How does one purify oneself from semen (mani), prostatic fluid (wadi), and pre-seminal fluid (madhi), especially if semen is discharged without a cause? And is it obligatory to repeat the prayer if one contented oneself with merely sprinkling water on the semen?

Scholars have differed regarding the purity of semen, and the preponderant opinion is that it is pure. As for wady and madhy, they are impure and must be purified with water, and wudu' must be performed after them. Some scholars are of the opinion that madhy can be purified by sprinkling water over it (nadh), but it is more cautious to wash it, unless it is difficult, in which case sprinkling suffices. There is no difference in this regard between being at home or outside. If purification is impossible and one fears the time for prayer will elapse, one should pray in their current state. The causes for the emission of madhy are minor pleasure, foreplay, thinking about or intending intercourse, and it may sometimes be emitted without any specific cause.