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  1. #include <iomanip>
  2. #include <iostream>
  3. #include <math.h>
  4. #include <stdlib.h>
  5. #include <time.h>
  6.  
  7. using namespace std;
  8.  
  9. enum subtractionMethod { REGULAR_SUBTRACTION, SHIFTED_SUBTRACTION, ARITHMETIC_CONJUGATE };
  10. double subtract(double& x, double& y, subtractionMethod theMethod)
  11. {
  12. 	//check for theMethod
  13. 	switch (theMethod)
  14. 	{
  15. 		case REGULAR_SUBTRACTION:
  16. 			return (x-y);
  17. 		case SHIFTED_SUBTRACTION:
  18. 		{
  19. 			//we will lose -log2(1-y/x) bits of precision
  20. 			int bitsLost = (int)ceil(-1*log2(1-y/x));
  21. 			int scaleFactor = (int)(pow(2,bitsLost));
  22. 			//attempting to multiply both arguments by 2^bitCount, subtract, and divide back
  23. 			return (x*scaleFactor-y*scaleFactor)/scaleFactor;
  24. 		}
  25. 		case ARITHMETIC_CONJUGATE:
  26. 			return (x*x-y*y)/(x+y);
  27. 		default:
  28. 			return 0;	//code should NEVER reach here!!
  29. 	}
  30. }
  31.  
  32. int main() 
  33. {
  34. 	double x = 0, y = 1000000;
  35. 	//seed the random number generator
  36. 	srand(time(0));
  37. 	//generate 2 random numbers between 1 and 1000000
  38. 	x = (double)(rand() % 1000000 + 1);
  39. 	while (y > x)
  40. 		y = (double)(rand() % 1000000 + 1);
  41. 	//divide both numbers by 1E15
  42. 	x /= 1E15;
  43. 	y /= 1E15;
  44. 	//report x and y
  45. 	cout << setprecision(15) << showpoint << fixed;
  46. 	cout << "x == " << x << "\ny == " << y << endl;
  47. 	//attempt to subtract them and print them to screen
  48. 	//first via straight subtraction
  49. 	cout << "x-y by straight subtraction is: " << subtract(x,y,REGULAR_SUBTRACTION) << endl;
  50. 	//next, by bit-shifting
  51. 	cout << "x-y by shifting is :" << subtract(x,y,SHIFTED_SUBTRACTION) << endl;
  52. 	//finally by arithmetic conjugate
  53. 	cout << "x-y by arithmetic conjugate is: " << subtract(x,y,ARITHMETIC_CONJUGATE) << endl;
  54.  
  55. 	return 0;
  56. }
Success #stdin #stdout 0s 3340KB
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stdin
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Standard input is empty
stdout
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x == 0.000000000547883
y == 0.000000000326355
x-y by straight subtraction is: 0.000000000221528
x-y by shifting is :0.000000000221528
x-y by arithmetic conjugate is: 0.000000000221528
https://ideone.com/wfkEUp
language:
C++ (gcc 8.3)
created:
10 years ago
visibility:
public

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