1 | |
---|

2 | /* @(#)s_asinh.c 5.1 93/09/24 */ |
---|

3 | /* |
---|

4 | * ==================================================== |
---|

5 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
---|

6 | * |
---|

7 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
---|

8 | * Permission to use, copy, modify, and distribute this |
---|

9 | * software is freely granted, provided that this notice |
---|

10 | * is preserved. |
---|

11 | * ==================================================== |
---|

12 | */ |
---|

13 | |
---|

14 | /* asinh(x) |
---|

15 | * Method : |
---|

16 | * Based on |
---|

17 | * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ] |
---|

18 | * we have |
---|

19 | * asinh(x) := x if 1+x*x=1, |
---|

20 | * := sign(x)*(log(x)+ln2)) for large |x|, else |
---|

21 | * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else |
---|

22 | * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2))) |
---|

23 | */ |
---|

24 | |
---|

25 | #include <libm/fdlibm.h> |
---|

26 | |
---|

27 | #ifdef __STDC__ |
---|

28 | static const double |
---|

29 | #else |
---|

30 | static double |
---|

31 | #endif |
---|

32 | one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ |
---|

33 | ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ |
---|

34 | huge= 1.00000000000000000000e+300; |
---|

35 | |
---|

36 | #ifdef __STDC__ |
---|

37 | double asinh(double x) |
---|

38 | #else |
---|

39 | double asinh(x) |
---|

40 | double x; |
---|

41 | #endif |
---|

42 | { |
---|

43 | double t,w; |
---|

44 | int n0,hx,ix; |
---|

45 | n0 = ((*(int*)&one)>>29)^1; |
---|

46 | hx = *(n0+(int*)&x); |
---|

47 | ix = hx&0x7fffffff; |
---|

48 | if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */ |
---|

49 | if(ix< 0x3e300000) { /* |x|<2**-28 */ |
---|

50 | if(huge+x>one) return x; /* return x inexact except 0 */ |
---|

51 | } |
---|

52 | if(ix>0x41b00000) { /* |x| > 2**28 */ |
---|

53 | w = __ieee754_log(fabs(x))+ln2; |
---|

54 | } else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */ |
---|

55 | t = fabs(x); |
---|

56 | w = __ieee754_log(2.0*t+one/(sqrt(x*x+one)+t)); |
---|

57 | } else { /* 2.0 > |x| > 2**-28 */ |
---|

58 | t = x*x; |
---|

59 | w =log1p(fabs(x)+t/(one+sqrt(one+t))); |
---|

60 | } |
---|

61 | if(hx>0) return w; else return -w; |
---|

62 | } |
---|