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  • Arbitrary-precision arithmetic Explanation

    - by TT
    I'm trying to learn C and have come across the inability to work with REALLY big numbers (i.e., 100 digits, 1000 digits, etc.). I am aware that there exist libraries to do this, but I want to attempt to implement it myself. I just want to know if anyone has or can provide a very detailed, dumbed down explanation of arbitrary-precision arithmetic. Thanks!

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  • Implementing a hilbert map of the internet

    - by Martin
    In the XKCD comic 195 a design for a map of the internet address space is suggested using a hilbert curve so that items from a similar IPs will be clustered together. Given an IP address, how would I calculate the 2D coordinates (in the range zero to one) that this IP is located on such a map?

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  • PHP given a series of arbitrary numbers, how can I choose a logical max value on a line graph?

    - by stormist
    I am constructing a line graph in PHP. I was setting the max value of the line graph to the max value of my collection of items, but this ended up making the graph less readable you are unable to view the highest line on the graph as it intersects with the top of it. So what I need is basically a formula to take a set of numbers and calculate what the logical max value of on the line graph should be.. so some examples 3500 250 10049 45394 434 312 Max value on line graph should probably be 50000 493 412 194 783 457 344 max value on line graph would ideally be 1000 545 649 6854 5485 11545 In this case, 12000 makes sense as max value So something as simple as rounding upward to the nearest thousandth might work but I'd need it to progressively increase as the numbers got bigger. (50000 instead of 46,000 in first example) The maximum these numbers will ever be is about a million. Any recommendations would be greatly appreciated, thank you.

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  • Efficiency of manually written loops vs operator overloads (C++)

    - by Sagekilla
    Hi all, in the program I'm working on I have 3-element arrays, which I use as mathematical vectors for all intents and purposes. Through the course of writing my code, I was tempted to just roll my own Vector class with simple +, -, *, /, etc overloads so I can simplify statements like: for (int i = 0; i < 3; i++) r[i] = r1[i] - r2[i]; // becomes: r = r1 - r2; Which should be more or less identical in generated code. But when it comes to more complicated things, could this really impact my performance heavily? One example that I have in my code is this: Manually written version: for (int j = 0; j < 3; j++) { p.vel[j] = p.oldVel[j] + (p.oldAcc[j] + p.acc[j]) * dt2 + (p.oldJerk[j] - p.jerk[j]) * dt12; p.pos[j] = p.oldPos[j] + (p.oldVel[j] + p.vel[j]) * dt2 + (p.oldAcc[j] - p.acc[j]) * dt12; } Using a Vector class with operator overloads: p.vel = p.oldVel + (p.oldAcc + p.acc) * dt2 + (p.oldJerk - p.jerk) * dt12; p.pos = p.oldPos + (p.oldVel + p.vel) * dt2 + (p.oldAcc - p.acc) * dt12; I am compiling my code for maximum possible speed, as it's extremely important that this code runs quickly and calculates accurately. So will me relying on my Vector's for these sorts of things really affect me? For those curious, this is part of some numerical integration code which is not trivial to run in my program. Any insight would be appreciated, as would any idioms or tricks I'm unaware of.

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  • Built in raytracing?

    - by acidzombie24
    Relating to this question i was wondering if .NET has any libs (or a function) i can use to detect if one point collides with another. I am not sure what angles i should use but is there some function like this func(point src, rect target, angle, distanceOfVision, listPointOrRectOfWalls) Pretty unlikely but i dont know a formula or how to start. Its a quick and dirty prototype. I am thinking of writing the func about but dropping angle and just make line of sight a rectangle and check if any points is between src and target.

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  • Can someone explain how this works?

    - by Dan Howard
    Key in the first three digits of your phone number (NOT the Area code...) Multiply by 80 Add 1 Multiply by 250 Add to this the last 4 digits of your phone number Add to this the last 4 digits of your phone number again. Subtract 250 Divide number by 2 Do you recognize the answer??

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  • Distance between hyperplanes

    - by michael dillard
    I'm trying to teach myself some machine learning, and have been using the MNIST database (http://yann.lecun.com/exdb/mnist/) do so. The author of that site wrote a paper in '98 on all different kinds of handwriting recognition techniques, available at http://yann.lecun.com/exdb/publis/pdf/lecun-98.pdf. The 10th method mentioned is a "Tangent Distance Classifier". The idea being that if you place each image in a (NxM)-dimensional vector space, you can compute the distance between two images as the distance between the hyperplanes formed by each where the hyperplane is given by taking the point, and rotating the image, rescaling the image, translating the image, etc. I can't figure out enough to fill in the missing details. I understand that most of these are indeed linear operators, so how does one use that fact to then create the hyperplane? And once we have a hyperplane, how do we take its distance with other hyperplanes?

