[java] Is there an upper bound to BigInteger?

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What does BigInteger having no limit mean?

The Javadoc for BigInteger does not define any maximum or minimum. However, it does say:

(emphasis added)

Immutable arbitrary-precision integers

Is there such a maximum, even in theory? Or is the way BigInteger operates fundamentally different, such that there is in reality no maximum except for the amount of memory available on the computer?

BigInteger would only be used if you know it will not be a decimal and there is a possibility of the long data type not being large enough. BigInteger has no cap on its max size (as large as the RAM on the computer can hold).

From here.

It is implemented using an int[]:

  110       /**
  111        * The magnitude of this BigInteger, in <i>big-endian</i> order: the
  112        * zeroth element of this array is the most-significant int of the
  113        * magnitude.  The magnitude must be "minimal" in that the most-significant
  114        * int ({@code mag[0]}) must be non-zero.  This is necessary to
  115        * ensure that there is exactly one representation for each BigInteger
  116        * value.  Note that this implies that the BigInteger zero has a
  117        * zero-length mag array.
  118        */
  119       final int[] mag;

From the source

From the Wikipedia article Arbitrary-precision arithmetic:

Several modern programming languages have built-in support for bignums, and others have libraries available for arbitrary-precision integer and floating-point math. Rather than store values as a fixed number of binary bits related to the size of the processor register, these implementations typically use variable-length arrays of digits.

The first maximum you would hit is the length of a String which is 2³¹-1 digits. It's much smaller than the maximum of a BigInteger but IMHO it loses much of its value if it can't be printed.