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This was confusing.=0A= > I believe it did only remove the "very slow" paths.=0A= =0A= I've updated the title in v2.=0A= =0A= > here are the claimed bounds and the maximal errors I found so far after= =0A= > applying Wilco's patches (rounded up to 3 digits):=0A= >=0A= >=A0=A0=A0=A0=A0 claimed found so far=0A= > acos=A0 0.52=A0=A0=A0 0.523=0A= > asin=A0 0.523=A0=A0 0.516=0A= > atan=A0 0.56=A0=A0=A0 0.523=0A= > tan=A0=A0 0.62=A0=A0=A0 0.612=0A= > atan2 0.56=A0=A0=A0 0.524=0A= =0A= Thanks for that, I have added these bounds at the start of each function.= =0A= =0A= > I have only one further remark:=0A= >=0A= > -typedef union { int4 i[2]; double x; } mynumber;=0A= > +typedef union { int4 i[2]; double x; double d; } mynumber;=0A= >=0A= > Why did you add another 'double' field d? Only the 'd' field is used in= =0A= > e_atan2.c, why not replace it by 'x'? Maybe to avoid a too large diff?=0A= =0A= Yes, the purpose is just to remove the slow paths and minimise the=0A= changes, so this was the quickest and simplest way to remove the uses=0A= of 'number'.=0A= =0A= Cheers,=0A= Wilco=