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  • logic question about factorials

    - by Syom
    I have a problem and can't solve it alone. My teacher gives me one logic task today, and i'm sure you can help me. How can I count the number of zeroes at the end of factorial(41). (on paper) I understand that it has nothing to do with programing, but I'm sure programers can help me. Thanks in advance.

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  • NZEC in spoj FACKT

    - by frodo
    I was trying to solve this problem http://www.spoj.pl/problems/FACKT/, and I keep getting a Non-Zero Exit Code (NZEC). How exactly do I figure out what to change in the code to overcome this? Here is the code import math import sys def cal_num(n): i = 1 f = 1 while f<n: f *= i i = i + 1 return i-1 while 1: line = sys.stdin.readline() if line == "": break n = int(line) x = cal_num(n) y = math.factorial(2*x) l = int(math.ceil(math.log(y,10))) print (x,l) Any suggestion would be welcome.

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  • The best cross platform (portable) arbitrary precision math library

    - by Siu Ching Pong - Asuka Kenji
    Dear ninjas / hackers / wizards, I'm looking for a good arbitrary precision math library in C or C++. Could you please give me some advices / suggestions? The primary requirements: It MUST handle arbitrarily big integers (my primary interest is on integers). In case that you don't know what the word arbitrarily big means, imagine something like 100000! (the factorial of 100000). The precision MUST NOT NEED to be specified during library initialization / object creation. The precision should ONLY be constrained by the available resources of the system. It SHOULD utilize the full power of the platform, and should handle "small" numbers natively. That means on a 64-bit platform, calculating 2^33 + 2^32 should use the available 64-bit CPU instructions. The library SHOULD NOT calculate this in the same way as it does with 2^66 + 2^65 on the same platform. It MUST handle addition (+), subtraction (-), multiplication (*), integer division (/), remainder (%), power (**), increment (++), decrement (--), gcd(), factorial(), and other common integer arithmetic calculations efficiently. Ability to handle functions like sqrt() (square root), log() (logarithm) that do not produce integer results is a plus. Ability to handle symbolic computations is even better. Here are what I found so far: Java's BigInteger and BigDecimal class: I have been using these so far. I have read the source code, but I don't understand the math underneath. It may be based on theories / algorithms that I have never learnt. The built-in integer type or in core libraries of bc / Python / Ruby / Haskell / Lisp / Erlang / OCaml / PHP / some other languages: I have ever used some of these, but I have no idea on which library they are using, or which kind of implementation they are using. What I have already known: Using a char as a decimal digit, and a char* as a decimal string and do calculations on the digits using a for-loop. Using an int (or a long int, or a long long) as a basic "unit" and an array of it as an arbitrary long integer, and do calculations on the elements using a for-loop. Booth's multiplication algorithm What I don't know: Printing the binary array mentioned above in decimal without using naive methods. Example of a naive method: (1) add the bits from the lowest to the highest: 1, 2, 4, 8, 16, 32, ... (2) use a char* string mentioned above to store the intermediate decimal results). What I appreciate: Good comparisons on GMP, MPFR, decNumber (or other libraries that are good in your opinion). Good suggestions on books / articles that I should read. For example, an illustration with figures on how a un-naive arbitrarily long binary to decimal conversion algorithm works is good. Any help. Please DO NOT answer this question if: you think using a double (or a long double, or a long long double) can solve this problem easily. If you do think so, it means that you don't understand the issue under discussion. you have no experience on arbitrary precision mathematics. Thank you in advance! Asuka Kenji

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  • What is up with the Joy of Clojure 2nd edition?

    - by kurofune
    Manning just released the second edition of the beloved Joy of Clojure book, and while I share that love I get the feeling that many of the examples are already outdated. In particular, in the chapter on optimization the recommended type-hinting seems not to be allowed by the compiler. I don't know if this was allowable for older versions of Clojure. For example: (defn factorial-f [^long original-x] (loop [x original-x, acc 1] (if (>= 1 x) acc (recur (dec x) (*' x acc))))) returns: clojure.lang.Compiler$CompilerException: java.lang.UnsupportedOperationException: Can't type hint a primitive local, compiling:(null:3:1) Likewise, the chapter on core.logic seems be using an old API and I have to find workarounds for each example to accommodate the recent changes. For example, I had to turn this: (logic/defrel orbits orbital body) (logic/fact orbits :mercury :sun) (logic/fact orbits :venus :sun) (logic/fact orbits :earth :sun) (logic/fact orbits :mars :sun) (logic/fact orbits :jupiter :sun) (logic/fact orbits :saturn :sun) (logic/fact orbits :uranus :sun) (logic/fact orbits :neptune :sun) (logic/run* [q] (logic/fresh [orbital body] (orbits orbital body) (logic/== q orbital))) into this, leveraging the pldb lib: (pldb/db-rel orbits orbital body) (def facts (pldb/db [orbits :mercury :sun] [orbits :venus :sun] [orbits :earth :sun] [orbits :mars :sun] [orbits :jupiter :sun] [orbits :saturn :sun] [orbits :uranus :sun] [orbits :neptune :sun])) (pldb/with-db facts (logic/run* [q] (logic/fresh [orbital body] (orbits orbital body) (logic/== q orbital)))) I am still pulling teeth to get the later examples to work. I am relatively new programming, myself, so I wonder if I am naively looking over something here, or are if these points I'm making legitimate concerns? I really want to get good at this stuff like type-hinting and core.logic, but wanna make sure I am studying up to date materials. Any illuminating facts to help clear up my confusion would be most welcome.

