/* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_coshl.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. * ==================================================== */ /* coshl(x) * Method : * mathematically coshl(x) if defined to be (exp(x)+exp(-x))/2 * 1. Replace x by |x| (coshl(x) = coshl(-x)). * 2. * [ exp(x) - 1 ]^2 * 0 <= x <= ln2/2 : coshl(x) := 1 + ------------------- * 2*exp(x) * * exp(x) + 1/exp(x) * ln2/2 <= x <= 22 : coshl(x) := ------------------- * 2 * 22 <= x <= lnovft : coshl(x) := expl(x)/2 * lnovft <= x <= ln2ovft: coshl(x) := expl(x/2)/2 * expl(x/2) * ln2ovft < x : coshl(x) := huge*huge (overflow) * * Special cases: * coshl(x) is |x| if x is +INF, -INF, or NaN. * only coshl(0)=1 is exact for finite x. */ #include "libm.h" #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 long double coshl(long double x) { return cosh(x); } #elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384 static const long double huge = 1.0e4900L; long double coshl(long double x) { long double t,w; int32_t ex; uint32_t mx,lx; /* High word of |x|. */ GET_LDOUBLE_WORDS(ex, mx, lx, x); ex &= 0x7fff; /* x is INF or NaN */ if (ex == 0x7fff) return x*x; /* |x| in [0,0.5*ln2], return 1+expm1l(|x|)^2/(2*expl(|x|)) */ if (ex < 0x3ffd || (ex == 0x3ffd && mx < 0xb17217f7u)) { t = expm1l(fabsl(x)); w = 1.0 + t; if (ex < 0x3fbc) return w; /* cosh(tiny) = 1 */ return 1.0+(t*t)/(w+w); } /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */ if (ex < 0x4003 || (ex == 0x4003 && mx < 0xb0000000u)) { t = expl(fabsl(x)); return 0.5*t + 0.5/t; } /* |x| in [22, ln(maxdouble)] return 0.5*exp(|x|) */ if (ex < 0x400c || (ex == 0x400c && mx < 0xb1700000u)) return 0.5*expl(fabsl(x)); /* |x| in [log(maxdouble), log(2*maxdouble)) */ if (ex == 0x400c && (mx < 0xb174ddc0u || (mx == 0xb174ddc0u && lx < 0x31aec0ebu))) { w = expl(0.5*fabsl(x)); t = 0.5*w; return t*w; } /* |x| >= log(2*maxdouble), cosh(x) overflow */ return huge*huge; } #endif