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 #include <sys/cdefs.h> 14 __FBSDID("$FreeBSD$"); 15 16 /* asinh(x) 17 * Method : 18 * Based on 19 * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ] 20 * we have 21 * asinh(x) := x if 1+x*x=1, 22 * := sign(x)*(log(x)+ln2)) for large |x|, else 23 * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else 24 * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2))) 25 */ 26 27 #include <float.h> 28 29 #include "math.h" 30 #include "math_private.h" 31 32 static const double 33 one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ 34 ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ 35 huge= 1.00000000000000000000e+300; 36 37 double 38 asinh(double x) 39 { 40 double t,w; 41 int32_t hx,ix; 42 GET_HIGH_WORD(hx,x); 43 ix = hx&0x7fffffff; 44 if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */ 45 if(ix< 0x3e300000) { /* |x|<2**-28 */ 46 if(huge+x>one) return x; /* return x inexact except 0 */ 47 } 48 if(ix>0x41b00000) { /* |x| > 2**28 */ 49 w = __ieee754_log(fabs(x))+ln2; 50 } else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */ 51 t = fabs(x); 52 w = __ieee754_log(2.0*t+one/(__ieee754_sqrt(x*x+one)+t)); 53 } else { /* 2.0 > |x| > 2**-28 */ 54 t = x*x; 55 w =log1p(fabs(x)+t/(one+__ieee754_sqrt(one+t))); 56 } 57 if(hx>0) return w; else return -w; 58 } 59 60 #if LDBL_MANT_DIG == 53 61 __weak_reference(asinh, asinhl); 62 #endif 63