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Hey peoples! Tonight, some meta-words. As you know I am fascinated by compilers and language implementations, and I just want to know all the things and implement all the fun stuff: intermediate representations, flow-sensitive source-to-source optimization passes, register allocation, instruction selection, garbage collection, all of that. It started long ago with a combination of curiosity and a hubris to satisfy that curiosity. The usual way to slake such a thirst is structured higher education followed by industry apprenticeship, but for whatever reason my path sent me through a nuclear engineering bachelor’s program instead of computer science, and continuing that path was so distasteful that I noped out all the way to rural Namibia for a couple years. Fast-forward, after 20 years in the programming industry, and having picked up some language implementation experience, a few years ago I returned to garbage collection. I have a good level of language implementation chops but never wrote a memory manager, and Guile’s performance was limited by its use of the Boehm collector. I had been on the lookout for something that could help, and when I learned of it seemed to me that the only thing missing was an appropriate implementation for Guile, and hey I could do that!Immix I started with the idea of an -style interface to a memory manager that was abstract enough to be implemented by a variety of different collection algorithms. This kind of abstraction is important, because in this domain it’s easy to convince oneself that a given algorithm is amazing, just based on vibes; to stay grounded, I find I always need to compare what I am doing to some fixed point of reference. This GC implementation effort grew into , but as it did so a funny thing happened: the as a direct replacement for the Boehm collector maintained mark bits in a side table, which I realized was a suitable substrate for Immix-inspired bump-pointer allocation into holes. I ended up building on that to develop an Immix collector, but without lines: instead each granule of allocation (16 bytes for a 64-bit system) is its own line.MMTkWhippetmark-sweep collector that I prototyped The is funny, because it defines itself as a new class of collector, fundamentally different from the three other fundamental algorithms (mark-sweep, mark-compact, and evacuation). Immix’s are blocks (64kB coarse-grained heap divisions) and lines (128B “fine-grained” divisions); the innovation (for me) is the discipline by which one can potentially defragment a block without a second pass over the heap, while also allowing for bump-pointer allocation. See the papers for the deets!Immix papermark-regionregionsoptimistic evacuation However what, really, are the regions referred to by ? If they are blocks, then the concept is trivial: everyone has a block-structured heap these days. If they are spans of lines, well, how does one choose a line size? As I understand it, Immix’s choice of 128 bytes was to be fine-grained enough to not lose too much space to fragmentation, while also being coarse enough to be eagerly swept during the GC pause.mark-region This constraint was odd, to me; all of the mark-sweep systems I have ever dealt with have had lazy or concurrent sweeping, so the lower bound on the line size to me had little meaning. Indeed, as one reads papers in this domain, it is hard to know the real from the rhetorical; the review process prizes novelty over nuance. Anyway. What if we cranked the precision dial to 16 instead, and had a line per granule? That was the process that led me to Nofl. It is a space in a collector that came from mark-sweep with a side table, but instead uses the side table for bump-pointer allocation. Or you could see it as an Immix whose line size is 16 bytes; it’s certainly easier to explain it that way, and that’s the tack I took in a .recent paper submission to ISMM’25 Wait what! I have a fine job in industry and a blog, why write a paper? Gosh I have meditated on this for a long time and the answers are very silly. Firstly, one of my language communities is Scheme, which was a research hotbed some 20-25 years ago, which means many practitioners—people I would be pleased to call peers—came up through the PhD factories and published many interesting results in academic venues. These are the folks I like to hang out with! This is also what academic conferences are, chances to shoot the shit with far-flung fellows. In Scheme this is fine, my work on Guile is enough to pay the intellectual cover charge, but I need more, and in the field of GC I am not a proven player. So I did an atypical thing, which is to cosplay at being an independent researcher without having first been a dependent researcher, and just solo-submit a paper. Kids: if you see yourself here, just go get a doctorate. It is not easy but I can only think it is a much more direct path to goal. And the result? Well, friends, it is this blog post :) I got the usual assortment of review feedback, from the very sympathetic to the less so, but ultimately people were confused by leading with a comparison to Immix but ending without an evaluation against Immix. This is fair and the paper does not mention that, you know, I don’t have an Immix lying around. To my eyes it was a good paper, an , but, you know, just a try. I’ll try again sometime.80% paper In the meantime, I am driving towards getting Whippet into Guile. I am hoping that sometime next week I will have excised all the uses of the BDW (Boehm GC) API in Guile, which will finally allow for testing Nofl in more than a laboratory environment. Onwards and upwards! whippet regions? paper??!?
