generic
type Float_Type is digits <>;
package Normal_CDF_Inverse is
function Normal_CDF_Inverse(p: Float_Type'Base) return Float_Type'Base;
end Normal_CDF_Inverse;
with Ada.Numerics.Generic_Elementary_Functions;
package body Normal_CDF_Inverse is
package Elementary_Functions is new Ada.Numerics.Generic_Elementary_Functions(Float_Type'Base);
use Elementary_Functions;
function Rational_Approximation(t: Float_Type'Base) return Float_Type'Base is
c: constant array(0..2) of Float_Type'Base := (2.515517, 0.802853, 0.010328);
d: constant array(0..2) of Float_Type'Base := (1.432788, 0.189269, 0.001308);
numerator, denominator: Float_Type'Base;
begin
-- Abramowitz and Stegun formula 26.2.23.
-- The absolute value of the error should be less than 4.5 e-4.
numerator := (c(2)*t + c(1))*t + c(0);
denominator := ((d(2)*t + d(1))*t + d(0))*t + 1.0;
return t - numerator / denominator;
end Rational_Approximation;
function Normal_CDF_Inverse(p: Float_Type'Base) return Float_Type'Base is
begin
if p <= 0.0 or else p >= 1.0 then
raise Ada.Numerics.Argument_Error;
end if;
-- See article above for explanation of this section.
if p < 0.5 then
-- F^-1(p) = - G^-1(p)
return -Rational_Approximation( Sqrt(-2.0*Log(p)) );
else
-- F^-1(p) = G^-1(1-p)
return Rational_Approximation( Sqrt(-2.0*Log(1.0-p)) );
end if;
end Normal_CDF_Inverse;
end Normal_CDF_Inverse;