As a simple test one could look at the distribution of the random numbers. A good quality generator should distribute the numbers uniformly (and pseudo generators usually do this by construction). I have been counting for 10 buckets and 500,000 trials. ($freq{ int TRNGrand $r }++ for 1..$n; with $r=10; and $n=500000;). One would expect 10% of the numbers in each bucket (ie 50,000). The maximum relative error is around 10.5% in this exercise, ie +/-5000. Using rand, the maximum relative error is around 0.5%.

This would most likely lead to a failure of the usual statistical test like Diehard_tests but then you might want to see whether this deviation is a welcome additional source of randomness or leads to a predictable bias that could be exploited when you use your numbers for encryption (as one example).

In any case, generating those 500,000 numbers took nearly 8 hours (rand took less than a second), so I will refrain from more comprehensive testing of your code.