Question: Cache Coherence Analysis Using the ESI Protocol

Background:

We studied the ESI cache coherence protocol for a bus$-$based system. This protocol ensures data consistency across multiple processors in a shared memory system. In this example, we analyze the behavior of two processors with private L$1$ data caches and a shared memory accessible via a snoopy cache coherence protocol over a shared bus.

System Details:

Caches:

Each processor has its own private L$1$ data cache. Cache size: $16$KiB $(16*1024$ bytes$).$Line size: $64$ bytes.Direct$-$mapped configuration.

ESI Protocol:

Exclusive $($E$)$: A cache line is only in one cache and clean.Shared $($S$)$: A cache line is in multiple caches and clean.Invalid $($I$)$: A cache line is invalid.

Memory Behavior:

Cache hits and misses are determined based on the coherence state and access type $($read$/$write$).$

Task:

Analyze the following memory operations and determine for each step:

The cache coherence state of the referenced address in both Processor $1$ and Processor $2.$

Whether the operation results in a cache hit or cache miss.

Memory Reference Trace:

Time Step $2$: CPU $2$ reads address $0$x$0004.$

Time Step $3$: CPU $2$ writes to address $0$x$4004.$

Time Step $4$: CPU $2$ reads address $0$x$0008.$

Time Step $5$: CPU $1$ writes to address $0$x$8000.$

Time Step $6$: CPU $1$ writes to address $0$x$0008.$

Time Step $7$: CPU $2$ writes to address $0$x$0008.$

Time Step $8$: CPU $1$ reads address $0$x$0004.$

Time Step $9$: CPU $1$ reads address $0$x$4004.$

Instructions:

For each time step, document:

The state of the cache line $($Exclusive$,$ Shared, Invalid$)$ for both Processor $1$ and Processor $2.$Whether the access results in a hit or miss.