xref: /illumos-gate/usr/src/lib/libm/common/C/cosh.c (revision ddc0e0b5)
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2125c28e83SPiotr Jasiukajtis /*
2225c28e83SPiotr Jasiukajtis  * Copyright 2011 Nexenta Systems, Inc.  All rights reserved.
2325c28e83SPiotr Jasiukajtis  */
2425c28e83SPiotr Jasiukajtis /*
2525c28e83SPiotr Jasiukajtis  * Copyright 2005 Sun Microsystems, Inc.  All rights reserved.
2625c28e83SPiotr Jasiukajtis  * Use is subject to license terms.
2725c28e83SPiotr Jasiukajtis  */
2825c28e83SPiotr Jasiukajtis 
29*ddc0e0b5SRichard Lowe #pragma weak __cosh = cosh
3025c28e83SPiotr Jasiukajtis 
3125c28e83SPiotr Jasiukajtis /* INDENT OFF */
3225c28e83SPiotr Jasiukajtis /*
3325c28e83SPiotr Jasiukajtis  * cosh(x)
3425c28e83SPiotr Jasiukajtis  * Code originated from 4.3bsd.
3525c28e83SPiotr Jasiukajtis  * Modified by K.C. Ng for SUN 4.0 libm.
3625c28e83SPiotr Jasiukajtis  * Method :
3725c28e83SPiotr Jasiukajtis  *	1. Replace x by |x| (cosh(x) = cosh(-x)).
3825c28e83SPiotr Jasiukajtis  *	2.
3925c28e83SPiotr Jasiukajtis  *                                       [ exp(x) - 1 ]^2
4025c28e83SPiotr Jasiukajtis  *  0        <= x <= 0.3465  :  cosh(x) := 1 + -------------------
4125c28e83SPiotr Jasiukajtis  *								      2*exp(x)
4225c28e83SPiotr Jasiukajtis  *
4325c28e83SPiotr Jasiukajtis  *		                                   exp(x) +  1/exp(x)
4425c28e83SPiotr Jasiukajtis  *  0.3465   <= x <= 22      :  cosh(x) := -------------------
4525c28e83SPiotr Jasiukajtis  *								           2
4625c28e83SPiotr Jasiukajtis  *  22       <= x <= lnovft  :  cosh(x) := exp(x)/2
4725c28e83SPiotr Jasiukajtis  *  lnovft   <= x <  INF     :  cosh(x) := scalbn(exp(x-1024*ln2),1023)
4825c28e83SPiotr Jasiukajtis  *
4925c28e83SPiotr Jasiukajtis  *	Note: .3465 is a number near one half of ln2.
5025c28e83SPiotr Jasiukajtis  *
5125c28e83SPiotr Jasiukajtis  * Special cases:
5225c28e83SPiotr Jasiukajtis  *	cosh(x) is |x| if x is +INF, -INF, or NaN.
5325c28e83SPiotr Jasiukajtis  *	only cosh(0)=1 is exact for finite x.
5425c28e83SPiotr Jasiukajtis  */
5525c28e83SPiotr Jasiukajtis /* INDENT ON */
5625c28e83SPiotr Jasiukajtis 
5725c28e83SPiotr Jasiukajtis #include "libm.h"
5825c28e83SPiotr Jasiukajtis 
5925c28e83SPiotr Jasiukajtis static const double
6025c28e83SPiotr Jasiukajtis 	ln2 = 6.93147180559945286227e-01,
6125c28e83SPiotr Jasiukajtis 	ln2hi = 6.93147180369123816490e-01,
6225c28e83SPiotr Jasiukajtis 	ln2lo = 1.90821492927058770002e-10,
6325c28e83SPiotr Jasiukajtis 	lnovft = 7.09782712893383973096e+02;
6425c28e83SPiotr Jasiukajtis 
6525c28e83SPiotr Jasiukajtis double
cosh(double x)6625c28e83SPiotr Jasiukajtis cosh(double x) {
6725c28e83SPiotr Jasiukajtis 	double t, w;
6825c28e83SPiotr Jasiukajtis 
6925c28e83SPiotr Jasiukajtis 	w = fabs(x);
7025c28e83SPiotr Jasiukajtis 	if (!finite(w))
7125c28e83SPiotr Jasiukajtis 		return (w * w);
7225c28e83SPiotr Jasiukajtis 	if (w < 0.3465) {
7325c28e83SPiotr Jasiukajtis 		t = expm1(w);
7425c28e83SPiotr Jasiukajtis 		w = 1.0 + t;
7525c28e83SPiotr Jasiukajtis 		if (w != 1.0)
7625c28e83SPiotr Jasiukajtis 			w = 1.0 + (t * t) / (w + w);
7725c28e83SPiotr Jasiukajtis 		return (w);
7825c28e83SPiotr Jasiukajtis 	} else if (w < 22.0) {
7925c28e83SPiotr Jasiukajtis 		t = exp(w);
8025c28e83SPiotr Jasiukajtis 		return (0.5 * (t + 1.0 / t));
8125c28e83SPiotr Jasiukajtis 	} else if (w <= lnovft) {
8225c28e83SPiotr Jasiukajtis 		return (0.5 * exp(w));
8325c28e83SPiotr Jasiukajtis 	} else {
8425c28e83SPiotr Jasiukajtis 		w = (w - 1024 * ln2hi) - 1024 * ln2lo;
8525c28e83SPiotr Jasiukajtis 		if (w >= ln2)
8625c28e83SPiotr Jasiukajtis 			return (_SVID_libm_err(x, x, 5));
8725c28e83SPiotr Jasiukajtis 		else
8825c28e83SPiotr Jasiukajtis 			return (scalbn(exp(w), 1023));
8925c28e83SPiotr Jasiukajtis 	}
9025c28e83SPiotr Jasiukajtis }
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