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验证数值正确性

将结果与参考值进行比较

验证数值正确性 是 CoddyKit 上的免费 Mojo Academy 课时。 这是第 4 节课，共 4 节。 你可以在下方免费阅读本课时的完整内容 — 然后在浏览器中使用内置代码编辑器和全天候 AI 导师进行实践。 这是 Mojo Academy 学习路径的一部分，你的进度在网页和 CoddyKit 应用中同步。 Mojo Academy 课程共包含 4 节课。

本课时的部分内容尚未翻译，以英文显示。

Fast but Wrong Is Useless

An optimized kernel only counts if it computes the right answer. Always verify before you trust a speedup.

Keep a Reference

Hold on to the simple, obviously correct version. It is your reference, the source of truth every fast kernel must match.

Floats Are Not Exact

Floating-point math rounds, so reordering sums can shift the last digits. Optimized results may differ slightly without being wrong.

Avoid Exact Equality

Because of rounding, never compare floats with ==. Tiny differences will make correct code look broken.

if fast == ref:  # fragile, avoid

Compare With a Tolerance

Instead, check that values are close within a small tolerance. If the gap is under epsilon, treat them as equal.

if abs(fast - ref) <= 1e-5:
    pass  # close enough

Absolute vs Relative Error

Absolute error is the raw gap; relative error scales it by magnitude. Big numbers need relative checks to stay fair.

rel = abs(fast - ref) / abs(ref)

Check Every Element

Loop over the whole result and test each cell. One mismatch beyond tolerance means the optimization broke something.

for i in range(n):
    if abs(fast[i] - ref[i]) > tol:
        print("mismatch at", i)

Track the Worst Gap

Record the largest difference you see. The max error across all elements is a clear, single health number for the kernel.

Test the Edge Cases

Try empty inputs, a single element, and odd sizes that do not divide evenly by the SIMD width. Edges expose tail bugs fast.

Use Known Answers

Multiply by the identity matrix or sum a vector of ones. Predictable inputs give answers you can verify by hand.

Automate the Check

Wrap verification in a small test that fails loudly on any mismatch. Run it after every change so regressions never slip by.

Quick Check

Your SIMD matmul is off from the reference by 0.0000007. What should you conclude?

Recap

Verify fast code against a trusted reference, compare with a tolerance not ==, check edges and known answers, and automate it. ✅

常见问题解答

「验证数值正确性」课时是免费的吗？

是的 — 「验证数值正确性」的完整文本可在网页上免费阅读。要进行交互式练习（内置代码编辑器和全天候 AI 导师）并解锁 Mojo Academy 课程的其余内容，请升级到 CoddyKit PRO。 Mojo Academy 课程共包含 4 节课。

「验证数值正确性」这节课中我会学到什么？

将结果与参考值进行比较 你通过在浏览器中直接运行的动手代码来练习 Mojo Academy，全天候 AI 导师会在你学习这节课的过程中回答你的问题。

学习 Mojo Academy 需要有经验吗？

无需任何先前经验。CoddyKit 上的 Mojo Academy 课程适合初学者到高级学习者，你可以从这里开始或从头开始，按照自己的节奏学习。 这是第 4 节课，共 4 节。

「验证数值正确性」课时需要多长时间？

大多数 CoddyKit 课程大约需要 5–10 分钟。每节课都很精短且互动，所以你能稳步进步，并在网页和应用中从离开的地方继续。

我能在这节 Mojo Academy 课中编写并运行代码吗？

能。每节 Mojo Academy 课都包含内置代码编辑器，你可以在浏览器中直接编写并运行真实代码，并获得即时 AI 反馈 — 无需本地设置。

此课程中的所有课时

  1. 在 Mojo 中建模张量
  2. 逐步构建矩阵乘法
  3. 优化内积
  4. 验证数值正确性
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