s_asinh.c revision 21673
1193326Sed/* @(#)s_asinh.c 5.1 93/09/24 */ 2193326Sed/* 3193326Sed * ==================================================== 4193326Sed * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 5193326Sed * 6193326Sed * Developed at SunPro, a Sun Microsystems, Inc. business. 7193326Sed * Permission to use, copy, modify, and distribute this 8193326Sed * software is freely granted, provided that this notice 9193326Sed * is preserved. 10193326Sed * ==================================================== 11193326Sed */ 12193326Sed 13193326Sed#ifndef lint 14193326Sedstatic char rcsid[] = "$FreeBSD: head/lib/msun/src/s_asinh.c 21673 1997-01-14 07:20:47Z jkh $"; 15193326Sed#endif 16193326Sed 17226633Sdim/* asinh(x) 18193326Sed * Method : 19263508Sdim * Based on 20193326Sed * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ] 21193326Sed * we have 22193326Sed * asinh(x) := x if 1+x*x=1, 23193326Sed * := sign(x)*(log(x)+ln2)) for large |x|, else 24193326Sed * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else 25193326Sed * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2))) 26234353Sdim */ 27234353Sdim 28193326Sed#include "math.h" 29239462Sdim#include "math_private.h" 30193326Sed 31193326Sed#ifdef __STDC__ 32193326Sedstatic const double 33193326Sed#else 34193326Sedstatic double 35193326Sed#endif 36193326Sedone = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ 37193326Sedln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ 38193326Sedhuge= 1.00000000000000000000e+300; 39193326Sed 40193326Sed#ifdef __STDC__ 41193326Sed double asinh(double x) 42193326Sed#else 43193326Sed double asinh(x) 44198092Srdivacky double x; 45193326Sed#endif 46193326Sed{ 47193326Sed double t,w; 48193326Sed int32_t hx,ix; 49198092Srdivacky GET_HIGH_WORD(hx,x); 50193326Sed ix = hx&0x7fffffff; 51193326Sed if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */ 52193326Sed if(ix< 0x3e300000) { /* |x|<2**-28 */ 53198092Srdivacky if(huge+x>one) return x; /* return x inexact except 0 */ 54193326Sed } 55193326Sed if(ix>0x41b00000) { /* |x| > 2**28 */ 56193326Sed w = __ieee754_log(fabs(x))+ln2; 57226633Sdim } else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */ 58226633Sdim t = fabs(x); 59226633Sdim w = __ieee754_log(2.0*t+one/(sqrt(x*x+one)+t)); 60249423Sdim } else { /* 2.0 > |x| > 2**-28 */ 61249423Sdim t = x*x; 62249423Sdim w =log1p(fabs(x)+t/(one+sqrt(one+t))); 63249423Sdim } 64226633Sdim if(hx>0) return w; else return -w; 65193326Sed} 66193326Sed