s_tanh.c 2.1 KB

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  1. /* @(#)s_tanh.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_tanh.c,v 1.7 1995/05/10 20:48:22 jtc Exp $";
  14. #endif
  15. /* Tanh(x)
  16. * Return the Hyperbolic Tangent of x
  17. *
  18. * Method :
  19. * x -x
  20. * e - e
  21. * 0. tanh(x) is defined to be -----------
  22. * x -x
  23. * e + e
  24. * 1. reduce x to non-negative by tanh(-x) = -tanh(x).
  25. * 2. 0 <= x <= 2**-55 : tanh(x) := x*(one+x)
  26. * -t
  27. * 2**-55 < x <= 1 : tanh(x) := -----; t = expm1(-2x)
  28. * t + 2
  29. * 2
  30. * 1 <= x <= 22.0 : tanh(x) := 1- ----- ; t=expm1(2x)
  31. * t + 2
  32. * 22.0 < x <= INF : tanh(x) := 1.
  33. *
  34. * Special cases:
  35. * tanh(NaN) is NaN;
  36. * only tanh(0)=0 is exact for finite argument.
  37. */
  38. #include "math.h"
  39. #include "math_private.h"
  40. #ifdef __STDC__
  41. static const double one=1.0, two=2.0, tiny = 1.0e-300;
  42. #else
  43. static double one=1.0, two=2.0, tiny = 1.0e-300;
  44. #endif
  45. #ifdef __STDC__
  46. double tanh(double x)
  47. #else
  48. double tanh(x)
  49. double x;
  50. #endif
  51. {
  52. double t,z;
  53. int32_t jx,ix;
  54. /* High word of |x|. */
  55. GET_HIGH_WORD(jx,x);
  56. ix = jx&0x7fffffff;
  57. /* x is INF or NaN */
  58. if(ix>=0x7ff00000) {
  59. if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */
  60. else return one/x-one; /* tanh(NaN) = NaN */
  61. }
  62. /* |x| < 22 */
  63. if (ix < 0x40360000) { /* |x|<22 */
  64. if (ix<0x3c800000) /* |x|<2**-55 */
  65. return x*(one+x); /* tanh(small) = small */
  66. if (ix>=0x3ff00000) { /* |x|>=1 */
  67. t = expm1(two*fabs(x));
  68. z = one - two/(t+two);
  69. } else {
  70. t = expm1(-two*fabs(x));
  71. z= -t/(t+two);
  72. }
  73. /* |x| > 22, return +-1 */
  74. } else {
  75. z = one - tiny; /* raised inexact flag */
  76. }
  77. return (jx>=0)? z: -z;
  78. }
  79. libm_hidden_def(tanh)