s_asinh.c revision 176451
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 13176451Sdas#include <sys/cdefs.h> 14176451Sdas__FBSDID("$FreeBSD: head/lib/msun/src/s_asinh.c 176451 2008-02-22 02:30:36Z das $"); 152116Sjkh 162116Sjkh/* asinh(x) 172116Sjkh * Method : 188870Srgrimes * Based on 192116Sjkh * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ] 202116Sjkh * we have 212116Sjkh * asinh(x) := x if 1+x*x=1, 222116Sjkh * := sign(x)*(log(x)+ln2)) for large |x|, else 232116Sjkh * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else 248870Srgrimes * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2))) 252116Sjkh */ 262116Sjkh 272116Sjkh#include "math.h" 282116Sjkh#include "math_private.h" 292116Sjkh 308870Srgrimesstatic const double 312116Sjkhone = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ 322116Sjkhln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ 338870Srgrimeshuge= 1.00000000000000000000e+300; 342116Sjkh 3597413Salfreddouble 3697413Salfredasinh(double x) 378870Srgrimes{ 382116Sjkh double t,w; 392116Sjkh int32_t hx,ix; 402116Sjkh GET_HIGH_WORD(hx,x); 412116Sjkh ix = hx&0x7fffffff; 422116Sjkh if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */ 432116Sjkh if(ix< 0x3e300000) { /* |x|<2**-28 */ 442116Sjkh if(huge+x>one) return x; /* return x inexact except 0 */ 458870Srgrimes } 462116Sjkh if(ix>0x41b00000) { /* |x| > 2**28 */ 472116Sjkh w = __ieee754_log(fabs(x))+ln2; 482116Sjkh } else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */ 492116Sjkh t = fabs(x); 5023579Sbde w = __ieee754_log(2.0*t+one/(__ieee754_sqrt(x*x+one)+t)); 512116Sjkh } else { /* 2.0 > |x| > 2**-28 */ 522116Sjkh t = x*x; 5323579Sbde w =log1p(fabs(x)+t/(one+__ieee754_sqrt(one+t))); 542116Sjkh } 552116Sjkh if(hx>0) return w; else return -w; 562116Sjkh} 57