/* @(#)e_sinh.c 1.3 95/01/18 */ /* * ==================================================== * 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. * ==================================================== */ #include <sys/cdefs.h> __FBSDID("$FreeBSD$"); /* __ieee754_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 <float.h> #include "math.h" #include "math_private.h" static const double one = 1.0, shuge = 1.0e307; double __ieee754_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 */ if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */ 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*__ieee754_exp(fabs(x)); /* |x| in [log(maxdouble), overflowthresold] */ if (ix<=0x408633CE) return h*2.0*__ldexp_exp(fabs(x), -1); /* |x| > overflowthresold, sinh(x) overflow */ return x*shuge; } #if (LDBL_MANT_DIG == 53) __weak_reference(sinh, sinhl); #endif