[unix-history] / usr / src / lib / libm / common_source / cosh.c

/*
 * Copyright (c) 1985 Regents of the University of California.
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 * 3. All advertising materials mentioning features or use of this software
 *    must display the following acknowledgement:
 *	This product includes software developed by the University of
 *	California, Berkeley and its contributors.
 * 4. Neither the name of the University nor the names of its contributors
 *    may be used to endorse or promote products derived from this software
 *    without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
 * SUCH DAMAGE.
 */

#ifndef lint
static char sccsid[] = "@(#)cosh.c	5.6 (Berkeley) 10/9/90";
#endif /* not lint */

/* COSH(X)
 * RETURN THE HYPERBOLIC COSINE OF X
 * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
 * CODED IN C BY K.C. NG, 1/8/85; 
 * REVISED BY K.C. NG on 2/8/85, 2/23/85, 3/7/85, 3/29/85, 4/16/85.
 *
 * Required system supported functions :
 *	copysign(x,y)
 *	scalb(x,N)
 *
 * Required kernel function:
 *	exp(x) 
 *	exp__E(x,c)	...return exp(x+c)-1-x for |x|<0.3465
 *
 * Method :
 *	1. Replace x by |x|. 
 *	2. 
 *		                                        [ exp(x) - 1 ]^2 
 *	    0        <= x <= 0.3465  :  cosh(x) := 1 + -------------------
 *			       			           2*exp(x)
 *
 *		                                   exp(x) +  1/exp(x)
 *	    0.3465   <= x <= 22      :  cosh(x) := -------------------
 *			       			           2
 *	    22       <= x <= lnovfl  :  cosh(x) := exp(x)/2 
 *	    lnovfl   <= x <= lnovfl+log(2)
 *				     :  cosh(x) := exp(x)/2 (avoid overflow)
 *	    log(2)+lnovfl <  x <  INF:  overflow to INF
 *
 *	Note: .3465 is a number near one half of ln2.
 *
 * Special cases:
 *	cosh(x) is x if x is +INF, -INF, or NaN.
 *	only cosh(0)=1 is exact for finite x.
 *
 * Accuracy:
 *	cosh(x) returns the exact hyperbolic cosine of x nearly rounded.
 *	In a test run with 768,000 random arguments on a VAX, the maximum
 *	observed error was 1.23 ulps (units in the last place).
 *
 * Constants:
 * The hexadecimal values are the intended ones for the following constants.
 * The decimal values may be used, provided that the compiler will convert
 * from decimal to binary accurately enough to produce the hexadecimal values
 * shown.
 */

#include "mathimpl.h"

vc(mln2hi, 8.8029691931113054792E1   ,0f33,43b0,2bdb,c7e2,   7, .B00F33C7E22BDB)
vc(mln2lo,-4.9650192275318476525E-16 ,1b60,a70f,582a,279e, -50,-.8F1B60279E582A)
vc(lnovfl, 8.8029691931113053016E1   ,0f33,43b0,2bda,c7e2,   7, .B00F33C7E22BDA)

ic(mln2hi, 7.0978271289338397310E2,    10, 1.62E42FEFA39EF)
ic(mln2lo, 2.3747039373786107478E-14, -45, 1.ABC9E3B39803F)
ic(lnovfl, 7.0978271289338397310E2,     9, 1.62E42FEFA39EF)

#ifdef vccast
#define   mln2hi    vccast(mln2hi)
#define   mln2lo    vccast(mln2lo)
#define   lnovfl    vccast(lnovfl)
#endif

#if defined(vax)||defined(tahoe)
static max = 126                      ;
#else	/* defined(vax)||defined(tahoe) */
static max = 1023                     ;
#endif	/* defined(vax)||defined(tahoe) */

double cosh(x)
double x;
{	
	static const double half=1.0/2.0,
		one=1.0, small=1.0E-18; /* fl(1+small)==1 */
	double t;

#if !defined(vax)&&!defined(tahoe)
	if(x!=x) return(x);	/* x is NaN */
#endif	/* !defined(vax)&&!defined(tahoe) */
	if((x=copysign(x,one)) <= 22)
	    if(x<0.3465) 
		if(x<small) return(one+x);
		else {t=x+exp__E(x,0.0);x=t+t; return(one+t*t/(2.0+x)); }

	    else /* for x lies in [0.3465,22] */
	        { t=exp(x); return((t+one/t)*half); }

	if( lnovfl <= x && x <= (lnovfl+0.7)) 
        /* for x lies in [lnovfl, lnovfl+ln2], decrease x by ln(2^(max+1)) 
         * and return 2^max*exp(x) to avoid unnecessary overflow 
         */
	    return(scalb(exp((x-mln2hi)-mln2lo), max)); 

