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While studying virtual memory concepts, I understood that a virtual address (generated by a processor to access memory location) contains page number and page offset. we use a page table to get the physical address (frame number essentially) corresponding to this page number.
Now, if these addresses (physical/virtual) operate in terms of pages/frames, how does the processor access a cache which operates in terms of blocks/lines?
Also, if the virtual address consists of only page number and page offset, where does the tag bits come from which is used to check if the cache set (specified by index/set bits) contains the required data or not?
I figured out the answer to this question.
Same address can be used/interpreted for accessing two different addressing schemes. (Thanks #PeterCordes for pointing this out)
Scheme 1 (To access the TLB): PageNumber + PageOffset
Scheme 2 (To access the cache): Tag + Set/Index + Offset
Usually in VIPT caches, the page number comes from higher-order TAG bits, and the page offset comes from lower-order TAG bits along with SET and OFFSET bits. To prevent aliasing (multiple virtual addresses mapping to same physical address), it is important that SET/INDEX bits come fully from page offset. This restriction limits the size of the cache.
I am not able to entirely grasp the concept of synonyms or aliasing in VIPT caches.
Consider the address split as:-
Here, suppose we have 2 pages with different VA's mapped to same physical address(or frame no).
The pageno part of VA (bits 13-39) which are different gets translated to PFN of PA(bits 12-35) and the PFN remains same for both the VA's as they are mapped to same physical frame.
Now the pageoffset part(bits 0-13) of both the VA's are same as the data which they want to access from a particular frame no is same.
As the pageoffset part of both VA's are same, bits (5-13) will also be same, so the index or set no is the same and hence there should be no aliasing as only single set or index no is mapped to a physical frame no.
How is bit 12 as shown in the diagram, responsible for aliasing ? I am not able to understand that.
It would be great if someone could give an example with the help of addresses.
Note: this diagram has a minor error that doesn't affect the question: 36 - 12 = 24-bit tags for 36-bit physical addresses, not 28. MIPS64 R4x00 CPUs do in fact have 40-bit virtual, 36-bit physical addresses, and 24-bit tags, according to chapters 4 and 11 of the manual.
This diagram is from http://www.cse.unsw.edu.au/~cs9242/02/lectures/03-cache/node8.html which does label it as being for MIPS R4x00.
The page offset is bits 0-11, not 0-13. Look at your bottom diagram: the page offset is the low 12 bits, so you have 4k pages (like x86 and other common architectures).
If any of the index bits come from above the page offset, VIPT no longer behaves like a PIPT with free translation for the index bits. That's the case here.
A process can have the same physical page (frame) mapped to 2 different virtual pages.
Your claim that The pageno part of VA (bits 13-39) which are different gets translated to PFN of PA(bits 12-35) and the PFN remains same for both the VA's is totally bogus. Translation can change bit #12. So one of the index bits really is virtual and not also physical, so two entries for the same physical line can go in different sets.
I think my main confusion is regarding the page offset range. Is it the same for both PA and VA (that is 0-11) or is it 0-12 for VA and 0-11 for PA? Will they always be same?
It's always the same for PA and VA. The page offset isn't marked on the VA part of your diagram, only the range of bits used as the index.
It wouldn't make sense for it to be any different: virtual and physical memory are both byte-addressable (or word-addressable). And of course a page frame (physical page) is the same size as a virtual page. Right or left shifting an address during translation from virtual to physical would make no sense.
As discussed in comments:
I did eventually find http://www.cse.unsw.edu.au/~cs9242/02/lectures/03-cache/node8.html (which includes the diagram in the question!). It says the same thing: physical tagging does solve the cache homonym problem as an alternative to flushing on context switch.
But not the synonym problem. For that, you can have the OS ensure that bit 12 of every VA = bit 12 of every PA. This is called page coloring.
Page coloring would also solve the homonym problem without the hardware doing overlapping tag bits, because it gives 1 more bit that's the same between physical and virtual address. phys idx = virt idx. (But then the HW would be relying on software to be correct, if it wanted to depend on this invariant.)
Another reason for having the tag overlap the index is write-back during eviction:
Outer caches are almost always PIPT, and memory itself obviously needs the physical address. So you need the physical address of a line when you send it out the memory hierarchy.
A write-back cache needs to be able to evict dirty lines (send them to L2 or to physical RAM) long after the TLB check for the store was done. Unlike a load, you don't still have the TLB result floating around unless you stored it somewhere. How does the VIPT to PIPT conversion work on L1->L2 eviction
Having the tag include all the physical address bits above the page offset solves this problem: given the page-offset index bits and the tag, you can construct the full physical address.
(Another solution would be a write-through cache, so you do always have the physical address from the TLB to send with the data, even if it's not reconstructable from the cache tag+index. Or for read-only caches, e.g. instruction caches, there is no write-back; eviction = drop.)