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  • Call methods in main method

    - by Niloo
    this is my main method that gets 3 integers from command line and I parse then in my validating method. However I have one operation method that calls 3 other methods, but i don't know what type of data and howmany I have to put in my operatinMethod() " cuase switch only gets one); AND also in my mainMethod() for calling the operationMehod(); itself? please let me know if i'm not clear? Thanx! main method: public class test { // Global Constants final static int MIN_NUMBER = 1; final static int MAX_PRIME = 10000; final static int MAX_FACTORIAL = 12; final static int MAX_LEAPYEAR = 4000; //Global Variables static int a,b,c; public static void main (String[] args) { for(int i =0; i< args.length; i++){} if(validateInput(args[0],args[1],args[2])){ performOperations(); } } //Validate User Input public static boolean validateInput(String num1,String num2,String num3){ boolean isValid = false; try{ try{ try{ a = Integer.parseInt(num1); if(!withinRange(a,MIN_NUMBER, MAX_PRIME)) { System.out.println("The entered value " + num1 +" is out of range [1 TO 10000]."); } isValid = true; } catch(Exception ex) { System.out.println("The entered value " + num1 + " is not a valid integer. Please try again."); } b = Integer.parseInt(num2); if(!withinRange(b,MIN_NUMBER, MAX_FACTORIAL)) { System.out.println("The entered value " + num2 +" is out of range [1 TO 12]."); } isValid = true; } catch(Exception ex) { System.out.println("The entered value " + num2 + " is not a valid integer. Please try again."); } c = Integer.parseInt(num3); if(!withinRange(c,MIN_NUMBER, MAX_LEAPYEAR)) { System.out.println("The entered value " + num3 +" is out of range [1 TO 4000]."); } isValid = true; } catch(Exception ex) { System.out.println("The entered value " + num3 + " is not a valid integer. Please try again."); } return isValid; } //Check the value within the specified range private static boolean withinRange(int userInput ,int min, int max){ boolean isInRange = true; if(userInput < min || userInput > max){ isInRange = false; } return isInRange; } //Perform operations private static void performOperations(int userInput) { switch(userInput) { case 1: // count Prime numbers countPrimes(a); break; case 2: // Calculate factorial getFactorial(b); break; case 3: // find Leap year isLeapYear(c); break; } } // Verify Prime Number private static boolean isPrime(int prime) { for(int i = 2; i <= Math.sqrt(prime) ; i++) { if ((prime % i) == 0) { return false; } } return true; } // Calculate Prime private static int countPrimes(int userInput){ int count =0; for(int i=userInput; i<=MAX_PRIME; i++) { if(isPrime(i)){ count++; } } System.out.println("Exactly "+ count + " prime numbers exist between "+ a + " and 10,000."); return count; } // Calculate the factorial value private static int getFactorial(int userInput){ int ans = userInput; if(userInput >1 ){ ans*= (getFactorial(userInput-1)); //System.out.println("The value of "+ b +"! is "+ getFactorial(userInput)); } return ans; } // Determine whether the integer represents a leap year private static boolean isLeapYear(int userInput){ if (userInput % 4 == 0 && userInput % 400 == 0 && userInput % 100 ==0){ System.out.println("The year "+ c +" is a leap year"); } else { System.out.println("The year "+ c +" is a not leap year"); } return false; } }

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  • Add child to scene from within a class.

