Oxford University Press, Cambridge. It is an excellent source of information about Piri Reis and his map of 1513. It has an extensive discussion concerning the source maps and cartographic data from which he compiled Piri Reis Map of 1513.
Someone needs to provide some sort of evidence that it is indeed an accurate map.
The examinations that I have made of it show all sorts of errors that certainly falsify any claim of unusual accuracy for this map. Also, the methodology used to determine the longitude and latitude of the map allowed all sorts of unintentional fudging. After deciding that these incorrect grids had probably been added much later by persons other than the original draftsman, I removed them and worked out what I consider to be the correct grids. The basic assumption of Mallery is that the maps were originally accurate and any errors are the result of later copying and compilation. However, these reconstructed source maps may have no basis in fact because no proof is offered that the errors that they corrected were indeed the result of the copying and compilation process and not actually part of the actual source map.