SAS memory usage and sorting - sas

I'm curious about SAS's use of memory, sorting, and why it seems to be so inefficient.
I have a quad core xeon with 8GB ram. I have a 3GB dataset. Why, at any given time during a standard proc sort, is a mere 120MB of ram being used and a meager 15-20% CPU utilization? This seems like something horribly inefficient is going on with the procedure.
In my opinion, as I have the available memory, it would load the entire dataset and then proceed to obliterate all available CPU cycles. But only 15%? It's a stunning waste of available resources and bothers me. It seems like it's constantly going back and forth to
the disk which is painfully slow.
Is there some magical setting that says "SAS, you can utilize everything to go faster" I'm missing?
64bit OS running 64bit SAS, btw.

You might check your MEMSIZE and SORTSIZE settings. More discussion about sort performance is here.

The thing with sort is that it's not the sorting that takes the time, generally it's the reading the data set in and writing it out again. Sorting is, comparatively, quick. So with a 3GB data set significant time is taken just waiting for the disk to supply all of the data. It can overlap sorting parts of the data with reading more of it in, but it's still likely to be I/O bound.
That said, MEMSIZE and SORTSIZE will at least allow you to make maximum use of your available memory. You need to ensure that SAS will be reading the entire data set in and sorting it in one go and then writing it out again. With lower memory, or if MEMSIZE/SORTSIZE are not suitably configured, it will sort the data set in chunks and then have to merge those chunks. You really want to avoid "multi-pass sort" if at all possible as it will double the time it takes (has to go through the whole data set sorting chunks, then to through all the data again, merging those chunks). I think you get hints from the SASLOG as to whether it is multi-pass sorting or not.

In general, that's not how SAS works. SAS keeps your data on your disk drives and only reads a small portion of it at a time. To, me that's the advantage of SAS: I use SAS for stuff that can't fit in RAM.
You might be interested in Stata, R, or another package that keeps your data in RAM. It's pretty easy to move back & forth between the programs, even for the same project.

Related

C++: Is it more efficient to store data or continually read it

Ok so I'm working on a game project. Just finished rebuilding a game engine I designed some time ago. I'm looking at making a proprietary file type to store data rather than using a database like sqlite.
Looking at making this work with the game as efficiently and quickly as possible right off the bat without going too deep into it. And then improving over time.
My question is: Is it more efficient overall to load the data from the file and store it in a data manager class to be reused? Or is it more efficient overall to continually pull from the file?
Assuming the file follows some form of consistent structure for it's data. And we're looking at the largest "table" being something like 30 columns with roughly 1000 rows of data.
Here's a handy chart of "Latency Numbers Every Computer Programmer Should Know"
The far right hand side of the chart (red) has the time it takes to read 1 MB from disk. The green column has the same value read from RAM.
What this shows us is that you should do almost anything to avoid having to directly interact with the disk. Keeping data in RAM is good. Keeping data on disk is bad. (Memory mapped files might provide a way to handle this.)
This aside, reinventing the wheel is almost always the wrong solution. Sqlite works and works well. If it's not ideally suited for your needs, there are other file types out there.
If you're "looking at making this work with the game as efficiently and quickly as possible right off the bat without going too deep into it. And then improving over time", you'll find that's easiest to do if you reuse preexisting solutions to common problems.
Keeping reading from a file is generally not a good idea; modern operating systems do keep large IO caches (so if you keep reading the same stuff it won't really hit the disk), but syscalls are of course way more onerous than straight accessing memory - although, whether this is actually going to be a performance problem for your specific case is impossible to judge with the information you provided. On the other hand, if you have a lot of data to access keeping it all in memory can be wasteful, slow to load and, when under memory pressure, lead to paging.
The easy way out of this conundrum is to map the file in memory; the data is automatically fetched from disk when required and, unless the system is under memory pressure, frequently accessed pages remain cached in RAM, guaranteeing you fast access.
Of course this is feasible only if the data you need to map is smaller than the address space, but given the example you provided (30 columns/1000 rows, which is really small) it shouldn't be a problem at all.
If you can hold the data in RAM then it is more efficient. This is because it is quicker for your computer to access values that are in RAM, a cache or the CPU's registers than it is to get it from the hard drive. Reading from the hard drive requires alot of time from the drivers of the operating system; therefore holding the data is more efficient

Not enough memory in C++ : write to file instead, read data in when needed?

