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Diffstat (limited to 'e_cosh.c')
-rw-r--r-- | e_cosh.c | 89 |
1 files changed, 89 insertions, 0 deletions
diff --git a/e_cosh.c b/e_cosh.c new file mode 100644 index 0000000..a5c5ae6 --- /dev/null +++ b/e_cosh.c @@ -0,0 +1,89 @@ + +/* @(#)e_cosh.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, 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 ieee_cosh(x) if defined to be (ieee_exp(x)+ieee_exp(-x))/2 + * 1. Replace x by |x| (ieee_cosh(x) = ieee_cosh(-x)). + * 2. + * [ ieee_exp(x) - 1 ]^2 + * 0 <= x <= ln2/2 : ieee_cosh(x) := 1 + ------------------- + * 2*ieee_exp(x) + * + * ieee_exp(x) + 1/ieee_exp(x) + * ln2/2 <= x <= 22 : ieee_cosh(x) := ------------------- + * 2 + * 22 <= x <= lnovft : ieee_cosh(x) := ieee_exp(x)/2 + * lnovft <= x <= ln2ovft: ieee_cosh(x) := ieee_exp(x/2)/2 * ieee_exp(x/2) + * ln2ovft < x : ieee_cosh(x) := huge*huge (overflow) + * + * Special cases: + * cosh(x) is |x| if x is +INF, -INF, or NaN. + * only ieee_cosh(0)=1 is exact for finite x. + */ + +#include "fdlibm.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; + int ix; + unsigned lx; + + /* High word of |x|. */ + ix = __HI(x); + ix &= 0x7fffffff; + + /* x is INF or NaN */ + if(ix>=0x7ff00000) return x*x; + + /* |x| in [0,0.5*ln2], return 1+ieee_expm1(|x|)^2/(2*ieee_exp(|x|)) */ + if(ix<0x3fd62e43) { + t = ieee_expm1(ieee_fabs(x)); + w = one+t; + if (ix<0x3c800000) return w; /* ieee_cosh(tiny) = 1 */ + return one+(t*t)/(w+w); + } + + /* |x| in [0.5*ln2,22], return (ieee_exp(|x|)+1/ieee_exp(|x|)/2; */ + if (ix < 0x40360000) { + t = __ieee754_exp(ieee_fabs(x)); + return half*t+half/t; + } + + /* |x| in [22, ieee_log(maxdouble)] return half*ieee_exp(|x|) */ + if (ix < 0x40862E42) return half*__ieee754_exp(ieee_fabs(x)); + + /* |x| in [log(maxdouble), overflowthresold] */ + lx = *( (((*(unsigned*)&one)>>29)) + (unsigned*)&x); + if (ix<0x408633CE || + (ix==0x408633ce)&&(lx<=(unsigned)0x8fb9f87d)) { + w = __ieee754_exp(half*ieee_fabs(x)); + t = half*w; + return t*w; + } + + /* |x| > overflowthresold, ieee_cosh(x) overflow */ + return huge*huge; +} |