/* | |

* ==================================================== | |

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

* | |

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

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

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

* is preserved. | |

* ==================================================== | |

*/ | |

/* Changes for 128-bit long double are | |

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

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

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

copying permissions. These modifications are distributed here under | |

the following terms: | |

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

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

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

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

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

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

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

Lesser General Public License for more details. | |

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

License along with this library; if not, see | |

<http://www.gnu.org/licenses/>. */ | |

/* coshq(x) | |

* Method : | |

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

* 1. Replace x by |x| (coshl(x) = coshl(-x)). | |

* 2. | |

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

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

* 2*exp(x) | |

* | |

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

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

* 2 | |

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

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

* ln2ovft < x : coshl(x) := huge*huge (overflow) | |

* | |

* Special cases: | |

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

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

*/ | |

#include "quadmath-imp.h" | |

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

ovf_thresh = 1.1357216553474703894801348310092223067821E4Q; | |

__float128 | |

coshq (__float128 x) | |

{ | |

__float128 t, w; | |

int32_t ex; | |

ieee854_float128 u; | |

u.value = x; | |

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

/* Absolute value of x. */ | |

u.words32.w0 = ex; | |

/* x is INF or NaN */ | |

if (ex >= 0x7fff0000) | |

return x * x; | |

/* |x| in [0,0.5*ln2], return 1+expm1q(|x|)^2/(2*expq(|x|)) */ | |

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

{ | |

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

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

t = expm1q (u.value); | |

w = one + t; | |

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

} | |

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

if (ex < 0x40044000) | |

{ | |

t = expq (u.value); | |

return half * t + half / t; | |

} | |

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

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

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

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

if (u.value <= ovf_thresh) | |

{ | |

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

t = half * w; | |

return t * w; | |

} | |

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

return huge * huge; | |

} |