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Diffstat (limited to 'lib/libm/common_source/sinh.c')
| -rw-r--r-- | lib/libm/common_source/sinh.c | 121 |
1 files changed, 121 insertions, 0 deletions
diff --git a/lib/libm/common_source/sinh.c b/lib/libm/common_source/sinh.c new file mode 100644 index 000000000000..0516849cff13 --- /dev/null +++ b/lib/libm/common_source/sinh.c @@ -0,0 +1,121 @@ +/* + * 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[] = "@(#)sinh.c 8.1 (Berkeley) 6/4/93"; +#endif /* not lint */ + +/* SINH(X) + * RETURN THE HYPERBOLIC SINE 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, 3/7/85, 3/24/85, 4/16/85. + * + * Required system supported functions : + * copysign(x,y) + * scalb(x,N) + * + * Required kernel functions: + * expm1(x) ...return exp(x)-1 + * + * Method : + * 1. reduce x to non-negative by sinh(-x) = - sinh(x). + * 2. + * + * expm1(x) + expm1(x)/(expm1(x)+1) + * 0 <= x <= lnovfl : sinh(x) := -------------------------------- + * 2 + * lnovfl <= x <= lnovfl+ln2 : sinh(x) := expm1(x)/2 (avoid overflow) + * lnovfl+ln2 < x < INF : overflow to INF + * + * + * Special cases: + * sinh(x) is x if x is +INF, -INF, or NaN. + * only sinh(0)=0 is exact for finite argument. + * + * Accuracy: + * sinh(x) returns the exact hyperbolic sine of x nearly rounded. In + * a test run with 1,024,000 random arguments on a VAX, the maximum + * observed error was 1.93 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 sinh(x) +double x; +{ + static const double one=1.0, half=1.0/2.0 ; + double t, sign; +#if !defined(vax)&&!defined(tahoe) + if(x!=x) return(x); /* x is NaN */ +#endif /* !defined(vax)&&!defined(tahoe) */ + sign=copysign(one,x); + x=copysign(x,one); + if(x<lnovfl) + {t=expm1(x); return(copysign((t+t/(one+t))*half,sign));} + + else if(x <= lnovfl+0.7) + /* subtract x by ln(2^(max+1)) and return 2^max*exp(x) + to avoid unnecessary overflow */ + return(copysign(scalb(one+expm1((x-mln2hi)-mln2lo),max),sign)); + + else /* sinh(+-INF) = +-INF, sinh(+-big no.) overflow to +-INF */ + return( expm1(x)*sign ); +} |