Custom data types and arbitrary-precision arithmetic are often key for efficient hardware designs on Field Programmable Gate Array (FPGA) platforms. Current end-to-end flows incorporating quantization are not only domain-specific, but also tightly integrated and not repurposable. Abstractions for arbitrary-precision arithmetic are generally vendor-specific, and results are hardly portable across platforms. In this work, we present a new Intermediate Representation (IR), base2, to address the programmability issues of custom data types in reconfigurable hardware. We contextualize our proposal in the greater LLVM (llvm) ecosystem, where we show how existing abstractions can be simplified and unified. We implement base2 in Multi-Level Intermediate Representation (MLIR), which allows it to be used in a variety of existing and future target-agnostic front-ends. We demonstrate the power of our model by applying it to sample kernels and evaluating the accuracy of the result. For these samples, we achieve interoperability with an existing end-to-end High-Level Synthesis (HLS) flow.