Today, some more words on memory management, on the practicalities of a system with conservatively-traced references. The context is that I have finally started banging into , initially in a configuration that continues to use the conservative Boehm-Demers-Weiser (BDW) collector behind the scene. In that way I can incrementally migrate over all of the uses of the BDW API in Guile to use Whippet API instead, and then if all goes well, I should be able to switch Whippet to use another GC algorithm, probably the . MMC scales better than BDW for multithreaded mutators, and it can eliminate fragmentation via Immix-inspired optimistic evacuation.WhippetGuilemostly-marking collector (MMC) A garbage-collected heap consists of memory, which is a set of addressable locations. An object is a disjoint part of a heap, and is the unit of allocation. A field is memory within an object that may refer to another object by address. Objects are nodes in a directed graph in which each edge is a field containing an object reference. A root is an edge into the heap from outside. Garbage collection reclaims memory from objects that are not reachable from the graph that starts from a set of roots. Reclaimed memory is available for new allocations. In the course of its work, a collector may want to relocate an object, moving it to a different part of the heap. The collector can do so if it can update all edges that refer to the object to instead refer to its new location. Usually a collector arranges things so all edges have the same representation, for example an aligned word in memory; updating an edge means replacing the word’s value with the new address. Relocating objects can improve locality and reduce fragmentation, so it is a good technique to have available. (Sometimes we say evacuate, move, or compact instead of relocate; it’s all the same.) Some collectors allow edges: words in memory whose value may be the address of an object, or might just be scalar data. Ambiguous edges usually come about if a compiler doesn’t precisely record which stack locations or registers contain GC-managed objects. Such ambiguous edges must be traced : the collector adds the object to its idea of the set of live objects, as if the edge were a real reference. This tracing mode isn’t supported by all collectors.ambiguousconservatively Any object that might be the target of an ambiguous edge cannot be relocated by the collector; a collector that allows conservative edges cannot rely on relocation as part of its reclamation strategy. Still, if the collector can know that a given object will not be the referent of an ambiguous edge, relocating it is possible. How can one know that an object is not the target of an ambiguous edge? We have to partition the heap somehow into possibly-conservatively-referenced and definitely-not-conservatively-referenced. The two ways that I know to do this are spatially and temporally. Spatial partitioning means that regardless of the set of root and intra-heap edges, there are some objects that will never be conservatively referenced. This might be the case for a type of object that is “internal” to a language implementation; third-party users that may lack the discipline to precisely track roots might not be exposed to objects of a given kind. Still, link-time optimization tends to weather these boundaries, so I don’t see it as being too reliable over time. Temporal partitioning is more robust: if all ambiguous references come from roots, then if one traces roots before intra-heap edges, then any object not referenced after the roots-tracing phase is available for relocation. So let’s talk about Guile! Guile uses BDW currently, which considers edges to be ambiguous by default. However, given that objects carry type tags, Guile can, with relatively little effort, switch to precisely tracing most edges. “Most”, however, is not sufficient; to allow for relocation, we need to intra-heap ambiguous edges, to confine conservative tracing to the roots-tracing phase.eliminate Conservatively tracing references from C stacks or even from static data sections is not a problem: these are roots, so, fine. Guile currently traces Scheme stacks almost-precisely: its compiler emits stack maps for every call site, which uses liveness analysis to only mark those slots that are Scheme values that will be used in the continuation. However it’s possible that any given frame is marked conservatively. The most common case is when using the BDW collector and a thread is pre-empted by a signal; then its most recent stack frame is likely not at a safepoint and indeed is likely undefined in terms of Guile’s VM. It can also happen if there is a call site within a VM operation, for example to a builtin procedure, if it throws an exception and recurses, or causes GC itself. Also, when are enabled, we can run Scheme between any two Guile VM operations.per-instruction traps So, Guile could change to trace Scheme stacks fully precisely, but this is a lot of work; in the short term we will probably just trace Scheme stacks as roots instead of during the main trace. However, there is one more significant source