Vanilla Option - Price - Black Scholes - Close Form

To calculate vanilla option price by B/S

The Black-Scholes formulas for the prices of European call and put options are:
c=S_0 e^(-r_f T) N(d_1 )- Ke^(-r_d T) N(d_2)
and
p=Ke^(-r_d T) N(-d_2 )- S_0 e^(-r_f T) N(-d_1)
where
d_1=(ln⁡(S_0/K)+(r_d-r_f+σ^2/2)T)/(σ√T)
d_2=(ln⁡(S_0/K)+(r_d-r_f-σ^2/2)T)/(σ√T)=d_1-σ√T