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• Calculating odds distribution with 6-sided dice

  - by Stephen

  I'm trying to calculate the odds distribution of a changing number of 6-sided die rolls. For example, 3d6 ranges from 3 to 18 as follows: 3:1, 4:3, 5:6, 6:10, 7:15, 8:21, 9:25, 10:27, 11:27, 12:25, 13:21, 14:15, 15:10, 16:6, 17:3, 18:1 I wrote this php program to calculate it: function distributionCalc($numberDice,$sides=6) { for ( $i=0; $i<pow($sides,$numberDice); $i++) { $sum=0; for ($j=0; $j<$numberDice; $j++) { $sum+=(1+(floor($i/pow($sides,$j))) % $sides); } $distribution[$sum]++; } return $distribution; } The inner $j for-loop uses the magic of the floor and modulus functions to create a base-6 counting sequence with the number of digits being the number of dice, so 3d6 would count as: 111,112,113,114,115,116,121,122,123,124,125,126,131,etc. The function takes the sum of each, so it would read as: 3,4,5,6,7,8,4,5,6,7,8,9,5,etc. It plows through all 3^6 possible results and adds 1 to the corresponding slot in the $distribution array between 3 and 18. Pretty straightforward. However, it only works until about 8d6, afterward i get server time-outs because it's now doing billions of calculations. But I don't think it's necessary because die probability follows a sweet bell-curve distribution. I'm wondering if there's a way to skip the number crunching and go straight to the curve itself. Is there a way to do this, so, for example, with 80d6 (80-480)? Can the distribution be projected without doing 6^80 calculations? I'm not a professional coder and probability is still new to me, so thanks for all the help! Stephen

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• Draw LINE_STRIP with Unity

  - by Boozzz

  For a new project I am thinking about whether to use OpenGL or Unity3d. I have a bit of experience with OpenGL, but I am completely new to Unity. I already read through the Unity documentation and tutorials on the Unity Website. However, I could not find a way to draw a simple Line-Strip with Unity. In the following example (C#, OpenGL/SharpGL) I draw a round trajectory from a predifined point to an obstacle, which can be imagined as a divided circle with midpoint [cx,cy] and radius r. The position (x-y coordinates) of the obstacle is given by obst_x and obst_y. Question 1: How could I do the same with Unity? Question 2: In my new project, I will have to draw quite a lot of such geometric primitives. Does it make any sense to use Unity for those things? void drawCircle(float cx, float cy, float r, const float obst_x, const float obst_y) { float theta = 0.0f, pos_x, pos_y, dist; const float delta = 0.1; glBegin(GL_LINE_STRIP); while (theta < 180) { theta += delta; //get the current angle float x = r * cosf(theta); //calculate the x component float y = r * sinf(theta); //calculate the y component pos_x = x + cx; //calculate current x position pos_y = y + cy; //calculate current y position //calculate distance from current vertex to obstacle dist = sqrt(pow(pos_x - obst_x) + pow(pos_y - obst_y)); //check if current vertex intersects with obstacle if dist <= 0 { break; //stop drawing circle } else { glVertex2f(pos_x, pos_y); //draw vertex } } glEnd(); }

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• Optimal two variable linear regression SQL statement (censoring outliers)

  - by Dave Jarvis

  Problem Am looking to apply the y = mx + b equation (where m is SLOPE, b is INTERCEPT) to a data set, which is retrieved as shown in the SQL code. The values from the (MySQL) query are: SLOPE = 0.0276653965651912 INTERCEPT = -57.2338357550468 SQL Code SELECT ((sum(t.YEAR) * sum(t.AMOUNT)) - (count(1) * sum(t.YEAR * t.AMOUNT))) / (power(sum(t.YEAR), 2) - count(1) * sum(power(t.YEAR, 2))) as SLOPE, ((sum( t.YEAR ) * sum( t.YEAR * t.AMOUNT )) - (sum( t.AMOUNT ) * sum(power(t.YEAR, 2)))) / (power(sum(t.YEAR), 2) - count(1) * sum(power(t.YEAR, 2))) as INTERCEPT FROM (SELECT D.AMOUNT, Y.YEAR FROM CITY C, STATION S, YEAR_REF Y, MONTH_REF M, DAILY D WHERE -- For a specific city ... -- C.ID = 8590 AND -- Find all the stations within a 15 unit radius ... -- SQRT( POW( C.LATITUDE - S.LATITUDE, 2 ) + POW( C.LONGITUDE - S.LONGITUDE, 2 ) ) <15 AND -- Gather all known years for that station ... -- S.STATION_DISTRICT_ID = Y.STATION_DISTRICT_ID AND -- The data before 1900 is shaky; insufficient after 2009. -- Y.YEAR BETWEEN 1900 AND 2009 AND -- Filtered by all known months ... -- M.YEAR_REF_ID = Y.ID AND -- Whittled down by category ... -- M.CATEGORY_ID = '001' AND -- Into the valid daily climate data. -- M.ID = D.MONTH_REF_ID AND D.DAILY_FLAG_ID <> 'M' GROUP BY Y.YEAR ORDER BY Y.YEAR ) t Data The data is visualized here (with five outliers highlighted): Questions How do I return the y value against all rows without repeating the same query to collect and collate the data? That is, how do I "reuse" the list of t values? How would you change the query to eliminate outliers (at an 85% confidence interval)? The following results (to calculate the start and end points of the line) appear incorrect. Why are the results off by ~10 degrees (e.g., outliers skewing the data)? (1900 * 0.0276653965651912) + (-57.2338357550468) = -4.66958228 (2009 * 0.0276653965651912) + (-57.2338357550468) = -1.65405406 I would have expected the 1900 result to be around 10 (not -4.67) and the 2009 result to be around 11.50 (not -1.65). Thank you!

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• Precision of cos(atan2(y,x)) versus using complex <double>, C++

  - by Ivan

  Hi all, I'm writing some coordinate transformations (more specifically the Joukoswky Transform, Wikipedia Joukowsky Transform), and I'm interested in performance, but of course precision. I'm trying to do the coordinate transformations in two ways: 1) Calculating the real and complex parts in separate, using double precision, as below: double r2 = chi.x*chi.x + chi.y*chi.y; //double sq = pow(r2,-0.5*n) + pow(r2,0.5*n); //slow!!! double sq = sqrt(r2); //way faster! double co = cos(atan2(chi.y,chi.x)); double si = sin(atan2(chi.y,chi.x)); Z.x = 0.5*(co*sq + co/sq); Z.y = 0.5*si*sq; where chi and Z are simple structures with double x and y as members. 2) Using complex : Z = 0.5 * (chi + (1.0 / chi)); Where Z and chi are complex . There interesting part is that indeed the case 1) is faster (about 20%), but the precision is bad, giving error in the third decimal number after the comma after the inverse transform, while the complex gives back the exact number. So, the problem is on the cos(atan2), sin(atan2)? But if it is, how the complex handles that? Thanks!

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• C#: Wrong answer when finding "cool" numbers.

