prefetching data at L1 and L2

This statement :

the level-2 cache cannot prefetch more than one line at a time.

is incorrect

In fact, the L2 prefetchers are often stronger and more aggressive than L1 prefetchers. It depends on the actual machine you use, but Intels’ L2 prefetcher for e.g. can trigger 2 prefetches for each request, while the L1 is usually limited (there are several types of prefetches that can coexist in the L1, but they’re likely to be competing on a more limited BW than the L2 has at its disposal, so there will probably be less prefetches coming out of the L1.

The optimization guide, in Section (Data Prefetching) counts the following prefetcher types:

Two hardware prefetchers load data to the L1 DCache:
- Data cache unit (DCU) prefetcher: This prefetcher, also known as the streaming prefetcher, is triggered by an ascending access to very recently loaded data. The processor assumes that this access is part of a streaming algorithm and automatically fetches the next line.
- Instruction pointer (IP)-based stride prefetcher: This prefetcher keeps track of individual load instructions. If a load instruction is detected to have a regular stride, then a prefetch is sent to the next address which is the sum of the current address and the stride. This prefetcher can prefetch forward or backward and can detect strides of up to 2K bytes.

 Data Prefetch to the L2 and Last Level Cache - 
 - Spatial Prefetcher: This prefetcher strives to complete every cache line fetched to  the L2 cache with the pair line that completes it to a 128-byte aligned chunk.
 - Streamer: This prefetcher monitors read requests from the L1 cache for ascending and descending sequences of addresses. Monitored read requests include L1 DCache requests initiated by load and store operations and by the hardware prefetchers, and L1 ICache requests for code fetch. When a forward or backward stream of requests is detected, the anticipated cache lines are prefetched. Prefetched cache lines must be in the same 4K page. 

And a bit further ahead:

... The streamer may issue two prefetch requests on every L2 lookup. The streamer can run up to 20 lines ahead of the load request.

Of the above, only the IP-based can handle strides greater than one cache line (the streaming ones can deal with anything that uses consecutive cachelines, meaning up to 64byte stride (or actually up to 128 bytes if you don’t mind some extra lines). To use that, make sure that loads/stores at a given address would perform strided accesses – that’s usually the case already in loops going over arrays. Compiler loop-unrolling may split that into multiple different stride streams with larger strides – that would work even better (the lookahead would be larger), unless you exceed the number of outstanding tracked IPs – again, that depends on the exact implementation.

However, if your access pattern does consist of consecutive lines, the L2 streamer is much more efficient than the L1 since it runs ahead faster.

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