1 | /* s_tanhl.c -- __float128 version of s_tanh.c. |
---|---|

2 | * Conversion to __float128 by Ulrich Drepper, |

3 | * Cygnus Support, drepper@cygnus.com. |

4 | */ |

5 | |

6 | /* |

7 | * ==================================================== |

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

9 | * |

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

11 | * Permission to use, copy, modify, and distribute this |

12 | * software is freely granted, provided that this notice |

13 | * is preserved. |

14 | * ==================================================== |

15 | */ |

16 | |

17 | /* Changes for 128-bit __float128 contributed by |

18 | Stephen L. Moshier <moshier@na-net.ornl.gov> */ |

19 | |

20 | /* tanhl(x) |

21 | * Return the Hyperbolic Tangent of x |

22 | * |

23 | * Method : |

24 | * x -x |

25 | * e - e |

26 | * 0. tanhl(x) is defined to be ----------- |

27 | * x -x |

28 | * e + e |

29 | * 1. reduce x to non-negative by tanhl(-x) = -tanhl(x). |

30 | * 2. 0 <= x <= 2**-57 : tanhl(x) := x*(one+x) |

31 | * -t |

32 | * 2**-57 < x <= 1 : tanhl(x) := -----; t = expm1l(-2x) |

33 | * t + 2 |

34 | * 2 |

35 | * 1 <= x <= 40.0 : tanhl(x) := 1- ----- ; t=expm1l(2x) |

36 | * t + 2 |

37 | * 40.0 < x <= INF : tanhl(x) := 1. |

38 | * |

39 | * Special cases: |

40 | * tanhl(NaN) is NaN; |

41 | * only tanhl(0)=0 is exact for finite argument. |

42 | */ |

43 | |

44 | #include "quadmath-imp.h" |

45 | |

46 | static const __float128 one = 1.0Q, two = 2.0Q, tiny = 1.0e-4900Q; |

47 | |

48 | __float128 |

49 | tanhq (__float128 x) |

50 | { |

51 | __float128 t, z; |

52 | uint32_t jx, ix; |

53 | ieee854_float128 u; |

54 | |

55 | /* Words of |x|. */ |

56 | u.value = x; |

57 | jx = u.words32.w0; |

58 | ix = jx & 0x7fffffff; |

59 | /* x is INF or NaN */ |

60 | if (ix >= 0x7fff0000) |

61 | { |

62 | /* for NaN it's not important which branch: tanhl(NaN) = NaN */ |

63 | if (jx & 0x80000000) |

64 | return one / x - one; /* tanhl(-inf)= -1; */ |

65 | else |

66 | return one / x + one; /* tanhl(+inf)=+1 */ |

67 | } |

68 | |

69 | /* |x| < 40 */ |

70 | if (ix < 0x40044000) |

71 | { |

72 | if (u.value == 0) |

73 | return x; /* x == +- 0 */ |

74 | if (ix < 0x3fc60000) /* |x| < 2^-57 */ |

75 | { |

76 | math_check_force_underflow (x); |

77 | return x * (one + tiny); /* tanh(small) = small */ |

78 | } |

79 | u.words32.w0 = ix; /* Absolute value of x. */ |

80 | if (ix >= 0x3fff0000) |

81 | { /* |x| >= 1 */ |

82 | t = expm1q (two * u.value); |

83 | z = one - two / (t + two); |

84 | } |

85 | else |

86 | { |

87 | t = expm1q (-two * u.value); |

88 | z = -t / (t + two); |

89 | } |

90 | /* |x| > 40, return +-1 */ |

91 | } |

92 | else |

93 | { |

94 | z = one - tiny; /* raised inexact flag */ |

95 | } |

96 | return (jx & 0x80000000) ? -z : z; |

97 | } |

98 |