1 /* s_tanhl.c -- long double version of s_tanh.c.
5 * ====================================================
6 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
8 * Developed at SunPro, a Sun Microsystems, Inc. business.
9 * Permission to use, copy, modify, and distribute this
10 * software is freely granted, provided that this notice
12 * ====================================================
15 #if defined(LIBM_SCCS) && !defined(lint)
16 static char rcsid
[] = "$NetBSD: $";
20 * Return the Hyperbolic Tangent of x
25 * 0. tanhl(x) is defined to be -----------
28 * 1. reduce x to non-negative by tanhl(-x) = -tanhl(x).
29 * 2. 0 <= x <= 2**-55 : tanhl(x) := x*(one+x)
31 * 2**-55 < x <= 1 : tanhl(x) := -----; t = expm1l(-2x)
34 * 1 <= x <= 23.0 : tanhl(x) := 1- ----- ; t=expm1l(2x)
36 * 23.0 < x <= INF : tanhl(x) := 1.
40 * only tanhl(0)=0 is exact for finite argument.
45 #include <math_private.h>
46 #include <math-underflow.h>
47 #include <libm-alias-ldouble.h>
49 static const long double one
=1.0, two
=2.0, tiny
= 1.0e-4900L;
51 long double __tanhl(long double x
)
57 /* High word of |x|. */
58 GET_LDOUBLE_WORDS(se
,j0
,j1
,x
);
63 /* for NaN it's not important which branch: tanhl(NaN) = NaN */
64 if (se
&0x8000) return one
/x
-one
; /* tanhl(-inf)= -1; */
65 else return one
/x
+one
; /* tanhl(+inf)=+1 */
69 if (ix
< 0x4003 || (ix
== 0x4003 && j0
< 0xb8000000u
)) {/* |x|<23 */
71 return x
; /* x == +- 0 */
72 if (ix
<0x3fc8) /* |x|<2**-55 */
74 math_check_force_underflow (x
);
75 return x
*(one
+tiny
); /* tanh(small) = small */
77 if (ix
>=0x3fff) { /* |x|>=1 */
78 t
= __expm1l(two
*fabsl(x
));
79 z
= one
- two
/(t
+two
);
81 t
= __expm1l(-two
*fabsl(x
));
84 /* |x| > 23, return +-1 */
86 z
= one
- tiny
; /* raised inexact flag */
88 return (se
&0x8000)? -z
: z
;
90 libm_alias_ldouble (__tanh
, tanh
)