I'm developing a tool for wavelet image analysis and machine learning on Linux machines in C++.
It is limited by the size of the images, the number of scales and their corresponding filters (up to 2048x2048 doubles) for each of N orientations as well as additional memory and processing overhead by a machine learning algorithm.
Unfortunately my skills of Linux system programming are shallow at best,
so I'm currently using no swap but figure it should be possible somehow?
I'm required to keep the imaginary and real part of the
filtered images of each scale and orientation, as well as the corresponding wavelets for reconstruction purposes. I keep them in memory for additional speed for small images.
Regarding the memory use: I already
store everything no more than once,
only what is needed,
cut out any double entries or redundancy,
pass by reference only,
use pointers over temporary objects,
free memory as soon as it is not required any more and
limit the number of calculations to the absolute minimum.
As with most data processing tools, speed is at the essence. As long as there
is enough memory the tool is about 3x as fast compared to the same implementation in Matlab code.
But as soon as I'm out of memory nothing goes any more. Unfortunately most of the images I'm training the algorithm on are huge (raw data 4096x4096 double entries, after symmetric padding even larger), therefore I hit the ceiling quite often.
Would it be bad practise to temporarily write data that is not needed for the current calculation / processing step from memory to the disk?
What approach / data format would be most suitable to do that?
I was thinking of using rapidXML to read and write an XML to a binary file and then read out only the required data. Would this work?
Is a memory-mapped file what I need? https://en.wikipedia.org/wiki/Memory-mapped_file
I'm aware that this will result in performance loss, but it is more important that the software runs smoothly and does not freeze.
I know that there are libraries out there that can do wavelet image analysis, so please spare the "Why reinvent the wheel, just use XYZ instead". I'm using very specific wavelets, I'm required to do it myself and I'm not supposed to use external libraries.
Yes, writing data to the disk to save memory is bad practice.
There is usually no need to manually write your data to the disk to save memory, unless you are reaching the limits of what you can address (4GB on 32bit machines, much more in 64bit machines).
The reason for this is that the OS is already doing exactly the same thing. It is very possible that your own solution would be slower than what the OS is doing. Read this Wikipedia article if you are not familiar with the concept of paging and virtual memory.
Did you look into using mmap and munmap to bring the images (and temporary results) into your address space and discard them when you no longer need them. mmap allows you to map the content of a file directly in memory. no more fread/fwrite. Direct memory access. Writes to the memory region are written back to the file too and bringing back that intermediate state later on is no harder than redoing an mmap.
The big advantages are:
no encoding in a bloated format like XML
perfectly suitable for transient results such as matrices that are represented in contiguous memory regions.
Dead simple to implement.
Completely delegate to the OS the decision of when to swap in and out.
This doesn't solve your fundamental problem, but: Are you sure you need to be doing everything in double precision? You may not be able to use integer coefficient wavelets, but storing the image data itself in doubles is usually pretty wasteful. Also, 4k images aren't very big ... I'm assuming you are actually using frames of some sort so have redundant entries, otherwise your numbers don't seem to add up (and are you storing them sparsely?) ... or maybe you are just using a large number at once.
As for "should I write to disk"? This can help, particularly if you are getting a 4x increase (or more) by taking image data to double precision. You can answer it for yourself though, just measure the time to load and compare to your compute time to see if this is worth pursuing. The wavelet itself should be very cheap, so I'm guess you're mostly dominated by your learning algorithm. In that case, go ahead and throw out original data or whatever until you need it again.