As far as my understanding goes, the CPU always generates a virtual address that is made-up of 2 parts- the page number and the page offset. The page number is used for indexing the page table (the corresponding mapping gives the starting address of the frame in the RAM). Now, please consider the following questions. Consider that the word size of the machine is 4 bytes, and the page size is equal to the frame size = 4096 bytes.
Supposing that the page number is 4 and the offset is 3. Then Page 4 in the logical memory maps to frame 8 in the virtual memory. This means that the starting address of the frame is 8.
Now, each frame will contain 4096/4= 1024 words. Does the offset imply for a word inside the frame, since the machine will always fetch a word at a time? What I mean is that does it mean the 3rd word in frame 8?
Is the particular word given to the CPU, or the entire frame? If former, then why does everyone talk about transfer in terms of frames and pages rather than words?
Suppose a page fault occurs. What this means is that the particular page in not in memory. Does it mean that the physical address mapped contains some other page? Does the mapping even exist in such a case when the invalid bit is 1.
Can someone clear-up things for me? One moment I seem to get it, and the very next, I get into a maze.
The key point of paging is that it deals with "chunks" of memory.
It is a map, a function, that translates virtual addresses into physical addresses but not on an address-by-address base. Rather, a "chunk" of continuous virtual addresses is translated together into another continuous "chunk" of, now physical, addresses.
You can think of it as a "translation" or "shuffle" of "chunks" of memory.
The correct term for "chunk" is page.
If try to do a sample mapping you can see that each page contains a set of addresses that all have a peculiarity: their lower bits don't change when passing from virtual to physical. The upper bits instead are arbitrary.
This dichotomy of the address value defines the Offset and Page/Frame number.
The offset is the part of the address value that don't undergo any translation.
In a page of 4KiB there are 4096 addresses, each one with its offset, so the offset has size log2(4096) = log2(212) = 12 * log2(2) = 12 bits.
In short the page size determines the offset size.
It is necessary to break the memory into pages and not words or byte, or in another view it is necessary to group the addresses to translate into pages.
Without pages, the metadata used for the translation, in jargon the page tables of various level, would occupy more memory that the one that under translation!
Offsets are relative to their page/frame thanks to the way their are defined: the offset 1024 (in hex 400h) in the frame 8 means the address 8000h + 400h = 8400h; if the page is mapped to the frame 12 the offset 1024 is still 1024 bytes after the beginning of the frame, 0c000h + 400h = 0c400h.
Being an address, an offset usually denotes a byte, event in architecture where bytes are not addressable. However this is not a standard convention, to know if an offset denotes a word or a byte (e.g. if offset 10 of frame 0 is the byte 40 or the byte 10) check the architecture manual. The first sections are usually dedicated to establishing a terminology to use throughout the book.
Paging happens before the CPU accesses the memory, you can think of it as an high level process. The unit that accesses the memory/bus is mostly unaware of it, as such the CPU read the data that the instruction is telling it to read (a word, a byte, and so on).
People talk about moving a page because a page is the smallest unit that can be characterized.
You can mark a page as non present, but not a word. You can make a page read-only but not a word.
If you need to map, say 16 bytes, you still need to map a whole page since 16 bytes are not characterizable. So we might as well read a whole page.
When a page-fault occurs it means that the page accessed is, at any level in the page-tables, non present.
This may mean a wide range of things, from the fact that the Present bit has been simply toggled (with the page still there), to the fact that the page has been saved to disk and zero-ed in memory.
Since the mapping function is total, meaning that every value is a valid value, the CPU need a way to know when a value is not valid.
The Present bit does this: tell the CPU that a translation must not be performed and that an exception must be raised instead.
The OS use this exception to be notified of when a page is needed, it doesn't need to reassign the mapping to another page or zero the memory.
When people say that a page is removed they mean that it is removed from the mapping, all modern OSes also zero-d the page to prevent leaking of information to other processes though.
So if a physical frame is not mapped it doesn't mean that another page in another process is mapping it, it simply mean that that range of addresses cannot be accessed.
As said above there are a lot of reasons for an OS to do this, including protection.
You have things a bit backwards. The operating system defines a logical address space for each process. The logic address space is divided into units of memory called PAGES.
The operating system logically maps the pages of the address to either physical page frames or secondary storage If the operating system maps pages to secondary storage then is using virtual memory.
In ye olde days all systems that did logical memory translation always did virtual memory mappings to secondary storage. That is why the terms virtual memory translation and logical memory translation are often conflated. These days it is becoming increasingly common to have logical translation without virtual memory.
All address accesses through a process are to logical addresses. The processor translates the logical address to page frames. If logical page exists but is mapped to secondary storage, accessing that page triggers a page fault. The operating system must handle the fault, remap the logical/virtual page to a physical page frame; load the data from secondary storage to the page frame; and restart the instructions.
Supposing that the page number is 4 and the offset is 3. Then Page 4 in the logical memory maps to frame 8 in the virtual memory. This means that the starting address of the frame is 8.
