The machinery with __kBitConversionBuffer is tied to little endian systems.
On big endian systems, the two slots on __kBitConversionInts are swapped.

To illustrate, consider

JSBI.LT(JSBI.BigInt("4294967296"), 4294967296);

On big endian environments, the above expression evaluates to true, which is wrong.
(In this specific example, the execution path starts to diverge here.)

Perhaps the most prominent example of big-endian environment is that emulated by typedarray.

Thank you for the library.