The Android Open Source Project | b07e1d9 | 2009-03-03 19:29:30 -0800 | [diff] [blame] | 1 | |
| 2 | /* @(#)s_asinh.c 1.3 95/01/18 */ |
| 3 | /* |
| 4 | * ==================================================== |
| 5 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
| 6 | * |
| 7 | * Developed at SunSoft, a Sun Microsystems, Inc. business. |
| 8 | * Permission to use, copy, modify, and distribute this |
| 9 | * software is freely granted, provided that this notice |
| 10 | * is preserved. |
| 11 | * ==================================================== |
| 12 | */ |
| 13 | |
| 14 | /* asinh(x) |
| 15 | * Method : |
| 16 | * Based on |
| 17 | * asinh(x) = sign(x) * log [ |x| + ieee_sqrt(x*x+1) ] |
| 18 | * we have |
| 19 | * asinh(x) := x if 1+x*x=1, |
| 20 | * := sign(x)*(ieee_log(x)+ln2)) for large |x|, else |
| 21 | * := sign(x)*ieee_log(2|x|+1/(|x|+ieee_sqrt(x*x+1))) if|x|>2, else |
| 22 | * := sign(x)*ieee_log1p(|x| + x^2/(1 + ieee_sqrt(1+x^2))) |
| 23 | */ |
| 24 | |
| 25 | #include "fdlibm.h" |
| 26 | |
| 27 | #ifdef __STDC__ |
| 28 | static const double |
| 29 | #else |
| 30 | static double |
| 31 | #endif |
| 32 | one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ |
| 33 | ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ |
| 34 | huge= 1.00000000000000000000e+300; |
| 35 | |
| 36 | #ifdef __STDC__ |
| 37 | double asinh(double x) |
| 38 | #else |
| 39 | double asinh(x) |
| 40 | double x; |
| 41 | #endif |
| 42 | { |
| 43 | double t,w; |
| 44 | int hx,ix; |
| 45 | hx = __HI(x); |
| 46 | ix = hx&0x7fffffff; |
| 47 | if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */ |
| 48 | if(ix< 0x3e300000) { /* |x|<2**-28 */ |
| 49 | if(huge+x>one) return x; /* return x inexact except 0 */ |
| 50 | } |
| 51 | if(ix>0x41b00000) { /* |x| > 2**28 */ |
| 52 | w = __ieee754_log(ieee_fabs(x))+ln2; |
| 53 | } else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */ |
| 54 | t = ieee_fabs(x); |
| 55 | w = __ieee754_log(2.0*t+one/(ieee_sqrt(x*x+one)+t)); |
| 56 | } else { /* 2.0 > |x| > 2**-28 */ |
| 57 | t = x*x; |
| 58 | w =ieee_log1p(ieee_fabs(x)+t/(one+ieee_sqrt(one+t))); |
| 59 | } |
| 60 | if(hx>0) return w; else return -w; |
| 61 | } |