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  • Least common multiple for 3 or more numbers

    - by paan
    How do you calculate the least common multiple of multiple numbers? So far I've only been able to calculate it between two numbers. But have no idea how to expand it to calculate 3 or more numbers. So far this is how I did it LCM = num1 * num2 / gcd ( num1 , num2 ) With gcd is the function to calculate the greatest common divisor for the numbers. Using euclidean algorithm But I can't figure out how to calculate it for 3 or more numbers.

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  • Interesting task using random numbers only

    - by psihodelia
    Given any number of the random real numbers from the interval [0,1] is there exist any method to construct a floating point number with zero decimal part? Your algorithm can use only random() function calls and no variables or constants. No constants and variables are allowed, no type casting is allowed. You can use for/while, if/else or any other programming language operands.

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  • How to get colliding effect or bouncy when ball hits the track.

    - by Chandan Shetty SP
    I am using below formula to move the ball circular, where accelX and accelY are the values from accelerometer, it is working fine. But the problem in this code is mRadius (I fixed its value to 50), i need to change mRadius according to accelerometer values and also i need bouncing effect when it touches the track. Currently i am developing code by assuming only one ball is on the board. float degrees = -atan2(accelX, accelY) * 180 / 3.14159; int x = cCentrePoint.x + mRadius * cos(degreesToRadians(degrees)); int y = cCentrePoint.y + mRadius * sin(degreesToRadians(degrees)); Here is the snap of the game i want to develop: Updated: I am sending the updated code... mRadius = 5; mRange = NSMakeRange(0,60); -(void) updateBall: (UIAccelerationValue) accelX withY:(UIAccelerationValue)accelY { float degrees = -atan2(accelX, accelY) * 180 / 3.14159; int x = cCentrePoint.x + mRadius * cos(degreesToRadians(degrees)); int y = cCentrePoint.y + mRadius * sin(degreesToRadians(degrees)); //self.targetRect is rect of ball Object self.targetRect = CGRectMake(newX, newY, 8, 9); self.currentRect = self.targetRect; //http://books.google.co.in/books?id=WV9glgdrrrUC&pg=PA455#v=onepage&q=&f=false static NSDate *lastDrawTime; if(lastDrawTime!=nil) { NSTimeInterval secondsSinceLastDraw = -([lastDrawTime timeIntervalSinceNow]); ballXVelocity = ballXVelocity + (accelX * secondsSinceLastDraw) * [self isTouchedTrack:mRadius andRange:mRange]; ballYVelocity = ballYVelocity + -(accelY * secondsSinceLastDraw) * [self isTouchedTrack:mRadius andRange:mRange]; distXTravelled = distXTravelled + secondsSinceLastDraw * ballXVelocity * 50; distYTravelled = distYTravelled + secondsSinceLastDraw * ballYVelocity * 50; CGRect temp = self.targetRect; temp.origin.x += distXTravelled; temp.origin.y += distYTravelled; int radius = (temp.origin.x - cCentrePoint.x) / cos(degreesToRadians(degrees)); if( !NSLocationInRange(abs(radius),mRange)) { //Colided with the tracks...Need a better logic here ballXVelocity = -ballXVelocity; } else { // Need a better logic here self.targetRect = temp; } //NSLog(@"angle = %f",degrees); } [lastDrawTime release]; lastDrawTime = [ [NSDate alloc] init]; } In the above code i have initialized mRadius and mRange(indicate track) to some constant for testing, i am not getting the moving of the ball as i expected( bouncing effect when Collided with track ) with respect to accelerometer. Help me to recognize where i went wrong or send some code snippets or links which does the similar job. I am searching for better logic than my code, if you found share with me.

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  • How to create pulsating value from 0..1..0..1..0 etc for a given duration?

    - by pollux
    Hi I'm working on some code where I have a Time object with a member time. Time.time gives me the time since my application started in seconds (float value). Now I want to create a pulsating value between 0 and 1 and then from 1 to 0 again, which continues doing thins untill the application stops. I was thinking to use sin() but don't know what to pass to it as paramters to create this pulsing value. How would I create this pulsating value? Kind regards, Pollux

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  • Counting point size based on chart area during zooming/unzoomin