  - by user300484

  Hello you all! In my application, a "cool" number is a number that is both a square and a cube, like for example: 64 = 8^2 and 64 = 4^3. My application is supposed to find the number of "cool numbers" between a range given by the user. I wrote my code and the application runs fine, but it is giving me the wrong answer. Can you help me here please? for example: IMPUT 1 100 OUTPUT 1 using System; using System.Collections.Generic; using System.Linq; using System.Text; namespace ConsoleApplication1 { class Program { static void Main(string[] args) { double a = Convert.ToDouble(Console.ReadLine()); // first number in the range double b = Convert.ToDouble(Console.ReadLine()); // second number in the range long x = 0; for (double i = a; i <= b; i++) { double cube = 1.0 / 3.0; double cuad = 1.0 / 2.0; double crt = Math.Pow(i, cube); // cube root double sqrt = Math.Pow(i, cuad); // square root if ((crt * 10) % 10 == 0 || (sqrt * 10) % 10 == 0) // condition to determine if it is a cool number. x++; } Console.WriteLine(x); Console.ReadLine(); } } }

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• Optimal two variable linear regression SQL statement

  - by Dave Jarvis

  Problem Am looking to apply the y = mx + b equation (where m is SLOPE, b is INTERCEPT) to a data set, which is retrieved as shown in the SQL code. The values from the (MySQL) query are: SLOPE = 0.0276653965651912 INTERCEPT = -57.2338357550468 SQL Code SELECT ((sum(t.YEAR) * sum(t.AMOUNT)) - (count(1) * sum(t.YEAR * t.AMOUNT))) / (power(sum(t.YEAR), 2) - count(1) * sum(power(t.YEAR, 2))) as SLOPE, ((sum( t.YEAR ) * sum( t.YEAR * t.AMOUNT )) - (sum( t.AMOUNT ) * sum(power(t.YEAR, 2)))) / (power(sum(t.YEAR), 2) - count(1) * sum(power(t.YEAR, 2))) as INTERCEPT FROM (SELECT D.AMOUNT, Y.YEAR FROM CITY C, STATION S, YEAR_REF Y, MONTH_REF M, DAILY D WHERE -- For a specific city ... -- C.ID = 8590 AND -- Find all the stations within a 5 unit radius ... -- SQRT( POW( C.LATITUDE - S.LATITUDE, 2 ) + POW( C.LONGITUDE - S.LONGITUDE, 2 ) ) <15 AND -- Gather all known years for that station ... -- S.STATION_DISTRICT_ID = Y.STATION_DISTRICT_ID AND -- The data before 1900 is shaky; and insufficient after 2009. -- Y.YEAR BETWEEN 1900 AND 2009 AND -- Filtered by all known months ... -- M.YEAR_REF_ID = Y.ID AND -- Whittled down by category ... -- M.CATEGORY_ID = '001' AND -- Into the valid daily climate data. -- M.ID = D.MONTH_REF_ID AND D.DAILY_FLAG_ID <> 'M' GROUP BY Y.YEAR ORDER BY Y.YEAR ) t Data The data is visualized here: Questions How do I return the y value against all rows without repeating the same query to collect and collate the data? That is, how do I "reuse" the list of t values? How would you change the query to eliminate outliers (at an 85% confidence interval)? The following results (to calculate the start and end points of the line) appear incorrect. Why are the results off by ~10 degrees (e.g., outliers skewing the data)? (1900 * 0.0276653965651912) + (-57.2338357550468) = -4.66958228 (2009 * 0.0276653965651912) + (-57.2338357550468) = -1.65405406 I would have expected the 1900 result to be around 10 (not -4.67) and the 2009 result to be around 11.50 (not -1.65). Thank you!

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• Optimal two variable linear regression calculation

  - by Dave Jarvis

  Problem Am looking to apply the y = mx + b equation (where m is SLOPE, b is INTERCEPT) to a data set, which is retrieved as shown in the SQL code. The values from the (MySQL) query are: SLOPE = 0.0276653965651912 INTERCEPT = -57.2338357550468 SQL Code SELECT ((sum(t.YEAR) * sum(t.AMOUNT)) - (count(1) * sum(t.YEAR * t.AMOUNT))) / (power(sum(t.YEAR), 2) - count(1) * sum(power(t.YEAR, 2))) as SLOPE, ((sum( t.YEAR ) * sum( t.YEAR * t.AMOUNT )) - (sum( t.AMOUNT ) * sum(power(t.YEAR, 2)))) / (power(sum(t.YEAR), 2) - count(1) * sum(power(t.YEAR, 2))) as INTERCEPT, FROM (SELECT D.AMOUNT, Y.YEAR FROM CITY C, STATION S, YEAR_REF Y, MONTH_REF M, DAILY D WHERE -- For a specific city ... -- C.ID = 8590 AND -- Find all the stations within a 15 unit radius ... -- SQRT( POW( C.LATITUDE - S.LATITUDE, 2 ) + POW( C.LONGITUDE - S.LONGITUDE, 2 ) ) < 15 AND -- Gather all known years for that station ... -- S.STATION_DISTRICT_ID = Y.STATION_DISTRICT_ID AND -- The data before 1900 is shaky; insufficient after 2009. -- Y.YEAR BETWEEN 1900 AND 2009 AND -- Filtered by all known months ... -- M.YEAR_REF_ID = Y.ID AND -- Whittled down by category ... -- M.CATEGORY_ID = '001' AND -- Into the valid daily climate data. -- M.ID = D.MONTH_REF_ID AND D.DAILY_FLAG_ID <> 'M' GROUP BY Y.YEAR ORDER BY Y.YEAR ) t Data The data is visualized here: Question The following results (to calculate the start and end points of the line) appear incorrect. Why are the results off by ~10 degrees (e.g., outliers skewing the data)? (1900 * 0.0276653965651912) + (-57.2338357550468) = -4.66958228 (2009 * 0.0276653965651912) + (-57.2338357550468) = -1.65405406 I would have expected the 1900 result to be around 10 (not -4.67) and the 2009 result to be around 11.50 (not -1.65). Related Sites Least absolute deviations Robust regression Thank you!

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• Choosing between instance methods and separate functions?

  - by StackedCrooked

  Adding functionality to a class can be done by adding a method or by defining a function that takes an object as its first parameter. Most programmers that I know would choose for the solution of adding a instance method. However, I sometimes prefer to create a separate function. For example, in the example code below Area and Diagonal are defined as separate functions instead of methods. I find it better this way because I think these functions provide enhancements rather than core functionality. Is this considered a good/bad practice? If the answer is "it depends", then what are the rules for deciding between adding method or defining a separate function? class Rect { public: Rect(int x, int y, int w, int h) : mX(x), mY(y), mWidth(w), mHeight(h) { } int x() const { return mX; } int y() const { return mY; } int width() const { return mWidth; } int height() const { return mHeight; } private: int mX, mY, mWidth, mHeight; }; int Area(const Rect & inRect) { return inRect.width() * inRect.height(); } float Diagonal(const Rect & inRect) { return std::sqrt(std::pow(static_cast<float>(inRect.width()), 2) + std::pow(static_cast<float>(inRect.height()), 2)); }

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• OnClickListener error: Source not found

  - by fordays

  Hi, I'm brand new to Android development and right now I am building a simple calculator for healthcare workers. My program implements the OnClickListener class, but every time I click on the button to initiate the calculation, I get an error saying the "Source is not Found". Here is the code: public class KidneyeGFR extends Activity implements OnClickListener { /** Called when the activity is first created. */ @Override public void onCreate(Bundle savedInstanceState) { super.onCreate(savedInstanceState); setContentView(R.layout.main); Calculate = (Button)this.findViewById(R.id.Calculate); Calculate.setOnClickListener(this); } public void onClick(View v) { if (Female.isChecked()) { gender = 0.742; } else { gender = 1.0; } if (African.isChecked()) { race = 1.212; } else { race = 1.0; } calculateBone(); } protected void calculateBone() { int age = Integer.parseInt(EditAge.getText().toString()); double serum = Double.parseDouble(EditSerum.getText().toString()); finalgfr = BONECONST * Math.pow(serum, -1.154) * Math.pow(age, -0.203) * gender * race; BONEtext.setText(Double.toString(finalbone)); }

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• How do I make this nested for loop, testing sums of cubes, more efficient?

