diff options
Diffstat (limited to 'libm/e_cosh.c')
| -rw-r--r-- | libm/e_cosh.c | 93 |
1 files changed, 93 insertions, 0 deletions
diff --git a/libm/e_cosh.c b/libm/e_cosh.c new file mode 100644 index 000000000..3f9ed63b4 --- /dev/null +++ b/libm/e_cosh.c @@ -0,0 +1,93 @@ +/* @(#)e_cosh.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_cosh.c,v 1.7 1995/05/10 20:44:58 jtc Exp $"; +#endif + +/* __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" + +#ifdef __STDC__ +static const double one = 1.0, half=0.5, huge = 1.0e300; +#else +static double one = 1.0, half=0.5, huge = 1.0e300; +#endif + +#ifdef __STDC__ + double __ieee754_cosh(double x) +#else + double __ieee754_cosh(x) + double x; +#endif +{ + double t,w; + int32_t ix; + u_int32_t lx; + + /* High word of |x|. */ + GET_HIGH_WORD(ix,x); + ix &= 0x7fffffff; + + /* x is INF or NaN */ + if(ix>=0x7ff00000) return x*x; + + /* |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; */ + if (ix < 0x40360000) { + 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| > overflowthresold, cosh(x) overflow */ + return huge*huge; +} |