Optimizar el producto escalar

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

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

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

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

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

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

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

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

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

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.

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

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

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