> Maybe I am crazy, or the labels here are wrong, but that looks like the > error is three times as *big* after the patch. I.e. it worsened instead > of improving.
Oh, sorry. I was not clear in my previous message. The error did not improved with regard to the original formula. What I meant is with regard to the original (1-x*x) simplification. But you are right, the above error is about 3 times bigger than the original formula, but before the error was about 300 times bigger. You are not crazy :P On Fri, Oct 19, 2018 at 10:46 AM Segher Boessenkool <seg...@kernel.crashing.org> wrote: > > Hi all, > > On Fri, Oct 19, 2018 at 09:21:07AM -0300, Giuliano Augusto Faulin Belinassi > wrote: > > > Did you enable FMA? I'd expect 1 - x*x to be accurate with FMA, so the > > > relative error > > > should be much better. If there is no FMA, 2*(1-fabs(x)) - (1-fabs(x))^2 > > > should be > > > more accurate when abs(x)>0.5 and still much faster. > > > > No, but I will check how to enable it if FMA is available. > > I did a minor test with your formula and the precision improved a lot. > > Here is an example for floats > > > > with input : = 9.99999880790710449218750000000000000000000000000000e-01 > > cosh: before: = 2.04800000000000000000000000000000000000000000000000e+03 > > cosh: after : = 2.04800024414062500000000000000000000000000000000000e+03 > > cosh: mpfr : = 2.04800006103515897848424084406334262726138617589463e+03 > > error before: = 6.10351589784842408440633426272613861758946325324235e-05 > > error after : = 1.83105466021515759155936657372738613824105367467577e-04 > > Maybe I am crazy, or the labels here are wrong, but that looks like the > error is three times as *big* after the patch. I.e. it worsened instead > of improving. > > > Segher