of ambiguous roots, and that is reified continuation objects. Unlike active stacks, these have to be discovered during a trace and cannot be partitioned out to the root phase. For delimited continuations, these consist of a slice of the Scheme stack. Traversing a stack slice precisely is less problematic than for active stacks, because it isn’t in motion, and it is captured at a known point; but we will have to deal with stack frames that are pre-empted in unexpected locations due to exceptions within builtins. If a stack map is missing, probably the solution there is to reconstruct one using local flow analysis over the bytecode of the stack frame’s function; time-consuming, but it should be robust as we do it elsewhere. Undelimited continuations (those captured by ) contain a slice of the C stack also, for historical reasons, and there we can’t trace it precisely at all. Therefore either we disable relocation if there are any live undelimited continuation objects, or we eagerly pin any object referred to by a freshly captured stack slice.call/cc If you want to follow along with the Whippet-in-Guile work, see the branch in Git. I’ve bumped its version to 4.0 because, well, why the hell not; if it works, it will certainly be worth it. Until next time, happy hacking!wip-whippet problem statement: how to manage ambiguous edges kinds of ambiguous edges in guile fin
Earlier this weekGuileWhippet But now I do! Today’s note is about how we can support untagged allocations of a few different kinds in Whippet’s .mostly-marking collector Why bother supporting untagged allocations at all? Well, if I had my way, I wouldn’t; I would just slog through Guile and fix all uses to be tagged. There are only a finite number of use sites and I could get to them all in a month or so. The problem comes for uses of from outside itself, in C extensions and embedding programs. These users are loathe to adapt to any kind of change, and garbage-collection-related changes are the worst. So, somehow, we need to support these users if we are not to break the Guile community.scm_gc_malloclibguile The problem with , though, is that it is missing an expression of intent, notably as regards tagging. You can use it to allocate an object that has a tag and thus can be traced precisely, or you can use it to allocate, well, anything else. I think we will have to add an API for the tagged case and assume that anything that goes through is requesting an untagged, conservatively-scanned block of memory. Similarly for : you could be allocating a tagged object that happens to not contain pointers, or you could be allocating an untagged array of whatever. A new API is needed there too for pointerless untagged allocations.scm_gc_mallocscm_gc_mallocscm_gc_malloc_pointerless Recall that the mostly-marking collector can be built in a number of different ways: it can support conservative and/or precise roots, it can trace the heap precisely or conservatively, it can be generational or not, and the collector can use multiple threads during pauses or not. Consider a basic configuration with precise roots. You can make tagged pointerless allocations just fine: the trace function for that tag is just trivial. You would like to extend the collector with the ability to make pointerless allocations, for raw data. How to do this?untagged Consider first that when the collector goes to trace an object, it can’t use bits inside the object to discriminate between the tagged and untagged cases. Fortunately though . Of those 8 bits, 3 are used for the mark (five different states, allowing for future concurrent tracing), two for the , one to indicate whether the object is pinned or not, and one to indicate the end of the object, so that we can determine object bounds just by scanning the metadata byte array. That leaves 1 bit, and we can use it to indicate untagged pointerless allocations. Hooray!the main space of the mostly-marking collector has one metadata byte for each 16 bytes of payloadprecise field-logging write barrier However there is a wrinkle: when Whippet decides the it should evacuate an object, it tracks the evacuation state in the object itself; the embedder has to provide an implementation of a , allowing the collector to detect whether an object is forwarded or not, to claim an object for forwarding, to commit a forwarding pointer, and so on. We can’t do that for raw data, because all bit states belong to the object, not the collector or the embedder. So, we have to set the “pinned” bit on the object, indicating that these objects can’t move.little state machine We could in theory manage the forwarding state in the metadata byte, but we don’t have the bits to do that currently; maybe some day. For now, untagged pointerless allocations are pinned. You might also want to support untagged allocations that contain pointers to other GC-managed objects. In this case you would want these untagged allocations to be scanned conservatively. We can do this, but if we do, it will pin all objects. Thing is, conservative stack roots is a kind of a sweet spot in language run-time design. You get to avoid constraining your