C++ Reading from several sections of a file is too slow

I need to read byte arrays from several locations of a big file.
I have already optimized the file so that as few sections as possible have to be read, and the sections are as closely together as possible.
I have 20 calls like this one:
m_content.resize(iByteCount);
fseek(iReadFile,iStartPos ,SEEK_SET);
size_t readElements = fread(&m_content[0], sizeof(unsigned char), iByteCount, iReadFile);
iByteCount is around 5000 on average.
Before using fread, I used a memory-mapped file, but the results were approximately the same.
My calls are still too slow (around 200 ms) when called for the first time. When I repeat the same call with the same sections of bytes to read, it is very fast (around 1 ms), but that does not really help me.
The file is big (around 200 mb).
After this call, I have to read double values from a different section of the file, but I can not avoid this.
I don't want to split it up in 2 files. I have seen the "huge file approach" used by other people, too, and they overcame this problem somehow.
If I use memory-mapping, the first call of reading is always slow. If I then repeat reading from this section, it is lightening fast. When I then read from a different section, it is slow for the first time, but then lightening fast the second time.
I have no idea why this is so.
Does anybody have any more ideas for me?
Thank you.
Disk drives have two (actually three) factors that limit their speed: access time, sequential bandwidth, and bus latency/bandwidth.
What you feel most is access time. Access time is typically in the millisecond ballpark. Having to do a seek takes upwards of 5 (often more than 10) milliseconds on a typical harddisk. Note that the number printed on a disk drive is the "average" time, not the worst time (and, in some cases it seems that it's much closer to "best" than "average").
Sequential read bandwidth is typically upwards of 60-80 MiB/s even for a slow disk, and 120-150 MiB/s for a faster disk (or >400MiB on solid state). Bus bandwidth and latency are something you usually don't care about as bus speed usually exceeds the drive speed (except if you use a modern solid state disk on SATA-2, or a 15k harddisk on SATA-1, or any disk over USB).
Also note that you cannot change the drive's bandwidth, nor the bus bandwidth. Nor can you change the seek time. However, you can change the number of seeks.
In practice, this means you must avoid seeks as much as you can. If that means reading in data that you do not need, do not be afraid of doing so. It is much faster to read 100 kiB than to read 5 kiB, seek ahead 90 kilobytes, and read another 5 kiB.
If you can, read the whole file in one go, and only use the parts you are interested in. 200 MiB should not be a big hindrance on a modern computer. Reading in 200 MiB with fread into an allocated buffer might however be forbidding (that depends on your target architecture, and what else your program is doing). But don't worry, you have already had the best solution to the problem: memory mapping.
While memory mapping is not a "magic accelerator", it is nevertheless as close to "magic" as you can get.
The big advantage of memory mapping is that you can directly read from the buffer cache. Which means that the OS will prefetch pages, and you can even ask it to more aggressively prefetch, so effectively all your reads will be "instantaneous". Also, what is stored in the buffer cache is in some sense "free".
Unluckily, memory mapping is not always easy to get right (especially since the documentation and the hint flags typically supplied by operating systems are deceptive or counter-productive).
While you have no guarantee that what has been read once stays in the buffers, in practice this is the case for anyting of "reasonable" size. Of course the operating system cannot and will not keep a terabyte of data in RAM, but something around 200 MiB will quite reliably stay in the buffers on a "normal" modern computer. Reading from buffers works more or less in zero time.
So, your goal is to get the operating system to read the file into its buffers, as sequentially as possible. Unless the machine runs out of physical memory so it is forced to discard buffer pages, this will be lightning fast (and if that happens, every other solution will be equally slow).
Linux has the readahead syscall which lets you prefetch data. Unluckily, it blocks until data has been fetched, which is not what you probably want (you would thus have to use an extra thread for this). madvise(MADV_WILLNEED) is a less reliable, but probably better alternative. posix_fadvise may work too, but note that Linux limits the readahead to twice the default readahead size (i.e. 256kiB).
Do not have yourself being fooled by the docs, as the docs are deceptive. It may seem that MADV_RANDOM is a better choice, as your access is "random". It makes sense to be honest to the OS about what you're doing, doesn't it? Usually yes, but not here. This, simply turns off prefetching, which is the exact opposite of what you really want. I don't know the rationale behind this, maybe some ill-advised attempt to converve memory -- in any case it is detrimental to your performance.
Windows (since Windows 8, for desktop only) has PrefetchVirtualMemory which does exactly what one would want here, but unluckily it's only available on the newest version. On older versions, there is just... nothing.
A very easy, efficient, and portable way of populating the pages in your mapping is to launch a worker thread that faults every page. This sounds horrendous, but it works very nicely, and is operating-system agnostic.
Something like volatile int x = 0; for(int i = 0; i < len; i += 4096) x += map[i]; is entirely sufficient. I am using such code to pre-fault pages prior to accessing them, it works at speeds unrivalled to any other method of populating buffers and uses very little CPU.
(moved to an answer as requested by the OP)
You cannot read from a file any quicker (there is no magic flag to say "read faster"). There is either an issue with your hardware or 200mS is how long it is supposed to take
1) The difference in access speed between your first read and subsequent ones is perfectly understandable : your first call actually read the file from the disk, and this takes time. However your kernel (not mentioning the disk controller) keep the accessed data buffered so when you access it a second time it is a pure memory access (1ms).
Even if you only need to access really tiny portions of the file, libc/kernel/controller optimizations access the disk in quite large chunk. You can read the libc/OS/controller doc to try and align your reads on these chunks.
2) You're using stream input, try using direct open/read/close functions : low-level I/O have less overhead (obviously). Nothing gets faster than this, so if you still find this too slow, you have an OS or hardware issue.
as it look you have a good benchmark, try to switch the size and the count in your fread call. reading 1 times 1000 bytes will be faster than 1000 x 1 byte.
Disk is slow, and as you pointed out, the delay comes from the first access - that's the disk spinning up and accessing the sectors necessary. You're always going to pay that cost one time.
You could improve your performance a little by using memory mapped IO. See either mmap (Linux) or CreateFileMapping+MapViewOfFile (Windows).
I have already optimized the file so that as few sections as possible have to be read
Correct me if I'm wrong, but in reference to the file being optimised, I'm assuming you mean you've ordered the sections to minimize the number of reads that take place and not what I'm going to suggest.
Being bound by IO here is likely due to the seek times, so other than getting a faster storage medium, your options are limited.
Two possible ideas I had are: -
1) Compress the data that is stored, which may give you slightly faster read times, but will still not help with seek time. You'd have to test if this benefits at all.
2) If relevant, as soon as you've retrieved one block of data, move it to a thread and start processing it while another read takes place. You may be doing this already, but if not, I thought it worth mentioning.