    - by Fecal Brunch
    Hi, I'm new to flash in general and have been writing a program with two classes that extend MovieClip (Stems and Star). I need to create a new Stems object as a child of the scene when the user stops dragging a Star object, but do not know how to reference the scene from within the Star class's code. I've tried passing the scene into the constructor of the Star and doing sometihng like: this.scene.addChild (new Stems ()); But apparently that's not how to do it... Below is the code for Stems and Stars, any advice would be appreciated greatly. package { import flash.display.MovieClip; import flash.events.*; import flash.utils.Timer; public class Stems extends MovieClip { public const centreX=1026/2; public const centreY=600/2; public var isFlowing:Boolean; public var flowerType:Number; public const outerLimit=210; public const innerLimit=100; public function Stems(fType:Number) { this.isFlowing=false; this.scaleX=this.scaleY= .0007* distanceFromCentre(this.x, this.y); this.setXY(); trace(distanceFromCentre(this.x, this.y)); if (fType==2) { gotoAndStop("Aplant"); } } public function distanceFromCentre(X:Number, Y:Number):int { return (Math.sqrt((X-centreX)*(X-centreX)+(Y-centreY)*(Y-centreY))); } public function rotateAwayFromCentre():void { var theX:int=centreX-this.x; var theY:int = (centreY - this.y) * -1; var angle = Math.atan(theY/theX)/(Math.PI/180); if (theX<0) { angle+=180; } if (theX>=0&&theY<0) { angle+=360; } this.rotation = ((angle*-1) + 90)+180; } public function setXY() { do { var tempX=Math.random()*centreX*2; var tempY=Math.random()*centreY*2; } while (distanceFromCentre (tempX, tempY)>this.outerLimit || distanceFromCentre (tempX, tempY)<this.innerLimit); this.x=tempX; this.y=tempY; rotateAwayFromCentre(); } public function getFlowerType():Number { return this.flowerType; } } } package { import flash.display.MovieClip; import flash.events.*; import flash.utils.Timer; public class Star extends MovieClip { public const sWide=1026; public const sTall=600; public var startingX:Number; public var startingY:Number; public var starColor:Number; public var flicker:Timer; public var canUpdatePos:Boolean=true; public const innerLimit=280; public function Star(color:Number, basefl:Number, factorial:Number) { this.setXY(); this.starColor=color; this.flicker = new Timer (basefl + factorial * (Math.ceil(100* Math.random ()))); this.flicker.addEventListener(TimerEvent.TIMER, this.tick); this.addEventListener(MouseEvent.MOUSE_OVER, this.hover); this.addEventListener(MouseEvent.MOUSE_UP, this.drop); this.addEventListener(MouseEvent.MOUSE_DOWN, this.drag); this.addChild (new Stems (2)); this.flicker.start(); this.updateAnimation(0, false); } public function distanceOK(X:Number, Y:Number):Boolean { if (Math.sqrt((X-(sWide/2))*(X-(sWide/2))+(Y-(sTall/2))*(Y-(sTall/2)))>innerLimit) { return true; } else { return false; } } public function setXY() { do { var tempX=this.x=Math.random()*sWide; var tempY=this.y=Math.random()*sTall; } while (distanceOK (tempX, tempY)==false); this.startingX=tempX; this.startingY=tempY; } public function tick(event:TimerEvent) { if (this.canUpdatePos) { this.setXY(); } this.updateAnimation(0, false); this.updateAnimation(this.starColor, false); } public function updateAnimation(color:Number, bright:Boolean) { var brightStr:String; if (bright) { brightStr="bright"; } else { brightStr="low"; } switch (color) { case 0 : this.gotoAndStop("none"); break; case 1 : this.gotoAndStop("N" + brightStr); break; case 2 : this.gotoAndStop("A" + brightStr); break; case 3 : this.gotoAndStop("F" + brightStr); break; case 4 : this.gotoAndStop("E" + brightStr); break; case 5 : this.gotoAndStop("S" + brightStr); break; } } public function hover(event:MouseEvent):void { this.updateAnimation(this.starColor, true); this.canUpdatePos=false; } public function drop(event:MouseEvent):void { this.stopDrag(); this.x=this.startingX; this.y=this.startingY; this.updateAnimation(0, false); this.canUpdatePos=true; } public function drag(event:MouseEvent):void { this.startDrag(false); this.canUpdatePos=false; } } }

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  • Power Analysis in [R] for Two-Way Anova

    - by Thomas
    I am trying to calculate the necessary sample size for a 2x2 factorial design. I have two questions. 1) I am using the package pwr and the one way anova function to calculate the necessary sample size using the following code pwr.anova.test(k = , n = , f = , sig.level = , power = ) However, I would like to look at two way anova, since this is more efficient at estimating group means than one way anova. There is no two-way anova function that I could find. Is there a package or routine in [R] to do this? 2) Moreover, am I safe in assuming that since I am using a one-way anova power calculations, that the sample size will be more conservative (i.e. larger)?