compiler, you avoid a class of bugs related to rooting, but you can still support compaction of the heap. How is this, you ask? Well, consider that you can move any object for which we can precisely enumerate the incoming references. This is trivially the case for precise roots and precise tracing. For conservative roots, we don’t know whether a given edge is really an object reference or not, so we have to conservatively avoid moving those objects. But once you are done tracing conservative edges, any live object that hasn’t yet been traced is fair game for evacuation, because none of its predecessors have yet been visited. But once you add conservatively-traced objects back into the mix, you don’t know when you are done tracing conservative edges; you could always discover another conservatively-traced object later in the trace, so you have to pin everything. The good news, though, is that we have gained an easier migration path. I can now shove Whippet into Guile and get it running even before I have removed untagged allocations. Once I have done so, I will be able to allow for compaction / evacuation; things only get better from here. Also as a side benefit, the mostly-marking collector’s heap-conservative configurations are now faster, because we have metadata attached to objects which allows tracing to skip known-pointerless objects. This regains an optimization that BDW has long had via its , used in Guile since time out of mind.GC_malloc_atomic With support for untagged allocations, I think I am finally ready to start getting Whippet into Guile itself. Happy hacking, and see you on the other side! inside and outside on intent on data on slop fin
Salutations, populations. Today’s note is more of a work-in-progress than usual; I have been finally starting to look at getting into , and there are some open questions.WhippetGuile I started by taking a look at how Guile uses the ‘s API, to make sure I had all my bases covered for an eventual switch to something that was not BDW. I think I have a good overview now, and have divided the parts of BDW-GC used by Guile into seven categories.Boehm-Demers-Weiser collector Firstly there are the ways in which Guile’s run-time and compiler depend on BDW-GC’s behavior, without actually using BDW-GC’s API. By this I mean principally that we assume that any reference to a GC-managed object from any thread’s stack will keep that object alive. The same goes for references originating in global variables, or static data segments more generally. Additionally, we rely on GC objects not to move: references to GC-managed objects in registers or stacks are valid across a GC boundary, even if those references are outside the GC-traced graph: all objects are pinned. Some of these “uses” are internal to Guile’s implementation itself, and thus amenable to being changed, albeit with some effort. However some escape into the wild via Guile’s API, or, as in this case, as implicit behaviors; these are hard to change or evolve, which is why I am putting my hopes on Whippet’s , which allows for conservative roots.mostly-marking collector Then there are the uses of BDW-GC’s API, not to accomplish a task, but to protect the mutator from the collector: , explicitly enabling or disabling GC, calls to that take BDW-GC’s use of POSIX signals into account, and so on. BDW-GC can stop any thread at any time, between any two instructions; for most users is anodyne, but if ever you use weak references, things start to get really gnarly.GC_call_with_alloc_locksigmask Of course a new collector would have its own constraints, but switching to cooperative instead of pre-emptive safepoints would be a welcome relief from this mess. On the other hand, we will require client code to explicitly mark their threads as inactive during calls in more cases, to ensure that all threads can promptly reach safepoints at all times. Swings and roundabouts? Did you know that the Boehm collector allows for precise tracing? It does! It’s slow and truly gnarly, but when you need precision, precise tracing nice to have. (This is the interface.) Guile uses it to mark Scheme stacks, allowing it to avoid treating unboxed locals as roots. When it loads compiled files, Guile also adds some sliced of the mapped files to the root set. These interfaces will need to change a bit in a switch to Whippet but are ultimately internal, so that’s fine.GC_new_kind What is not fine is that Guile allows C users to hook into precise tracing, notably via . This is not only the wrong interface, not allowing for copying collection, but these functions are just truly gnarly. I don’t know know what to do with them yet; are our external users ready to forgo this interface entirely? We have been working on them over time, but I am not sure.scm_smob_set_mark Weak references, weak maps of various kinds: the implementation of these in terms of BDW’s API is incredibly gnarly and ultimately unsatisfying. We will be able to replace all of these with ephemerons and tables of ephemerons, which are natively supported by Whippet. The same goes with finalizers. The same goes for constructs built on top of finalizers, such