c++: how to optimize IO?

I am working on a mathematical problem that has the advantage of being able to "pre-compute" about half of the problem, save this information to file, and then reuse it many times to compute various 'instances' of my problem. The difficulty is that uploading all of this information in order to solve the actual problem is a major bottleneck.
More specifically:
I can pre-compute a huge amount of information - tons of probabilities (long double), a ton of std::map<int,int>, and much more - and save all this stuff to disk (several Gb).
The second half of my program accepts an input argument D. For each D, I need to perform a great many computations that involve a combination of the pre-computed data (from file), and some other data that are specific to D (so that the problem is different for each D).
Sometimes I will need to pick out certain pieces of pre-computed information from the files. Other times, I will need to upload every piece of data from a (large) file.
Are there any strategies for making the IO faster?
I already have the program parallelized (MPI, via boost::mpi) for other reasons, but regardless, accessing files on the disk is making my compute time unbearable.
Any strategies or optimizations?
Currently I am doing everything with cstdio, i.e. no iostream. Will that make a big difference?
Certainly the fastest (but the fragilest) solution would be to mmap the data to a fixed address. Slap it all in one big struct, and instantiate the std:::map with an allocator which will allocate in a block attached to the end of the struct. It's not simple, but it will be fast; one call to mmap, and the data is in your (virtual) memory. And because you're forcing the address in mmap, you can even store the pointers, etc.
As mentioned above, in addition to requiring a fair amount of work, it's fragile. Recompile your application, and the targeted address might not be available, or the layout might be different, or whatever. But since it's really just an optimization, this might not be an issue; anytime a compatibility issue arises, just drop the old file and start over. It will make the first run after a change which breaks compatibility extremely slow, but if you don't break compatibility too often...
The stuff that isn't in a map is easy. You put everything in one contiguous chunk of memory that you know (like a big array, or a struct/class with no pointers), and then use write() to write it out. Later use read() to read it in, in a single operation. If the size might vary, then use one operation to read a single int with the size, allocate the memory, and then use a single read() to pull it in.
The map part is a bit harder, since you can't do it all in one operation. Here you need to come up with a convention for serializing it. To make the i/o as fast as possible, your best bet is to convert it from the map to an in-memory form that is all in one place and you can convert back to the map easily and quickly. If, for example your keys are ints, and your values are of constant size then you could make an array of keys, and an array of values, copy your keys into the one array and values into the other, and then write() the two arrays, possibly writing out their size as well. Again, you read things in with only two or three calls to read().
Note that nothing ever got translated to ASCII, and there are a minimum number of system calls. The file will not be human readable, but it will be compact, and fast to read in. Three things make i/o slow: 1) system calls, if you use small reads/writes; 2) translation to/from ASCII (printf, scanf); 3) disk speed. Hard to do much about 3) (other than an SSD). You can do the read in a background thread, but you might need to block waiting for the data to be in.
Some guidelines:
multiple calls to read() are more expensive than single call
binary files are faster than text files
single file is faster than multiple files for large values of "multiple"
use memory-mapped files if you can
use 64 bit OS to let OS manage the memory for you
Ideally, I'd try to put all long doubles into memory-mapped file, and all maps into binary files.
Divide and conquer: if 64 bits is not an option, try to break your data into large chunks in a way that all chunks are never used together, and the entire chunk is needed when it's needed. This way you could load the chunks when they needed and discard them when they are not.
These suggestions of uploading the whole data to the RAM are good when two conditions are met:
Sum of all I/O times during is much more than cost of loading all data to RAM
Relatively large portion of all data is being accessed during application run
