# picomath

### normal_cdf_inverse.a

```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;

package body Normal_CDF_Inverse is

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
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;
```