/* origin: FreeBSD /usr/src/lib/msun/src/e_sinh.c */ /* * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. * * Developed at SunSoft, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this * software is freely granted, provided that this notice * is preserved. * ==================================================== */ /* sinh(x) * Method : * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2 * 1. Replace x by |x| (sinh(-x) = -sinh(x)). * 2. * E + E/(E+1) * 0 <= x <= 22 : sinh(x) := --------------, E=expm1(x) * 2 * * 22 <= x <= lnovft : sinh(x) := exp(x)/2 * lnovft <= x <= ln2ovft: sinh(x) := exp(x/2)/2 * exp(x/2) * ln2ovft < x : sinh(x) := x*shuge (overflow) * * Special cases: * sinh(x) is |x| if x is +INF, -INF, or NaN. * only sinh(0)=0 is exact for finite x. */ #include "libm.h" static const double one = 1.0, huge = 1.0e307; double sinh(double x) { double t, h; int32_t ix, jx; /* High word of |x|. */ GET_HIGH_WORD(jx, x); ix = jx & 0x7fffffff; /* x is INF or NaN */ if (ix >= 0x7ff00000) return x + x; h = 0.5; if (jx < 0) h = -h; /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */ if (ix < 0x40360000) { /* |x|<22 */ if (ix < 0x3e300000) /* |x|<2**-28 */ /* raise inexact, return x */ if (huge+x > one) return x; t = expm1(fabs(x)); if (ix < 0x3ff00000) return h*(2.0*t - t*t/(t+one)); return h*(t + t/(t+one)); } /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */ if (ix < 0x40862E42) return h*exp(fabs(x)); /* |x| in [log(maxdouble), overflowthresold] */ if (ix <= 0x408633CE) return h * 2.0 * __expo2(fabs(x)); /* h is for sign only */ /* |x| > overflowthresold, sinh(x) overflow */ return x*huge; }