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  • Proper structure for many test cases in Python with unittest

    - by mellort
    I am looking into the unittest package, and I'm not sure of the proper way to structure my test cases when writing a lot of them for the same method. Say I have a fact function which calculates the factorial of a number; would this testing file be OK? import unittest class functions_tester(unittest.TestCase): def test_fact_1(self): self.assertEqual(1, fact(1)) def test_fact_2(self): self.assertEqual(2, fact(2)) def test_fact_3(self): self.assertEqual(6, fact(3)) def test_fact_4(self): self.assertEqual(24, fact(4)) def test_fact_5(self): self.assertFalse(1==fact(5)) def test_fact_6(self): self.assertRaises(RuntimeError, fact, -1) #fact(-1) if __name__ == "__main__": unittest.main() It seems sloppy to have so many test methods for one method. I'd like to just have one testing method and put a ton of basic test cases (ie 4! ==24, 3!==6, 5!==120, and so on), but unittest doesn't let you do that. What is the best way to structure a testing file in this scenario? Thanks in advance for the help.

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  • How to use Externel Triggers on Oracle 11g..

    - by RBA
    Hi, I want to fire a trigger whenever an insert command is fired.. The trigger will access a pl/sql file which can change anytime.. So the query is, if we design the trigger, how can we make sure this dynamic thing happens.. As during the stored procedure, it is not workingg.. I think - it should work for 1) External Procedures 2) Execute Statement Please correct me, if I am wrong.. I was working on External Procedures but i am not able to find the way to execute the external procedure from here on.. SQL> CREATE OR REPLACE FUNCTION Plstojavafac_func (N NUMBER) RETURN NUMBER AS 2 LANGUAGE JAVA 3 NAME 'Factorial.J_calcFactorial(int) return int'; 4 / @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ SQL> CREATE OR REPLACE TRIGGER student_after_insert 2 AFTER INSERT 3 ON student 4 FOR EACH ROW How to call the procedure from heree... And does my interpretations are right,, plz suggest.. Thanks.

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  • Postfix and right-associative operators in LR(0) parsers

    - by Ian
    Is it possible to construct an LR(0) parser that could parse a language with both prefix and postfix operators? For example, if I had a grammar with the + (addition) and ! (factorial) operators with the usual precedence then 1+3! should be 1 + 3! = 1 + 6 = 7, but surely if the parser were LR(0) then when it had 1+3 on the stack it would reduce rather than shift? Also, do right associative operators pose a problem? For example, 2^3^4 should be 2^(3^4) but again, when the parser have 2^3 on the stack how would it know to reduce or shift? If this isn't possible is there still a way to use an LR(0) parser, possibly by converting the input into Polish or Reverse Polish notation or adding brackets in the appropriate places? Would this be done before, during or after the lexing stage?

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  • how to exit recursive math formula and still get an answer

    - by calccrypto
    i wrote this python code, which from wolfram alpha says that its supposed to return the factorial of any positive value (i probably messed up somewhere), integer or not: from math import * def double_factorial(n): if int(n) == n: n = int(n) if [0,1].__contains__(n): return 1 a = (n&1) + 2 b = 1 while a<=n: b*=a a+= 2 return float(b) else: return factorials(n/2) * 2**(n/2) *(pi/2)**(.25 *(-1+cos(n * pi))) def factorials(n): return pi**(.5 * sin(n*pi)**2) * 2**(-n + .25 * (-1 + cos(2*n*pi))) * double_factorial(2*n) the problem is , say i input pi to 6 decimal places. 2*n will not become a float with 0 as its decimals any time soon, so the equation turns out to be pi**(.5 * sin(n*pi)**2) * 2**(-n + .25 * (-1 + cos(2*n*pi))) * double_factorial(loop(loop(loop(...))))) how would i stop the recursion and still get the answer? ive had suggestions to add an index to the definitions or something, but the problem is, if the code stops when it reaches an index, there is still no answer to put back into the previous "nests" or whatever you call them

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  • How to use External Procedures in Triggers on Oracle 11g..

