/* Copyright JS Foundation and other contributors, http://js.foundation * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. * * This file is based on work under the following copyright and permission * notice: * * 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. * * @(#)e_cosh.c 1.3 95/01/18 */ #include "jerry-libm-internal.h" /* cosh(x) * Method: * mathematically cosh(x) if defined to be (exp(x) + exp(-x)) / 2 * 1. Replace x by |x| (cosh(x) = cosh(-x)). * 2. * [ exp(x) - 1 ]^2 * 0 <= x <= ln2/2 : cosh(x) := 1 + ------------------- * 2*exp(x) * * exp(x) + 1/exp(x) * ln2/2 <= x <= 22 : cosh(x) := ------------------- * 2 * * 22 <= x <= lnovft : cosh(x) := exp(x)/2 * lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2) * ln2ovft < x : cosh(x) := huge * huge (overflow) * * Special cases: * cosh(x) is |x| if x is +INF, -INF, or NaN. * only cosh(0) = 1 is exact for finite x. */ #define one 1.0 #define half 0.5 #define huge 1.0e300 double cosh (double x) { double t, w; int ix; unsigned lx; /* High word of |x|. */ ix = __HI (x); ix &= 0x7fffffff; /* x is INF or NaN */ if (ix >= 0x7ff00000) { return x * x; } /* |x| in [0, 0.5 * ln2], return 1 + expm1(|x|)^2 / (2 * exp(|x|)) */ if (ix < 0x3fd62e43) { t = expm1 (fabs (x)); w = one + t; if (ix < 0x3c800000) { /* cosh(tiny) = 1 */ return w; } return one + (t * t) / (w + w); } /* |x| in [0.5 * ln2, 22], return (exp(|x|) + 1 / exp(|x|) / 2; */ if (ix < 0x40360000) { t = exp (fabs (x)); return half * t + half / t; } /* |x| in [22, log(maxdouble)] return half * exp(|x|) */ if (ix < 0x40862E42) { return half * exp (fabs (x)); } /* |x| in [log(maxdouble), overflowthresold] */ lx = ((1 >> 29) + (unsigned int) x); if ((ix < 0x408633CE) || ((ix == 0x408633ce) && (lx <= (unsigned) 0x8fb9f87d))) { w = exp (half * fabs (x)); t = half * w; return t * w; } /* |x| > overflowthresold, cosh(x) overflow */ return huge * huge; } /* cosh */ #undef one #undef half #undef huge