Radio telescopes produce large volumes of data that need to be processed to obtain high-resolution sky images. This is a complex task that requires computing systems that provide both high performance and high energy efficiency. Hardware accelerators such as GPUs (Graphics Processing Units) and FPGAs (Field Programmable Gate Arrays) can provide these two features and are thus an appealing option for this application. Most HPC (High-Performance Computing) systems operate in double precision (64-bit) or in single precision (32-bit), and radio-astronomical imaging is no exception. With reduced precision computing, smaller data types (e.g., 16-bit) are used to improve energy efficiency and throughput performance in noise-tolerant applications. We demonstrate that reduced precision can also be used to produce high-quality sky images. To this end, we analyze the gridding component (Image-Domain Gridding) of the widely-used WSClean imaging application. Gridding is typically one of the most time-consuming steps in the imaging process and, therefore, an excellent candidate for acceleration. We identify the minimum required exponent and mantissa bits for a custom floating-point data type. Then, we propose the first custom floating-point accelerator on a Xilinx Alveo U50 FPGA using High-Level Synthesis. Our reduced-precision implementation improves the throughput and energy efficiency of respectively 1.84\times and 2.03\times compared to the single-precision floating-point baseline on the same FPGA. Our solution is also 2.12\times faster and 3.46\times more energy-efficient than an Intel i9 9900k CPU (Central Processing Unit) and manages to keep up in throughput with an AMD RX 550 GPU.