as ; we’ll get to reimplement these on top of nice Whippet-supplied primitives. Whippet allows for resuscitation of finalized objects, so all is good here.guardians There is a long list of miscellanea: the interfaces to explicitly trigger GC, to get statistics, to control the number of marker threads, to initialize the GC; these will change, but all uses are internal, making it not a terribly big deal. I should mention one API concern, which is that BDW’s state is all implicit. For example, when you go to allocate, you don’t pass the API a handle which you have obtained for your thread, and which might hold some thread-local freelists; BDW will instead load thread-local variables in its API. That’s not as efficient as it could be and Whippet goes the explicit route, so there is some additional plumbing to do. Finally I should mention the true miscellaneous BDW-GC function: . Guile exposes it via an API, . It was already vestigial and we should just remove it, as it has no sensible semantics or implementation.GC_freescm_gc_free That brings me to what I wanted to write about today, but am going to have to finish tomorrow: the actual allocation routines. BDW-GC provides two, essentially: and . The difference is that “atomic” allocations don’t refer to other GC-managed objects, and as such are well-suited to raw data. Otherwise you can think of atomic allocations as a pure optimization, given that BDW-GC mostly traces conservatively anyway.GC_mallocGC_malloc_atomic From the perspective of a user of BDW-GC looking to switch away, there are two broad categories of allocations, tagged and untagged. Tagged objects have attached metadata bits allowing their type to be inspected by the user later on. This is the happy path! We’ll be able to write a function that takes any object, does a switch on, say, some bits in the first word, dispatching to type-specific tracing code. As long as the object is sufficiently initialized by the time the next safepoint comes around, we’re good, and given cooperative safepoints, the compiler should be able to ensure this invariant.gc_trace_object Then there are untagged allocations. Generally speaking, these are of two kinds: temporary and auxiliary. An example of a temporary allocation would be growable storage used by a C run-time routine, perhaps as an unbounded-sized alternative to . Guile uses these a fair amount, as they compose well with non-local control flow as occurring for example in exception handling.alloca An auxiliary allocation on the other hand might be a data structure only referred to by the internals of a tagged object, but which itself never escapes to Scheme, so you never need to inquire about its type; it’s convenient to have the lifetimes of these values managed by the GC, and when desired to have the GC automatically trace their contents. Some of these should just be folded into the allocations of the tagged objects themselves, to avoid pointer-chasing. Others are harder to change, notably for mutable objects. And the trouble is that for external users of , I fear that we won’t be able to migrate them over, as we don’t know whether they are making tagged mallocs or not.scm_gc_malloc One conventional way to handle untagged allocations is to manage to fit your data into other tagged data structures; V8 does this in many places with instances of FixedArray, for example, and Guile should do more of this. Otherwise, you make new tagged data types. In either case, all auxiliary data should be tagged. I think there may be an alternative, which would be just to support the equivalent of untagged and ; but for that, I am out of time today, so type at y’all tomorrow. Happy hacking!GC_mallocGC_malloc_atomic inventory what is to be done? implicit uses defensive uses precise tracing reachability misc allocation
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In my first interview out of college I was asked the change counter problem: Given a set of coin denominations, find the minimum number of coins required to make change for a given number. IE for USA coinage and 37 cents, the minimum number is four (quarter, dime, 2 pennies). I implemented the simple greedy algorithm and immediately fell into the trap of the question: the greedy algorithm only works for "well-behaved" denominations. If the coin values were [10, 9, 1], then making 37 cents would take 10 coins in the greedy algorithm but only 4 coins optimally (10+9+9+9). The "smart" answer is to use a dynamic programming algorithm, which I didn't know how to do. So I failed the interview. But you only need dynamic programming if you're writing your own algorithm. It's really easy if you throw it into a constraint solver like MiniZinc and call it a day. int: total; array[int] of int: values = [10, 9, 1]; array[index_set(values)] of var 0..: coins; constraint sum (c in index_set(coins)) (coins[c] * values[c]) == total; solve minimize sum(coins); You can try this online here. It'll give you a prompt to put in total and then give you successively-better solutions: coins = [0, 0, 37]; ---------- coins = [0, 1, 28]; ---------- coins = [0, 2, 19]; ---------- coins = [0, 