    - by RBA
    Hi, I want to fire a trigger whenever an insert command is fired.. The trigger will access a pl/sql file which can change anytime.. So the query is, if we design the trigger, how can we make sure this dynamic thing happens.. As during the stored procedure, it is not workingg.. I think - it should work for 1) External Procedures 2) Execute Statement Please correct me, if I am wrong.. I was working on External Procedures but i am not able to find the way to execute the external procedure from here on.. SQL> CREATE OR REPLACE FUNCTION Plstojavafac_func (N NUMBER) RETURN NUMBER AS 2 LANGUAGE JAVA 3 NAME 'Factorial.J_calcFactorial(int) return int'; 4 / @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ SQL> CREATE OR REPLACE TRIGGER student_after_insert 2 AFTER INSERT 3 ON student 4 FOR EACH ROW How to call the procedure from heree... And does my interpretations are right,, plz suggest.. Thanks.

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  • What's some simple F# code that generates the .tail IL instruction?

    - by kld2010
    I'd like to see the .tail IL instruction, but the simple recursive functions using tail calls that I've been writing are apparently optimized into loops. I'm actually guessing on this, as I'm not entirely sure what a loop looks like in Reflector. I definitely don't see any .tail opcodes though. I have "Generate tail calls" checked in my project's properties. I've also tried both Debug and Release builds in Reflector. The code I used is from Programming F# by Chris Smith, page 190: let factorial x = // Keep track of both x and an accumulator value (acc) let rec tailRecursiveFactorial x acc = if x <= 1 then acc else tailRecursiveFactorial (x - 1) (acc * x) tailRecursiveFactorial x 1 Can anyone suggest some simple F# code which will indeed generate .tail?

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  • How to use Externel Procedures in Triggers on Oracle 11g..

    - by RBA
    Hi, I want to fire a trigger whenever an insert command is fired.. The trigger will access a pl/sql file which can change anytime.. So the query is, if we design the trigger, how can we make sure this dynamic thing happens.. As during the stored procedure, it is not workingg.. I think - it should work for 1) External Procedures 2) Execute Statement Please correct me, if I am wrong.. I was working on External Procedures but i am not able to find the way to execute the external procedure from here on.. SQL> CREATE OR REPLACE FUNCTION Plstojavafac_func (N NUMBER) RETURN NUMBER AS 2 LANGUAGE JAVA 3 NAME 'Factorial.J_calcFactorial(int) return int'; 4 / @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ SQL> CREATE OR REPLACE TRIGGER student_after_insert 2 AFTER INSERT 3 ON student 4 FOR EACH ROW How to call the procedure from heree... And does my interpretations are right,, plz suggest.. Thanks.

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  • which is the cleaner way to do this simple while?

    - by user363834
    I'm learning c++ and I want to make clean and readable code and I was wondering which way is better (while is supposed to make the factorial of 9) : 1 - int main(){ int i = 1,r = i; while (i < 10) { r *= ++i; } 2 - int main(){ int i = 1,r = i; while (i < 10) { i++ r *= i } 1 may be harder to understand but it's 1 less line, is it worth it? and what about performance. Obviously it wouldn't matter in such a trivial example but it would be a good practice to make fast code from the begining.

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  • What are basic programs like, recursion, Fibonacci, small trick programs?

    - by Mike
    This question may seem daft (I'm a new to 'programming' and should probably stop if this is the type of question I'm required to ask)... What are: "basic programs like, recursion, fibonacci, factorial, string manipulation, small trick programs"? I've recently read Coding Horror - the non programmer and followed the links to Kegel and How to get hired. Then I delved through some similar questions here (hence the block quote) and I realised that as a fully fledged non-programmer I probably wouldn't know if I knew recursion (or any of the others) because I wouldn't know what it looked like, or why it was used, and what the results would look like after it was used. I suppose I'm trying to get a picture of "the basics". What the principles are and why we learn them - where they'll be used and what result/s your looking for. If they'll be used as an interview question during my first interview sometime in 2020 I would like to look less ignorant than those 199 out of 200 who just don't know the how, or the why, of programming. As always...I'll get my coat. Thanks Mike

