-/* 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
return cosh(x);
}
#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
-static const long double one = 1.0, half = 0.5, 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 = one + t;
- if (ex < 0x3fbc) return w; /* cosh(tiny) = 1 */
- return one+(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 half*t + half/t;
+ union ldshape u = {x};
+ unsigned ex = u.i.se & 0x7fff;
+ uint32_t w;
+ long double t;
+
+ /* |x| */
+ u.i.se = ex;
+ x = u.f;
+ w = u.i.m >> 32;
+
+ /* |x| < log(2) */
+ if (ex < 0x3fff-1 || (ex == 0x3fff-1 && w < 0xb17217f7)) {
+ if (ex < 0x3fff-32) {
+ FORCE_EVAL(x + 0x1p120f);
+ return 1;
+ }
+ t = expm1l(x);
+ return 1 + t*t/(2*(1+t));
}
- /* |x| in [22, ln(maxdouble)] return half*exp(|x|) */
- if (ex < 0x400c || (ex == 0x400c && mx < 0xb1700000u))
- return half*expl(fabsl(x));
-
- /* |x| in [log(maxdouble), log(2*maxdouble)) */
- if (ex == 0x400c && (mx < 0xb174ddc0u ||
- (mx == 0xb174ddc0u && lx < 0x31aec0ebu)))
- {
- w = expl(half*fabsl(x));
- t = half*w;
- return t*w;
+ /* |x| < log(LDBL_MAX) */
+ if (ex < 0x3fff+13 || (ex == 0x3fff+13 && w < 0xb17217f7)) {
+ t = expl(x);
+ return 0.5*(t + 1/t);
}
- /* |x| >= log(2*maxdouble), cosh(x) overflow */
- return huge*huge;
+ /* |x| > log(LDBL_MAX) or nan */
+ t = expl(0.5*x);
+ return 0.5*t*t;
+}
+#elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384
+// TODO: broken implementation to make things compile
+long double coshl(long double x)
+{
+ return cosh(x);
}
#endif