e_atanh.c 1.9 KB

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  1. /* @(#)e_atanh.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: e_atanh.c,v 1.8 1995/05/10 20:44:55 jtc Exp $";
  14. #endif
  15. /* __ieee754_atanh(x)
  16. * Method :
  17. * 1.Reduced x to positive by atanh(-x) = -atanh(x)
  18. * 2.For x>=0.5
  19. * 1 2x x
  20. * atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
  21. * 2 1 - x 1 - x
  22. *
  23. * For x<0.5
  24. * atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
  25. *
  26. * Special cases:
  27. * atanh(x) is NaN if |x| > 1 with signal;
  28. * atanh(NaN) is that NaN with no signal;
  29. * atanh(+-1) is +-INF with signal.
  30. *
  31. */
  32. #include "math.h"
  33. #include "math_private.h"
  34. libm_hidden_proto(log1p)
  35. #ifdef __STDC__
  36. static const double one = 1.0, huge = 1e300;
  37. #else
  38. static double one = 1.0, huge = 1e300;
  39. #endif
  40. #ifdef __STDC__
  41. static const double zero = 0.0;
  42. #else
  43. static double zero = 0.0;
  44. #endif
  45. #ifdef __STDC__
  46. double attribute_hidden __ieee754_atanh(double x)
  47. #else
  48. double attribute_hidden __ieee754_atanh(x)
  49. double x;
  50. #endif
  51. {
  52. double t;
  53. int32_t hx,ix;
  54. u_int32_t lx;
  55. EXTRACT_WORDS(hx,lx,x);
  56. ix = hx&0x7fffffff;
  57. if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */
  58. return (x-x)/(x-x);
  59. if(ix==0x3ff00000)
  60. return x/zero;
  61. if(ix<0x3e300000&&(huge+x)>zero) return x; /* x<2**-28 */
  62. SET_HIGH_WORD(x,ix);
  63. if(ix<0x3fe00000) { /* x < 0.5 */
  64. t = x+x;
  65. t = 0.5*log1p(t+t*x/(one-x));
  66. } else
  67. t = 0.5*log1p((x+x)/(one-x));
  68. if(hx>=0) return t; else return -t;
  69. }