  - by Brian J. Fink

  I'm trying to iterate through all the combinations of pairs of positive long integers in Java and testing the sum of their cubes to discover if it's a Fibonacci number. I'm currently doing this by using the value of the outer loop variable as the inner loop's upper limit, with the effect being that the outer loop runs a little slower each time. Initially it appeared to run very quickly--I was up to 10 digits within minutes. But now after 2 full days of continuous execution, I'm only somewhere in the middle range of 15 digits. At this rate it may end up taking a whole year just to finish running this program. The code for the program is below: import java.lang.*; import java.math.*; public class FindFib { public static void main(String args[]) { long uLimit=9223372036854775807L; //long maximum value BigDecimal PHI=new BigDecimal(1D+Math.sqrt(5D)/2D); //Golden Ratio for(long a=1;a<=uLimit;a++) //Outer Loop, 1 to maximum for(long b=1;b<=a;b++) //Inner Loop, 1 to current outer { //Cube the numbers and add BigDecimal c=BigDecimal.valueOf(a).pow(3).add(BigDecimal.valueOf(b).pow(3)); System.out.print(c+" "); //Output result //Upper and lower limits of interval for Mobius test: [c*PHI-1/c,c*PHI+1/c] BigDecimal d=c.multiply(PHI).subtract(BigDecimal.ONE.divide(c,BigDecimal.ROUND_HALF_UP)), e=c.multiply(PHI).add(BigDecimal.ONE.divide(c,BigDecimal.ROUND_HALF_UP)); //Mobius test: if integer in interval (floor values unequal) Fibonacci number! if (d.toBigInteger().compareTo(e.toBigInteger())!=0) System.out.println(); //Line feed else System.out.print("\r"); //Carriage return instead } //Display final message System.out.println("\rDone. "); } } Now the use of BigDecimal and BigInteger was delibrate; I need them to get the necessary precision. Is there anything other than my variable types that I could change to gain better efficiency?

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• Silverlight 3 ArcSegment to always draw circle's

  - by kapaboo

  Hi everyone, Ok, my arcSegment must always draw Circle's. For this reason I calculate the Arc's Width with the following formula: arcXRadius = (4 * Math.Pow(height, 2) + Math.Pow(distanceArcPoints, 2)) / (8 * height); so Arcs.Size = (arcXRadius,height) But seems that the height is scaled down when drawn. I want to add a small Circle to the Arc's middle (highest point) so when you drag it it changes the arc Height but also changes the Width so it will remain a circle. Here's how I calculate the Circle's (highest) point: Point middlePoint = GetMiddlePoint(arcPointA,arcPointB); double arcYRadius = arcSegment.Size.Height; if (arcYRadius <= 0) return middlePoint; double angle = arcSegment.RotationAngle; Point ellinewPoint = new Point(); ellinewPoint.X = Math.Cos((angle + 90) * Math.PI / 180) * arcYRadius + middlePoint.X; ellinewPoint.Y = Math.Sin((angle + 90) * Math.PI / 180) * arcYRadius + middlePoint.Y; Until Arc's.Size.Height Property gets Closer to the Width my Circle is not at the right Point. So maybe someone can give me a hint or tell me what am I doing wrong. Cheers, kapaboo

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• Eliminate full table scan due to BETWEEN (and GROUP BY)

  - by Dave Jarvis

  Description According to the explain command, there is a range that is causing a query to perform a full table scan (160k rows). How do I keep the range condition and reduce the scanning? I expect the culprit to be: Y.YEAR BETWEEN 1900 AND 2009 AND Code Here is the code that has the range condition (the STATION_DISTRICT is likely superfluous). SELECT COUNT(1) as MEASUREMENTS, AVG(D.AMOUNT) as AMOUNT, Y.YEAR as YEAR, MAKEDATE(Y.YEAR,1) as AMOUNT_DATE FROM CITY C, STATION S, STATION_DISTRICT SD, YEAR_REF Y FORCE INDEX(YEAR_IDX), MONTH_REF M, DAILY D WHERE -- For a specific city ... -- C.ID = 10663 AND -- Find all the stations within a specific unit radius ... -- 6371.009 * SQRT( POW(RADIANS(C.LATITUDE_DECIMAL - S.LATITUDE_DECIMAL), 2) + (COS(RADIANS(C.LATITUDE_DECIMAL + S.LATITUDE_DECIMAL) / 2) * POW(RADIANS(C.LONGITUDE_DECIMAL - S.LONGITUDE_DECIMAL), 2)) ) <= 50 AND -- Get the station district identification for the matching station. -- S.STATION_DISTRICT_ID = SD.ID AND -- Gather all known years for that station ... -- Y.STATION_DISTRICT_ID = SD.ID AND -- The data before 1900 is shaky; insufficient after 2009. -- Y.YEAR BETWEEN 1900 AND 2009 AND -- Filtered by all known months ... -- M.YEAR_REF_ID = Y.ID AND -- Whittled down by category ... -- M.CATEGORY_ID = '003' AND -- Into the valid daily climate data. -- M.ID = D.MONTH_REF_ID AND D.DAILY_FLAG_ID <> 'M' GROUP BY Y.YEAR Update The SQL is performing a full table scan, which results in MySQL performing a "copy to tmp table", as shown here: +----+-------------+-------+--------+-----------------------------------+--------------+---------+-------------------------------+--------+-------------+ | id | select_type | table | type | possible_keys | key | key_len | ref | rows | Extra | +----+-------------+-------+--------+-----------------------------------+--------------+---------+-------------------------------+--------+-------------+ | 1 | SIMPLE | C | const | PRIMARY | PRIMARY | 4 | const | 1 | | | 1 | SIMPLE | Y | range | YEAR_IDX | YEAR_IDX | 4 | NULL | 160422 | Using where | | 1 | SIMPLE | SD | eq_ref | PRIMARY | PRIMARY | 4 | climate.Y.STATION_DISTRICT_ID | 1 | Using index | | 1 | SIMPLE | S | eq_ref | PRIMARY | PRIMARY | 4 | climate.SD.ID | 1 | Using where | | 1 | SIMPLE | M | ref | PRIMARY,YEAR_REF_IDX,CATEGORY_IDX | YEAR_REF_IDX | 8 | climate.Y.ID | 54 | Using where | | 1 | SIMPLE | D | ref | INDEX | INDEX | 8 | climate.M.ID | 11 | Using where | +----+-------------+-------+--------+-----------------------------------+--------------+---------+-------------------------------+--------+-------------+ Related http://dev.mysql.com/doc/refman/5.0/en/how-to-avoid-table-scan.html http://dev.mysql.com/doc/refman/5.0/en/where-optimizations.html http://stackoverflow.com/questions/557425/optimize-sql-that-uses-between-clause Thank you!

