MongoDB's NumberLong only 54 bit signed?
Is a MongoDB's NumberLong really 64 bit signed integer really 64 bit?
MongoDB's NumberLong is said to be a 64 bit signed integer, which should mean we can play with -2^开发者_运维问答63 <= x <= 2^63-1, where x is a NumberLong. However, adding 1 or subtracting 1 from a NumberLong(x) does not return the expected value for x <= -2^54 or x >= 2^54, but correct values are returned for -2^53 <= x <= 2^53.
The reliable NumberLong numbers therefor seem to be 54 bit signed integers.Why is this?
Am I doing someting wrong?Sample from the mongo shell:
> NumberLong( Math.pow(2,54) )
NumberLong("18014398509481984") // Expected
> NumberLong( Math.pow(2,54)-1 )
NumberLong("18014398509481984") // **NOT** Expected
> NumberLong( -Math.pow(2,54) )
NumberLong("-18014398509481984") // Expected
> NumberLong( -Math.pow(2,54)+1 )
NumberLong("-18014398509481984") // **NOT** Expected
> NumberLong( Math.pow(2,53) )
NumberLong("9007199254740992") // Expected
> NumberLong( Math.pow(2,53)-1 )
NumberLong("9007199254740991") // Expected
> NumberLong( -Math.pow(2,53) )
NumberLong("-9007199254740992") // Expected
> NumberLong( -Math.pow(2,53)+1 )
NumberLong("-9007199254740991") // Expected
Using MongoDB 2.0.0
Wow, this is puzzling. Clearly there is some sort of rounding error happening here.
> NumberLong("18014398509481984")-NumberLong("1");
18014398509481984
> NumberLong("18014398509481984")-NumberLong("2");
18014398509481982
> NumberLong("18014398509481984")+NumberLong("1");
18014398509481984
> NumberLong("18014398509481984")+NumberLong("2");
18014398509481984
> NumberLong("18014398509481984")+NumberLong("3");
18014398509481988
This is probably something wrong with the JavaScript engine that the shell runs in, rather than MongoDB itself. Check this out, for example--$inc
works fine:
> db.test.insert({twoTo54:NumberLong("18014398509481984")});
> db.test.update({},{$inc:{twoTo54:NumberLong("1")}});
> db.test.find();
{ "_id" : ObjectId("4f204847756aa806028abce1"), "twoTo54" : NumberLong("18014398509481985") }
> db.test.update({},{$inc:{twoTo54:NumberLong("1")}});
> db.test.find();
{ "_id" : ObjectId("4f204847756aa806028abce1"), "twoTo54" : NumberLong("18014398509481986") }
> db.test.update({},{$inc:{twoTo54:NumberLong("1")}});
> db.test.find();
{ "_id" : ObjectId("4f204847756aa806028abce1"), "twoTo54" : NumberLong("18014398509481987") }
You have to be careful, though. If you use just a normal literal 1
, it will convert the type to a Number, which then breaks the $inc
:
> db.test.update({},{$inc:{twoTo54:1}});
> db.test.find();
{ "_id" : ObjectId("4f204847756aa806028abce1"), "twoTo54" : 18014398509481988 }
> db.test.update({},{$inc:{twoTo54:1}});
> db.test.find();
{ "_id" : ObjectId("4f204847756aa806028abce1"), "twoTo54" : 18014398509481988 }
And even if you go back to $inc
with NumberLong("1")
, it's still broken:
> db.test.update({},{$inc:{twoTo54:NumberLong("1")}});
> db.test.find();
{ "_id" : ObjectId("4f204847756aa806028abce1"), "twoTo54" : 18014398509481988 }
Definitely good to keep in mind.
Math.pow
most likely operates on double
s. The integers are coerced to floats, and at 2^54, double precision numbers lose resolution at the 1's place. The information is already lost at the time you convert back to integer types.
do you get comparable results using left shift <<
or repeated multiplication?
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