| /* @(#)s_asinh.c 5.1 93/09/24 */ |
| /* |
| * ==================================================== |
| * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
| * |
| * Developed at SunPro, a Sun Microsystems, Inc. business. |
| * Permission to use, copy, modify, and distribute this |
| * software is freely granted, provided that this notice |
| * is preserved. |
| * ==================================================== |
| */ |
| |
| /* asinh(x) |
| * Method : |
| * Based on |
| * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ] |
| * we have |
| * asinh(x) := x if 1+x*x=1, |
| * := sign(x)*(log(x)+ln2)) for large |x|, else |
| * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else |
| * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2))) |
| */ |
| |
| #include <math.h> |
| #include <math_private.h> |
| |
| static const double |
| one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ |
| ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ |
| huge = 1.00000000000000000000e+300; |
| |
| double |
| __asinh (double x) |
| { |
| double w; |
| int32_t hx, ix; |
| GET_HIGH_WORD (hx, x); |
| ix = hx & 0x7fffffff; |
| if (__builtin_expect (ix < 0x3e300000, 0)) /* |x|<2**-28 */ |
| { |
| if (huge + x > one) |
| return x; /* return x inexact except 0 */ |
| } |
| if (__builtin_expect (ix > 0x41b00000, 0)) /* |x| > 2**28 */ |
| { |
| if (ix >= 0x7ff00000) |
| return x + x; /* x is inf or NaN */ |
| w = __ieee754_log (fabs (x)) + ln2; |
| } |
| else |
| { |
| double xa = fabs (x); |
| if (ix > 0x40000000) /* 2**28 > |x| > 2.0 */ |
| { |
| w = __ieee754_log (2.0 * xa + one / (__ieee754_sqrt (xa * xa + one) + |
| xa)); |
| } |
| else /* 2.0 > |x| > 2**-28 */ |
| { |
| double t = xa * xa; |
| w = __log1p (xa + t / (one + __ieee754_sqrt (one + t))); |
| } |
| } |
| return __copysign (w, x); |
| } |
| weak_alias (__asinh, asinh) |
| #ifdef NO_LONG_DOUBLE |
| strong_alias (__asinh, __asinhl) |
| weak_alias (__asinh, asinhl) |
| #endif |