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• power and modulo on the fly for big numbers

  - by user unknown

  I raise some basis b to the power p and take the modulo m of that. Let's assume b=55170 or 55172 and m=3043839241 (which happens to be the square of 55171). The linux-calculator bc gives the results (we need this for control): echo "p=5606;b=55171;m=b*b;((b-1)^p)%m;((b+1)^p)%m" | bc 2734550616 309288627 Now calculating 55170^5606 gives a somewhat large number, but since I have to do a modulooperation, I can circumvent the usage of BigInt, I thought, because of: (a*b) % c == ((a%c) * (b%c))%c i.e. (9*7) % 5 == ((9%5) * (7%5))%5 => 63 % 5 == (4 * 2) %5 => 3 == 8 % 5 ... and a^d = a^(b+c) = a^b * a^c, therefore I can divide b+c by 2, which gives, for even or odd ds d/2 and d-(d/2), so for 8^5 I can calculate 8^2 * 8^3. So my (defective) method, which always cut's off the divisor on the fly looks like that: def powMod (b: Long, pot: Int, mod: Long) : Long = { if (pot == 1) b % mod else { val pot2 = pot/2 val pm1 = powMod (b, pot, mod) val pm2 = powMod (b, pot-pot2, mod) (pm1 * pm2) % mod } } and feeded with some values, powMod (55170, 5606, 3043839241L) res2: Long = 1885539617 powMod (55172, 5606, 3043839241L) res4: Long = 309288627 As we can see, the second result is exactly the same as the one above, but the first one looks quiet different. I'm doing a lot of such calculations, and they seem to be accurate as long as they stay in the range of Int, but I can't see any error. Using a BigInt works as well, but is way too slow: def calc2 (n: Int, pri: Long) = { val p: BigInt = pri val p3 = p * p val p1 = (p-1).pow (n) % (p3) val p2 = (p+1).pow (n) % (p3) print ("p1: " + p1 + " p2: " + p2) } calc2 (5606, 55171) p1: 2734550616 p2: 309288627 (same result as with bc) Can somebody see the error in powMod?

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• C program - Seg fault, cause of

  - by resonant_fractal

  Running this gives me a seg fault (gcc filename.c -lm), when i enter 6 (int) as a value. Please help me get my head around this. The intended functionality has not yet been implemented, but I need to know why I'm headed into seg faults already. Thanks! #include<stdio.h> #include<math.h> int main (void) { int l = 5; int n, i, tmp, index; char * s[] = {"Sheldon", "Leonard", "Penny", "Raj", "Howard"}; scanf("%d", &n); //Solve Sigma(Ai*2^(i-1)) = (n - k)/l if (n/l <= 1) printf("%s\n", s[n-1]); else { tmp = n; for (i = 1;;) { tmp = tmp - (l * pow(2,i-1)); if (tmp <= 5) { // printf("Breaking\n"); break; } ++i; } printf("Last index = %d\n", i); // ***NOTE*** //Value lies in next array, therefore ++i; index = tmp + pow(2, n-1); printf("%d\n", index); } return 0; }

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• I just learned about C++ functions, can i use if statements onto functions?

  - by Sagistic

  What I am confused on is about the isNumPalindrome() function. It returns a boolean value of either true or false. How am I suppose to use that so I can display if its a palindrome or not. For ex. If (isNumPalindrome = true) cout "Your number is a palindrome" else "your number is not a palindrome." #include "stdafx.h" int _tmain(int argc, _TCHAR* argv[]) { return 0; } #include <iostream> #include <cmath> using namespace std; int askNumber(); bool isNumPalindrome(); int num, pwr; int main() { askNumber(); isNumPalindrome(); return 0; } bool isNumPalindrome() { int pwr = 0; if (num < 10) return true; else { while (num / static_cast<int>(pow(10.0, pwr)) >=10) pwr++; while (num >=10) { int tenTopwr = static_cast<int>(pow(10.0, pwr)); if ((num / tenTopwr) != (num% 10)) return false; else { num = num % tenTopwr; num = num / 10; pwr = pwr-2; } } return true; } } int askNumber() { cout << "Enter an integer in order to determine if it is a palindrome: " ; cin >> num; cout << endl; return num; }

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• Calculating distance between two X,Y coordinates

  - by Umopepisdn

  I am writing a tool for a game that involves calculating the distance between two coordinates on a spherical plane 500 units across. That is, [0,0] through [499,499] are valid coordinates, and [0,0] and [499,499] are also right next to each other. Currently, in my application, I am comparing the distance between a city with an [X,Y] location respective to the user's own [X,Y] location, which they have configured in advance. To do this, I found this algorithm, which kind of works: Math.sqrt ( dx * dx + dy * dy ); Because sorting a paged list by distance is a useful thing to be able to do, I implemented this algorithm in a MySQL query and have made it available to my application using the following part of my SELECT statement: SQRT( POW( ( ".strval($sourceX)." - cityX ) , 2 ) + POW( ( ".strval($sourceY)." - cityY ) , 2 ) ) AS distance This works fine for many calculations, but does not take into account the fact that [0,0] and [499,499] are kitty-corner to one another. Is there any way I can tweak this algorithm to generate an accurate distance, given that 0 and 499 are adjacent? Thanks, -Umo

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• Factorising program not working. Help required.

