| /* @(#)e_sinh.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. |
| * ==================================================== |
| */ |
| |
| #if defined(LIBM_SCCS) && !defined(lint) |
| static char rcsid[] = "$NetBSD: e_sinh.c,v 1.7 1995/05/10 20:46:13 jtc Exp $"; |
| #endif |
| |
| /* __ieee754_sinh(x) |
| * Method : |
| * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2 |
| * 1. Replace x by |x| (sinh(-x) = -sinh(x)). |
| * 2. |
| * E + E/(E+1) |
| * 0 <= x <= 22 : sinh(x) := --------------, E=expm1(x) |
| * 2 |
| * |
| * 22 <= x <= lnovft : sinh(x) := exp(x)/2 |
| * lnovft <= x <= ln2ovft: sinh(x) := exp(x/2)/2 * exp(x/2) |
| * ln2ovft < x : sinh(x) := x*shuge (overflow) |
| * |
| * Special cases: |
| * sinh(x) is |x| if x is +INF, -INF, or NaN. |
| * only sinh(0)=0 is exact for finite x. |
| */ |
| |
| #include <math.h> |
| #include <math_private.h> |
| |
| static const double one = 1.0, shuge = 1.0e307; |
| |
| double |
| __ieee754_sinh (double x) |
| { |
| double t, w, h; |
| int32_t ix, jx; |
| u_int32_t lx; |
| |
| /* High word of |x|. */ |
| GET_HIGH_WORD (jx, x); |
| ix = jx & 0x7fffffff; |
| |
| /* x is INF or NaN */ |
| if (__builtin_expect (ix >= 0x7ff00000, 0)) |
| return x + x; |
| |
| h = 0.5; |
| if (jx < 0) |
| h = -h; |
| /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */ |
| if (ix < 0x40360000) /* |x|<22 */ |
| { |
| if (__builtin_expect (ix < 0x3e300000, 0)) /* |x|<2**-28 */ |
| if (shuge + x > one) |
| return x; |
| /* sinh(tiny) = tiny with inexact */ |
| t = __expm1 (fabs (x)); |
| if (ix < 0x3ff00000) |
| return h * (2.0 * t - t * t / (t + one)); |
| return h * (t + t / (t + one)); |
| } |
| |
| /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */ |
| if (ix < 0x40862e42) |
| return h * __ieee754_exp (fabs (x)); |
| |
| /* |x| in [log(maxdouble), overflowthresold] */ |
| GET_LOW_WORD (lx, x); |
| if (ix < 0x408633ce || ((ix == 0x408633ce) && (lx <= (u_int32_t) 0x8fb9f87d))) |
| { |
| w = __ieee754_exp (0.5 * fabs (x)); |
| t = h * w; |
| return t * w; |
| } |
| |
| /* |x| > overflowthresold, sinh(x) overflow */ |
| return x * shuge; |
| } |
| strong_alias (__ieee754_sinh, __sinh_finite) |
