| /* Optimized by Ulrich Drepper <drepper@gmail.com>, 2011 */ |
| /* |
| * ==================================================== |
| * 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. |
| * ==================================================== |
| */ |
| |
| /* __ieee754_cosh(x) |
| * Method : |
| * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2 |
| * 1. Replace x by |x| (cosh(x) = cosh(-x)). |
| * 2. |
| * [ exp(x) - 1 ]^2 |
| * 0 <= x <= ln2/2 : cosh(x) := 1 + ------------------- |
| * 2*exp(x) |
| * |
| * exp(x) + 1/exp(x) |
| * ln2/2 <= x <= 22 : cosh(x) := ------------------- |
| * 2 |
| * 22 <= x <= lnovft : cosh(x) := exp(x)/2 |
| * lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2) |
| * ln2ovft < x : cosh(x) := huge*huge (overflow) |
| * |
| * Special cases: |
| * cosh(x) is |x| if x is +INF, -INF, or NaN. |
| * only cosh(0)=1 is exact for finite x. |
| */ |
| |
| #include <math.h> |
| #include <math_private.h> |
| |
| static const double one = 1.0, half = 0.5, huge = 1.0e300; |
| |
| double |
| __ieee754_cosh (double x) |
| { |
| double t, w; |
| int32_t ix; |
| u_int32_t lx; |
| |
| /* High word of |x|. */ |
| GET_HIGH_WORD (ix, x); |
| ix &= 0x7fffffff; |
| |
| /* |x| in [0,22] */ |
| if (ix < 0x40360000) |
| { |
| /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */ |
| if (ix < 0x3fd62e43) |
| { |
| t = __expm1 (fabs (x)); |
| w = one + t; |
| if (ix < 0x3c800000) |
| return w; /* cosh(tiny) = 1 */ |
| return one + (t * t) / (w + w); |
| } |
| |
| /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */ |
| t = __ieee754_exp (fabs (x)); |
| return half * t + half / t; |
| } |
| |
| /* |x| in [22, log(maxdouble)] return half*exp(|x|) */ |
| if (ix < 0x40862e42) |
| return half * __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 (half * fabs (x)); |
| t = half * w; |
| return t * w; |
| } |
| |
| /* x is INF or NaN */ |
| if (ix >= 0x7ff00000) |
| return x * x; |
| |
| /* |x| > overflowthresold, cosh(x) overflow */ |
| return huge * huge; |
| } |
| strong_alias (__ieee754_cosh, __cosh_finite) |