  - by Ender

  I am working on a factorisation problem using Fermat's Factorization and for small numbers it is working well. I've been able to calculate the factors (getting the answers from Wolfram Alpha) for small numbers, like the one on the Wikipedia page (5959). Just when I thought I had the problem licked I soon realised that my program was not working when it came to larger numbers. The program follows through the examples from the Wikipedia page, printing out the values a, b, a2 and b2; the results printed for large numbers are not correct. I've followed the pseudocode provided on the Wikipedia page, but am struggling to understand where to go next. Along with the Wikipedia page I have been following this guide. Once again, as my Math knowledge is pretty poor I cannot follow what I need to do next. The code I am using so far is as follows: import java.math.BigInteger; /** * * @author AlexT */ public class Fermat { private BigInteger a, b; private BigInteger b2; private static final BigInteger TWO = BigInteger.valueOf(2); public void fermat(BigInteger N) { // floor(sqrt(N)) BigInteger tmp = getIntSqrt(N); // a <- ceil(sqrt(N)) a = tmp.add(BigInteger.ONE); // b2 <- a*a-N b2 = (a.multiply(a)).subtract(N); final int bitLength = N.bitLength(); BigInteger root = BigInteger.ONE.shiftLeft(bitLength / 2); root = root.add(b2.divide(root)).divide(TWO); // while b2 not square root while(!(isSqrt(b2, root))) { // a <- a + 1 a = a.add(BigInteger.ONE); // b2 <- (a * a) - N b2 = (a.multiply(a)).subtract(N); root = root.add(b2.divide(root)).divide(TWO); } b = getIntSqrt(b2); BigInteger a2 = a.pow(2); // Wrong BigInteger sum = (a.subtract(b)).multiply((a.add(b))); //if(sum.compareTo(N) == 0) { System.out.println("A: " + a + "\nB: " + b); System.out.println("A^2: " + a2 + "\nB^2: " + b2); //} } /** * Is the number provided a perfect Square Root? * @param n * @param root * @return */ private static boolean isSqrt(BigInteger n, BigInteger root) { final BigInteger lowerBound = root.pow(2); final BigInteger upperBound = root.add(BigInteger.ONE).pow(2); return lowerBound.compareTo(n) <= 0 && n.compareTo(upperBound) < 0; } public BigInteger getIntSqrt(BigInteger x) { // It returns s where s^2 < x < (s+1)^2 BigInteger s; // final result BigInteger currentRes = BigInteger.valueOf(0); // init value is 0 BigInteger currentSum = BigInteger.valueOf(0); // init value is 0 BigInteger sum = BigInteger.valueOf(0); String xS = x.toString(); // change input x to a string xS int lengthOfxS = xS.length(); int currentTwoBits; int i=0; // index if(lengthOfxS % 2 != 0) {// if odd length, add a dummy bit xS = "0".concat(xS); // add 0 to the front of string xS lengthOfxS++; } while(i < lengthOfxS){ // go through xS two by two, left to right currentTwoBits = Integer.valueOf(xS.substring(i,i+2)); i += 2; // sum = currentSum*100 + currentTwoBits sum = currentSum.multiply(BigInteger.valueOf(100)); sum = sum.add(BigInteger.valueOf(currentTwoBits)); // subtraction loop do { currentSum = sum; // remember the value before subtract // in next 3 lines, we work out // currentRes = sum - 2*currentRes - 1 sum = sum.subtract(currentRes); // currentRes++ currentRes = currentRes.add(BigInteger.valueOf(1)); sum = sum.subtract(currentRes); } while(sum.compareTo(BigInteger.valueOf(0)) >= 0); // the loop stops when sum < 0 // go one step back currentRes = currentRes.subtract(BigInteger.valueOf(1)); currentRes = currentRes.multiply(BigInteger.valueOf(10)); } s = currentRes.divide(BigInteger.valueOf(10)); // go one step back return s; } /** * @param args the command line arguments */ public static void main(String[] args) { Fermat fermat = new Fermat(); //Works //fermat.fermat(new BigInteger("5959")); // Doesn't Work fermat.fermat(new BigInteger("90283")); } } If anyone can help me out with this problem I'll be eternally grateful.

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• Normal maps red in OpenGL?

  - by KaiserJohaan

  I am using Assimp to import 3d models, and FreeImage to parse textures. The problem I am having is that the normal maps are actually red rather than blue when I try to render them as normal diffuse textures. http://i42.tinypic.com/289ing3.png When I open the images in a image-viewing program they do indeed show up as blue. Heres when I create the texture; OpenGLTexture::OpenGLTexture(const std::vector<uint8_t>& textureData, uint32_t textureWidth, uint32_t textureHeight, TextureType textureType, Logger& logger) : mLogger(logger), mTextureID(gNextTextureID++), mTextureType(textureType) { glGenTextures(1, &mTexture); CHECK_GL_ERROR(mLogger); glBindTexture(GL_TEXTURE_2D, mTexture); CHECK_GL_ERROR(mLogger); glTexImage2D(GL_TEXTURE_2D, 0, GL_RGBA, textureWidth, textureHeight, 0, glTextureFormat, GL_UNSIGNED_BYTE, &textureData[0]); CHECK_GL_ERROR(mLogger); glGenerateMipmap(GL_TEXTURE_2D); CHECK_GL_ERROR(mLogger); glBindTexture(GL_TEXTURE_2D, 0); CHECK_GL_ERROR(mLogger); } Here is my fragment shader. You can see I just commented out the normal-map parsing and treated the normal map texture as the diffuse texture to display it and illustrate the problem. As for the rest of the code it interacts as expected with the diffuse textures so I dont see a obvious problem there. "#version 330 \n \ \n \ layout(std140) uniform; \n \ \n \ const int MAX_LIGHTS = 8; \n \ \n \ struct Light \n \ { \n \ vec4 mLightColor; \n \ vec4 mLightPosition; \n \ vec4 mLightDirection; \n \ \n \ int mLightType; \n \ float mLightIntensity; \n \ float mLightRadius; \n \ float mMaxDistance; \n \ }; \n \ \n \ uniform UnifLighting \n \ { \n \ vec4 mGamma; \n \ vec3 mViewDirection; \n \ int mNumLights; \n \ \n \ Light mLights[MAX_LIGHTS]; \n \ } Lighting; \n \ \n \ uniform UnifMaterial \n \ { \n \ vec4 mDiffuseColor; \n \ vec4 mAmbientColor; \n \ vec4 mSpecularColor; \n \ vec4 mEmissiveColor; \n \ \n \ bool mHasDiffuseTexture; \n \ bool mHasNormalTexture; \n \ bool mLightingEnabled; \n \ float mSpecularShininess; \n \ } Material; \n \ \n \ uniform sampler2D unifDiffuseTexture; \n \ uniform sampler2D unifNormalTexture; \n \ \n \ in vec3 frag_position; \n \ in vec3 frag_normal; \n \ in vec2 frag_texcoord; \n \ in vec3 frag_tangent; \n \ in vec3 frag_bitangent; \n \ \n \ out vec4 finalColor; " " \n \ \n \ void CalcGaussianSpecular(in vec3 dirToLight, in vec3 normal, out float gaussianTerm) \n \ { \n \ vec3 viewDirection = normalize(Lighting.mViewDirection); \n \ vec3 halfAngle = normalize(dirToLight + viewDirection); \n \ \n \ float angleNormalHalf = acos(dot(halfAngle, normalize(normal))); \n \ float exponent = angleNormalHalf / Material.mSpecularShininess; \n \ exponent = -(exponent * exponent); \n \ \n \ gaussianTerm = exp(exponent); \n \ } \n \ \n \ vec4 CalculateLighting(in Light light, in vec4 diffuseTexture, in vec3 normal) \n \ { \n \ if (light.mLightType == 1) // point light \n \ { \n \ vec3 positionDiff = light.mLightPosition.xyz - frag_position; \n \ float dist = max(length(positionDiff) - light.mLightRadius, 0); \n \ \n \ float attenuation = 1 / ((dist/light.mLightRadius + 1) * (dist/light.mLightRadius + 1)); \n \ attenuation = max((attenuation - light.mMaxDistance) / (1 - light.mMaxDistance), 0); \n \ \n \ vec3 dirToLight = normalize(positionDiff); \n \ float angleNormal = clamp(dot(normalize(normal), dirToLight), 0, 1); \n \ \n \ float gaussianTerm = 0.0; \n \ if (angleNormal > 0.0) \n \ CalcGaussianSpecular(dirToLight, normal, gaussianTerm); \n \ \n \ return diffuseTexture * (attenuation * angleNormal * Material.mDiffuseColor * light.mLightIntensity * light.mLightColor) + \n \ (attenuation * gaussianTerm * Material.mSpecularColor * light.mLightIntensity * light.mLightColor); \n \ } \n \ else if (light.mLightType == 2) // directional light \n \ { \n \ vec3 dirToLight = normalize(light.mLightDirection.xyz); \n \ float angleNormal = clamp(dot(normalize(normal), dirToLight), 0, 1); \n \ \n \ float gaussianTerm = 0.0; \n \ if (angleNormal > 0.0) \n \ CalcGaussianSpecular(dirToLight, normal, gaussianTerm); \n \ \n \ return diffuseTexture * (angleNormal * Material.mDiffuseColor * light.mLightIntensity * light.mLightColor) + \n \ (gaussianTerm * Material.mSpecularColor * light.mLightIntensity * light.mLightColor); \n \ } \n \ else if (light.mLightType == 4) // ambient light \n \ return diffuseTexture * Material.mAmbientColor * light.mLightIntensity * light.mLightColor; \n \ else \n \ return vec4(0.0); \n \ } \n \ \n \ void main() \n \ { \n \ vec4 diffuseTexture = vec4(1.0); \n \ if (Material.mHasDiffuseTexture) \n \ diffuseTexture = texture(unifDiffuseTexture, frag_texcoord); \n \ \n \ vec3 normal = frag_normal; \n \ if (Material.mHasNormalTexture) \n \ { \n \ diffuseTexture = vec4(normalize(texture(unifNormalTexture, frag_texcoord).xyz * 2.0 - 1.0), 1.0); \n \ // vec3 normalTangentSpace = normalize(texture(unifNormalTexture, frag_texcoord).xyz * 2.0 - 1.0); \n \ //mat3 tangentToWorldSpace = mat3(normalize(frag_tangent), normalize(frag_bitangent), normalize(frag_normal)); \n \ \n \ // normal = tangentToWorldSpace * normalTangentSpace; \n \ } \n \ \n \ if (Material.mLightingEnabled) \n \ { \n \ vec4 accumLighting = vec4(0.0); \n \ \n \ for (int lightIndex = 0; lightIndex < Lighting.mNumLights; lightIndex++) \n \ accumLighting += Material.mEmissiveColor * diffuseTexture + \n \ CalculateLighting(Lighting.mLights[lightIndex], diffuseTexture, normal); \n \ \n \ finalColor = pow(accumLighting, Lighting.mGamma); \n \ } \n \ else { \n \ finalColor = pow(diffuseTexture, Lighting.mGamma); \n \ } \n \ } \n"; Why is this? does normal-map textures need some sort of special treatment in opengl?