	else 
	    return(exp(x)*half);	/* for large x,  cosh(x)=exp(x)/2 */
}
Commit	Line	Data
4c182be8	1	/*
c77add16	2	* Copyright (c) 1985 Regents of the University of California.
4c182be8 KB	3	* All rights reserved.
4c182be8 KB	4	*
af359dea C	5	* Redistribution and use in source and binary forms, with or without
	6	* modification, are permitted provided that the following conditions
	7	* are met:
	8	* 1. Redistributions of source code must retain the above copyright
	9	* notice, this list of conditions and the following disclaimer.
	10	* 2. Redistributions in binary form must reproduce the above copyright
	11	* notice, this list of conditions and the following disclaimer in the
	12	* documentation and/or other materials provided with the distribution.
	13	* 3. All advertising materials mentioning features or use of this software
	14	* must display the following acknowledgement:
	15	* This product includes software developed by the University of
	16	* California, Berkeley and its contributors.
	17	* 4. Neither the name of the University nor the names of its contributors
	18	* may be used to endorse or promote products derived from this software
	19	* without specific prior written permission.
4c182be8	20	*
af359dea C	21	* THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
	22	* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
	23	* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
	24	* ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
	25	* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
	26	* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
	27	* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
	28	* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
	29	* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
	30	* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
	31	* SUCH DAMAGE.
c77add16 ZAL	32	*/
	33
	34	#ifndef lint
af359dea	35	static char sccsid[] = "@(#)cosh.c 5.6 (Berkeley) 10/9/90";
4c182be8	36	#endif /* not lint */
c77add16 ZAL	37
	38	/* COSH(X)
	39	* RETURN THE HYPERBOLIC COSINE OF X
	40	* DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
	41	* CODED IN C BY K.C. NG, 1/8/85;
	42	* REVISED BY K.C. NG on 2/8/85, 2/23/85, 3/7/85, 3/29/85, 4/16/85.
	43	*
	44	* Required system supported functions :
	45	* copysign(x,y)
	46	* scalb(x,N)
	47	*
	48	* Required kernel function:
	49	* exp(x)
	50	* exp__E(x,c) ...return exp(x+c)-1-x for \|x\|<0.3465
	51	*
	52	* Method :
	53	* 1. Replace x by \|x\|.
	54	* 2.
	55	* [ exp(x) - 1 ]^2
	56	* 0 <= x <= 0.3465 : cosh(x) := 1 + -------------------
	57	* 2*exp(x)
	58	*
	59	* exp(x) + 1/exp(x)
	60	* 0.3465 <= x <= 22 : cosh(x) := -------------------
	61	* 2
	62	* 22 <= x <= lnovfl : cosh(x) := exp(x)/2
	63	* lnovfl <= x <= lnovfl+log(2)
	64	* : cosh(x) := exp(x)/2 (avoid overflow)
	65	* log(2)+lnovfl < x < INF: overflow to INF
	66	*
	67	* Note: .3465 is a number near one half of ln2.
	68	*
	69	* Special cases:
	70	* cosh(x) is x if x is +INF, -INF, or NaN.
	71	* only cosh(0)=1 is exact for finite x.
	72	*
	73	* Accuracy:
	74	* cosh(x) returns the exact hyperbolic cosine of x nearly rounded.
	75	* In a test run with 768,000 random arguments on a VAX, the maximum
	76	* observed error was 1.23 ulps (units in the last place).
	77	*
	78	* Constants:
	79	* The hexadecimal values are the intended ones for the following constants.
	80	* The decimal values may be used, provided that the compiler will convert
	81	* from decimal to binary accurately enough to produce the hexadecimal values
	82	* shown.
	83	*/
	84
9eda3584 KB	85	#include "mathimpl.h"
	86
	87	vc(mln2hi, 8.8029691931113054792E1 ,0f33,43b0,2bdb,c7e2, 7, .B00F33C7E22BDB)
	88	vc(mln2lo,-4.9650192275318476525E-16 ,1b60,a70f,582a,279e, -50,-.8F1B60279E582A)
	89	vc(lnovfl, 8.8029691931113053016E1 ,0f33,43b0,2bda,c7e2, 7, .B00F33C7E22BDA)
	90
	91	ic(mln2hi, 7.0978271289338397310E2, 10, 1.62E42FEFA39EF)
	92	ic(mln2lo, 2.3747039373786107478E-14, -45, 1.ABC9E3B39803F)
	93	ic(lnovfl, 7.0978271289338397310E2, 9, 1.62E42FEFA39EF)
	94
	95	#ifdef vccast
	96	#define mln2hi vccast(mln2hi)
	97	#define mln2lo vccast(mln2lo)
	98	#define lnovfl vccast(lnovfl)
	99	#endif
c77add16	100
859dc438	101	#if defined(vax)\|\|defined(tahoe)
c77add16	102	static max = 126 ;
859dc438	103	#else /* defined(vax)\|\|defined(tahoe) */
c77add16	104	static max = 1023 ;
859dc438	105	#endif /* defined(vax)\|\|defined(tahoe) */
c77add16 ZAL	106
	107	double cosh(x)
	108	double x;
	109	{
9eda3584 KB	110	static const double half=1.0/2.0,
	111	one=1.0, small=1.0E-18; /* fl(1+small)==1 */
	112	double t;
c77add16	113
859dc438	114	#if !defined(vax)&&!defined(tahoe)
c77add16	115	if(x!=x) return(x); /* x is NaN */
859dc438	116	#endif /* !defined(vax)&&!defined(tahoe) */
c77add16 ZAL	117	if((x=copysign(x,one)) <= 22)
	118	if(x<0.3465)
	119	if(x<small) return(one+x);
	120	else {t=x+exp__E(x,0.0);x=t+t; return(one+t*t/(2.0+x)); }
	121
	122	else /* for x lies in [0.3465,22] */
	123	{ t=exp(x); return((t+one/t)*half); }
	124
	125	if( lnovfl <= x && x <= (lnovfl+0.7))
	126	/* for x lies in [lnovfl, lnovfl+ln2], decrease x by ln(2^(max+1))
	127	* and return 2^max*exp(x) to avoid unnecessary overflow
	128	*/
	129	return(scalb(exp((x-mln2hi)-mln2lo), max));
	130
	131	else
	132	return(exp(x)half); / for large x, cosh(x)=exp(x)/2 */
	133	}