VDR-LLM-Prolog on FPGA: Exact Integer Arithmetic in Custom Silicon: A 10-Core Q335 Processor on Zynq-7020

VDR-LLM-Prolog is an architecture for language models built on exact integer arithmetic, where every value is a triple [Value, Denominator, Remainder] of integers, data lives in scoped knowledge bases at integer addresses, and the language model orchestrates 448 deterministic primitives rather than generating computation as text. The arithmetic foundation uses Q335 — a fixed denominator of 2^335 providing 100 decimal digits of precision — where addition is one integer add and multiplication is one integer multiply followed by division by the fixed denominator. This paper presents a custom FPGA processor design that accelerates Q335 arithmetic and Prolog knowledge base operations on a Xilinx Zynq-7020 system-on-chip. The design exploits a structural property of the Q335 representation: because the denominator is a fixed power of two, division by the denominator is bit extraction — bits above position 335 are the quotient, bits below are the remainder. In digital logic, fixed-position bit extraction is wiring, not computation: zero logic cells, zero clock cycles beyond routing delay, zero power consumption. The processor implements ten VDR-Q335 cores, each with a 384-bit ALU (1-cycle addition, 9-cycle multiplication via iterative 128-bit tiling on DSP48E1 slices, 1-cycle comparison, 19-cycle cross-multiply for Prolog unification), a 2KB remainder tree in block RAM, and a 53-instruction ISA spanning wide arithmetic, remainder tree management, Prolog matching, and batch processing. A batch dispatcher distributes work across cores via DMA, and a binary reduction network combines partial results in 5 cycles. The system fits within 54.2% of available lookup tables and 73.4% of flip-flops, leaving headroom for timing closure and future additions. At 150 MHz, the design achieves single Prolog fact queries across 200 facts in approximately 200 nanoseconds, attention dot products for 64-dimensional vectors in approximately 6 microseconds, surrogate softmax over 100 logits in approximately 3.3 microseconds, and SGD parameter updates in approximately 15 cycles per element. The ARM host processor runs the Zig VDR-LLM-Prolog runtime — orchestrated inference, knowledge base management, sessions, grammar-directed generation, and language model passes — while the FPGA accelerates parallel data-plane operations through a register-mapped control interface and high-bandwidth DMA. Every accelerated operation produces results bit-identical to the software implementation, verified against the project's 884-test validation suite with zero arithmetic errors. The architecture scales linearly: the same core design targets 60 cores on Zynq-7045, 120 on Zynq-7100, and 200+ on UltraScale+ devices.