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• Extreme Optimization – Numerical Algorithm Support

  - by JoshReuben

  Function Delegates Many calculations involve the repeated evaluation of one or more user-supplied functions eg Numerical integration. The EO MathLib provides delegate types for common function signatures and the FunctionFactory class can generate new delegates from existing ones. RealFunction delegate - takes one Double parameter – can encapsulate most of the static methods of the System.Math class, as well as the classes in the Extreme.Mathematics.SpecialFunctions namespace: var sin = new RealFunction(Math.Sin); var result = sin(1); BivariateRealFunction delegate - takes two Double parameters: var atan2 = new BivariateRealFunction (Math.Atan2); var result = atan2(1, 2); TrivariateRealFunction delegate – represents a function takes three Double arguments ParameterizedRealFunction delegate - represents a function taking one Integer and one Double argument that returns a real number. The Pow method implements such a function, but the arguments need order re-arrangement: static double Power(int exponent, double x) { return ElementaryFunctions.Pow(x, exponent); } ... var power = new ParameterizedRealFunction(Power); var result = power(6, 3.2); A ComplexFunction delegate - represents a function that takes an Extreme.Mathematics.DoubleComplex argument and also returns a complex number. MultivariateRealFunction delegate - represents a function that takes an Extreme.Mathematics.LinearAlgebra.Vector argument and returns a real number. MultivariateVectorFunction delegate - represents a function that takes a Vector argument and returns a Vector. FastMultivariateVectorFunction delegate - represents a function that takes an input Vector argument and an output Matrix argument – avoiding object construction  The FunctionFactory class RealFromBivariateRealFunction and RealFromParameterizedRealFunction helper methods - transform BivariateRealFunction or a ParameterizedRealFunction into a RealFunction delegate by fixing one of the arguments, and treating this as a new function of a single argument. var tenthPower = FunctionFactory.RealFromParameterizedRealFunction(power, 10); var result = tenthPower(x); Note: There is no direct way to do this programmatically in C# - in F# you have partial value functions where you supply a subset of the arguments (as a travelling closure) that the function expects. When you omit arguments, F# generates a new function that holds onto/remembers the arguments you passed in and "waits" for the other parameters to be supplied. let sumVals x y = x + y     let sumX = sumVals 10     // Note: no 2nd param supplied.     // sumX is a new function generated from partially applied sumVals.     // ie "sumX is a partial application of sumVals." let sum = sumX 20     // Invokes sumX, passing in expected int (parameter y from original)  val sumVals : int -> int -> int val sumX : (int -> int) val sum : int = 30 RealFunctionsToVectorFunction and RealFunctionsToFastVectorFunction helper methods - combines an array of delegates returning a real number or a vector into vector or matrix functions. The resulting vector function returns a vector whose components are the function values of the delegates in the array. var funcVector = FunctionFactory.RealFunctionsToVectorFunction(     new MultivariateRealFunction(myFunc1),     new MultivariateRealFunction(myFunc2));  The IterativeAlgorithm<T> abstract base class Iterative algorithms are common in numerical computing - a method is executed repeatedly until a certain condition is reached, approximating the result of a calculation with increasing accuracy until a certain threshold is reached. If the desired accuracy is achieved, the algorithm is said to converge. This base class is derived by many classes in the Extreme.Mathematics.EquationSolvers and Extreme.Mathematics.Optimization namespaces, as well as the ManagedIterativeAlgorithm class which contains a driver method that manages the iteration process.  The ConvergenceTest abstract base class This class is used to specify algorithm Termination , convergence and results - calculates an estimate for the error, and signals termination of the algorithm when the error is below a specified tolerance. Termination Criteria - specify the success condition as the difference between some quantity and its actual value is within a certain tolerance – 2 ways: absolute error - difference between the result and the actual value. relative error is the difference between the result and the actual value relative to the size of the result. Tolerance property - specify trade-off between accuracy and execution time. The lower the tolerance, the longer it will take for the algorithm to obtain a result within that tolerance. Most algorithms in the EO NumLib have a default value of MachineConstants.SqrtEpsilon - gives slightly less than 8 digits of accuracy. ConvergenceCriterion property - specify under what condition the algorithm is assumed to converge. Using the ConvergenceCriterion enum: WithinAbsoluteTolerance / WithinRelativeTolerance / WithinAnyTolerance / NumberOfIterations Active property - selectively ignore certain convergence tests Error property - returns the estimated error after a run MaxIterations / MaxEvaluations properties - Other Termination Criteria - If the algorithm cannot achieve the desired accuracy, the algorithm still has to end – according to an absolute boundary. Status property - indicates how the algorithm terminated - the AlgorithmStatus enum values:NoResult / Busy / Converged (ended normally - The desired accuracy has been achieved) / IterationLimitExceeded / EvaluationLimitExceeded / RoundOffError / BadFunction / Divergent / ConvergedToFalseSolution. After the iteration terminates, the Status should be inspected to verify that the algorithm terminated normally. Alternatively, you can set the ThrowExceptionOnFailure to true. Result property - returns the result of the algorithm. This property contains the best available estimate, even if the desired accuracy was not obtained. IterationsNeeded / EvaluationsNeeded properties - returns the number of iterations required to obtain the result, number of function evaluations.  Concrete Types of Convergence Test classes SimpleConvergenceTest class - test if a value is close to zero or very small compared to another value. VectorConvergenceTest class - test convergence of vectors. This class has two additional properties. The Norm property specifies which norm is to be used when calculating the size of the vector - the VectorConvergenceNorm enum values: EuclidianNorm / Maximum / SumOfAbsoluteValues. The ErrorMeasure property specifies how the error is to be measured – VectorConvergenceErrorMeasure enum values: Norm / Componentwise ConvergenceTestCollection class - represent a combination of tests. The Quantifier property is a ConvergenceTestQuantifier enum that specifies how the tests in the collection are to be combined: Any / All  The AlgorithmHelper Class inherits from IterativeAlgorithm<T> and exposes two methods for convergence testing. IsValueWithinTolerance<T> method - determines whether a value is close to another value to within an algorithm's requested tolerance. IsIntervalWithinTolerance<T> method - determines whether an interval is within an algorithm's requested tolerance.

