9.999999333e-4 - 6.006003001e-11
= -9.999999934e-4 (all digits correct)