1 /* @(#)s_asinh.c 5.1 93/09/24 */ 2 /* 3 * ==================================================== 4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 5 * 6 * Developed at SunPro, a Sun Microsystems, Inc. business. 7 * Permission to use, copy, modify, and distribute this 8 * software is freely granted, provided that this notice 9 * is preserved. 10 * ==================================================== 11 */ 12 13 /* asinh(x) 14 * Method : 15 * Based on 16 * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ] 17 * we have 18 * asinh(x) := x if 1+x*x=1, 19 * := sign(x)*(log(x)+ln2)) for large |x|, else 20 * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else 21 * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2))) 22 */ 23 24 #include <float.h> 25 #include <math.h> 26 27 #include "math_private.h" 28 29 static const double 30 one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ 31 ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ 32 huge= 1.00000000000000000000e+300; 33 34 double 35 asinh(double x) 36 { 37 double t,w; 38 int32_t hx,ix; 39 GET_HIGH_WORD(hx,x); 40 ix = hx&0x7fffffff; 41 if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */ 42 if(ix< 0x3e300000) { /* |x|<2**-28 */ 43 if(huge+x>one) return x; /* return x inexact except 0 */ 44 } 45 if(ix>0x41b00000) { /* |x| > 2**28 */ 46 w = log(fabs(x))+ln2; 47 } else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */ 48 t = fabs(x); 49 w = log(2.0*t+one/(sqrt(x*x+one)+t)); 50 } else { /* 2.0 > |x| > 2**-28 */ 51 t = x*x; 52 w =log1p(fabs(x)+t/(one+sqrt(one+t))); 53 } 54 if(hx>0) return w; else return -w; 55 } 56 57 #if LDBL_MANT_DIG == DBL_MANT_DIG 58 __strong_alias(asinhl, asinh); 59 #endif /* LDBL_MANT_DIG == DBL_MANT_DIG */ 60