/* sinh.c * * Hyperbolic sine * * * * SYNOPSIS: * * double x, y, sinh(); * * y = sinh( x ); * * * * DESCRIPTION: * * Returns hyperbolic sine of argument in the range MINLOG to * MAXLOG. * * The range is partitioned into two segments. If |x| <= 1, a * rational function of the form x + x**3 P(x)/Q(x) is employed. * Otherwise the calculation is sinh(x) = ( exp(x) - exp(-x) )/2. * * * * ACCURACY: * * Relative error: * arithmetic domain # trials peak rms * DEC +- 88 50000 4.0e-17 7.7e-18 * IEEE +-MAXLOG 30000 2.6e-16 5.7e-17 * */ /* Cephes Math Library Release 2.8: June, 2000 Copyright 1984, 1995, 2000 by Stephen L. Moshier */ #include <math.h> #ifdef UNK static double P[] = { -7.89474443963537015605E-1, -1.63725857525983828727E2, -1.15614435765005216044E4, -3.51754964808151394800E5 }; static double Q[] = { /* 1.00000000000000000000E0,*/ -2.77711081420602794433E2, 3.61578279834431989373E4, -2.11052978884890840399E6 }; #endif #ifdef DEC static unsigned short P[] = { 0140112,0015377,0042731,0163255, 0142043,0134721,0146177,0123761, 0143464,0122706,0034353,0006017, 0144653,0140536,0157665,0054045 }; static unsigned short Q[] = { /*0040200,0000000,0000000,0000000,*/ 0142212,0155404,0133513,0022040, 0044015,0036723,0173271,0011053, 0145400,0150407,0023710,0001034 }; #endif #ifdef IBMPC static unsigned short P[] = { 0x3cd6,0xe8bb,0x435f,0xbfe9, 0xf4fe,0x398f,0x773a,0xc064, 0x6182,0xc71d,0x94b8,0xc0c6, 0xab05,0xdbf6,0x782b,0xc115 }; static unsigned short Q[] = { /*0x0000,0x0000,0x0000,0x3ff0,*/ 0x6484,0x96e9,0x5b60,0xc071, 0x2245,0x7ed7,0xa7ba,0x40e1, 0x0044,0xe4f9,0x1a20,0xc140 }; #endif #ifdef MIEEE static unsigned short P[] = { 0xbfe9,0x435f,0xe8bb,0x3cd6, 0xc064,0x773a,0x398f,0xf4fe, 0xc0c6,0x94b8,0xc71d,0x6182, 0xc115,0x782b,0xdbf6,0xab05 }; static unsigned short Q[] = { 0xc071,0x5b60,0x96e9,0x6484, 0x40e1,0xa7ba,0x7ed7,0x2245, 0xc140,0x1a20,0xe4f9,0x0044 }; #endif #ifdef ANSIPROT extern double fabs ( double ); extern double exp ( double ); extern double polevl ( double, void *, int ); extern double p1evl ( double, void *, int ); #else double fabs(), exp(), polevl(), p1evl(); #endif extern double INFINITY, MINLOG, MAXLOG, LOGE2; double sinh(x) double x; { double a; #ifdef MINUSZERO if( x == 0.0 ) return(x); #endif a = fabs(x); if( (x > (MAXLOG + LOGE2)) || (x > -(MINLOG-LOGE2) ) ) { mtherr( "sinh", DOMAIN ); if( x > 0 ) return( INFINITY ); else return( -INFINITY ); } if( a > 1.0 ) { if( a >= (MAXLOG - LOGE2) ) { a = exp(0.5*a); a = (0.5 * a) * a; if( x < 0 ) a = -a; return(a); } a = exp(a); a = 0.5*a - (0.5/a); if( x < 0 ) a = -a; return(a); } a *= a; return( x + x * a * (polevl(a,P,3)/p1evl(a,Q,3)) ); }