/* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_sinhl.c */ /* * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this * software is freely granted, provided that this notice * is preserved. * ==================================================== */ /* sinhl(x) * Method : * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2 * 1. Replace x by |x| (sinhl(-x) = -sinhl(x)). * 2. * E + E/(E+1) * 0 <= x <= 25 : sinhl(x) := --------------, E=expm1l(x) * 2 * * 25 <= x <= lnovft : sinhl(x) := expl(x)/2 * lnovft <= x <= ln2ovft: sinhl(x) := expl(x/2)/2 * expl(x/2) * ln2ovft < x : sinhl(x) := x*huge (overflow) * * Special cases: * sinhl(x) is |x| if x is +INF, -INF, or NaN. * only sinhl(0)=0 is exact for finite x. */ #include "libm.h" #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 long double sinhl(long double x) { return sinh(x); } #elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384 static const long double one = 1.0, huge = 1.0e4931L; long double sinhl(long double x) { long double t,w,h; uint32_t jx,ix,i0,i1; /* Words of |x|. */ GET_LDOUBLE_WORDS(jx, i0, i1, x); ix = jx & 0x7fff; /* x is INF or NaN */ if (ix == 0x7fff) return x + x; h = 0.5; if (jx & 0x8000) h = -h; /* |x| in [0,25], return sign(x)*0.5*(E+E/(E+1))) */ if (ix < 0x4003 || (ix == 0x4003 && i0 <= 0xc8000000)) { /* |x| < 25 */ if (ix < 0x3fdf) /* |x|<2**-32 */ if (huge + x > one) return x;/* sinh(tiny) = tiny with inexact */ t = expm1l(fabsl(x)); if (ix < 0x3fff) return h*(2.0*t - t*t/(t + one)); return h*(t + t/(t + one)); } /* |x| in [25, log(maxdouble)] return 0.5*exp(|x|) */ if (ix < 0x400c || (ix == 0x400c && i0 < 0xb17217f7)) return h*expl(fabsl(x)); /* |x| in [log(maxdouble), overflowthreshold] */ if (ix < 0x400c || (ix == 0x400c && (i0 < 0xb174ddc0 || (i0 == 0xb174ddc0 && i1 <= 0x31aec0ea)))) { w = expl(0.5*fabsl(x)); t = h*w; return t*w; } /* |x| > overflowthreshold, sinhl(x) overflow */ return x*huge; } #endif