122 lines
4.5 KiB
C
122 lines
4.5 KiB
C
/*
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* Copyright (c) 1985 Regents of the University of California.
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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* 3. All advertising materials mentioning features or use of this software
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* must display the following acknowledgement:
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* This product includes software developed by the University of
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* California, Berkeley and its contributors.
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* 4. Neither the name of the University nor the names of its contributors
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* may be used to endorse or promote products derived from this software
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* without specific prior written permission.
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*
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* THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
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* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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* ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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* SUCH DAMAGE.
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*/
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#ifndef lint
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static char sccsid[] = "@(#)sinh.c 5.6 (Berkeley) 10/9/90";
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#endif /* not lint */
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/* SINH(X)
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* RETURN THE HYPERBOLIC SINE OF X
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* DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
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* CODED IN C BY K.C. NG, 1/8/85;
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* REVISED BY K.C. NG on 2/8/85, 3/7/85, 3/24/85, 4/16/85.
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*
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* Required system supported functions :
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* copysign(x,y)
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* scalb(x,N)
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*
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* Required kernel functions:
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* expm1(x) ...return exp(x)-1
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*
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* Method :
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* 1. reduce x to non-negative by sinh(-x) = - sinh(x).
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* 2.
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*
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* expm1(x) + expm1(x)/(expm1(x)+1)
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* 0 <= x <= lnovfl : sinh(x) := --------------------------------
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* 2
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* lnovfl <= x <= lnovfl+ln2 : sinh(x) := expm1(x)/2 (avoid overflow)
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* lnovfl+ln2 < x < INF : overflow to INF
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*
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*
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* Special cases:
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* sinh(x) is x if x is +INF, -INF, or NaN.
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* only sinh(0)=0 is exact for finite argument.
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*
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* Accuracy:
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* sinh(x) returns the exact hyperbolic sine of x nearly rounded. In
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* a test run with 1,024,000 random arguments on a VAX, the maximum
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* observed error was 1.93 ulps (units in the last place).
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*
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* Constants:
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* The hexadecimal values are the intended ones for the following constants.
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* The decimal values may be used, provided that the compiler will convert
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* from decimal to binary accurately enough to produce the hexadecimal values
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* shown.
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*/
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#include "mathimpl.h"
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vc(mln2hi, 8.8029691931113054792E1 ,0f33,43b0,2bdb,c7e2, 7, .B00F33C7E22BDB)
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vc(mln2lo,-4.9650192275318476525E-16 ,1b60,a70f,582a,279e, -50,-.8F1B60279E582A)
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vc(lnovfl, 8.8029691931113053016E1 ,0f33,43b0,2bda,c7e2, 7, .B00F33C7E22BDA)
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ic(mln2hi, 7.0978271289338397310E2, 10, 1.62E42FEFA39EF)
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ic(mln2lo, 2.3747039373786107478E-14, -45, 1.ABC9E3B39803F)
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ic(lnovfl, 7.0978271289338397310E2, 9, 1.62E42FEFA39EF)
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#ifdef vccast
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#define mln2hi vccast(mln2hi)
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#define mln2lo vccast(mln2lo)
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#define lnovfl vccast(lnovfl)
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#endif
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#if defined(vax)||defined(tahoe)
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static max = 126 ;
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#else /* defined(vax)||defined(tahoe) */
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static max = 1023 ;
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#endif /* defined(vax)||defined(tahoe) */
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double sinh(x)
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double x;
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{
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static const double one=1.0, half=1.0/2.0 ;
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double t, sign;
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#if !defined(vax)&&!defined(tahoe)
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if(x!=x) return(x); /* x is NaN */
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#endif /* !defined(vax)&&!defined(tahoe) */
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sign=copysign(one,x);
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x=copysign(x,one);
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if(x<lnovfl)
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{t=expm1(x); return(copysign((t+t/(one+t))*half,sign));}
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else if(x <= lnovfl+0.7)
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/* subtract x by ln(2^(max+1)) and return 2^max*exp(x)
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to avoid unnecessary overflow */
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return(copysign(scalb(one+expm1((x-mln2hi)-mln2lo),max),sign));
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else /* sinh(+-INF) = +-INF, sinh(+-big no.) overflow to +-INF */
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return( expm1(x)*sign );
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}
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