interesting idea so,
I think that all know this game, so i've decided to remake it on a mobile version^^
for controls : auto speed or not, Left ( key 4 ) or Right( key 6 ) to move, Up ( key 2 ) to Increase Speed, Down ( key 8 ) to reduce Speed, and fire( key 5 ) to Jump !
[EDIT] ok so for just only the same button :
for controls : just Press the fire button to Jump, more you are holding the button, more your jump is higher
and of course, the game is with an autospeed for the character !