Export numeric data with preset decimal places

Question

I have a table of pairs of numbers, each with 300 decimal places, which are all important. If saved using Export["data.dat", data] and then imported back via Import["data.dat"] - then the 300 decimal places will become about 8 decimal places. What is the easiest way to overcome this? I don't really need the data file to be compatible with anything other than Mathematica.

This question is similar to this one.

Answer 1

Elaborating on my comment, the native mathematica package format precisely preserves the definition of symbols:

 lst = {1.3566789543235679098765432344564335, N[Pi, 50]};
 FullForm[lst[[1]]]

1.3566789543235679098765432344564335`34.132477087997515

 Export["test.m", lst];
 newlist = Import["test.m"];
 FullForm[newlist[[1]]]

1.3566789543235679098765432344564335`34.132477087997515

The "List" format chops to the nearest ascii representation and converts back on import,

Export["testfile", lst, "List"];
newlst = Import["testfile", "List"];
FullForm[newlst[[1]]]

1.3566789543235679098765432344564340000000000000000000000001`33.132477087997515

The difference is very subtle and perhaps inconsequential (here actually one bit difference in a 100+ bit binary representation ). I haven't tested it but I expect .m is faster too if you have large files to save. Of course the downside is .m is a unique format that would be difficult for anything else to parse.

Note the third argument to Export overrides whatever extension the file name has. The third argument corresponding to .m is "Package".

Also ".mx" is binary, which will be faster and smaller than ".m", but may not be portable across systems and versions. (Anybody know the "third argument" name for mx? )

Answer 2

The Export List format may be what your need. For instance, with

lst = {1.3566789543235679098765432344564335, N[Pi, 50]}

(not 300 digits, but a lot.)

Export["C:/Temp/tst", lst, "List"];
newlst = Import["C:/Temp/tst", "List"];
newlst
(* {1.35667895432356790987654323445643, 
    3.1415926535897932384626433832795028841971693993751} *)