Mesi Cache Coherence Table: Understanding Cache Hierarchy and Data Consistency

In modern computing systems, caches play a crucial role in improving performance by reducing memory access latency. However, with multiple processors accessing shared data, maintaining cache coherence becomes a significant challenge. The MESI (Modified, Exclusive, Shared, Invalid) protocol is a widely used cache coherence protocol that ensures data consistency across all caches in a multi-processor system.

Cache Coherence Table

The MESI protocol uses a table to track the state of each cache line. The table has four rows: Modified, Exclusive, Shared, and Invalid. Each row represents a different state of the cache line.

| State | Description |

| --- | --- |

| Modified | This copy is not shared by other caches and has been updated. |

| Exclusive | This is the only cache copy and is consistent with global memory. |

| Shared | There are multiple caches copies shared, and all words in both caches are clean. |

| Invalid | This cache line is invalid in all caches. |

Understanding MESI States

In a system implementing the MESI protocol, each cache line can be in one of these four states.

* Modified: When a processor updates a cache line, it becomes modified. The modified state indicates that the cache line has been updated and is not shared with other processors.

* Exclusive: An exclusive state means that only one processor has access to the cache line, and it is consistent with global memory.

* Shared: A shared state indicates that multiple processors have copies of the same cache line. In this case, all words in both caches are clean, meaning they do not contain any dirty data.

* Invalid: An invalid state means that a cache line is no longer valid or has been removed from the cache.

Cache Coherence Protocol

The MESI protocol ensures cache coherence by following these steps:

1. When a processor updates a cache line, it sets its state to Modified.

2. If another processor tries to access the same cache line, the MESI protocol sends an invalidation message to that processor's cache, which sets its state to Invalid.

3. The modified processor then broadcasts an update message to all other processors' caches, setting their states to Exclusive.

4. When a processor reads from a shared cache line, it sets its state to Shared.

Example Scenarios

Let's consider two example scenarios:

1. A four-processor shared-memory system implements the MESI protocol. Initially, each processor has an invalid copy of the variable `a` in their cache. For the following sequence of memory references, show the state of the line containing the variable `a` in each processor's cache after each reference is resolved.

Time | Operation | Content of Directory for X

-----|-----------|----------------------1 | Processor 0 - read | Modified (Processor 0)

2 | Processor 5 - read | Invalid (Processor 5)

3 | Processor 0 - writes to X | Modified (Processor 0)

In this scenario, Processor 0 updates the cache line containing `a`, setting its state to Modified. Processor 5 tries to access the same cache line but receives an invalidation message, setting its state to Invalid.

2. Consider a multiprocessing system with 8 processors that have their local caches and are connected to the main memory using Full Map Directory cache coherence protocol. What is the number of bits per directory?

Answer: Each processor requires 1 bit in the directory, so the total number of bits is 8 (2^3).

In conclusion, the MESI cache coherence protocol ensures data consistency across all caches in a multi-processor system by using a table to track the state of each cache line. Understanding the different states and how they are managed is crucial for designing efficient cache coherence protocols that maintain data consistency in shared-memory systems.

References

* 'Cache Coherence Protocols' by Intel Corporation

* 'MESI Protocol' by Wikipedia

Mesi cache coherence table