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
36 static const double one = 1.0, half=0.5, huge = 1.0e300;
37
__ieee754_cosh(double x)38 double __ieee754_cosh(double x)
39 {
40 double t,w;
41 int32_t ix;
42 u_int32_t lx;
43
44 /* High word of |x|. */
45 GET_HIGH_WORD(ix,x);
46 ix &= 0x7fffffff;
47
48 /* x is INF or NaN */
49 if(ix>=0x7ff00000) return x*x;
50
51 /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
52 if(ix<0x3fd62e43) {
53 t = expm1(fabs(x));
54 w = one+t;
55 if (ix<0x3c800000) return w; /* cosh(tiny) = 1 */
56 return one+(t*t)/(w+w);
57 }
58
59 /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
60 if (ix < 0x40360000) {
61 t = __ieee754_exp(fabs(x));
62 return half*t+half/t;
63 }
64
65 /* |x| in [22, log(maxdouble)] return half*exp(|x|) */
66 if (ix < 0x40862E42) return half*__ieee754_exp(fabs(x));
67
68 /* |x| in [log(maxdouble), overflowthresold] */
69 GET_LOW_WORD(lx,x);
70 if (ix<0x408633CE ||
71 ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) {
72 w = __ieee754_exp(half*fabs(x));
73 t = half*w;
74 return t*w;
75 }
76
77 /* |x| > overflowthresold, cosh(x) overflow */
78 return huge*huge;
79 }
80
81 /*
82 * wrapper cosh(x)
83 */
84 #ifndef _IEEE_LIBM
cosh(double x)85 double cosh(double x)
86 {
87 double z = __ieee754_cosh(x);
88 if (_LIB_VERSION == _IEEE_ || isnan(x))
89 return z;
90 if (fabs(x) > 7.10475860073943863426e+02)
91 return __kernel_standard(x, x, 5); /* cosh overflow */
92 return z;
93 }
94 #else
95 strong_alias(__ieee754_cosh, cosh)
96 #endif
97 libm_hidden_def(cosh)
98