The next step would be to use these properties to write a compiler to run normal source code as floating point integers, maybe with some kind of FFI to call regular OS APIs.
- Using IEEE floating-point error for ML transfer functions http://tom7.org/grad/
- Using IEEE NaN and infinity to build logic gates and a whole CPU http://tom7.org/nand/
This is a proof by construction that the Intel MMU's fault handling mechanism is Turing complete. We have constructed an assembler that translates 'Move, Branch if Zero, Decrement' instructions to C source that sets up various processor control tables. After this code has executed, the CPU computes by attempting to fault without ever executing a single instruction. Optionally, the assembler can also generate X86 instructions that will display variables in the VGA frame buffer and will cause control to be transferred between the native (display) instructions and 'weird machine' trap instructions.
The mov trick is akin to OISC, the "one instruction set computer". Here instead it's building logic circuits.