All of the ones designed for unarmored combat. Except for specialized swords used in armored combat, all longswords were double edged and sharp the entire length.
But you have to take into consideration the definition of "sharp". There are techniques that involve placing the edge near the hilt under the arms or against the neck. So you need it to be at least sharp enough to be uncomfortable, if not deadly. But you don't want to make the lower parts of the edges too thin because most of your parries are done with them.
So maybe you choose to sharpen them to a dull ax while near the tip you go for razor sharp. But this is more personal preference than something called out in the longsword manuals.
But no, no one felt it was necessary to explicitly call this out. Like "the pointy end goes towards the other guy", it was just assumed knowledge for two-handed swords.
What we do see in the one-handed sword of Viggiani is explicit instructions to sharpen both edges for their entire length.
ROD: It was certainly possible to do it, but the modern usage has rediscovered the most offensive way to be having the entire length of both sides to be sharp edges; because when one comes to the half sword in combat, the false edge of the forte of the sword is quite opportune; think of it, conte: it is very modern to have two edges from the hilt to the point; I would rule that in the time of David they were of this fashion. He says in the Psalms these words: “The highness of God in their mouths, and a double-edged sword in their hand, to inflict vengeance on the nations”; and I discussed with a Hebrew friend of mine in Mantua, that they are understood in the Hebrew language to be written thus as I have said.
The fact that he felt it necessary to call this out suggests that others of his time would disagree. But we haven't found any explicit examples.
Turning back to the specialized sword for armored dueling, Vadi says,
Take note and understand this addendum
If you wish to test the sword in armour,
Make the cutting edges four fingers from the point,
The idea here is that you aren't going to cut someone in full armor, so no need to make the edge sharp. But to add in the thrust (e.g. to the eyes, inside of elbows, back of the knees) you would sharpen the last 3-4 inches.
