-/* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_atanh.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.
- * ====================================================
- */
-/* atanhl(x)
- * Method :
- * 1.Reduced x to positive by atanh(-x) = -atanh(x)
- * 2.For x>=0.5
- * 1 2x x
- * atanhl(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
- * 2 1 - x 1 - x
- *
- * For x<0.5
- * atanhl(x) = 0.5*log1pl(2x+2x*x/(1-x))
- *
- * Special cases:
- * atanhl(x) is NaN if |x| > 1 with signal;
- * atanhl(NaN) is that NaN with no signal;
- * atanhl(+-1) is +-INF with signal.
- */
-
#include "libm.h"
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
return atanh(x);
}
#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
-static const long double zero = 0.0, one = 1.0, huge = 1e4900L;
-
+/* atanh(x) = log((1+x)/(1-x))/2 = log1p(2x/(1-x))/2 ~= x + x^3/3 + o(x^5) */
long double atanhl(long double x)
{
- long double t;
- int32_t ix;
- uint32_t se,i0,i1;
+ union {
+ long double f;
+ struct{uint64_t m; uint16_t se; uint16_t pad;} i;
+ } u = {.f = x};
+ unsigned e = u.i.se & 0x7fff;
+ unsigned s = u.i.se >> 15;
+
+ /* |x| */
+ u.i.se = e;
+ x = u.f;
- GET_LDOUBLE_WORDS(se, i0, i1, x);
- ix = se & 0x7fff;
- if ((ix+((((i0&0x7fffffff)|i1)|(-((i0&0x7fffffff)|i1)))>>31)) > 0x3fff)
- /* |x| > 1 */
- return (x-x)/(x-x);
- if (ix == 0x3fff)
- return x/zero;
- if (ix < 0x3fe3 && huge+x > zero) /* x < 2**-28 */
- return x;
- SET_LDOUBLE_EXP(x, ix);
- if (ix < 0x3ffe) { /* x < 0.5 */
- t = x + x;
- t = 0.5*log1pl(t + t*x/(one-x));
- } else
- t = 0.5*log1pl((x + x)/(one - x));
- if (se <= 0x7fff)
- return t;
- return -t;
+ if (e < 0x3fff - 1) {
+ /* |x| < 0.5, up to 1.7ulp error */
+ x = 0.5*log1pl(2*x + 2*x*x/(1-x));
+ } else {
+ x = 0.5*log1pl(2*x/(1-x));
+ }
+ return s ? -x : x;
}
#endif