/* origin: OpenBSD /usr/src/lib/libm/src/ld80/s_asinhl.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. * ==================================================== */ /* asinhl(x) * Method : * Based on * asinhl(x) = signl(x) * logl [ |x| + sqrtl(x*x+1) ] * we have * asinhl(x) := x if 1+x*x=1, * := signl(x)*(logl(x)+ln2)) for large |x|, else * := signl(x)*logl(2|x|+1/(|x|+sqrtl(x*x+1))) if|x|>2, else * := signl(x)*log1pl(|x| + x^2/(1 + sqrtl(1+x^2))) */ #include "libm.h" #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 long double asinhl(long double x) { return asinh(x); } #elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384 static const long double one = 1.000000000000000000000e+00L, /* 0x3FFF, 0x00000000, 0x00000000 */ ln2 = 6.931471805599453094287e-01L, /* 0x3FFE, 0xB17217F7, 0xD1CF79AC */ huge = 1.000000000000000000e+4900L; long double asinhl(long double x) { long double t,w; int32_t hx,ix; GET_LDOUBLE_EXP(hx, x); ix = hx & 0x7fff; if (ix == 0x7fff) return x + x; /* x is inf or NaN */ if (ix < 0x3fde) { /* |x| < 2**-34 */ /* return x, raise inexact if x != 0 */ if (huge+x > one) return x; } if (ix > 0x4020) { /* |x| > 2**34 */ w = logl(fabsl(x)) + ln2; } else if (ix > 0x4000) { /* 2**34 > |x| > 2.0 */ t = fabsl(x); w = logl(2.0*t + one/(sqrtl(x*x + one) + t)); } else { /* 2.0 > |x| > 2**-28 */ t = x*x; w =log1pl(fabsl(x) + t/(one + sqrtl(one + t))); } if (hx & 0x8000) return -w; return w; } #endif