/* origin: FreeBSD /usr/src/lib/msun/src/s_asinh.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. * ==================================================== */ /* asinh(x) * Method : * Based on * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ] * we have * asinh(x) := x if 1+x*x=1, * := sign(x)*(log(x)+ln2)) for large |x|, else * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2))) */ #include "libm.h" static const double ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ huge= 1.00000000000000000000e+300; double asinh(double x) { double t,w; int32_t hx,ix; GET_HIGH_WORD(hx, x); ix = hx & 0x7fffffff; if (ix >= 0x7ff00000) /* x is inf or NaN */ return x+x; if (ix < 0x3e300000) { /* |x| < 2**-28 */ /* return x inexact except 0 */ if (huge+x > 1.0) return x; } if (ix > 0x41b00000) { /* |x| > 2**28 */ w = log(fabs(x)) + ln2; } else if (ix > 0x40000000) { /* 2**28 > |x| > 2.0 */ t = fabs(x); w = log(2.0*t + 1.0/(sqrt(x*x+1.0)+t)); } else { /* 2.0 > |x| > 2**-28 */ t = x*x; w =log1p(fabs(x) + t/(1.0+sqrt(1.0+t))); } if (hx > 0) return w; return -w; }