    - by Gacek
    Hi folks. I heave a quite simple task. I know (I suppose) it should be easy, but from the reasons I cannot understand, I try to solve it since 2 days and I don't know where I'm making the mistake. So, the problem is as follows: - we have a chart with some points - The chart starts with some known area and points have known size - we would like to "emulate" the zooming effect. So when we zoom to some part of the chart, the size of points is getting proportionally bigger. In other words, the smaller part of the chart we select, the bigger the point should get. So, we have something like that. We know this two parameters: initialArea; // Initial area - area of the whole chart, counted as width*height initialSize; // initial size of the points Now lets assume we are handling some kind of OnZoom event. We selected some part of the chart and would like to count the current size of the points float CountSizeOnZoom() { float currentArea = CountArea(...); // the area is counted for us. float currentSize = initialSize * initialArea / currentArea; return currentSize; } And it works. But the rate of change is too fast. In other words, the points are getting really big too soon. So I would like the currentSize to be invertly proportional to currentArea, but with some scaling coefficient. So I created the second function: float CountSizeOnZoom() { float currentArea = CountArea(...); % the area is counted for us. // Lets assume we want the size of points to change ten times slower, than area of the chart changed. float currentSize = initialSize + 0.1f* initialSize * ((initialArea / currentArea) -1); return currentSize; } Lets do some calculations in mind. if currentArea is smaller than initialArea, initialArea/currentArea > 1 and then we add "something" small and postive to initialSize. Checked, it works. Lets check what happens if we would un-zoom. currentArea will be equal to initialArea, so we would have 0 at the right side (1-1), so new size should be equal to initialSize. Right? Yeah. So lets check it... and it doesn't work. My question is: where is the mistake? Or maybe you have any ideas how to count this scaled size depending on current area in some other way?

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  • Code Golf: Countdown Number Game

    - by Noldorin
    Challenge Here is the task, inspired by the well-known British TV game show Countdown. The challenge should be pretty clear even without any knowledge of the game, but feel free to ask for clarifications. And if you fancy seeing a clip of this game in action, check out this YouTube clip. It features the wonderful late Richard Whitely in 1997. You are given 6 numbers, chosen at random from the set {1, 2, 3, 4, 5, 6, 8, 9, 10, 25, 50, 75, 100}, and a random target number between 100 and 999. The aim is to make use the six given numbers and the four common arithmetic operations (addition, subtraction, multiplication, division; all over the rational numbers) to generate the target - or as close as possible either side. Each number may only be used once at most, while each arithmetic operator may be used any number of times (including zero.) Note that it does not matter how many numbers are used. Write a function that takes the target number and set of 6 numbers (can be represented as list/collection/array/sequence) and returns the solution in any standard numerical notation (e.g. infix, prefix, postfix). The function must always return the closest-possible result to the target, and must run in at most 1 minute on a standard PC. Note that in the case where more than one solution exists, any single solution is sufficient. Examples: {50, 100, 4, 2, 2, 4}, target 203 e.g. 100 * 2 + 2 + (4 / 4) e.g. (100 + 50) * 4 * 2 / (4 + 2) {25, 4, 9, 2, 3, 10}, target 465 e.g. (25 + 10 - 4) * (9 * 2 - 3) {9, 8, 10, 5, 9, 7), target 241 e.g. ((10 + 9) * 9 * 7) + 8) / 5 Rules Other than mentioned in the problem statement, there are no further restrictions. You may write the function in any standard language (standard I/O is not necessary). The aim as always is to solve the task with the smallest number of characters of code. Saying that, I may not simply accept the answer with the shortest code. I'll also be looking at elegance of the code and time complexity of the algorithm! My Solution I'm attempting an F# solution when I find the free time - will post it here when I have something! Format Please post all answers in the following format for the purpose of easy comparison: Language Number of characters: ??? Fully obfuscated function: (code here) Clear (ideally commented) function: (code here) Any notes on the algorithm/clever shortcuts it takes.

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  • C - How to implement Set data structure?

    - by psihodelia
    Is there any tricky way to implement a set data structure (a collection of unique values) in C? All elements in a set will be of the same type and there is a huge RAM memory. As I know, for integers it can be done really fast'N'easy using value-indexed arrays. But I'd like to have a very general Set data type. And it would be nice if a set could include itself.

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  • analyzing hashes

    - by calccrypto
    Is anyone willing to devote some time to helping me analyze a (hopefully cryptographically secure) hash? I honestly have no idea what im doing, so i need someone to show me how to, to teach me. almost all of the stuff ive found online have been really long, tedious, and vague the code is in python because for some reason i dont know c/c++. all i know about the hash: 1. there are no collisions (so far) and 2. differences between two similar inputs results in wildly different differences and please dont tell me that if i dont know what im doing, i shouldnt be doing it.

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  • Is OOP based on any branch of mathematics?

    - by ektrules
    I know relational databases are based on set-theory, functional programming is based on lambda calculus, logic programming is based on logic (of course :)), and now that I think of it; I'm not sure if imperative and generic programming is based on any particular branch of mathematics either.

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  • simplify expression k/m%n

    - by aaa
    hello. Simple question, is it possible to simplify (or replace division or modulo by less-expensive operation) (k/m)%n where variables are integers and operators are C style division and modulo operators. what about the case where m and n are constants (both or just one), not based 2? Thank you

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