(they are usually met when some application is running for a long time processing different data)
However for other cases other options might be considered.
E.g. it is essential to understand if access pattern is truly random. If no, look into reordering data to ensure that items that are accessible together are close to each other. This will ensure that OS caching is performing at its best, and also will reduce HDD seek times (not a case for SSD of course).
If accesses are truly random, and application is not running as long as needed to ammortize one-time data loading cost I would look into architecture, e.g. by extracting this data manager into separate module that will keep this data preloaded.
For Windows it might be system service, for other OSes other options are available.
Cache, cache, cache. If it's only several GB it should be feasible to cache most if not all of your data in something like memcached. This is an especially good solution if you're using MPI across multiple machines rather than just multiple processors on the same machine.
If it's all running on the same machine, consider a shared memory cache if you have the memory available.
Also, make sure your file writes are being done on a separate thread. No need to block an entire process waiting for a file to write.
As was said, cache as much as you can in memory.
If you're finding that the amount you need to cache is larger than your memory will allow, try swapping out the caches between memory and disk how it is often done when virtual memory pages need to be swapped to disk. It is essentially the same problem.
One common method is the Least Recently Used Algorithm for determining which page will be swapped.
It really depends on how much memory is available and what the access pattern is.
The simplest solution is to use memory mapped files. This generally requires that the file has been layed out as if the objects were in memory, so you will need to only use POD data with no pointers (but you can use relative indexes).
You need to study your access pattern to see if you can group together the values that are often used together. This will help the OS in better caching those values (ie, keeping them in memory for you, rather than always going to the disk to read them).
Another option will be to split the file into several chunks, preferably in a logical way. It might be necessary to create an index file that map a range of values to the file that contain them.
Then, you can only access the set of files required.
Finally, for complex data structures (where memory mapped files fail) or for sparse reading (when you only ever extract only a small piece of information from a given file), it might be interesting to read about LRU caches.
The idea will be to use serialization and compression. You write several files, among which an index, and compress all of them (zip). Then, at launch time, you start by loading the index and save it in memory.
Whenever you need to access a value, you first try your cache, if it is not it, you access the file that contains it, decompress it in memory, dump its content in your cache. Note: if the cache is too small, you have to be picky about what you dump in... or reduce the size of the files.
The frequently accessed values will stay in cache, avoiding unnecessary round-trip, and because the file is zipped there will be less IO.
Structure your data in a way that caching can be effective. For instance, when you are reading "certain pieces," if those are all contiguous it won't have to seek around the disk to gather all of them.
Reading and writing in batches, instead of record by record will help if you are sharing disk access with another process.
More specifically: I can pre-compute a huge amount of information - tons of probabilities (long double), a ton of std::map, and much more - and save all this stuff to disk (several Gb).
As far as I understood the std::map are pre-calculated also and there are no insert/remove operations. Only search. How about an idea to replace the maps to something like std::hash_map or sparsehash. In theory it can give performance gain.
More specifically: I can pre-compute a huge amount of information - tons of probabilities (long double), a ton of std::map, and much more - and save all this stuff to disk (several Gb).
Don't reinvent the wheel. I'd suggest using a key-value data store, such as berkeley db: http://docs.oracle.com/cd/E17076_02/html/gsg/C/concepts.html
This will enable saving and sharing the files, caching the parts you actually use a lot and keeping other parts on disk.

how to memory map a huge matrix?

