1 /* from: FreeBSD: head/lib/msun/src/e_coshl.c XXX */
2
3 /*
4 * ====================================================
5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6 *
7 * Developed at SunPro, a Sun Microsystems, Inc. business.
8 * Permission to use, copy, modify, and distribute this
9 * software is freely granted, provided that this notice
10 * is preserved.
11 * ====================================================
12 */
13
14 #include <sys/cdefs.h>
15 __FBSDID("$FreeBSD$");
16
17 /*
18 * See e_cosh.c for complete comments.
19 *
20 * Converted to long double by Bruce D. Evans.
21 */
22
23 #include <float.h>
24 #ifdef __i386__
25 #include <ieeefp.h>
26 #endif
27
28 #include "fpmath.h"
29 #include "math.h"
30 #include "math_private.h"
31 #include "k_expl.h"
32
33 #if LDBL_MAX_EXP != 0x4000
34 /* We also require the usual expsign encoding. */
35 #error "Unsupported long double format"
36 #endif
37
38 #define BIAS (LDBL_MAX_EXP - 1)
39
40 static const volatile long double huge = 0x1p10000L, tiny = 0x1p-10000L;
41 #if LDBL_MANT_DIG == 64
42 /*
43 * Domain [-1, 1], range ~[-1.8211e-21, 1.8211e-21]:
44 * |cosh(x) - c(x)| < 2**-68.8
45 */
46 static const union IEEEl2bits
47 C4u = LD80C(0xaaaaaaaaaaaaac78, -5, 4.16666666666666682297e-2L);
48 #define C4 C4u.e
49 static const double
50 C2 = 0.5,
51 C6 = 1.3888888888888616e-3, /* 0x16c16c16c16b99.0p-62 */
52 C8 = 2.4801587301767953e-5, /* 0x1a01a01a027061.0p-68 */
53 C10 = 2.7557319163300398e-7, /* 0x127e4fb6c9b55f.0p-74 */
54 C12 = 2.0876768371393075e-9, /* 0x11eed99406a3f4.0p-81 */
55 C14 = 1.1469537039374480e-11, /* 0x1938c67cd18c48.0p-89 */
56 C16 = 4.8473490896852041e-14; /* 0x1b49c429701e45.0p-97 */
57 #elif LDBL_MANT_DIG == 113
58 /*
59 * Domain [-1, 1], range ~[-2.3194e-37, 2.3194e-37]:
60 * |cosh(x) - c(x)| < 2**-121.69
61 */
62 static const long double
63 C4 = 4.16666666666666666666666666666666225e-2L, /* 0x1555555555555555555555555554e.0p-117L */
64 C6 = 1.38888888888888888888888888889434831e-3L, /* 0x16c16c16c16c16c16c16c16c1dd7a.0p-122L */
65 C8 = 2.48015873015873015873015871870962089e-5L, /* 0x1a01a01a01a01a01a01a017af2756.0p-128L */
66 C10 = 2.75573192239858906525574318600800201e-7L, /* 0x127e4fb7789f5c72ef01c8a040640.0p-134L */
67 C12 = 2.08767569878680989791444691755468269e-9L, /* 0x11eed8eff8d897b543d0679607399.0p-141L */
68 C14= 1.14707455977297247387801189650495351e-11L, /* 0x193974a8c07c9d24ae169a7fa9b54.0p-149L */
69 C16 = 4.77947733238737883626416876486279985e-14L; /* 0x1ae7f3e733b814d4e1b90f5727fe4.0p-157L */
70 static const double
71 C2 = 0.5,
72 C18 = 1.5619206968597871e-16, /* 0x16827863b9900b.0p-105 */
73 C20 = 4.1103176218528049e-19, /* 0x1e542ba3d3c269.0p-114 */
74 C22 = 8.8967926401641701e-22, /* 0x10ce399542a014.0p-122 */
75 C24 = 1.6116681626523904e-24, /* 0x1f2c981d1f0cb7.0p-132 */
76 C26 = 2.5022374732804632e-27; /* 0x18c7ecf8b2c4a0.0p-141 */
77 #else
78 #error "Unsupported long double format"
79 #endif /* LDBL_MANT_DIG == 64 */
80
81 /* log(2**16385 - 0.5) rounded up: */
82 static const float
83 o_threshold = 1.13572168e4; /* 0xb174de.0p-10 */
84
85 long double
coshl(long double x)86 coshl(long double x)
87 {
88 long double hi,lo,x2,x4;
89 double dx2;
90 uint16_t ix;
91
92 GET_LDBL_EXPSIGN(ix,x);
93 ix &= 0x7fff;
94
95 /* x is INF or NaN */
96 if(ix>=0x7fff) return x*x;
97
98 ENTERI();
99
100 /* |x| < 1, return 1 or c(x) */
101 if(ix<0x3fff) {
102 if (ix<BIAS-(LDBL_MANT_DIG+1)/2) /* |x| < TINY */
103 RETURNI(1+tiny); /* cosh(tiny) = 1(+) with inexact */
104 x2 = x*x;
105 #if LDBL_MANT_DIG == 64
106 x4 = x2*x2;
107 RETURNI(((C16*x2 + C14)*x4 + (C12*x2 + C10))*(x4*x4*x2) +
108 ((C8*x2 + C6)*x2 + C4)*x4 + C2*x2 + 1);
109 #elif LDBL_MANT_DIG == 113
110 dx2 = x2;
111 RETURNI((((((((((((C26*dx2 + C24)*dx2 + C22)*dx2 +
112 C20)*x2 + C18)*x2 +
113 C16)*x2 + C14)*x2 + C12)*x2 + C10)*x2 + C8)*x2 + C6)*x2 +
114 C4)*(x2*x2) + C2*x2 + 1);
115 #endif
116 }
117
118 /* |x| in [1, 64), return accurate exp(|x|)/2+1/exp(|x|)/2 */
119 if (ix < 0x4005) {
120 k_hexpl(fabsl(x), &hi, &lo);
121 RETURNI(lo + 0.25/(hi + lo) + hi);
122 }
123
124 /* |x| in [64, o_threshold], return correctly-overflowing exp(|x|)/2 */
125 if (fabsl(x) <= o_threshold)
126 RETURNI(hexpl(fabsl(x)));
127
128 /* |x| > o_threshold, cosh(x) overflow */
129 RETURNI(huge*huge);
130 }
131