1 /* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_sinhl.c */
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6 * Developed at SunPro, a Sun Microsystems, Inc. business.
7 * Permission to use, copy, modify, and distribute this
8 * software is freely granted, provided that this notice
10 * ====================================================
14 * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
15 * 1. Replace x by |x| (sinhl(-x) = -sinhl(x)).
18 * 0 <= x <= 25 : sinhl(x) := --------------, E=expm1l(x)
21 * 25 <= x <= lnovft : sinhl(x) := expl(x)/2
22 * lnovft <= x <= ln2ovft: sinhl(x) := expl(x/2)/2 * expl(x/2)
23 * ln2ovft < x : sinhl(x) := x*huge (overflow)
26 * sinhl(x) is |x| if x is +INF, -INF, or NaN.
27 * only sinhl(0)=0 is exact for finite x.
32 #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
33 long double sinhl(long double x)
37 #elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
38 static const long double one = 1.0, huge = 1.0e4931L;
40 long double sinhl(long double x)
46 GET_LDOUBLE_WORDS(jx, i0, i1, x);
50 if (ix == 0x7fff) return x + x;
55 /* |x| in [0,25], return sign(x)*0.5*(E+E/(E+1))) */
56 if (ix < 0x4003 || (ix == 0x4003 && i0 <= 0xc8000000)) { /* |x| < 25 */
57 if (ix < 0x3fdf) /* |x|<2**-32 */
59 return x;/* sinh(tiny) = tiny with inexact */
62 return h*(2.0*t - t*t/(t + one));
63 return h*(t + t/(t + one));
66 /* |x| in [25, log(maxdouble)] return 0.5*exp(|x|) */
67 if (ix < 0x400c || (ix == 0x400c && i0 < 0xb17217f7))
68 return h*expl(fabsl(x));
70 /* |x| in [log(maxdouble), overflowthreshold] */
71 if (ix < 0x400c || (ix == 0x400c && (i0 < 0xb174ddc0 ||
72 (i0 == 0xb174ddc0 && i1 <= 0x31aec0ea)))) {
73 w = expl(0.5*fabsl(x));
78 /* |x| > overflowthreshold, sinhl(x) overflow */