| lh | 9ed821d | 2023-04-07 01:36:19 -0700 | [diff] [blame^] | 1 | /* |
| 2 | * ==================================================== |
| 3 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
| 4 | * |
| 5 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
| 6 | * Permission to use, copy, modify, and distribute this |
| 7 | * software is freely granted, provided that this notice |
| 8 | * is preserved. |
| 9 | * ==================================================== |
| 10 | */ |
| 11 | |
| 12 | /* asinh(x) |
| 13 | * Method : |
| 14 | * Based on |
| 15 | * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ] |
| 16 | * we have |
| 17 | * asinh(x) := x if 1+x*x=1, |
| 18 | * := sign(x)*(log(x)+ln2)) for large |x|, else |
| 19 | * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else |
| 20 | * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2))) |
| 21 | */ |
| 22 | |
| 23 | #include "math.h" |
| 24 | #include "math_private.h" |
| 25 | |
| 26 | static const double |
| 27 | one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ |
| 28 | ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ |
| 29 | huge= 1.00000000000000000000e+300; |
| 30 | |
| 31 | double asinh(double x) |
| 32 | { |
| 33 | double t,w; |
| 34 | int32_t hx,ix; |
| 35 | GET_HIGH_WORD(hx,x); |
| 36 | ix = hx&0x7fffffff; |
| 37 | if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */ |
| 38 | if(ix< 0x3e300000) { /* |x|<2**-28 */ |
| 39 | if(huge+x>one) return x; /* return x inexact except 0 */ |
| 40 | } |
| 41 | if(ix>0x41b00000) { /* |x| > 2**28 */ |
| 42 | w = __ieee754_log(fabs(x))+ln2; |
| 43 | } else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */ |
| 44 | t = fabs(x); |
| 45 | w = __ieee754_log(2.0*t+one/(__ieee754_sqrt(x*x+one)+t)); |
| 46 | } else { /* 2.0 > |x| > 2**-28 */ |
| 47 | t = x*x; |
| 48 | w =log1p(fabs(x)+t/(one+__ieee754_sqrt(one+t))); |
| 49 | } |
| 50 | if(hx>0) return w; else return -w; |
| 51 | } |
| 52 | libm_hidden_def(asinh) |