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  1. #include <stdio.h>
  2. #include <math.h>
  3.  
  4. #define EPS 1e-6
  5. #define PI 3.14159
  6. static int j_;
  7.  
  8. float taylor_series(float x) {
  9. 	j_ = 1;
  10.  
  11. 	if (fabs(x) < EPS) 
  12. 		return x;
  13.  
  14. 	float w = x * x;
  15. 	float y = x;
  16. 	float z = 1.0;
  17. 	float s = x;
  18.  
  19. 	for ( ; ; ) {
  20. 		y *= -w;
  21. 		z *= ++j_;
  22. 		z *= ++j_;
  23. 		float t = y / z;
  24. 		if (fabs(t) < EPS) break;
  25. 		s += t;
  26. 	}
  27.  
  28. 	return s;
  29. }
  30.  
  31. int main(void) {
  32. 	printf("%f\t", taylor_series(PI * 0.5));
  33. 	printf("%f\t", sin(PI * 0.5));
  34. 	printf("%d\n", j_);
  35. 	printf("%f\t", taylor_series(0.000123));
  36. 	printf("%f\t", sin(0.000123));
  37. 	printf("%d\n", j_);
  38. 	printf("%f\t", taylor_series(PI * 0.25));
  39. 	printf("%f\t", sin(PI * 0.25));
  40. 	printf("%d\n", j_);
  41. 	printf("%f\t", taylor_series(PI * 1.25));
  42. 	printf("%f\t", sin(PI * 1.25));
  43. 	printf("%d\n", j_);
  44. 	printf("%f\t", taylor_series(PI * 2.25));
  45. 	printf("%f\t", sin(PI * 2.25));
  46. 	printf("%d\n", j_);
  47. 	printf("%f\t", taylor_series(PI * 3.25));
  48. 	printf("%f\t", sin(PI * 3.25));
  49. 	printf("%d\n", j_);
  50. 	return 0;
  51. }
  52.  
Success #stdin #stdout 0.01s 5288KB
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stdin
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Standard input is empty
stdout
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1.000000	1.000000	13
0.000123	0.000123	3
0.707106	0.707106	9
-0.707105	-0.707104	21
0.707094	0.707103	29
-0.707314	-0.707101	35
https://ideone.com/fgDpzm
The growth of factorials is much limited in reality
language:
C (gcc 8.3)
created:
13 days ago
visibility:
public

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