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path: root/src/math/s_asinh.c
blob: 260160912e5bcc9dbf7160ce2224d8b7b743a672 (plain)
 ```1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 ``` ``````/* @(#)s_asinh.c 5.1 93/09/24 */ /* * ==================================================== * 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 #include "math_private.h" static const double one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ 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) return x+x; /* x is inf or NaN */ if(ix< 0x3e300000) { /* |x|<2**-28 */ if(huge+x>one) return x; /* return x inexact except 0 */ } 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+one/(sqrt(x*x+one)+t)); } else { /* 2.0 > |x| > 2**-28 */ t = x*x; w =log1p(fabs(x)+t/(one+sqrt(one+t))); } if(hx>0) return w; else return -w; } ``````