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c++ – While allocating appropriate amount of space for big integers why does the needed space increase with the integer’s value?

I am trying to learn about integer overflows in C and C++ from a website. In its tutorial, it uses these lines of code:

info_size = (*n * sizeof(int)); //value of the number multiplied by sizeof(int), assumed to be 4 bytes
buffer = malloc(info_size)

where *n is the integer we are trying to store. It gives an example by storing 24 which leads to it allocating 96 bytes. Even if I were to store 2147483647 shouldn’t it be just 32 bits of 1, therefore only 4 bytes?

Is Cache allocated separate space?

There is a “Temporary Internet Files” folder on my PC, which I believe stores browser cache. Currently, it has 310 MB worth of data. Is this data space fixed? I mean, is this space pre-allocated for browser cache specifically?

If yes, then suppose that I just bought my PC, and started browsing on the internet for days to weeks to months until 310 MB worth of cache is created. What happens after that? If I browse further, will the old cache get deleted to free up space for the new cache arising from my continued browsing? I think the answer is yes and let me explain why I believe so. This website has so many sentences that make me strongly believe that this “browser cache” thing is allocated a separate storage space:

“Unfortunately, cached Data isn’t stored forever. It gets overwritten and deleted regularly. This is a problem if you depend on your cache to streamline your browsing experience.”

“There are a few reasons that data gets lost: The most common reason is that it is simply overwritten. Every time that you see new media, it gets written to your cache filed. (sic)”

“This means that the storage capacity (for browser cache) is much more limited. You can usually only store about 300 to 400 MB of data at a time.”

All these sentences seem to indicate that Cache is something that is separately stored in a folder and that has to be continuously deleted (of course automatically) to free up space and has to be overwritten over the allocated space (they mention 300-400 MB).

Is this understanding right?

upgrade – Drop tables but space not claimed in postgres 12

I have upgraded Postgresql 9.5 to Postgresql 12.4 a few days back using pg_upgrade utility with link (-k) option.

So basically I am having two data directories i.e. One is old data directory (v9.5) and the current one in running state (v12.4).

Yesterday I have dropped two tables of size 700MB and 300MB.

After connecting to postgres using psql utility I can see database size whose tables was dropped got decreased (with l+ ) but what is making me worry is that only a few MBs have been freed from storage partition.

I have checked if any deleted open file is there on OS level using lsof but there is none. I have run vacuumdb only on that database but no luck

Looking for the solution.

complexity theory – Configuration of a space bounded turing machine

A configuration of a turing machine is defined as the following:

an ordered triple (x, q, k) ∈ Σ∗ × K × N, where x denotes the string
on the tape, q denotes the machine’s current state, and k denotes the
position of the machine on the tape

I have read in a paper that a space bounded non-deterministic turing machine (NSPACE), has at most 2^(d*n) configurations on an input of length n, where d is a constant, how do we know that this is true? what is d? and how can we prove it?

periodic functions – The space $M$ is densely embedding in $N$?

Let $L>0$ fixed. Consider the space
$$mathcal{P}:=C_{per}^{infty}((0,L))={f: mathbb{R} longrightarrow mathbb{C}; ; ; f : text{is infinitely differentiable and periodic with period}: L}.$$

Consider the Sobolev Space $H^1_{per}((0,L))$. This space can be interpreted as the set of $f in mathcal{P}’$ such that
$$f, f’ in L^2_{per}((0,L)),$$
where
$$L^2_{per}((0,L))={f: mathbb{R} longrightarrow mathbb{C} ; ; ; f : text{is periodic with period} ; L ; text{and} ; f|_{(0,L)} in L^2((0,L))}. $$

Define
$$M := left{ u in H^1_{per}((0,L)) ; ; ; int_{0}^{L} u(x) ; dx =0 right} quad text{and} quad N := left{ u in L^2_{per}((0,L)) ; ; ; int_{0}^{L} u(x) ; dx =0 right}.$$

I know that $H^1_{per}((0,L))$ is densely embedding $L^2_{per}((0,L)).$ And know also $M$ is a closed subspace of $H^1_{per}((0,L))$ and $N$ is a closed subspace of $L^2_{per}((0,L))$

Question. The space $M$ is densely embedding in $N$?

ripple – Disk Space of Rippled testnet server

I am planning to create rippled testnet server.
According to below site, I need 360 GB Disk Space for 750,000 Ledger versions.
I believe the estimate is for mainnet, but is it same for testnet?
https://xrpl.org/capacity-planning.html

When I run rippled locally on testnet, it seems like ledger size of testnet is less than that of mainnet.
However, I couldn’t find any specification regarding disk space or ledger size of testnet.

optics – Aperture iris in front of lenses (in object space)

In general putting the aperture at the front or outside is avoided because not good; best is to put the aperture more or less in the center of the objective. With the aperture in front you’ll have more aberrations and/or need bigger and more expensive design.
Only in two cases the front aperture design is used:

  1. if the lens is very small and simple, like, really just one group (see the Kodak vest camera and the Triplet), here you cannot put the aperture in the middle! Choose, in the front or in the back.
  2. Otherwise, you put the aperture in front only if you are absolutely forced to do that, typically for coupling with other optical systems.

Small & simple:
Mobile phone lenses; to make them so compact, the aperture is usually placed at the brim of the front lens. Not really outside, but on the brim.

Forced:
Pinholes and many probe objectives, that need to peep from an hole; the hole is the natural aperture and the lens must be built to use all the light that goes through such hole; putting another aperture will cause vignetting. Nice example the SO spy lenses by Zeiss Jena:
Marco Cavina or see the catalog of Marshall Electronics.

Non-photographic lenses:

  • Laser scanning lenses, called F-theta Rogonar; the laser light is coming form the aperture position.
  • All eyepieces: the aperture is well outside, at the “exit pupil”, so I can place my eye with my iris in this place.

If you are curious about aberrations etc, the best short introduction I’ve found are those slides from Jena:
Gross Jena 2017; lecture 11/3, stop position.

design – How to reliably implement disk space quotas in an application?

Suppose we have a service which allows users to store files on a disk. The service should keep track of disk space used by a user and enforce a limit on the available space. Google Drive or Dropbox are obvious examples of such services.

But furthermore suppose that size is tracked recursively for all of the user’s directories. Effectively, such a service caches / pre-computes the result of du for all directories.

What are some good designs to keep track of disk usage per directory? I am especially interested in trade-offs involving atomicity and consistency.

Some ideas:

  1. Keep the directory size in a dedicated, hidden file in that directory (e.g. .__size__). When adding / subtracting bytes from a directory, modify sizes of all parent directories as well. The downside of this would be a lack of atomicity if the application fails halfway through modifying parent directory sizes.
  2. As a fix to aforementioned lack of atomicity and therefore possible inconsistencies, run a worker which traverses the directory tree, checking and fixing sizes. This would ensure eventual consistency.
  3. Emit domain events when bytes are written / deleted, e.g. to a message broker, and process those events asynchronously to update sizes. This would ensure eventual consistency, but how would we ensure atomicity or idempotence on retries when processing such events?
  4. Keep directory sizes in a relational database and update within a transaction.

Any thoughts?
3.