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  • argv Memory Allocation

    - by Joshua Green
    I was wondering if someone could tell me what I am doing wrong that I get this Unhandled Exception error message: 0xC0000005: Access violation reading location 0x0000000c. with a green pointer pointing at my first Prolog code (fid_t): Here is my header file: class UserTaskProlog { public: UserTaskProlog( ArRobot* r ); ~UserTaskProlog( ); protected: int cycles; char* argv[ 1 ]; term_t tf; term_t tx; term_t goal_term; functor_t goal_functor; ArRobot* robot; void logTask( ); }; And here is my main code: UserTaskProlog::UserTaskProlog( ArRobot* r ) : robot( r ), robotTaskFunc( this, &UserTaskProlog::logTask ) { cycles = 0; argv[ 0 ] = "libpl.dll"; argv[ 1 ] = NULL; PL_initialise( 1, argv ); PlCall( "consult( 'myPrologFile.pl' )" ); robot->addSensorInterpTask( "UserTaskProlog", 50, &robotTaskFunc ); } UserTaskProlog::~UserTaskProlog( ) { robot->remSensorInterpTask( &robotTaskFunc ); } void UserTaskProlog::logTask( ) { cycles++; fid_t fid = PL_open_foreign_frame( ); tf = PL_new_term_ref( ); PL_put_integer( tf, 5 ); tx = PL_new_term_ref( ); goal_term = PL_new_term_ref( ); goal_functor = PL_new_functor( PL_new_atom( "factorial" ), 2 ); PL_cons_functor( goal_term, goal_functor, tf, tx ); int fact; if ( PL_call( goal_term, NULL ) ) { PL_get_integer( tx, &fact ); cout << fact << endl; } PL_discard_foreign_frame( fid ); } int main( int argc, char** argv ) { ArRobot robot; ArArgumentParser argParser( &argc, argv ); UserTaskProlog talk( &robot ); } Thank you,

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  • In Perl, is a while loop generally faster than a for loop?

    - by Mike
    I've done a small experiment as will be shown below and it looks like that a while loop is faster than a for loop in Perl. But since the experiment was rather crude, and the subject might be a lot more complicated than it seems, I'd like to hear what you have to say about this. Thanks as always for any comments/suggestions :) In the following two small scripts, I've tried while and for loops separately to calcaulte the factorial of 100,000. The one that has the while loop took 57 minutes 17 seconds to finish while the for loop equivalent took 1 hour 7 minutes 54 seconds. Script that has while loop: use strict; use warnings; use bigint; my $now = time; my $n =shift; my $s=1; while(1){ $s *=$n; $n--; last if $n==2; } print $s*$n; $now = time - $now; printf("\n\nTotal running time: %02d:%02d:%02d\n\n", int($now / 3600), int(($now % 3600) / 60), int($now % 60)); Script that has for loop: use strict; use warnings; use bigint; my $now = time; my $n =shift; my $s=1; for (my $i=2; $i<=$n;$i++) { $s = $s*$i; } print $s; $now = time - $now; printf("\n\nTotal running time: %02d:%02d:%02d\n\n", int($now / 3600), int(($now % 3600) / 60), int($now % 60));

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  • Which languages support *recursive* function literals / anonymous functions?

    - by Hugh Allen
    It seems quite a few mainstream languages support function literals these days. They are also called anonymous functions, but I don't care if they have a name. The important thing is that a function literal is an expression which yields a function which hasn't already been defined elsewhere, so for example in C, &printf doesn't count. EDIT to add: if you have a genuine function literal expression <exp>, you should be able to pass it to a function f(<exp>) or immediately apply it to an argument, ie. <exp>(5). I'm curious which languages let you write function literals which are recursive. Wikipedia's "anonymous recursion" article doesn't give any programming examples. Let's use the recursive factorial function as the example. Here are the ones I know: JavaScript / ECMAScript can do it with callee: function(n){if (n<2) {return 1;} else {return n * arguments.callee(n-1);}} it's easy in languages with letrec, eg Haskell (which calls it let): let fac x = if x<2 then 1 else fac (x-1) * x in fac and there are equivalents in Lisp and Scheme. Note that the binding of fac is local to the expression, so the whole expression is in fact an anonymous function. Are there any others?

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  • Natural problems to solve using closures

    - by m.u.sheikh
    I have read quite a few articles on closures, and, embarassingly enough, I still don't understand this concept! Articles explain how to create a closure with a few examples, but I don't see any point in paying much attention to them, as they largely look contrived examples. I am not saying all of them are contrived, just that the ones I found looked contrived, and I dint see how even after understanding them, I will be able to use them. So in order to understand closures, I am looking at a few real problems, that can be solved very naturally using closures. For instance, a natural way to explain recursion to a person could be to explain the computation of n!. It is very natural to understand a problem like computing the factorial of a number using recursion. Similarly, it is almost a no-brainer to find an element in an unsorted array by reading each element, and comparing with the number in question. Also, at a different level, doing Object-oriented programming also makes sense. So I am trying to find a number of problems that could be solved with or without closures, but using closures makes thinking about them and solving them easier. Also, there are two types to closures, where each call to a closure can create a copy of the environment variables, or reference the same variables. So what sort of problems can be solved more naturally in which of the closure implementations?

