This is a high speed switching diode. Looking at its virtues, it has a 4ns switching time and 3pf capacity.
Looking at the National Semiconductor data sheet for a 1N4148 we discover, that this also is a high speed switching diode with 4ns 4pf.
Besides that, they tell you itīs identical to 1N914.
This is not my humble opinion, the datasheet tells so.
A 1N400x btw is a VASTLY different diode. It is dramatically slower and has higher capacitance. Any MOSFET intrinsic diode is very very much slower.
For a circuit demanding this diode, the 1n4148 is a perfect substitute. I can imagine that a fast diode does react differently than a slow one, so a diode with comparable speed/capacity will produce comparable results. Anything beyond that I do not believe.
I guess the 1s1588 was chosen, because this was ubiquitous in the place/time the circuit was designed, no other reason.