s_asinh.c revision 8870
12116Sjkh/* @(#)s_asinh.c 5.1 93/09/24 */ 22116Sjkh/* 32116Sjkh * ==================================================== 42116Sjkh * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 52116Sjkh * 62116Sjkh * Developed at SunPro, a Sun Microsystems, Inc. business. 72116Sjkh * Permission to use, copy, modify, and distribute this 88870Srgrimes * software is freely granted, provided that this notice 92116Sjkh * is preserved. 102116Sjkh * ==================================================== 112116Sjkh */ 122116Sjkh 132116Sjkh#ifndef lint 148870Srgrimesstatic char rcsid[] = "$Id: s_asinh.c,v 1.1.1.1 1994/08/19 09:39:45 jkh Exp $"; 152116Sjkh#endif 162116Sjkh 172116Sjkh/* asinh(x) 182116Sjkh * Method : 198870Srgrimes * Based on 202116Sjkh * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ] 212116Sjkh * we have 222116Sjkh * asinh(x) := x if 1+x*x=1, 232116Sjkh * := sign(x)*(log(x)+ln2)) for large |x|, else 242116Sjkh * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else 258870Srgrimes * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2))) 262116Sjkh */ 272116Sjkh 282116Sjkh#include "math.h" 292116Sjkh#include "math_private.h" 302116Sjkh 312116Sjkh#ifdef __STDC__ 328870Srgrimesstatic const double 332116Sjkh#else 348870Srgrimesstatic double 352116Sjkh#endif 362116Sjkhone = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ 372116Sjkhln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ 388870Srgrimeshuge= 1.00000000000000000000e+300; 392116Sjkh 402116Sjkh#ifdef __STDC__ 412116Sjkh double asinh(double x) 422116Sjkh#else 432116Sjkh double asinh(x) 442116Sjkh double x; 452116Sjkh#endif 468870Srgrimes{ 472116Sjkh double t,w; 482116Sjkh int32_t hx,ix; 492116Sjkh GET_HIGH_WORD(hx,x); 502116Sjkh ix = hx&0x7fffffff; 512116Sjkh if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */ 522116Sjkh if(ix< 0x3e300000) { /* |x|<2**-28 */ 532116Sjkh if(huge+x>one) return x; /* return x inexact except 0 */ 548870Srgrimes } 552116Sjkh if(ix>0x41b00000) { /* |x| > 2**28 */ 562116Sjkh w = __ieee754_log(fabs(x))+ln2; 572116Sjkh } else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */ 582116Sjkh t = fabs(x); 592116Sjkh w = __ieee754_log(2.0*t+one/(sqrt(x*x+one)+t)); 602116Sjkh } else { /* 2.0 > |x| > 2**-28 */ 612116Sjkh t = x*x; 622116Sjkh w =log1p(fabs(x)+t/(one+sqrt(one+t))); 632116Sjkh } 642116Sjkh if(hx>0) return w; else return -w; 652116Sjkh} 66