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  • Reversible numerical calculations in Prolog

    - by user8472
    While reading SICP I came across logic programming chapter 4.4. Then I started looking into the Prolog programming language and tried to understand some simple assignments in Prolog. I found that Prolog seems to have troubles with numerical calculations. Here is the computation of a factorial in standard Prolog: f(0, 1). f(A, B) :- A > 0, C is A-1, f(C, D), B is A*D. The issues I find is that I need to introduce two auxiliary variables (C and D), a new syntax (is) and that the problem is non-reversible (i.e., f(5,X) works as expected, but f(X,120) does not). Naively, I expect that at the very least C is A-1, f(C, D) above may be replaced by f(A-1,D), but even that does not work. My question is: Why do I need to do this extra "stuff" in numerical calculations but not in other queries? I do understand (and SICP is quite clear about it) that in general information on "what to do" is insufficient to answer the question of "how to do it". So the declarative knowledge in (at least some) math problems is insufficient to actually solve these problems. But that begs the next question: How does this extra "stuff" in Prolog help me to restrict the formulation to just those problems where "what to do" is sufficient to answer "how to do it"?

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  • Numerical calculations in Prolog

    - by user8472
    While reading SICP I came across logic programming chapter 4.4. Then I started looking into the Prolog programming language and tried to understand some simple assignments in Prolog. I found that Prolog seems to have troubles with numerical calculations. Here is the computation of a factorial in standard Prolog: f(0, 1). f(A, B) :- A > 0, C is A-1, f(C, D), B is A*D. The issues I find is that I need to introduce two auxiliary variables (C and D), a new syntax (is) and that the problem is non-reversible (i.e., f(5,X) works as expected, but f(X,120) does not). Naively, I expect that at the very least C is A-1, f(C, D) above may be replaced by f(A-1,D), but even that does not work. My question is: Why do I need to do this extra "stuff" in numerical calculations but not in other queries? I do understand (and SICP is quite clear about it) that in general information on "what to do" is insufficient to answer the question of "how to do it". So the declarative knowledge in (at least some) math problems is insufficient to actually solve these problems. But that begs the next question: How does this extra "stuff" in Prolog help me to restrict the formulation to just those problems where "what to do" is sufficient to answer "how to do it"?

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  • Implementing a Custom Coherence PartitionAssignmentStrategy

    - by jpurdy
    A recent A-Team engagement required the development of a custom PartitionAssignmentStrategy (PAS). By way of background, a PAS is an implementation of a Java interface that controls how a Coherence partitioned cache service assigns partitions (primary and backup copies) across the available set of storage-enabled members. While seemingly straightforward, this is actually a very difficult problem to solve. Traditionally, Coherence used a distributed algorithm spread across the cache servers (and as of Coherence 3.7, this is still the default implementation). With the introduction of the PAS interface, the model of operation was changed so that the logic would run solely in the cache service senior member. Obviously, this makes the development of a custom PAS vastly less complex, and in practice does not introduce a significant single point of failure/bottleneck. Note that Coherence ships with a default PAS implementation but it is not used by default. Further, custom PAS implementations are uncommon (this engagement was the first custom implementation that we know of). The particular implementation mentioned above also faced challenges related to managing multiple backup copies but that won't be discussed here. There were a few challenges that arose during design and implementation: Naive algorithms had an unreasonable upper bound of computational cost. There was significant complexity associated with configurations where the member count varied significantly between physical machines. Most of the complexity of a PAS is related to rebalancing, not initial assignment (which is usually fairly simple). A custom PAS may need to solve several problems simultaneously, such as: Ensuring that each member has a similar number of primary and backup partitions (e.g. each member has the same number of primary and backup partitions) Ensuring that each member carries similar responsibility (e.g. the most heavily loaded member has no more than one partition more than the least loaded). Ensuring that each partition is on the same member as a corresponding local resource (e.g. for applications that use partitioning across message queues, to ensure that each partition is collocated with its corresponding message queue). Ensuring that a given member holds no more than a given number of partitions (e.g. no member has more than 10 partitions) Ensuring that backups are placed far enough away from the primaries (e.g. on a different physical machine or a different blade enclosure) Achieving the above goals while ensuring that partition movement is minimized. These objectives can be even more complicated when the topology of the cluster is irregular. For example, if multiple cluster members may exist on each physical machine, then clearly the possibility exists that at certain points (e.g. following a member failure), the number of members on each machine may vary, in certain cases significantly so. Consider the case where there are three physical machines, with 3, 3 and 9 members each (respectively). This introduces complexity since the backups for the 9 members on the the largest machine must be spread across the other 6 members (to ensure placement on different physical machines), preventing an even distribution. For any given problem like this, there are usually reasonable compromises available, but the key point is that objectives may conflict under extreme (but not at all unlikely) circumstances. The most obvious general purpose partition assignment algorithm (possibly the only general purpose one) is to define a scoring function for a given mapping of partitions to members, and then apply that function to each possible permutation, selecting the most optimal permutation. This would result in N! (factorial) evaluations of the scoring function. This is clearly impractical for all but the smallest values of N (e.g. a partition count in the single digits). It's difficult to prove that more efficient general purpose algorithms don't exist, but the key take away from this is that algorithms will tend to either have exorbitant worst case performance or may fail to find optimal solutions (or both) -- it is very important to be able to show that worst case performance is acceptable. This quickly leads to the conclusion that the problem must be further constrained, perhaps by limiting functionality or by using domain-specific optimizations. Unfortunately, it can be very difficult to design these more focused algorithms. In the specific case mentioned, we constrained the solution space to very small clusters (in terms of machine count) with small partition counts and supported exactly two backup copies, and accepted the fact that partition movement could potentially be significant (preferring to solve that issue through brute force). We then used the out-of-the-box PAS implementation as a fallback, delegating to it for configurations that were not supported by our algorithm. Our experience was that the PAS interface is quite usable, but there are intrinsic challenges to designing PAS implementations that should be very carefully evaluated before committing to that approach.

