s_asinh.c 1.7 KB

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  1. /* @(#)s_asinh.c 5.1 93/09/24 */
  2. /*
  3. * ====================================================
  4. * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
  5. *
  6. * Developed at SunPro, a Sun Microsystems, Inc. business.
  7. * Permission to use, copy, modify, and distribute this
  8. * software is freely granted, provided that this notice
  9. * is preserved.
  10. * ====================================================
  11. */
  12. #if defined(LIBM_SCCS) && !defined(lint)
  13. static char rcsid[] = "$NetBSD: s_asinh.c,v 1.9 1995/05/12 04:57:37 jtc Exp $";
  14. #endif
  15. /* asinh(x)
  16. * Method :
  17. * Based on
  18. * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
  19. * we have
  20. * asinh(x) := x if 1+x*x=1,
  21. * := sign(x)*(log(x)+ln2)) for large |x|, else
  22. * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
  23. * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))
  24. */
  25. #include "math.h"
  26. #include "math_private.h"
  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. #ifdef __STDC__
  36. double asinh(double x)
  37. #else
  38. double asinh(x)
  39. double x;
  40. #endif
  41. {
  42. double t,w;
  43. int32_t hx,ix;
  44. GET_HIGH_WORD(hx,x);
  45. ix = hx&0x7fffffff;
  46. if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */
  47. if(ix< 0x3e300000) { /* |x|<2**-28 */
  48. if(huge+x>one) return x; /* return x inexact except 0 */
  49. }
  50. if(ix>0x41b00000) { /* |x| > 2**28 */
  51. w = __ieee754_log(fabs(x))+ln2;
  52. } else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */
  53. t = fabs(x);
  54. w = __ieee754_log(2.0*t+one/(__ieee754_sqrt(x*x+one)+t));
  55. } else { /* 2.0 > |x| > 2**-28 */
  56. t = x*x;
  57. w =log1p(fabs(x)+t/(one+__ieee754_sqrt(one+t)));
  58. }
  59. if(hx>0) return w; else return -w;
  60. }