3, 10]; ---------- coins = [0, 4, 1]; ---------- coins = [1, 3, 0]; ---------- Lots of similar interview questions are this kind of mathematical optimization problem, where we have to find the maximum or minimum of a function corresponding to constraints. They're hard in programming languages because programming languages are too low-level. They are also exactly the problems that constraint solvers were designed to solve. Hard leetcode problems are easy constraint problems.1 Here I'm using MiniZinc, but you could just as easily use Z3 or OR-Tools or whatever your favorite generalized solver is. More examples This was a question in a different interview (which I thankfully passed): Given a list of stock prices through the day, find maximum profit you can get by buying one stock and selling one stock later. It's easy to do in O(n^2) time, or if you are clever, you can do it in O(n). Or you could be not clever at all and just write it as a constraint problem: array[int] of int: prices = [3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 8]; var int: buy; var int: sell; var int: profit = prices[sell] - prices[buy]; constraint sell > buy; constraint profit > 0; solve maximize profit; Reminder, link to trying it online here. While working at that job, one interview question we tested out was: Given a list, determine if three numbers in that list can be added or subtracted to give 0? This is a satisfaction problem, not a constraint problem: we don't need the "best answer", any answer will do. We eventually decided against it for being too tricky for the engineers we were targeting. But it's not tricky in a solver; include "globals.mzn"; array[int] of int: numbers = [3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 8]; array[index_set(numbers)] of var {0, -1, 1}: choices; constraint sum(n in index_set(numbers)) (numbers[n] * choices[n]) = 0; constraint count(choices, -1) + count(choices, 1) = 3; solve satisfy; Okay, one last one, a problem I saw last year at Chipy AlgoSIG. Basically they pick some leetcode problems and we all do them. I failed to solve this one: Given an array of integers heights representing the histogram's bar height where the width of each bar is 1, return the area of the largest rectangle in the histogram. The "proper" solution is a tricky thing involving tracking lots of bookkeeping states, which you can completely bypass by expressing it as constraints: array[int] of int: numbers = [2,1,5,6,2,3]; var 1..length(numbers): x; var 1..length(numbers): dx; var 1..: y; constraint x + dx <= length(numbers); constraint forall (i in x..(x+dx)) (y <= numbers[i]); var int: area = (dx+1)*y; solve maximize area; output ["(\(x)->\(x+dx))*\(y) = \(area)"] There's even a way to automatically visualize the solution (using vis_geost_2d), but I didn't feel like figuring it out in time for the newsletter. Is this better? Now if I actually brought these questions to an interview the interviewee could ruin my day by asking "what's the runtime complexity?" Constraint solvers runtimes are unpredictable and almost always than an ideal bespoke algorithm because they are more expressive, in what I refer to as the capability/tractability tradeoff. But even so, they'll do way better than a bad bespoke algorithm, and I'm not experienced enough in handwriting algorithms to consistently beat a solver. The real advantage of solvers, though, is how well they handle new constraints. Take the stock picking problem above. I can write an O(n²) algorithm in a few minutes and the O(n) algorithm if you give me some time to think. Now change the problem to Maximize the profit by buying and selling up to max_sales stocks, but you can only buy or sell one stock at a given time and you can only hold up to max_hold stocks at a time? That's a way harder problem to write even an inefficient algorithm for! While the constraint problem is only a tiny bit more complicated: include "globals.mzn"; int: max_sales = 3; int: max_hold = 2; array[int] of int: prices = [3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 8]; array [1..max_sales] of var int: buy; array [1..max_sales] of var int: sell; array [index_set(prices)] of var 0..max_hold: stocks_held; var int: profit = sum(s in 1..max_sales) (prices[sell[s]] - prices[buy[s]]); constraint forall (s in 1..max_sales) (sell[s] > buy[s]); constraint profit > 0; constraint forall(i in index_set(prices)) (stocks_held[i] = (count(s in 1..max_sales) (buy[s] <= i) - count(s in 1..max_sales) (sell[s] <= i))); constraint alldifferent(buy ++ sell); solve maximize profit; output ["buy at \(buy)\n", "sell at \(sell)\n", "for \(profit)"]; Most constraint solving examples online are puzzles, like Sudoku or "SEND + MORE = MONEY". Solving leetcode problems would be a more interesting demonstration. And you get more interesting opportunities to teach optimizations, like symmetry breaking. Because my dad will email me if I don't explain this: "leetcode" is slang for "tricky algorithmic interview questions that have little-to-no relevance in the actual job you're interviewing for." It's from leetcode.com. ↩
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