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Diffstat (limited to 'REORG.TODO/sysdeps/ieee754/dbl-64/e_cosh.c')
-rw-r--r-- | REORG.TODO/sysdeps/ieee754/dbl-64/e_cosh.c | 88 |
1 files changed, 88 insertions, 0 deletions
diff --git a/REORG.TODO/sysdeps/ieee754/dbl-64/e_cosh.c b/REORG.TODO/sysdeps/ieee754/dbl-64/e_cosh.c new file mode 100644 index 0000000000..52a5d5007d --- /dev/null +++ b/REORG.TODO/sysdeps/ieee754/dbl-64/e_cosh.c @@ -0,0 +1,88 @@ +/* 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) + { + if (ix < 0x3c800000) + return one; /* cosh(tiny) = 1 */ + t = __expm1 (fabs (x)); + w = one + t; + 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 math_narrow_eval (huge * huge); +} +strong_alias (__ieee754_cosh, __cosh_finite) |