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Diffstat (limited to 'lib/libm/common_source/cosh.c')
| -rw-r--r-- | lib/libm/common_source/cosh.c | 133 |
1 files changed, 133 insertions, 0 deletions
diff --git a/lib/libm/common_source/cosh.c b/lib/libm/common_source/cosh.c new file mode 100644 index 000000000000..e2b30731b8c1 --- /dev/null +++ b/lib/libm/common_source/cosh.c @@ -0,0 +1,133 @@ +/* + * Copyright (c) 1985, 1993 + * The 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 8.1 (Berkeley) 6/4/93"; +#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 */ +} |