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  1. #include <stdio.h>
  2. #include <math.h>
  3.  
  4. float sqrt_(float x) {
  5. 	static const float T[7] = { 0.545253866f, 0.594603558f, 0.648419777f, 0.707106781f, 0.771105413f, 0.840896415f, 0.917004043f };
  6. 	static const float C0[2][8] = {
  7. 		{2.075945786f, 1.987932496f, 1.903650680f, 1.822942136f, 1.745655370f, 1.671645309f, 1.600773032f, 1.532905508f },
  8. 		{1.467915343f, 1.405680548f, 1.346084305f, 1.289014746f, 1.234364750f, 1.182031734f, 1.131917466f, 1.083927879f },
  9. 	};
  10. 	static const float C1[2][8] = {
  11. 		{-1.324459632f, -1.163042545f, -1.021297991f, -0.896828402f, -0.787528409f, -0.691549235f, -0.607267419f, -0.533257358f },
  12. 		{-0.936534387f, -0.822395271f, -0.722166735f, -0.634153445f, -0.556866678f, -0.488999154f, -0.429402910f, -0.377069894f },
  13. 	};
  14.  
  15. 	if (x < 0.f) {
  16. 		return NAN;
  17. 	}
  18.  
  19. 	int e;
  20. 	float f = frexpf(x, &e);
  21. 	int e_div_2 = e >> 1;
  22. 	int e_mod_2 = e & 1;
  23. 	int n = 3;
  24. 	int m = 4;
  25. 	for (int i = 0; i < 3; i++) {
  26. 		if (f < T[n]) {
  27. 			m >>= 1;
  28. 			n -= m;
  29. 		}
  30. 		else {
  31. 			m = (m + 1 >> 1);
  32. 			n += m;
  33. 		}
  34. 	}
  35. 	x = C0[e_mod_2][n] + C1[e_mod_2][n] * f;
  36. 	f = ldexpf(f, e_mod_2);
  37. 	x += .5f * x * (1.f - f * x * x);
  38. 	return ldexpf(f * x, e_div_2);
  39. }
  40.  
  41. int main() {
  42. 	float TABLE1[] = { 0.958202441f, 0.99999994f, 1.f };
  43. 	float TABLE2[] = { .5f, 0.545253866f, 0.594603558f, 0.648419777f, 0.707106781f, 0.771105413f, 0.840896415f, 0.917004043f };
  44. 	float TABLE3[] = { 0.125f, 0.25f, 0.5f, 1.f, 2.f, 4.f, 8.f, 16.f, 32.f };
  45. 	for (float x3 : TABLE3) {
  46. 		for (float x2 : TABLE2) {
  47. 			for (float x1 : TABLE1) {
  48. 				float x = x1 * x2 * x3;
  49. 				float y1 = sqrt_(x);
  50. 				float y0 = sqrt(x);
  51. 				printf("%e\n", (double)y1 / (double)y0 - 1.);
  52. 			}
  53. 		}
  54. 	}
  55. 	return 0;
  56. }
  57.  
Success #stdin #stdout 0.01s 5564KB
comments (?)
stdin 
Standard input is empty
stdout 
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https://ideone.com/x29AQb
language:
C++ (gcc 8.3)
created:
3 years ago
visibility:
public

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