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优化内积

将点积向量化并展开循环

优化内积 是 CoddyKit 上的免费 Mojo Academy 课时。这是第 3 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。

The Dot Product Core

The inner product multiplies two sequences element by element and adds the results. Speeding it up speeds your whole matmul.

var acc: Float32 = 0.0
for k in range(K):
    acc += a[k] * b[k]

One Lane at a Time Is Slow

A plain loop handles a single pair per step. Modern CPUs can do many at once, so scalar code leaves lanes idle.

Enter SIMD

A SIMD value packs several numbers and applies one operation to all of them together, doing real work in parallel per instruction.

var v = SIMD[DType.float32, 4](1, 2, 3, 4)

Load a Chunk at Once

Instead of one float, load a whole SIMD-width slice of each array in a single move, ready for vector math.

var va = a.load[width=4](k)
var vb = b.load[width=4](k)

Multiply Whole Vectors

Multiplying two SIMD values yields a vector of products in one step. The element-wise work happens across all lanes together.

var prod = va * vb  # 4 products at once

Accumulate Into a Vector

Keep a SIMD accumulator and add each product vector into it. You delay the final sum until the loop is done.

var acc = SIMD[DType.float32, 4](0)
acc += va * vb

Step by the Width

The loop now advances by the SIMD width, not by one. Four lanes wide means a quarter as many iterations.

for k in range(0, K, 4):
    acc += a.load[width=4](k) * b.load[width=4](k)

Reduce at the End

After the loop, collapse the lane accumulator into one number with a horizontal reduce, giving the final dot product.

var total = acc.reduce_add()

Unrolling the Loop

Unrolling processes several widths per iteration, cutting loop overhead and exposing more independent work to the CPU.

Handle the Remainder

If K is not a multiple of the width, a few elements are left over. A small tail loop finishes them one at a time.

for k in range(K - K % 4, K):
    total += a[k] * b[k]

Let Mojo Help

Mojo offers the vectorize helper to apply a width-parameterized body across a range, handling stepping and the tail for you.

Quick Check

After a SIMD-width dot product loop, why do you call reduce_add at the end?

Recap

Vectorize the inner product by loading SIMD chunks, multiplying lanes together, accumulating, then reduce; unroll and clean up the tail. ⚡

常见问题解答

「优化内积」课时是免费的吗？

是的 — 「优化内积」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。

「优化内积」这节课中我会学到什么？

将点积向量化并展开循环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 3 节课，共 4 节。

「优化内积」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

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