With dmd 2.055 under Linux x86-64, (BigInt(10)^^p)^^2 doesn't return the correct result starting from p == 32:

import std.stdio, std.bigint;
void main() {
	for( int p = 0 ; p < 40 ; p++ ) {
		BigInt n = BigInt(10)^^p;
		BigInt a = n*n;
		BigInt b = n^^2;
		if( a != b ) {
			writefln( "%s %s %s %s", p, n, a, b );
		}
	}
}

It also fails with BigInt(2)^^p (from p==32 too) and BigInt(20)^^p (from p==16).

Values like (BigInt(2)^^32+1)^^2 are computed correctly.