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• How to display all methods in a JavaScript object?

  - by GeekTantra

  I wanted a way in which I could get all methods available in a Javascript Object like following alert( show_all_methods( Math ) ); should alert abs, acos, asin, atan, atan2, ceil, cos, exp, floor, log, max, min, pow, random,round, sin, sqrt, tan.

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• Are there any working implementations of the rolling hash function used in the Rabin-Karp string sea

  - by c14ppy

  I'm looking to use a rolling hash function so I can take hashes of n-grams of a very large string. For example: "stackoverflow", broken up into 5 grams would be: "stack", "tacko", "ackov", "ckove", "kover", "overf", "verfl", "erflo", "rflow" This is ideal for a rolling hash function because after I calculate the first n-gram hash, the following ones are relatively cheap to calculate because I simply have to drop the first letter of the first hash and add the new last letter of the second hash. I know that in general this hash function is generated as: H = c1ak - 1 + c2ak - 2 + c3ak - 3 + ... + cka0 where a is a constant and c1,...,ck are the input characters. If you follow this link on the Rabin-Karp string search algorithm , it states that "a" is usually some large prime. I want my hashes to be stored in 32 bit integers, so how large of a prime should "a" be, such that I don't overflow my integer? Does there exist an existing implementation of this hash function somewhere that I could already use? Here is an implementation I created: public class hash2 { public int prime = 101; public int hash(String text) { int hash = 0; for(int i = 0; i < text.length(); i++) { char c = text.charAt(i); hash += c * (int) (Math.pow(prime, text.length() - 1 - i)); } return hash; } public int rollHash(int previousHash, String previousText, String currentText) { char firstChar = previousText.charAt(0); char lastChar = currentText.charAt(currentText.length() - 1); int firstCharHash = firstChar * (int) (Math.pow(prime, previousText.length() - 1)); int hash = (previousHash - firstCharHash) * prime + lastChar; return hash; } public static void main(String[] args) { hash2 hashify = new hash2(); int firstHash = hashify.hash("mydog"); System.out.println(firstHash); System.out.println(hashify.hash("ydogr")); System.out.println(hashify.rollHash(firstHash, "mydog", "ydogr")); } } I'm using 101 as my prime. Does it matter if my hashes will overflow? I think this is desirable but I'm not sure. Does this seem like the right way to go about this?

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• Calculating the square of BigInteger

  - by brickner

  Hi, I'm using .NET 4's System.Numerics.BigInteger structure. I need to calculate the square (x^2) of very large numbers. If x is a BigInteger, What is the time complexity of: x*x; or BigInteger.Pow(x,2); ? If it's worse than O(n^2), do you have a better implementation? Maybe something like Schönhage–Strassen algorithm?

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• Using scipy.interpolate.splrep function

