1 /* 2 * ==================================================== 3 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 4 * 5 * Developed at SunPro, a Sun Microsystems, Inc. business. 6 * Permission to use, copy, modify, and distribute this 7 * software is freely granted, provided that this notice 8 * is preserved. 9 * ==================================================== 10 */ 11 12 /* asinh(x) 13 * Method : 14 * Based on 15 * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ] 16 * we have 17 * asinh(x) := x if 1+x*x=1, 18 * := sign(x)*(log(x)+ln2)) for large |x|, else 19 * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else 20 * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2))) 21 */ 22 23 #include <float.h> 24 25 #include "math.h" 26 #include "math_private.h" 27 28 static const double 29 one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ 30 ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ 31 huge= 1.00000000000000000000e+300; 32 33 double 34 asinh(double x) 35 { 36 double t,w; 37 int32_t hx,ix; 38 GET_HIGH_WORD(hx,x); 39 ix = hx&0x7fffffff; 40 if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */ 41 if(ix< 0x3e300000) { /* |x|<2**-28 */ 42 if(huge+x>one) return x; /* return x inexact except 0 */ 43 } 44 if(ix>0x41b00000) { /* |x| > 2**28 */ 45 w = log(fabs(x))+ln2; 46 } else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */ 47 t = fabs(x); 48 w = log(2.0*t+one/(sqrt(x*x+one)+t)); 49 } else { /* 2.0 > |x| > 2**-28 */ 50 t = x*x; 51 w =log1p(fabs(x)+t/(one+sqrt(one+t))); 52 } 53 if(hx>0) return w; else return -w; 54 } 55 56 #if LDBL_MANT_DIG == 53 57 __weak_reference(asinh, asinhl); 58 #endif 59