This make no sense. A logical page is virtual when it is mapped to secondary storage. If the page number is 4 the 4th logical page can:
a) have no mapping at all (access violation)
b) map to a physical page frame
c) map to a secondary storage (virtual memory)
Now, each frame will contain 4096/4= 1024 words. Does the offset imply for a word inside the frame, since the machine will always fetch a word at a time? What I mean is that does it mean the 3rd word in frame 8?
In nearly all (if not all) current processors there are no memory words; only bytes. The system bus fetches memory and the "word size" of the bus can be (and often is) different from the "word size" of the processor.
Is the particular word given to the CPU, or the entire frame? If former, then why does everyone talk about transfer in terms of frames and pages rather than words?
The process sees transfers in sizes related to the instruction being executed. The operand size can be larger or smaller than the machine word. The bus transfers data to memory and that size is frequently different from the word size of the machine.
Suppose a page fault occurs. What this means is that the particular page in not in memory. Does it mean that the physical address mapped contains some other page? Does the mapping even exist in such a case when the invalid bit is 1.
I gave the three possibilities for logical page mappings above. How those are indicated are system specific. Some systems use 2 bits to indicate a, b, or c. Others use a single bit to indicate (b) and require the operating system to determine whether it's (a) or (c).
Whether or not a page fault is triggered depended upon the state of the page table.
Generally a page fault means that the page frame is not in memory. However, it is often possible for the physical page frame to be in memory but not mapped in the page table (a soft page fault). (This occurs when the operating system has unmapped page frames to free some up but has not reallocated them.) In this case, the operating system simply needs to update the page table to point to the page frame and restart the instruction (no need to load from secondary storage).
Lets consider that size of page is equal to 1 KB. One entry in table
takes 2B. Table of pages takes not more than one page (so <= 1KB).
Can we conclude that size of operational memory is <= 512 KB ?
A correct answer is No, however I can't understand it. For me, answer is yes - look at my reasoning at show me where I am wrong, please.
Table contains <=1024B/2B=512=2^9 entries in table of pages. Size of page is 1024B=2^10B, so offset takes not more than <=10 bits. Number of page takes <=9 bits - because we have 512=2^9 entries. Hence, 9+10=19. Therefore <=2^19 bits make it possible to address <= 2^19 B=2^9KB=512KB.
Where am I wrong?
A page table entry is 2B, so a table entry can point to one of 2^16 physical pages. That's 2*16 kiB (because pages are 1kB). So a kernel can make use of up to 65536 kiB (64MiB) of physical memory.
This assumes that the entire page table entry (PTE) is a physical page number. That can work if the position of a PTE within the page table associates it with a virtual address. i.e. 9 bits of a virtual address are used as an index into the PT, to select a PTE.
We can't assume that the machine does work this way, but similarly we can't assume that it doesn't, until we have more information.
Given just the info in the question, we can conclude:
Usable physical memory can be anything up to 65536kiB.
Up to 512 virtual pages can be mapped at once (512kiB).
Not much else! Many possibilities are open.
A more likely design would have a valid/invalid bit in each PTE.
If a PTE's contents (rather than its location) indicate which virtual page it maps, it would be possible to map a large virtual address space onto very few physical pages. This address space would necessarily be sparsely mapped, but the kernel could give a process the illusion of having a lot of active mappings by keeping a separate table of what the mappings should be.
So on a page fault, the kernel checks to see if the page should have been mapped. If so, it puts the mapping in the PTE and resumes the process. (This kind of thing happens in real OSes, and it's called a minor page fault.)
In this design, the kernel's use of the page table to hold a subset of the real mappings would be analogous to a software-managed TLB. (Of course, this architecture could have a non-coherent TLB that requires invalidation after every PTE modification, so this would probably perform horribly).
When I study OS,I find a concept Logical Memory.So Why there is a need for a Logical Memory?How does a CPU generate Logical Memory?The output of "&ptr" operator is Logical or physical Address?Is Logical Memory and Virtual Memory same?
If you're talking about C's and C++'s sizeof, it returns a size and never an address. And the CPU does not generate any memory.
On x86 CPUs there are several layers in address calculations and translations. x86 programs operate with logical addresses comprised of two items: a segment selector (this one isn't always specified explicitly in instructions and may come from the cs, ds, ss or es segment register) and an offset.
The segment selector is then translated into the segment base address (either directly (multiplied by 16 in the real address mode and in the virtual 8086 mode of the CPU) or by using a special segment descriptor table (global or local, GDT or LDT, in the protected mode of the CPU), the selector is used as an index into the descriptor table, from where the base address is pulled).
Then the sum segment base address + offset forms a linear address (AKA virtual address).
If the CPU is in the real address mode, that's the final, physical address.
If the CPU is in the protected mode (or virtual 8086), that linear/virtual address can be further translated into the physical address by means of page tables (if page translation is enabled, of course, otherwise, it's the final physical address as well).
Physical memory is your RAM or ROM (or flash). Virtual memory is physical memory extended by the space of disk storage (could be flash as well as we now have SSDs).
You really need to read up on this. You seem to have no idea.