Here is my code snippet:  inline uint8_t &amp;AT(uint16_t addr) { // non-const version     return (addr &lt; 0x2000 ? Ram[addr &amp; 0x7ff]:        \     addr &lt; 0x4000 ? PPURegister[(addr - 0x2000) &amp; 0x7]: \     addr &lt; 0x4020 ? APUIORegister[(addr - 0x4000)]:     \     addr &lt; 0x6000 ? ExpansionRom[addr - 0x4020]:        \     addr &lt; 0x8000 ? SRam[addr - 0x6000]:                \     addr &lt; 0xc000 ? LowerPRGRom[addr - 0x8000]:         \     UpperPRGRom[addr - 0xc000]); }  inline const uint8_t &amp;AT(uint16_t addr) const { // const version     return AT(addr); // Function `AT` will recurses infinitely! But I don't want to copy the body of non-const function here. }   There are functions uses it:  uint8_t &amp;operator[](uint16_t addr) { return AT(addr); } const uint8_t &amp;operator[](uint16_t addr) const { return AT(addr); }   so, how to implement the function which returns const simply and clearly?
Let's say I have the following class X where I want to return access to an internal member:  class Z {     // details };  class X {     std::vector&lt;Z&gt; vecZ;  public:     Z&amp; Z(size_t index)     {         // massive amounts of code for validating index          Z&amp; ret = vecZ[index];          // even more code for determining that the Z instance         // at index is *exactly* the right sort of Z (a process         // which involves calculating leap years in which         // religious holidays fall on Tuesdays for         // the next thousand years or so)          return ret;     }     const Z&amp; Z(size_t index) const     {         // identical to non-const X::Z(), except printed in         // a lighter shade of gray since         // we're running low on toner by this point     } };   The two member functions X::Z() and X::Z() const have identical code inside the braces.  This is duplicate code and can cause maintenance problems for long functions with complex logic.    Is there a way to avoid this code duplication?
How to prove that a number is irrational I have a dataframe with many observations and many variables. Some of them are categorical (unordered) and the others are numerical.  I'm looking for associations between these variables. I've been able to compute correlation for numerical variables (Spearman's correlation) but :   I don't know how to measure correlation between unordered categorical variables. I don't know how to measure correlation between unordered categorical variables and numerical variables.   Does anyone know how this could be done? If so, are there R functions implementing these methods? How to replace the domain name in a Wordpress database? I have a Wordpress database which was installed in a development environment... thus, all references to the site itself have a fixed IP address (say 192.168.16.2). Now, I have to migrate that database to a new Wordpress installation on a hosting. The problem is that the SQL dump contains a lot of references to the IP address, and I have to replace it with: my_domain.com.  I could use sed or some other command to change the that from the command line, the problem is that there are a lot of configuration data which uses JSON. So what? Well, as you know, JSON arrays uses things like: s:4: to know how many chars an element has, and thus, if I just replace the IP with the domain name, the configuration files will get corrupted.  I used an app for Windows some years ago that allows to change values in a database and takes care of the JSON arrays. Unfortunately, I forgot the name of the app... so the question is: do you know any app that allows me to do what I want? Can I export Shotwell pictures database saving all the tags? I've imported lots of pictures into Shotwell and spent some time setting tags. Are those tags locked-in in Shotwell or I can export them (and import again or use with other software)? I have a project that needs a different voltage (or multiple voltages) than what I have available. Sometimes I need DC instead of AC, or I need a lower or higher voltage. How do I convert from one to another? Should I use resistors or a regulator or something else?  I've heard of converters, transformers, regulators, inverters, step-down, step-up, buck, boost, switching, linear, and other terms. Or acronyms (initialisms) like PMIC and LDO. Can someone shed some light on all this? Casting nines and elevens in other bases (radix) and doing check sums for binary Question  Let $X_n\geq 0$ be independent for $n\geq 1$. The following are equivalent.  $\sum_{n=1}^\infty X_n&lt;\infty$ a.s. $\sum_{n=1}^\infty[P(X_n&gt;1)+E(X_nI(X_n\leq 1)]&lt;\infty$ $\sum_{n=1}^\infty E(X_n/(1+X_n))&lt;\infty$   My attempt I was able to prove $(1)$ implies $(2)$ and $(2)$ implies $(3)$ but not $(3)$ implies $(1)$. For $(1)$ implies $(2)$, observe that by Borel-Cantelli $\sum_{n=1}^\infty P(X_n&gt;1)&lt;\infty$, else $X_n&gt;1$ infinitely often w.p.1 so that $(1)$ is violated. To see that $\sum_{n=1}^\infty E(X_nI(X_n\leq 1)]&lt;\infty$, apply Kolmogorov three-series theorem (I think). For $(2)$ implies $(3)$ we can write that $$ \begin{align} \frac{X_n}{1+X_n}&amp; =\frac{X_n}{1+X_n}I(X_n\leq 1)+\frac{X_n}{1+X_n}I(X_n&gt;1)\\ &amp;\leq X_nI(X_n\leq 1)+ I(X_n&gt;1). \end{align} $$ Now take the expectation of both sides and sum on $n$ using $(2)$ to conclude $(3)$. For the last implication $(3)$ implies $(1)$, I tried to use Kolmogorov three series theorem. To this end put $Y_n=X_nI(X_n\leq 1)$. First note that $\sum_{n=1}^\infty P(X_n&gt;1)&lt;\infty$ since $$ P(X_n&gt;1)\leq P\left(\frac{X_n}{1+X_n}&gt;\frac{1}{2}\right)\leq 2E\frac{X_n}{1+X_n} $$ by Markov's inequality. But I am unable to show that $\sum EY_n&lt;\infty$ and $\sum\text{Var}(Y_n)&lt;\infty$. Any help is appreciated. How do I sort a list of dictionaries by a value of the dictionary? What is the JVM thread scheduling algorithm? What's the main difference between int.Parse() and Convert.ToInt32 What is the main difference between int.Parse() and Convert.ToInt32()? Which one is to be preferred What to do when someone other than the author changes a question to fix a substantive problem with the code See . Someone other than the OP changed the code to address a substantial problem with the it that was addressed as part of my answer. The problem was admittedly peripheral to the core question, but it was a primary differentiator between my answer and another answer submitted at the same time.  Any suggestions on what to do in this situation? Leave it be? Edit it back? Something else?  Update: I just found , from the "Related Links" section on the right, which is pretty relevant. I have to keep remembering to check there rather than just searching for answers. Can a multiclass sorcerer make spell slots for their other class using sorcery points?  For example: can a multiclassed sorcerer 3 / warlock 1 use Flexible Casting to create a warlock spell slot? How can I render an object with an hdr background? I have an object with an hdr for the background. What do I do in Cycles to render the background with my object?  How is this different from an ordinary render in Cycles?  The hdr is a big one, 350MB. $n,a,b \mathbb \in \mathbb Z^+$ , such that $n\mid a^n-b^n$ ; to show $n\mid \frac {a^n-b^n}{a-b}$ Dubai (UAE) visa requirements when staying in the airport for a French citizen? Doom-style 2.5D Movement Animations I've started working on a demo for my 2.5D game. For a basic scene I figured I would just use the good old fashioned doom sprites textured to a double sided plane. Simple enough. But I've been scratching my head as to how to display the proper sprite animation relative to the player viewing the sprite...if that makes since.  For example suppose I have three players in the scene Players A, B, and C as such:    Player C should see player A as: Here's an example of what I think player A should look like from C's perspective:    While player B would see player A as follows:    My current idea is that for any given player, I will need to know the current direction of each other player, and where they are located/moving to relativly. From this, I could calculate which sprite image is required.  Is this correct? What improvements/optimizations could be made?  ** EDIT ** Total number of directions will be 8 as depicted below:    For each direction there are two sprites (to show walking movement, sprites for the right hand directions are mirrors of the left):    ** EDIT 2 ** Got this working and have a simple javascript/threejs example for anyone interested: How to run xrandr commands at startup in Ubuntu How can I run the following xrandrcommand on startup?  xrandr   cvt 1368 768  xrandr --newmode "1368x768_60.00"   85.25  1368 1440 1576 1784  768 771 781 798 -hsync +vsync xrandr --addmode VGA1 1368x768_60.00 xrandr --output VGA1 --mode 1368x768_60.00 Personal Hotspot not working over Wi-Fi on iOS 13 After upgrade to iOS 13 from 12.4, I noticed that personal hotspot isn't working anymore over Wi-Fi (via USB is ok).  Tested on two computers with Win7. The PC can connect to Wi-Fi, but no valid IP (IPv4) is assigned and no connection is working to internet. Convergence of the sequence $\sqrt{1+2\sqrt{1}},\sqrt{1+2\sqrt{1+3\sqrt{1}}},\sqrt{1+2\sqrt{1+3\sqrt{1+4\sqrt{1}}}},\cdots$ I recently came across this problem     Q1 Show that $\lim\limits_{n \rightarrow \infty} \underbrace{{\sqrt{1+2\sqrt{1+3\sqrt{1+4\sqrt{1+\cdots+n\sqrt{1}}}}}}}_{n \textrm{ times  }} = 3$   After trying it I looked at the solution from that book which was very ingenious but it was incomplete because it assumed that the limit already exists.  So my question is     Q2 Prove that the sequence$$\sqrt{1+2\sqrt{1}},\sqrt{1+2\sqrt{1+3\sqrt{1}}},\sqrt{1+2\sqrt{1+3\sqrt{1+4\sqrt{1}}}},\cdots,\sqrt{1+2\sqrt{1+3\sqrt{1+4\sqrt{1+\cdots+n\sqrt{1}}}}}$$ converges.   Though I only need solution for Q2, if you happen to know any complete solution for Q1 it would be a great help .  If the solution from that book is required I can post it but it is not complete as I mentioned.   Edit: I see that a similar question was asked before on this site but it was not proved that limit should exist. Execution order of event receivers and workflow on a list