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/* __ieee754_cosh(x)
13 * Method :
14 * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2
15 * 1. Replace x by |x| (cosh(x) = cosh(-x)).
16 * 2.
17 * [ exp(x) - 1 ]^2
18 * 0 <= x <= ln2/2 : cosh(x) := 1 + -------------------
19 * 2*exp(x)
20 *
21 * exp(x) + 1/exp(x)
22 * ln2/2 <= x <= 22 : cosh(x) := -------------------
23 * 2
24 * 22 <= x <= lnovft : cosh(x) := exp(x)/2
25 * lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2)
26 * ln2ovft < x : cosh(x) := huge*huge (overflow)
27 *
28 * Special cases:
29 * cosh(x) is |x| if x is +INF, -INF, or NaN.
30 * only cosh(0)=1 is exact for finite x.
31 */
32
33#include <math.h>
34#include <math_private.h>
35#include <math-narrow-eval.h>
36#include <libm-alias-finite.h>
37
38static const double one = 1.0, half=0.5, huge = 1.0e300;
39
40double
41__ieee754_cosh (double x)
42{
43 double t,w;
44 int32_t ix;
45
46 /* High word of |x|. */
47 GET_HIGH_WORD(ix,x);
48 ix &= 0x7fffffff;
49
50 /* |x| in [0,22] */
51 if (ix < 0x40360000) {
52 /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
53 if(ix<0x3fd62e43) {
54 if (ix<0x3c800000) /* cosh(tiny) = 1 */
55 return one;
56 t = __expm1(fabs(x));
57 w = one+t;
58 return one+(t*t)/(w+w);
59 }
60
61 /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
62 t = __ieee754_exp(fabs(x));
63 return half*t+half/t;
64 }
65
66 /* |x| in [22, log(maxdouble)] return half*exp(|x|) */
67 if (ix < 0x40862e42) return half*__ieee754_exp(fabs(x));
68
69 /* |x| in [log(maxdouble), overflowthresold] */
70 int64_t fix;
71 EXTRACT_WORDS64(fix, x);
72 fix &= UINT64_C(0x7fffffffffffffff);
73 if (fix <= UINT64_C(0x408633ce8fb9f87d)) {
74 w = __ieee754_exp(half*fabs(x));
75 t = half*w;
76 return t*w;
77 }
78
79 /* x is INF or NaN */
80 if(ix>=0x7ff00000) return x*x;
81
82 /* |x| > overflowthresold, cosh(x) overflow */
83 return math_narrow_eval (huge * huge);
84}
85libm_alias_finite (__ieee754_cosh, __cosh)
86