1 /* $NetBSD: n_sinh.c,v 1.8 2014/10/10 20:58:09 martin Exp $ */
2 /*
3 * Copyright (c) 1985, 1993
4 * The Regents of the University of California. All rights reserved.
5 *
6 * Redistribution and use in source and binary forms, with or without
7 * modification, are permitted provided that the following conditions
8 * are met:
9 * 1. Redistributions of source code must retain the above copyright
10 * notice, this list of conditions and the following disclaimer.
11 * 2. Redistributions in binary form must reproduce the above copyright
12 * notice, this list of conditions and the following disclaimer in the
13 * documentation and/or other materials provided with the distribution.
14 * 3. Neither the name of the University nor the names of its contributors
15 * may be used to endorse or promote products derived from this software
16 * without specific prior written permission.
17 *
18 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
19 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
20 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
21 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
22 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
23 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
24 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
25 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
26 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
27 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
28 * SUCH DAMAGE.
29 */
30
31 #ifndef lint
32 #if 0
33 static char sccsid[] = "@(#)sinh.c 8.1 (Berkeley) 6/4/93";
34 #endif
35 #endif /* not lint */
36
37 /* SINH(X)
38 * RETURN THE HYPERBOLIC SINE OF X
39 * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
40 * CODED IN C BY K.C. NG, 1/8/85;
41 * REVISED BY K.C. NG on 2/8/85, 3/7/85, 3/24/85, 4/16/85.
42 *
43 * Required system supported functions :
44 * copysign(x,y)
45 * scalb(x,N)
46 *
47 * Required kernel functions:
48 * expm1(x) ...return exp(x)-1
49 *
50 * Method :
51 * 1. reduce x to non-negative by sinh(-x) = - sinh(x).
52 * 2.
53 *
54 * expm1(x) + expm1(x)/(expm1(x)+1)
55 * 0 <= x <= lnovfl : sinh(x) := --------------------------------
56 * 2
57 * lnovfl <= x <= lnovfl+ln2 : sinh(x) := expm1(x)/2 (avoid overflow)
58 * lnovfl+ln2 < x < INF : overflow to INF
59 *
60 *
61 * Special cases:
62 * sinh(x) is x if x is +INF, -INF, or NaN.
63 * only sinh(0)=0 is exact for finite argument.
64 *
65 * Accuracy:
66 * sinh(x) returns the exact hyperbolic sine of x nearly rounded. In
67 * a test run with 1,024,000 random arguments on a VAX, the maximum
68 * observed error was 1.93 ulps (units in the last place).
69 *
70 * Constants:
71 * The hexadecimal values are the intended ones for the following constants.
72 * The decimal values may be used, provided that the compiler will convert
73 * from decimal to binary accurately enough to produce the hexadecimal values
74 * shown.
75 */
76
77 #define _LIBM_STATIC
78 #include "../src/namespace.h"
79 #include "mathimpl.h"
80
81 #ifdef __weak_alias
82 __weak_alias(sinh, _sinh);
83 __weak_alias(_sinhl, _sinh);
84 __weak_alias(sinhf, _sinhf);
85 #endif
86
87 vc(mln2hi, 8.8029691931113054792E1 ,0f33,43b0,2bdb,c7e2, 7, .B00F33C7E22BDB)
88 vc(mln2lo,-4.9650192275318476525E-16 ,1b60,a70f,582a,279e, -50,-.8F1B60279E582A)
89 vc(lnovfl, 8.8029691931113053016E1 ,0f33,43b0,2bda,c7e2, 7, .B00F33C7E22BDA)
90
91 ic(mln2hi, 7.0978271289338397310E2, 10, 1.62E42FEFA39EF)
92 ic(mln2lo, 2.3747039373786107478E-14, -45, 1.ABC9E3B39803F)
93 ic(lnovfl, 7.0978271289338397310E2, 9, 1.62E42FEFA39EF)
94
95 #ifdef vccast
96 #define mln2hi vccast(mln2hi)
97 #define mln2lo vccast(mln2lo)
98 #define lnovfl vccast(lnovfl)
99 #endif
100
101 #if defined(__vax__)||defined(tahoe)
102 static const int max = 126 ;
103 #else /* defined(__vax__)||defined(tahoe) */
104 static const int max = 1023 ;
105 #endif /* defined(__vax__)||defined(tahoe) */
106
107
108 double
sinh(double x)109 sinh(double x)
110 {
111 static const double one=1.0, half=1.0/2.0 ;
112 double t, sign;
113 #if !defined(__vax__)&&!defined(tahoe)
114 if(x!=x) return(x); /* x is NaN */
115 #endif /* !defined(__vax__)&&!defined(tahoe) */
116 sign=copysign(one,x);
117 x=copysign(x,one);
118 if(x<lnovfl)
119 {t=expm1(x); return(copysign((t+t/(one+t))*half,sign));}
120
121 else if(x <= lnovfl+0.7)
122 /* subtract x by ln(2^(max+1)) and return 2^max*exp(x)
123 to avoid unnecessary overflow */
124 return(copysign(scalb(one+expm1((x-mln2hi)-mln2lo),max),sign));
125
126 else /* sinh(+-INF) = +-INF, sinh(+-big no.) overflow to +-INF */
127 return( expm1(x)*sign );
128 }
129
130 float
sinhf(float x)131 sinhf(float x)
132 {
133 return(sinh((double)x));
134 }
135