Calculating Cache Memory Hit and Miss, and Calculating Rows in Cache

Question

I am studying an old exam for an upcoming exam, and the final questions consist of what the title describes. Now, I am familiar with assembly language instructions and I somewhat know what the code means. But, what the exam question actually wants me to do is confusing. I would really appreciate if someone could explain this question.

The question:

• I am given a cache-memory which has room for 512 bytes and every row is 8 bytes long. The memory is direct-mapped and an "address" is 32 bits long. Also, the cache-memory is empty from the start. After that, I get some instructions and am supposed to explain if it becomes a cache-hit or cache-miss. It should also be assumed that the instructions are all sequential and all data that is added/modified in an instruction still exists for the next instruction.

The instructions I get are

1. movia r8, 0xBEDA12C4
2. ldw r10, 0( r8 )
3. ldw r11, 8( r8 )
4. stw r10, 16( r8 )
5. ldw r10, 24(r8)
6. ldw r18, 32(r8)

Now I would really appreciate if someone could explain the details to me:

• The cache-memory has room for a total of 512 bytes. What is this? Is it the total memory the cache is able to store? Also, I heard from somewhere that this is how you calculate rows in cache. For example, 512 bytes of memory and every row is 16 bytes. 512/16 = 32 rows in cache. For this example 512/8 = 64 rows. Which one is it? What does this mean!?

• It also states that every row is 16 bytes long. I've seen the example with TAG, ROW, BYTE where they try to illustrate the cache. But how do I understand the 16 bytes per row? At least it doesn't seem to take part of the length on TAG, ROW, BYTE. What is this for?

• Direct-mapped cache. I understand this somewhat. It's just a big row of slots of order which are empty or not, yeah? I found some information on this here. http://www.cs.umd.edu/class/sum2003/cmsc311/Notes/Memory/direct.html

*Updated link: https://web.archive.org/web/20150213025748/http://www.cs.umd.edu/class/sum2003/cmsc311/Notes/Memory/direct.html

• Now to the main part. How do I calculate for each instruction if it will be a cache miss or hit? My guess is that the first instruction ought to be a miss, since the question said that the cache memory is empty from the start. The second instruction also must be a cache miss but from this point on I am not sure how to calculate if the instruction generates a cache hit or miss. To be honest, I am not even sure what a hit would be.

I would really appreciate if someone could show me how to calculate each step and how I know whether an instruction creates a cache hit or miss. The instructions we get for calculating this are really confusing. Thank you so much!

Answer 1

Generally you have to look at it as at a separate memory space, with only 512 bytes, addressable, readable and writable as arrays 8 bytes each. If you need byte 2, the address will be 0, you read the whole array and select byte 3 from it. If you need byte 8, the address will be 1, and you select byte 0 from the array. Such small memory have one huge advantage - it is fast. It alone can store the contents of some larger memory space, only first 512 bytes. If you store something to address 1 of larger memory space, it will go to that smaller memory instead, the address will become 0 and offset 1, internally for that small amount of memory. If you access beyond that, for example, 1000, you will have to wait more. In this case it would be just memory mapped "registers" - it would be actually faster and better in some cases, than "cache" - unfortunately for some reason processor makers generally won't let you use the cache in that way (probably marketing and support reasons - to sell other products as a separate market share, with higher price).
If you add some more space to each array to store some other value, you can store a part of address there. Without hardware support you could store there virtually anything, that second part is called tag. Now if you have some address fffff000, you can read the second space (assuming that you have the commands to do so), from address 0 - for simplicity and speed you can obtain the address from the primary memory space by masking all the bits except bits 3..8 and 0-2 (which are used to obtain offset in 8 byte array), and check the tag part from that address. One bit in that tag may be used to indicate whether there is something stored there, the other bits may be used to store the part of address from main memory. If you want to save something cached there, you set the bit indicating that the array is not "empty", and assign the upper bits of the main address there, and copy the 8 bytes from the main memory. Next time, before reading something within that range in memory, you read the tag part of the smaller memory array first, then decide whether to read from slow main memory, or from that smaller but faster part (and it would be cache hit).
If you write something with an address of (+-)x512 bytes in main memory, you would have to read the already mentioned array of 8 bytes, copy it into main memory, whole 8 bytes, and write what you want into the very same cell, and then modify the address with a new value. But you would lose the previous copy of your data in the smaller memory area (but faster). If you need the previous value again (any of those 8 bytes), you would have to copy it again from main memory (cache miss). The same goes for all other arrays of that "cache" memory. So we have a sequence of cache checking, writing, reading and copying the data to or from main memory.
That is called 1 way associativity, for 2 ways there would be one more array (same) of 512 bytes, which can store different addresses though (with the step of 512 from main memory), the tags of those 2 arrays may be checked simultaneously, and if some array has the copy of that memory range it can return it instead of reading it from main memory. Without tag checking (extra cycles for that), the "cache" is essentially a small amount of memory.