1 | /* |
---|---|

2 | * ==================================================== |

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

4 | * |

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

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

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

8 | * is preserved. |

9 | * ==================================================== |

10 | */ |

11 | |

12 | /* Changes for 128-bit __float128 are |

13 | Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov> |

14 | and are incorporated herein by permission of the author. The author |

15 | reserves the right to distribute this material elsewhere under different |

16 | copying permissions. These modifications are distributed here under |

17 | the following terms: |

18 | |

19 | This library is free software; you can redistribute it and/or |

20 | modify it under the terms of the GNU Lesser General Public |

21 | License as published by the Free Software Foundation; either |

22 | version 2.1 of the License, or (at your option) any later version. |

23 | |

24 | This library is distributed in the hope that it will be useful, |

25 | but WITHOUT ANY WARRANTY; without even the implied warranty of |

26 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |

27 | Lesser General Public License for more details. |

28 | |

29 | You should have received a copy of the GNU Lesser General Public |

30 | License along with this library; if not, write to the Free Software |

31 | Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */ |

32 | |

33 | /* coshq(x) |

34 | * Method : |

35 | * mathematically coshq(x) if defined to be (exp(x)+exp(-x))/2 |

36 | * 1. Replace x by |x| (coshq(x) = coshq(-x)). |

37 | * 2. |

38 | * [ exp(x) - 1 ]^2 |

39 | * 0 <= x <= ln2/2 : coshq(x) := 1 + ------------------- |

40 | * 2*exp(x) |

41 | * |

42 | * exp(x) + 1/exp(x) |

43 | * ln2/2 <= x <= 22 : coshq(x) := ------------------- |

44 | * 2 |

45 | * 22 <= x <= lnovft : coshq(x) := expq(x)/2 |

46 | * lnovft <= x <= ln2ovft: coshq(x) := expq(x/2)/2 * expq(x/2) |

47 | * ln2ovft < x : coshq(x) := huge*huge (overflow) |

48 | * |

49 | * Special cases: |

50 | * coshq(x) is |x| if x is +INF, -INF, or NaN. |

51 | * only coshq(0)=1 is exact for finite x. |

52 | */ |

53 | |

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

55 | |

56 | static const __float128 one = 1.0Q, half = 0.5Q, huge = 1.0e4900Q, |

57 | ovf_thresh = 1.1357216553474703894801348310092223067821E4Q; |

58 | |

59 | __float128 |

60 | coshq (__float128 x) |

61 | { |

62 | __float128 t, w; |

63 | int32_t ex; |

64 | ieee854_float128 u; |

65 | |

66 | u.value = x; |

67 | ex = u.words32.w0 & 0x7fffffff; |

68 | |

69 | /* Absolute value of x. */ |

70 | u.words32.w0 = ex; |

71 | |

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

73 | if (ex >= 0x7fff0000) |

74 | return x * x; |

75 | |

76 | /* |x| in [0,0.5*ln2], return 1+expm1l(|x|)^2/(2*expq(|x|)) */ |

77 | if (ex < 0x3ffd62e4) /* 0.3465728759765625 */ |

78 | { |

79 | if (ex < 0x3fb80000) /* |x| < 2^-116 */ |

80 | return one; /* cosh(tiny) = 1 */ |

81 | t = expm1q (u.value); |

82 | w = one + t; |

83 | |

84 | return one + (t * t) / (w + w); |

85 | } |

86 | |

87 | /* |x| in [0.5*ln2,40], return (exp(|x|)+1/exp(|x|)/2; */ |

88 | if (ex < 0x40044000) |

89 | { |

90 | t = expq (u.value); |

91 | return half * t + half / t; |

92 | } |

93 | |

94 | /* |x| in [22, ln(maxdouble)] return half*exp(|x|) */ |

95 | if (ex <= 0x400c62e3) /* 11356.375 */ |

96 | return half * expq (u.value); |

97 | |

98 | /* |x| in [log(maxdouble), overflowthresold] */ |

99 | if (u.value <= ovf_thresh) |

100 | { |

101 | w = expq (half * u.value); |

102 | t = half * w; |

103 | return t * w; |

104 | } |

105 | |

106 | /* |x| > overflowthresold, cosh(x) overflow */ |

107 | return huge * huge; |

108 | } |

109 |