Welcome to my new series covering mathematics and algorithms with FPGAs. Whatever hardware you’re designing, you’re likely to be working with numbers. This series begins with the basics of Verilog numbers, covers simple mathematics, including division and CORDIC, before looking at more complex algorithms, such as data compression. In this first post, we examine how integers (whole numbers) are represented and dig into the challenges of signed numbers in Verilog. Read more

In this FPGA recipe, we’re going to look at a straightforward method for generating sine and cosine using a lookup table. There are more precise methods, but this one is fast and simple and will suffice for many applications. This post is part of a series of handy recipes to solve common FPGA development problems. There are also posts on fixed-point numbers, division, and square root. Updated 2021-10-19. Get in touch with @WillFlux or open an issue on GitHub. Read more

The square root is useful in many circumstances, including statistics, graphics, and signal processing. In this FPGA recipe, we’re going to look at a straightforward digit-by-digit square root algorithm for integer and fixed-point numbers. There are lower-latency methods, but this one is simple, using only subtraction and bit shifts. This post is part of a series of handy recipes to solve common FPGA development problems. There are also posts on fixed-point numbers, division, and sine & cosine. Read more

Division is a fundamental arithmetic operation; one we take for granted in most contexts. FPGAs are different; Verilog can’t synthesize division: we need to do it ourselves. In this FPGA recipe, we’re going to look at a straightforward division algorithm for positive integers and fixed-point numbers. For integers, this method takes one cycle per bit: 32 cycles for 32-bit numbers. This post is part of a series of handy recipes to solve common FPGA development problems. Read more

Sometimes you need more precision than integers can provide, but floating-point computation is not trivial (try reading IEEE 754). You could use a library or IP block, but simple fixed point maths can often get the job done with little effort. Furthermore, most FPGAs have dedicated DSP blocks that make multiplication and addition of integers fast; we can take advantage of that with a fixed-point approach. This post is part of a series of handy recipes to solve common FPGA development problems. Read more