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172 lines
4.2 KiB
C
172 lines
4.2 KiB
C
/* sinh.c
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*
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* Hyperbolic sine
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*
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*
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*
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* SYNOPSIS:
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*
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* double x, y, sinh();
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*
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* y = sinh( x );
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*
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*
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*
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* DESCRIPTION:
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*
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* Returns hyperbolic sine of argument in the range MINLOG to
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* MAXLOG.
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*
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* The range is partitioned into two segments. If |x| <= 1, a
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* rational function of the form x + x**3 P(x)/Q(x) is employed.
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* Otherwise the calculation is sinh(x) = ( exp(x) - exp(-x) )/2.
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*
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*
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*
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* ACCURACY:
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*
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* Relative error:
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* arithmetic domain # trials peak rms
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* DEC +- 88 50000 4.0e-17 7.7e-18
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* IEEE +-MAXLOG 30000 2.6e-16 5.7e-17
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*
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*/
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/*
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Cephes Math Library Release 2.8: June, 2000
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Copyright 1984, 1995, 2000 by Stephen L. Moshier
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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 are met:
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1. Redistributions of source code must retain the above copyright notice,
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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. Neither the name of the <ORGANIZATION> nor the names of its
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contributors may be used to endorse or promote products derived from
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this software without specific prior written permission.
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THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
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AND 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 COPYRIGHT OWNER OR CONTRIBUTORS BE
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LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
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CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
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SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
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INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
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CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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POSSIBILITY OF SUCH DAMAGE.
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*/
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#include "mconf.h"
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#ifdef UNK
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static double P[] = {
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-7.89474443963537015605E-1,
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-1.63725857525983828727E2,
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-1.15614435765005216044E4,
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-3.51754964808151394800E5
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};
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static double Q[] = {
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/* 1.00000000000000000000E0,*/
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-2.77711081420602794433E2,
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3.61578279834431989373E4,
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-2.11052978884890840399E6
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};
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#endif
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#ifdef DEC
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static unsigned short P[] = {
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0140112,0015377,0042731,0163255,
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0142043,0134721,0146177,0123761,
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0143464,0122706,0034353,0006017,
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0144653,0140536,0157665,0054045
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};
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static unsigned short Q[] = {
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/*0040200,0000000,0000000,0000000,*/
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0142212,0155404,0133513,0022040,
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0044015,0036723,0173271,0011053,
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0145400,0150407,0023710,0001034
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};
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#endif
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#ifdef IBMPC
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static unsigned short P[] = {
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0x3cd6,0xe8bb,0x435f,0xbfe9,
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0xf4fe,0x398f,0x773a,0xc064,
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0x6182,0xc71d,0x94b8,0xc0c6,
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0xab05,0xdbf6,0x782b,0xc115
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};
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static unsigned short Q[] = {
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/*0x0000,0x0000,0x0000,0x3ff0,*/
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0x6484,0x96e9,0x5b60,0xc071,
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0x2245,0x7ed7,0xa7ba,0x40e1,
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0x0044,0xe4f9,0x1a20,0xc140
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};
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#endif
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#ifdef MIEEE
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static unsigned short P[] = {
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0xbfe9,0x435f,0xe8bb,0x3cd6,
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0xc064,0x773a,0x398f,0xf4fe,
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0xc0c6,0x94b8,0xc71d,0x6182,
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0xc115,0x782b,0xdbf6,0xab05
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};
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static unsigned short Q[] = {
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0xc071,0x5b60,0x96e9,0x6484,
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0x40e1,0xa7ba,0x7ed7,0x2245,
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0xc140,0x1a20,0xe4f9,0x0044
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};
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#endif
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#ifdef ANSIPROT
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extern double fabs ( double );
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extern double c_exp ( double );
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extern double polevl ( double, void *, int );
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extern double p1evl ( double, void *, int );
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#else
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double fabs(), c_exp(), polevl(), p1evl();
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#endif
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extern double INFINITY, MINLOG, MAXLOG, LOGE2;
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double c_sinh(x)
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double x;
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{
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double a;
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#ifdef MINUSZERO
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if( x == 0.0 )
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return(x);
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#endif
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a = fabs(x);
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if( (x > (MAXLOG + LOGE2)) || (x > -(MINLOG-LOGE2) ) )
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{
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mtherr( "sinh", DOMAIN );
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if( x > 0 )
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return( INFINITY );
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else
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return( -INFINITY );
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}
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if( a > 1.0 )
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{
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if( a >= (MAXLOG - LOGE2) )
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{
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a = c_exp(0.5*a);
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a = (0.5 * a) * a;
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if( x < 0 )
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a = -a;
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return(a);
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}
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a = c_exp(a);
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a = 0.5*a - (0.5/a);
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if( x < 0 )
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a = -a;
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return(a);
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}
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a *= a;
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return( x + x * a * (polevl(a,P,3)/p1evl(a,Q,3)) );
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}
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