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* arcsin and arccos: improve accuracy at small arguments by replacing sqr(1-x*x) with sqr((1-x)*(1+x)).

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* arcosh: likewise, error near 1.0 decreases approx. from 80*eps to 4*eps.
* artahn: improve accuracy by replacing ln(x+1) with lnxp1(x).

git-svn-id: trunk@26091 -
This commit is contained in:
sergei 2013-11-14 18:26:34 +00:00
parent b6d279d4aa
commit 141b2f7066
1 changed files with 11 additions and 11 deletions
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22
rtl/objpas/math.pp
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@ -743,21 +743,20 @@ begin
end;
{ ArcSin and ArcCos from Arjan van Dijk (arjan.vanDijk@User.METAIR.WAU.NL) }
function arcsin(x : float) : float;
begin
if abs(x) > 1 then InvalidArgument
else if abs(x) < 0.5 then
arcsin := arctan(x/sqrt(1-sqr(x)))
else
arcsin := sign(x) * (pi*0.5 - arctan(sqrt(1 / sqr(x) - 1)));
arcsin:=arctan2(x,sqrt((1.0-x)*(1.0+x)));
end;
function Arccos(x : Float) : Float;
begin
arccos := pi*0.5 - arcsin(x);
if abs(x)=1.0 then
if x<0.0 then
arccos:=Pi
else
arccos:=0
else
arccos:=arctan2(sqrt((1.0-x)*(1.0+x)),x);
end;
@ -827,7 +826,8 @@ function arctanh(x : float) : float;inline;
function arcosh(x : float) : float;
begin
arcosh:=Ln(x+Sqrt(x*x-1));
{ Provides accuracy about 4*eps near 1.0 }
arcosh:=Ln(x+Sqrt((x-1.0)*(x+1.0)));
end;
function arsinh(x : float) : float;
@ -837,7 +837,7 @@ function arsinh(x : float) : float;
function artanh(x : float) : float;
begin
artanh:=(Ln((1+x)/(1-x)))*0.5;
artanh:=(lnxp1(x)-lnxp1(-x))*0.5;
end;
function hypot(x,y : float) : float;