It's even hard to come up with all the relevant test cases - if you miss a corner case in the implementation, it is likely you will oversee it also in the test case generation. Only an exhaustive search would somehow be able to discover this.
With e.g. templates in C++, this is possible in some cases. You can test a template version using the limited range of an unsigned char, while your real implementation will use a uint64.
But instead of implementing e.g. a binary search, I prefer to take a proven implementation from e.g. the STL and adapt it for my needs. Experience and programmer lazyness have taught me this is a good way :)
With e.g. templates in C++, this is possible in some cases. You can test a template version using the limited range of an unsigned char, while your real implementation will use a uint64.
But instead of implementing e.g. a binary search, I prefer to take a proven implementation from e.g. the STL and adapt it for my needs. Experience and programmer lazyness have taught me this is a good way :)