xref: /freebsd/lib/msun/src/e_coshl.c (revision da5432eda807c4b7232d030d5157d5b417ea4f52)
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 /*
16  * See e_cosh.c for complete comments.
17  *
18  * Converted to long double by Bruce D. Evans.
19  */
20 
21 #include <float.h>
22 #ifdef __i386__
23 #include <ieeefp.h>
24 #endif
25 
26 #include "fpmath.h"
27 #include "math.h"
28 #include "math_private.h"
29 #include "k_expl.h"
30 
31 #if LDBL_MAX_EXP != 0x4000
32 /* We also require the usual expsign encoding. */
33 #error "Unsupported long double format"
34 #endif
35 
36 #define	BIAS	(LDBL_MAX_EXP - 1)
37 
38 static const volatile long double huge = 0x1p10000L, tiny = 0x1p-10000L;
39 #if LDBL_MANT_DIG == 64
40 /*
41  * Domain [-1, 1], range ~[-1.8211e-21, 1.8211e-21]:
42  * |cosh(x) - c(x)| < 2**-68.8
43  */
44 static const union IEEEl2bits
45 C4u = LD80C(0xaaaaaaaaaaaaac78, -5,  4.16666666666666682297e-2L);
46 #define	C4	C4u.e
47 static const double
48 C2  =  0.5,
49 C6  =  1.3888888888888616e-3,		/*  0x16c16c16c16b99.0p-62 */
50 C8  =  2.4801587301767953e-5,		/*  0x1a01a01a027061.0p-68 */
51 C10 =  2.7557319163300398e-7,		/*  0x127e4fb6c9b55f.0p-74 */
52 C12 =  2.0876768371393075e-9,		/*  0x11eed99406a3f4.0p-81 */
53 C14 =  1.1469537039374480e-11,		/*  0x1938c67cd18c48.0p-89 */
54 C16 =  4.8473490896852041e-14;		/*  0x1b49c429701e45.0p-97 */
55 #elif LDBL_MANT_DIG == 113
56 /*
57  * Domain [-1, 1], range ~[-2.3194e-37, 2.3194e-37]:
58  * |cosh(x) - c(x)| < 2**-121.69
59  */
60 static const long double
61 C4  =  4.16666666666666666666666666666666225e-2L,	/*  0x1555555555555555555555555554e.0p-117L */
62 C6  =  1.38888888888888888888888888889434831e-3L,	/*  0x16c16c16c16c16c16c16c16c1dd7a.0p-122L */
63 C8  =  2.48015873015873015873015871870962089e-5L,	/*  0x1a01a01a01a01a01a01a017af2756.0p-128L */
64 C10 =  2.75573192239858906525574318600800201e-7L,	/*  0x127e4fb7789f5c72ef01c8a040640.0p-134L */
65 C12 =  2.08767569878680989791444691755468269e-9L,	/*  0x11eed8eff8d897b543d0679607399.0p-141L */
66 C14=  1.14707455977297247387801189650495351e-11L,	/*  0x193974a8c07c9d24ae169a7fa9b54.0p-149L */
67 C16 =  4.77947733238737883626416876486279985e-14L;	/*  0x1ae7f3e733b814d4e1b90f5727fe4.0p-157L */
68 static const double
69 C2  =  0.5,
70 C18 =  1.5619206968597871e-16,		/*  0x16827863b9900b.0p-105 */
71 C20 =  4.1103176218528049e-19,		/*  0x1e542ba3d3c269.0p-114 */
72 C22 =  8.8967926401641701e-22,		/*  0x10ce399542a014.0p-122 */
73 C24 =  1.6116681626523904e-24,		/*  0x1f2c981d1f0cb7.0p-132 */
74 C26 =  2.5022374732804632e-27;		/*  0x18c7ecf8b2c4a0.0p-141 */
75 #else
76 #error "Unsupported long double format"
77 #endif /* LDBL_MANT_DIG == 64 */
78 
79 /* log(2**16385 - 0.5) rounded up: */
80 static const float
81 o_threshold =  1.13572168e4;		/*  0xb174de.0p-10 */
82 
83 long double
84 coshl(long double x)
85 {
86 	long double hi,lo,x2,x4;
87 #if LDBL_MANT_DIG == 113
88 	double dx2;
89 #endif
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