Suppose you got a huge (40+ GB) feature value (floating-point) matrix, rows are different features and columns are the samples/images.
The table is precomputed column-wise.
Then it is completely accessed row-wise and multi-threaded (each thread loads a whole row) several times.
What would be the best way to handle this matrix? I'm especially pondering over 5 points:
Since it's run on an x64 PC I could memory map the whole matrix at once but would that make sense?
What about the effects of multithreading (multithreaded initial computation as well?)?
How to layout the matrix: row or column major?
Would it help to mark the matrix as read-only after the precomputation has been finished?
Could something like http://www.kernel.org/doc/man-pages/online/pages/man2/madvise.2.html be used to speed it up?
Memory mapping the whole file could make the process much easier.
You want to lay out your data to optimize for the most common access pattern. It sounds like the data is going to be written once (column-wise) and read several times (row-wise). That suggests the data should be stored in row-major order.
Marking the matrix read-only once the pre-computation is done probably won't help performance (there are some possible low-level optimizations, but I don't think anything implements them), but it will prevent bugs from accidentally writing to data you don't intend to. Might as well.
madvise could end up being useful, once you've got your application written and working.
My overall advice: write the program in the simplest way you can, sequentially at first, and then put timers around the whole thing and the various major operations. Make sure the major operation times sum to the overall time, so you can be sure you're not missing anything. Then target your performance improvement efforts toward the components that are actually taking the most time.
Per JimR's mention of 4MB pages in his comment, you may end up wanting to look into hugetlbfs or using a Linux Kernel release with transparent huge page support (merged for 2.6.38, could probably be patched into earlier versions). This would likely save you a whole lot of TLB misses, and convince the kernel to do the disk IO in sufficiently large chunks to amortize any seek overhead.
Maybe, see below.
The size of the total working set of all threads must not exceed available RAM, otherwise the program will run at snail speed because of swapping.
Layout should match access patterns, as long as condition 2 is respected.
What do you mean by "mark as read only"?
Measure it.
Re 3: If you have, e.g., 8 CPUs but do not have enough RAM to load 8 rows, you should make each thread process its row sequentially in manageable chunks. In this case, block-layout of a matrix would make sense. If the thread MUST have the whole row in memory to process it, I'm afraid that you can't use all the CPUs, as the process will start thrashing, i.e., kicking out some subset of the matrix out of the ram and reloading another needed subset. This is slightly less bad than full swapping as the matrix is never modified, so the contents of the pages do not need to be written to the swap file before being kicked out. But it still hurts performance badly.
Also, doing random access I/O from multiple threads is a bad idea, which is what you'll end up doing if you use mmap(). You have (presumably) only a single disk, and parallel I/O will just make it slower. So mmap() might not make sense and you could achieve better I/O performance by reading data sequentially into ram.
Note that 40GB is approximately 10.5 million pages of 4096 bytes. By doing mmap(), you will, in the worst case, slow down computation by that many hard disk seeks. At 8ms per seek (taken from wikipedia), you'll end up wasting 83666 seconds, i.e., almost a whole day!
If you could fit the whole thing into main memory, then yes: memory map it all, and it doesn't matter whether it's column major or row major. However, at 40+ Gb, I'm sure it's too big for main memory. In which case:
No, don't map the whole thing! At least, don't expect the memory to work like normal memory if you map it all. Your program will take forever if you don't properly deal with the i/o issues.
The multi-threaded access issue is solved if you store it row-major (it sounds like you don't have multi-threaded column writes).
You should lay it out row-wise, assuming each cell is written once and then read many times.
Yes, I think it would help to mark the matrix as read-only after it's been written, but purely as a way to prevent bugs (accidental writes). It won't affect performance.
No, no amount of clever kernel read-ahead is going to solve your performance problems. You need to solve it at the algorithm level.
I think you are going to have a performance problem with a naive implementation. Either the computer with thrash while writing (if you store it row major) or it will thrash while querying (if you store it column major). The latter is presumably worse, but it's a problem both ways.
The right solution is to use an intermediate representation which is neither row-major nor column-major but 'large squares'. Take the first 50,000 columns and store them in a memory-mapped file (phase 1). It doesn't matter if it's column major or row major since it'll be purely memory resident. Then, take each row and write it into the final row-major memory-mapped file (phase 2). Then repeat the cycle for the next 50,000 columns, and so on.