Can I Control Floating Point Precision in Operations?

You can influence precision by selecting specific data types, which determine the bit sizes used for calculations. Options like float8, float16, float32, and float64 exist, but note that float8 and half precision formats are typically supported only on GPUs. While you can't set an arbitrary precision directly, you can scale your values to fit your precision needs, use the `floor()` function, and then scale back down. So, while hardware limits precision, you can control it somewhat through type selection.

I actually do something similar by using integer math instead of floating point in my projects, especially for motion control tasks. Integer calculations are much faster and meet the precision requirements dictated by my hardware, like stepper motors. The key is managing whether you're dealing with absolute or relative values; that way, you can control potential cumulative errors effectively.

There is a concept called variable precision floating point, mainly handled in software, but there's ongoing research for hardware support. It's essential if you're working on specialized applications, like certain embedded systems where resource optimization is critical. Fixed-point arithmetic is another option, but it's more niche and applies mostly to lower-powered devices.

The processors we use daily, like Intel and AMD, mostly allow you to choose between 32-bit floats and 64-bit doubles for precision, but you can't set a specific precision just for operations like addition or multiplication. While there might be some performance gains from using lower precision in functions like square roots or trigonometric calculations, modern CPUs handle these operations so efficiently that reduced precision usage rarely becomes necessary. Look-up tables often provide faster results when dealing with complex calculations.

If you choose smaller floating point types like FP16 instead of doubles, you're effectively reducing precision without complicated setups. Just remember for simple operations like multiplications, the time saved might not outweigh the overhead of managing different precisions. And C++ provides options, like using `-ffast-math`, to help optimize performance with floats as well!