  - by Koustav Ghosal

  I am trying to fit a cubic spline to a given set of points. My points are not ordered. I CANNOT sort or reorder the points, since I need that information. But since the function scipy.interpolate.splrep works only on non-duplicate and monotonically increasing points I have defined a function that maps the x-coordinates to a monotonically increasing space. My old points are: xpoints=[4913.0, 4912.0, 4914.0, 4913.0, 4913.0, 4913.0, 4914.0, 4915.0, 4918.0, 4921.0, 4925.0, 4932.0, 4938.0, 4945.0, 4950.0, 4954.0, 4955.0, 4957.0, 4956.0, 4953.0, 4949.0, 4943.0, 4933.0, 4921.0, 4911.0, 4898.0, 4886.0, 4874.0, 4865.0, 4858.0, 4853.0, 4849.0, 4848.0, 4849.0, 4851.0, 4858.0, 4864.0, 4869.0, 4877.0, 4884.0, 4893.0, 4903.0, 4913.0, 4923.0, 4935.0, 4947.0, 4959.0, 4970.0, 4981.0, 4991.0, 5000.0, 5005.0, 5010.0, 5015.0, 5019.0, 5020.0, 5021.0, 5023.0, 5025.0, 5027.0, 5027.0, 5028.0, 5028.0, 5030.0, 5031.0, 5033.0, 5035.0, 5037.0, 5040.0, 5043.0] ypoints=[10557.0, 10563.0, 10567.0, 10571.0, 10575.0, 10577.0, 10578.0, 10581.0, 10582.0, 10582.0, 10582.0, 10581.0, 10578.0, 10576.0, 10572.0, 10567.0, 10560.0, 10550.0, 10541.0, 10531.0, 10520.0, 10511.0, 10503.0, 10496.0, 10490.0, 10487.0, 10488.0, 10488.0, 10490.0, 10495.0, 10504.0, 10513.0, 10523.0, 10533.0, 10542.0, 10550.0, 10556.0, 10559.0, 10560.0, 10559.0, 10555.0, 10550.0, 10543.0, 10533.0, 10522.0, 10514.0, 10505.0, 10496.0, 10490.0, 10486.0, 10482.0, 10481.0, 10482.0, 10486.0, 10491.0, 10497.0, 10506.0, 10516.0, 10524.0, 10534.0, 10544.0, 10552.0, 10558.0, 10564.0, 10569.0, 10573.0, 10576.0, 10578.0, 10581.0, 10582.0] Plots: The code for the mapping function and interpolation is: xnew=[] ynew=ypoints for c3,i in enumerate(xpoints): if np.isfinite(np.log(i*pow(2,c3))): xnew.append(np.log(i*pow(2,c3))) else: if c==0: xnew.append(np.random.random_sample()) else: xnew.append(xnew[c3-1]+np.random.random_sample()) xnew=np.asarray(xnew) ynew=np.asarray(ynew) constant1=10.0 nknots=len(xnew)/constant1 idx_knots = (np.arange(1,len(xnew)-1,(len(xnew)-2)/np.double(nknots))).astype('int') knots = [xnew[i] for i in idx_knots] knots = np.asarray(knots) int_range=np.linspace(min(xnew),max(xnew),len(xnew)) tck = interpolate.splrep(xnew,ynew,k=3,task=-1,t=knots) y1= interpolate.splev(int_range,tck,der=0) The code is throwing an error at the function interpolate.splrep() for some set of points like the above one. The error is: File "/home/neeraj/Desktop/koustav/res/BOS5/fit_spline3.py", line 58, in save_spline_f tck = interpolate.splrep(xnew,ynew,k=3,task=-1,t=knots) File "/usr/lib/python2.7/dist-packages/scipy/interpolate/fitpack.py", line 465, in splrep raise _iermessier(_iermess[ier][0]) ValueError: Error on input data But for other set of points it works fine. For example for the following set of points. xpoints=[1629.0, 1629.0, 1629.0, 1629.0, 1629.0, 1629.0, 1629.0, 1629.0, 1629.0, 1629.0, 1629.0, 1629.0, 1629.0, 1629.0, 1629.0, 1629.0, 1630.0, 1630.0, 1630.0, 1631.0, 1631.0, 1631.0, 1631.0, 1630.0, 1629.0, 1629.0, 1629.0, 1628.0, 1627.0, 1627.0, 1625.0, 1624.0, 1624.0, 1623.0, 1620.0, 1618.0, 1617.0, 1616.0, 1615.0, 1614.0, 1614.0, 1612.0, 1612.0, 1612.0, 1611.0, 1610.0, 1609.0, 1608.0, 1607.0, 1607.0, 1603.0, 1602.0, 1602.0, 1601.0, 1601.0, 1600.0, 1599.0, 1598.0] ypoints=[10570.0, 10572.0, 10572.0, 10573.0, 10572.0, 10572.0, 10571.0, 10570.0, 10569.0, 10565.0, 10564.0, 10563.0, 10562.0, 10560.0, 10558.0, 10556.0, 10554.0, 10551.0, 10548.0, 10547.0, 10544.0, 10542.0, 10541.0, 10538.0, 10534.0, 10532.0, 10531.0, 10528.0, 10525.0, 10522.0, 10519.0, 10517.0, 10516.0, 10512.0, 10509.0, 10509.0, 10507.0, 10504.0, 10502.0, 10500.0, 10501.0, 10499.0, 10498.0, 10496.0, 10491.0, 10492.0, 10488.0, 10488.0, 10488.0, 10486.0, 10486.0, 10485.0, 10485.0, 10486.0, 10483.0, 10483.0, 10482.0, 10480.0] Plots: Can anybody suggest what's happening ?? Thanks in advance......

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• Resultant of a polynomial with x^n–1

  - by devin.omalley

  Resultant of a polynomial with x^n–1 (mod p) I am implementing the NTRUSign algorithm as described in http://grouper.ieee.org/groups/1363/lattPK/submissions/EESS1v2.pdf , section 2.2.7.1 which involves computing the resultant of a polynomial. I keep getting a zero vector for the resultant which is obviously incorrect. private static CompResResult compResMod(IntegerPolynomial f, int p) { int N = f.coeffs.length; IntegerPolynomial a = new IntegerPolynomial(N); a.coeffs[0] = -1; a.coeffs[N-1] = 1; IntegerPolynomial b = new IntegerPolynomial(f.coeffs); IntegerPolynomial v1 = new IntegerPolynomial(N); IntegerPolynomial v2 = new IntegerPolynomial(N); v2.coeffs[0] = 1; int da = a.degree(); int db = b.degree(); int ta = da; int c = 0; int r = 1; while (db > 0) { c = invert(b.coeffs[db], p); c = (c * a.coeffs[da]) % p; IntegerPolynomial cb = b.clone(); cb.mult(c); cb.shift(da - db); a.sub(cb, p); IntegerPolynomial v2c = v2.clone(); v2c.mult(c); v2c.shift(da - db); v1.sub(v2c, p); if (a.degree() < db) { r *= (int)Math.pow(b.coeffs[db], ta-a.degree()); r %= p; if (ta%2==1 && db%2==1) r = (-r) % p; IntegerPolynomial temp = a; a = b; b = temp; temp = v1; v1 = v2; v2 = temp; ta = db; } da = a.degree(); db = b.degree(); } r *= (int)Math.pow(b.coeffs[0], da); r %= p; c = invert(b.coeffs[0], p); v2.mult(c); v2.mult(r); v2.mod(p); return new CompResResult(v2, r); } There is pseudocode in http://www.crypto.rub.de/imperia/md/content/texte/theses/da_driessen.pdf which looks very similar. Why is my code not working? Are there any intermediate results I can check? I am not posting the IntegerPolynomial code because it isn't too interesting and I have unit tests for it that pass. CompResResult is just a simple "Java struct".

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• Miller-rabin exception number?

  - by nightcracker

  Hey everyone. This question is about the number 169716931325235658326303. According to http://www.alpertron.com.ar/ECM.HTM it is prime. According to my miller-rabin implementation in python with 7 repetitions is is composite. With 50 repetitions it is still composite. With 5000 repetitions it is STILL composite. I thought, this might be a problem of my implementation. So I tried GNU MP bignum library, which has a miller-rabin primality test built-in. I tested with 1000000 repetitions. Still composite. This is my implementation of the miller-rabin primality test: def isprime(n, precision=7): if n == 1 or n % 2 == 0: return False elif n < 1: raise ValueError("Out of bounds, first argument must be > 0") d = n - 1 s = 0 while d % 2 == 0: d //= 2 s += 1 for repeat in range(precision): a = random.randrange(2, n - 2) x = pow(a, d, n) if x == 1 or x == n - 1: continue for r in range(s - 1): x = pow(x, 2, n) if x == 1: return False if x == n - 1: break else: return False return True And the code for the GMP test: #include <gmp.h> #include <stdio.h> int main(int argc, char* argv[]) { mpz_t test; mpz_init_set_str(test, "169716931325235658326303", 10); printf("%d\n", mpz_probab_prime_p(test, 1000000)); mpz_clear(test); return 0; } As far as I know there are no "exceptions" (which return false positives for any amount of repetitions) to the miller-rabin primality test. Have I stumpled upon one? Is my computer broken? Is the Elliptic Curve Method wrong? What is happening here? EDIT I found the issue, which is http://www.alpertron.com.ar/ECM.HTM. I trusted this applet, I'll contact the author his applet's implementation of the ECM is faulty for this number. Thanks. EDIT2 Hah, the shame! In the end it was something that went wrong with copy/pasting on my side. NOR the applet NOR the miller-rabin algorithm NOR my implementation NOR gmp's implementation of it is wrong, the only thing that's wrong is me. I'm sorry.

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