浮点运算手册

Hacker News 上怎么说

• SuchAnonMuchWow · 2023 年

  ……一个整数，所以我们需要其他解决方案。pow 函数（或者 exp、log、cos 等其他数学函数）究竟是如何计算的，这本身就是一个庞大的研究课题，但如果你感兴趣，《Handbook of Floating-Point Arithmetic》（https://perso.ens-lyon.fr/jean-michel.muller/Handbook.html）既是该领域（以及浮点数有限精度相关问题）的绝佳入门读物，同时也提供了一个……

  …an integer, so we need other solutions. How exactly the pow function (or other math function like exp, log, cos, ...) are computed is a vast research subject in itself, but if you are interested, the Handbook of Floating-Point Arithmetic (https://perso.ens-lyon.fr/jean-michel.muller/Handbook.html) is both a good introduction to the domain (and the problems associated with the finite precision of floating point number), and provides a…

• RossBencina · 2026 年

  EDIT：我看到 libbf 实现了操作的精确舍入（faithful rounding）。漂亮。涨姿势了（TIL）。另参见：Jean-Michel Muller 的书：《Handbook of Floating Point Arithmetic》和《Elementary Functions》。https://www.sollya.org/

  EDIT: I see that libbf implements faithful rounding of operations. Nice. TIL. See also: Jean-Michel Muller's books: "Handbook of Floating Point Arithmetic," and "Elementary Functions." https://www.sollya.org/

• brandmeyer · 2018 年

  如果你手里有高德纳的《计算机程序设计艺术》，讲半数值算法的那一节涵盖了软件浮点数的内容。另一个资料来源是《Handbook of Floating Point Arithmetic》，里面详细介绍了硬件和软件方法。源代码实现可以在 libgcc 中找到。如果我没记错的话（IIRC），它们的 ARM 汇编代码版本是现有的运行速度最快的例程之一……

  If you have a copy of Knuth's Art of Computer Programming, the section on seminumerical algorithms covers software floating point. Another source is the Handbook of Floating Point Arithmetic, which covers both hardware and software methods in detail. An implementation in source code may be found in libgcc. IIRC their ARM assembly code versions are some of the fastest routines available…

• thiazikara · 2022 年

  ……组件、理论等等，你很快就会迷失。到头来你真正能做的只有：1. 找本统计学书，从理论上入门 ML；2. 学习数值计算，我个人非常喜欢《Handbook of Floating Point Arithmetic》，但我从来没真正读完过；3. 很多库针对特定架构做了大量优化，事实上我记得有人演示过使用 numpy 时遇到了……

  …components, theories, etc that you get lost very soon At end all you can really do 1. Grab a statistics book and get into ML theoretically 2. Learn about numerical computations, I particularly enjoyed the Handbook of Floating Point Arithmetic, but I never really finished it 3. Libraries have lot of optimizations in it pertaining to the specific architecture, and in fact, I remember that someone gave a demonstration of using numpy and he faced…

• lntue · 2023 年

  ……pythonsollya（Sollya 的 Python 包装库）以及 SageMath。除此之外，关于 Remez 算法的一些综述类参考文献（应该更符合你的胃口），我比较喜欢的有：- J.M. Muller 等人编著的《Handbook of Floating-Point Arithmetic》第 10.3.2 节（以及该节引用的文献）。- N. Brisebarre 和 S. Chevillard 的论文《Efficient polynomial L-approximations》，第 18 届 IEEE 计算机算术研讨会（ARITH '07），这篇是……

  …pythonsollya (a Python wrapper for Sollya), and SageMath. Other than that, some of the overview references about Remez algorithm (should be a bit closer to your taste) that I like are: - J.M. Muller et. al., "Handbook of Floating-Point Arithmetic", section 10.3.2 (and follow references in that section). - N. Brisebarre and S. Chevillard, "Efficient polynomial L-approximations," 18th IEEE Symposium on Computer Arithmetic (ARITH '07), which is…

• nsajko · 2023 年

  一本很好的参考书是《Handbook of Floating-Point Arithmetic》。如果你能具体说说到底哪里不清楚，我会给出更详细的“证明”。哪怕你现在的态度有点像“海狮谬误”（sealioning）。> 连看都没看就直接发帖否定，这也太荒谬了……

  A good reference is the Handbook of Floating-Point Arithmetic. If you can be more specific about what is it that's not clear, I'll give more specific "proof". Even though you're being a bit "sealion"-y. > It's ridiculous to post a dismissal without even watching…

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