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  • LLVM JIT segfaults. What am I doing wrong?

    - by bugspy.net
    It is probably something basic because I am just starting to learn LLVM.. The following creates a factorial function and tries to git and execute it (I know the generated func is correct because I was able to static compile and execute it). But I get segmentation fault upon execution of the function (in EE-runFunction(TheF, Args)) #include <iostream> #include "llvm/Module.h" #include "llvm/Function.h" #include "llvm/PassManager.h" #include "llvm/CallingConv.h" #include "llvm/Analysis/Verifier.h" #include "llvm/Assembly/PrintModulePass.h" #include "llvm/Support/IRBuilder.h" #include "llvm/Support/raw_ostream.h" #include "llvm/ExecutionEngine/JIT.h" #include "llvm/ExecutionEngine/GenericValue.h" using namespace llvm; Module* makeLLVMModule() { // Module Construction LLVMContext& ctx = getGlobalContext(); Module* mod = new Module("test", ctx); Constant* c = mod->getOrInsertFunction("fact64", /*ret type*/ IntegerType::get(ctx,64), IntegerType::get(ctx,64), /*varargs terminated with null*/ NULL); Function* fact64 = cast<Function>(c); fact64->setCallingConv(CallingConv::C); /* Arg names */ Function::arg_iterator args = fact64->arg_begin(); Value* x = args++; x->setName("x"); /* Body */ BasicBlock* block = BasicBlock::Create(ctx, "entry", fact64); BasicBlock* xLessThan2Block= BasicBlock::Create(ctx, "xlst2_block", fact64); BasicBlock* elseBlock = BasicBlock::Create(ctx, "else_block", fact64); IRBuilder<> builder(block); Value *One = ConstantInt::get(Type::getInt64Ty(ctx), 1); Value *Two = ConstantInt::get(Type::getInt64Ty(ctx), 2); Value* xLessThan2 = builder.CreateICmpULT(x, Two, "tmp"); //builder.CreateCondBr(xLessThan2, xLessThan2Block, cond_false_2); builder.CreateCondBr(xLessThan2, xLessThan2Block, elseBlock); /* Recursion */ builder.SetInsertPoint(elseBlock); Value* xMinus1 = builder.CreateSub(x, One, "tmp"); std::vector<Value*> args1; args1.push_back(xMinus1); Value* recur_1 = builder.CreateCall(fact64, args1.begin(), args1.end(), "tmp"); Value* retVal = builder.CreateBinOp(Instruction::Mul, x, recur_1, "tmp"); builder.CreateRet(retVal); /* x<2 */ builder.SetInsertPoint(xLessThan2Block); builder.CreateRet(One); return mod; } int main(int argc, char**argv) { long long x; if(argc > 1) x = atol(argv[1]); else x = 4; Module* Mod = makeLLVMModule(); verifyModule(*Mod, PrintMessageAction); PassManager PM; PM.add(createPrintModulePass(&outs())); PM.run(*Mod); // Now we going to create JIT ExecutionEngine *EE = EngineBuilder(Mod).create(); // Call the function with argument x: std::vector<GenericValue> Args(1); Args[0].IntVal = APInt(64, x); Function* TheF = cast<Function>(Mod->getFunction("fact64")) ; /* The following CRASHES.. */ GenericValue GV = EE->runFunction(TheF, Args); outs() << "Result: " << GV.IntVal << "\n"; delete Mod; return 0; }

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