e_atanh.c 1.8 KB

123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475
  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. #ifdef __STDC__
  35. static const double one = 1.0, huge = 1e300;
  36. #else
  37. static double one = 1.0, huge = 1e300;
  38. #endif
  39. #ifdef __STDC__
  40. static const double zero = 0.0;
  41. #else
  42. static double zero = 0.0;
  43. #endif
  44. #ifdef __STDC__
  45. double attribute_hidden __ieee754_atanh(double x)
  46. #else
  47. double attribute_hidden __ieee754_atanh(x)
  48. double x;
  49. #endif
  50. {
  51. double t;
  52. int32_t hx,ix;
  53. u_int32_t lx;
  54. EXTRACT_WORDS(hx,lx,x);
  55. ix = hx&0x7fffffff;
  56. if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */
  57. return (x-x)/(x-x);
  58. if(ix==0x3ff00000)
  59. return x/zero;
  60. if(ix<0x3e300000&&(huge+x)>zero) return x; /* x<2**-28 */
  61. SET_HIGH_WORD(x,ix);
  62. if(ix<0x3fe00000) { /* x < 0.5 */
  63. t = x+x;
  64. t = 0.5*log1p(t+t*x/(one-x));
  65. } else
  66. t = 0.5*log1p((x+x)/(one-x));
  67. if(hx>=0) return t; else return -t;
  68. }