1*05a0b428SJohn Marino /* @(#)e_cosh.c 5.1 93/09/24 */
2*05a0b428SJohn Marino /*
3*05a0b428SJohn Marino * ====================================================
4*05a0b428SJohn Marino * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5*05a0b428SJohn Marino *
6*05a0b428SJohn Marino * Developed at SunPro, a Sun Microsystems, Inc. business.
7*05a0b428SJohn Marino * Permission to use, copy, modify, and distribute this
8*05a0b428SJohn Marino * software is freely granted, provided that this notice
9*05a0b428SJohn Marino * is preserved.
10*05a0b428SJohn Marino * ====================================================
11*05a0b428SJohn Marino */
12*05a0b428SJohn Marino
13*05a0b428SJohn Marino /* cosh(x)
14*05a0b428SJohn Marino * Method :
15*05a0b428SJohn Marino * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2
16*05a0b428SJohn Marino * 1. Replace x by |x| (cosh(x) = cosh(-x)).
17*05a0b428SJohn Marino * 2.
18*05a0b428SJohn Marino * [ exp(x) - 1 ]^2
19*05a0b428SJohn Marino * 0 <= x <= ln2/2 : cosh(x) := 1 + -------------------
20*05a0b428SJohn Marino * 2*exp(x)
21*05a0b428SJohn Marino *
22*05a0b428SJohn Marino * exp(x) + 1/exp(x)
23*05a0b428SJohn Marino * ln2/2 <= x <= 22 : cosh(x) := -------------------
24*05a0b428SJohn Marino * 2
25*05a0b428SJohn Marino * 22 <= x <= lnovft : cosh(x) := exp(x)/2
26*05a0b428SJohn Marino * lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2)
27*05a0b428SJohn Marino * ln2ovft < x : cosh(x) := huge*huge (overflow)
28*05a0b428SJohn Marino *
29*05a0b428SJohn Marino * Special cases:
30*05a0b428SJohn Marino * cosh(x) is |x| if x is +INF, -INF, or NaN.
31*05a0b428SJohn Marino * only cosh(0)=1 is exact for finite x.
32*05a0b428SJohn Marino */
33*05a0b428SJohn Marino
34*05a0b428SJohn Marino #include <float.h>
35*05a0b428SJohn Marino #include <math.h>
36*05a0b428SJohn Marino
37*05a0b428SJohn Marino #include "math_private.h"
38*05a0b428SJohn Marino
39*05a0b428SJohn Marino static const double one = 1.0, half=0.5, huge = 1.0e300;
40*05a0b428SJohn Marino
41*05a0b428SJohn Marino double
cosh(double x)42*05a0b428SJohn Marino cosh(double x)
43*05a0b428SJohn Marino {
44*05a0b428SJohn Marino double t,w;
45*05a0b428SJohn Marino int32_t ix;
46*05a0b428SJohn Marino u_int32_t lx;
47*05a0b428SJohn Marino
48*05a0b428SJohn Marino /* High word of |x|. */
49*05a0b428SJohn Marino GET_HIGH_WORD(ix,x);
50*05a0b428SJohn Marino ix &= 0x7fffffff;
51*05a0b428SJohn Marino
52*05a0b428SJohn Marino /* x is INF or NaN */
53*05a0b428SJohn Marino if(ix>=0x7ff00000) return x*x;
54*05a0b428SJohn Marino
55*05a0b428SJohn Marino /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
56*05a0b428SJohn Marino if(ix<0x3fd62e43) {
57*05a0b428SJohn Marino t = expm1(fabs(x));
58*05a0b428SJohn Marino w = one+t;
59*05a0b428SJohn Marino if (ix<0x3c800000) return w; /* cosh(tiny) = 1 */
60*05a0b428SJohn Marino return one+(t*t)/(w+w);
61*05a0b428SJohn Marino }
62*05a0b428SJohn Marino
63*05a0b428SJohn Marino /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
64*05a0b428SJohn Marino if (ix < 0x40360000) {
65*05a0b428SJohn Marino t = exp(fabs(x));
66*05a0b428SJohn Marino return half*t+half/t;
67*05a0b428SJohn Marino }
68*05a0b428SJohn Marino
69*05a0b428SJohn Marino /* |x| in [22, log(maxdouble)] return half*exp(|x|) */
70*05a0b428SJohn Marino if (ix < 0x40862E42) return half*exp(fabs(x));
71*05a0b428SJohn Marino
72*05a0b428SJohn Marino /* |x| in [log(maxdouble), overflowthresold] */
73*05a0b428SJohn Marino GET_LOW_WORD(lx,x);
74*05a0b428SJohn Marino if (ix<0x408633CE ||
75*05a0b428SJohn Marino ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) {
76*05a0b428SJohn Marino w = exp(half*fabs(x));
77*05a0b428SJohn Marino t = half*w;
78*05a0b428SJohn Marino return t*w;
79*05a0b428SJohn Marino }
80*05a0b428SJohn Marino
81*05a0b428SJohn Marino /* |x| > overflowthresold, cosh(x) overflow */
82*05a0b428SJohn Marino return huge*huge;
83*05a0b428SJohn Marino }
84*05a0b428SJohn Marino
85*05a0b428SJohn Marino #if LDBL_MANT_DIG == DBL_MANT_DIG
86*05a0b428SJohn Marino __strong_alias(coshl, cosh);
87*05a0b428SJohn Marino #endif /* LDBL_MANT_DIG == DBL_MANT_DIG */
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