new BigInteger(String) performance / complexity

Question

I\'m wondering about the performance/complexity of constructing BigInteger objects with the new BigInteger(String) constructor

Answer 1

Simplifying from the source somewhat, it's the case because in the "traditional" String parsing loop

for each digit y from left to right:
  x = 10 * x + y

you have the issue that 10 * x takes time linear in the length of x, unavoidably, and that length grows by more-or-less a constant factor for each digit, also unavoidably.

(The actual implementation is somewhat smarter than this -- it tries to parse an int's worth of binary digits at a time, and so the actual multiplier in the loop is more likely 1 or 2 billion -- but yeah, it's still quadratic overall.)

That said, a number with 10^6 digits is at least a googol, and that's bigger than any number I've heard of being used even for cryptographic purposes. You're parsing a string that takes two megabytes of memory. Yes, it'll take a while, but I suspect the JDK authors didn't see the point of optimizing for such a rare use case.

Answer 2

You're actually measuring the time it takes to parse a string and create the BigInteger. Numeric operations involving BigIntegers would be a lot more efficient than this.

Answer 3

The O(n^2) effort is caused by the decimal to binary conversion if the BigInteger is specified as decimal digits.

Also, 10^7 digits is a really huge number. For typical cryptographic algorithms like RSA you would deal with 10^3 to 10^4 digits. Most of the BigInteger operations are not optimized for such a large number of digits.