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{ ******************************************************************
Incomplete Gamma function and related functions.
Translated from C code in Cephes library (http://www.moshier.net)
****************************************************************** }
unit uigamma;
interface
uses
utypes, ugamma;
function IGamma(A, X : Float) : Float;
{ Incomplete Gamma function}
function JGamma(A, X : Float) : Float;
{ Complement of incomplete Gamma function }
function Erf(X : Float) : Float;
{ Error function }
function Erfc(X : Float) : Float;
{ Complement of error function }
implementation
function IGamma(A, X : Float) : Float;
var
Ans, Ax, C, R : Float;
begin
SetErrCode(FOk);
if (X <= 0.0) or (A <= 0.0) then
begin
IGamma := 0.0;
Exit;
end;
if (X > 1.0) and (X > A) then
begin
IGamma := 1.0 - JGamma(A, X);
Exit;
end;
Ax := A * Ln(X) - X - LnGamma(A);
if Ax < MinLog then
begin
IGamma := DefaultVal(FUnderflow, 0.0);
Exit;
end;
Ax := Exp(Ax);
{ Power series }
R := A;
C := 1.0;
Ans := 1.0;
repeat
R := R + 1.0;
C := C * X / R;
Ans := Ans + C;
until C / Ans <= MachEp;
IGamma := Ans * Ax / A;
end;
function JGamma(A, X : Float) : Float;
const
Big = 1.0 / MachEp;
var
Ans, C, Yc, Ax, Y, Z, R, T,
Pk, Pkm1, Pkm2, Qk, Qkm1, Qkm2 : Float;
begin
SetErrCode(FOk);
if (X <= 0.0) or (A <= 0.0) then
begin
JGamma := 1.0;
Exit;
end;
if (X < 1.0) or (X < A) then
begin
JGamma := 1.0 - IGamma(A, X);
Exit;
end;
Ax := A * Ln(X) - X - LnGamma(A);
if Ax < MinLog then
begin
JGamma := DefaultVal(FUnderflow, 0.0);
Exit;
end;
Ax := Exp(Ax);
{ Continued fraction }
Y := 1.0 - A;
Z := X + Y + 1.0;
C := 0.0;
Pkm2 := 1.0;
Qkm2 := X;
Pkm1 := X + 1.0;
Qkm1 := Z * X;
Ans := Pkm1 / Qkm1;
repeat
C := C + 1.0;
Y := Y + 1.0;
Z := Z + 2.0;
Yc := Y * C;
Pk := Pkm1 * Z - Pkm2 * Yc;
Qk := Qkm1 * Z - Qkm2 * Yc;
if Qk <> 0.0 then
begin
R := Pk / Qk;
T := Abs((Ans - R) / R);
Ans := R;
end
else
T := 1.0;
Pkm2 := Pkm1;
Pkm1 := Pk;
Qkm2 := Qkm1;
Qkm1 := Qk;
if Abs(Pk) > Big then
begin
Pkm2 := Pkm2 * MachEp;
Pkm1 := Pkm1 * MachEp;
Qkm2 := Qkm2 * MachEp;
Qkm1 := Qkm1 * MachEp;
end;
until T <= MachEp;
JGamma := Ans * Ax;
end;
function Erf(X : Float) : Float;
begin
if X < 0.0 then
Erf := - IGamma(0.5, Sqr(X))
else
Erf := IGamma(0.5, Sqr(X));
end;
function Erfc(X : Float) : Float;
begin
if X < 0.0 then
Erfc := 1.0 + IGamma(0.5, Sqr(X))
else
Erfc := JGamma(0.5, Sqr(X));
end;
end.
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