fact: Definition atan_fastP prec x := let xi := I.bnd x x in if F'.lt c1_2 x then let prec := F.incr_prec prec 2 in let pi4i := pi4 prec in if F'.lt c2 x then I.sub prec (I.mul2 prec pi4i) (atan_fast0 prec (I.inv prec xi)) else let xm1i := I.sub prec xi i1 in let xp1i := I.add prec xi i1 in I.add prec pi4i (atan_fast0 prec (I.div prec xm1i xp1i)) else atan_fast0 (F.incr_prec prec 1) xi.
imports: Coq(Reals Psatz) Flocq(Zaux Raux Digits) Stdlib Xreal Basic Sig Interval Float