关于Eigen/Eigen3矩阵库定点精度实数运算支持的技术问询

Great question! Let me break down Eigen's support for fixed-point operations based on my hands-on experience with the library:

• Core Eigen lacks native fixed-point type support: You’re correct that Eigen’s primary focus is on IEEE754 floating-point types (float, double) and basic integer types out of the box. There’s no built-in, official support for fixed-point real-number arithmetic in the core library.

• Custom fixed-point integration is possible via templates: Eigen’s heavily template-based design lets you plug in your own fixed-point type, as long as it meets the library’s required arithmetic and trait requirements. Here’s a quick overview of what you’ll need to do:

  1. Build a custom fixed-point class (e.g., FixedPoint<StorageType, FractionalBits>) that overloads core operators like +, -, *, /, and supports conversions to/from floating-point values.
  2. Specialize Eigen’s type traits (such as Eigen::NumTraits<YourFixedPointType>) to inform Eigen about your type’s properties—like whether it behaves like a floating-point type, its precision characteristics, etc.
  3. Optional: If you want to leverage Eigen’s vectorization optimizations, you’ll need to implement SIMD support for your fixed-point type.

• Community solutions exist: Many developers have rolled their own fixed-point integrations with Eigen. For example, some have adapted Qt’s QFixed type or custom in-house fixed-point implementations to work seamlessly with Eigen matrices and linear algebra operations. Note that these are third-party workarounds, not part of the official Eigen distribution.

• Key things to keep in mind: When using custom fixed-point types with Eigen, you’ll need to handle precision limits, overflow, and underflow behavior yourself—Eigen won’t manage these automatically. Additionally, some advanced Eigen features (like certain decomposition algorithms) may have implicit assumptions about numeric types, so thorough testing is a must.

内容的提问来源于stack exchange，提问作者picµ