[Gretl-devel] fdjac precision question

Dear all, First, a couple of numbers to introduce the question cos(0.1)~ 0.99500416 5278 025766095561987803870294838576225415084035959352... ### NOTE all results are on 32-bit Ubuntu 15.10 To compare a helper: function string as_string (scalar x) sprintf s "%.15g",x return s end function 1)  x={0.1} eval as_string(fdjac(x,sin(x))) 0.99500416 7780 28 2) set fdjac_quality 1 eval as_string(fdjac(x,sin(x))) 0.99500416 5451 974 3) set fdjac_quality 2 eval as_string(fdjac(x,sin(x))) 0.99500416 3123 667 A home-backed thing inspired by fdjac help : A helper: function scalar feval (string fun, scalar x) return @fun end function The main: function scalar sdj2 (string f, scalar x) if abs(x)>10^3 h = 10^3*sqrt(x/1000*$macheps) else h=10^(3)*sqrt($macheps) endif z = (8*(feval(f,x+h)-feval(f,x-h)) - (feval(f,x+2*h)-feval(f,x-2*h)))/(12*h) sz = as_string(z) return z end function We have eval as_string(sdj2("sin(x)",0.1)) 0.99500416 5277 274 recall: 0.99500416 5278 025766 In theory, fdjac should be better, since it uses the same formula as sdj2() and it should optimize the step h, but... Oleh