Welcome to my ongoing series covering mathematics and algorithms with FPGAs. This series begins with the basics of Verilog numbers, then considers fixed-point, division, square roots and CORDIC before covering more complex algorithms, such as data compression.| Project F
In this how to, 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.| Project F
The square root is useful in many circumstances, including statistics, graphics, and signal processing. In this how to, 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.| Project F
Division is a fundamental arithmetic operation we take for granted. FPGAs include dedicated hardware to perform addition, subtraction, and multiplication and will infer the necessary logic. Division is different: we need to do it ourselves. This post looks at a straightforward division algorithm for positive integers before extending it to cover fixed-point numbers and signed numbers.| Project F
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.| Project F