/* acoshl.c * * Inverse hyperbolic cosine, long double precision * * * * SYNOPSIS: * * long double x, y, acoshl(); * * y = acoshl( x ); * * * * DESCRIPTION: * * Returns inverse hyperbolic cosine of argument. * * If 1 <= x < 1.5, a rational approximation * * sqrt(2z) * P(z)/Q(z) * * where z = x-1, is used. Otherwise, * * acosh(x) = log( x + sqrt( (x-1)(x+1) ). * * * * ACCURACY: * * Relative error: * arithmetic domain # trials peak rms * IEEE 1,3 30000 2.0e-19 3.9e-20 * * * ERROR MESSAGES: * * message condition value returned * acoshl domain |x| < 1 0.0 * */ /* acosh.c */ /* Cephes Math Library Release 2.7: May, 1998 Copyright 1984, 1991, 1998 by Stephen L. Moshier */ /* acosh(1+x) = sqrt(2x) * R(x), interval 0 < x < 0.5 */ #include <math.h> #ifdef UNK static long double P[] = { 2.9071989653343333587238E-5L, 3.2906030801088967279449E-3L, 6.3034445964862182128388E-2L, 4.1587081802731351459504E-1L, 1.0989714347599256302467E0L, 9.9999999999999999999715E-1L, }; static long double Q[] = { 1.0443462486787584738322E-4L, 6.0085845375571145826908E-3L, 8.7750439986662958343370E-2L, 4.9564621536841869854584E-1L, 1.1823047680932589605190E0L, 1.0000000000000000000028E0L, }; #endif #ifdef IBMPC static unsigned short P[] = { 0x4536,0x4dba,0x9f55,0xf3df,0x3fef, XPD 0x23a5,0xf9aa,0x289c,0xd7a7,0x3ff6, XPD 0x7e8b,0x8645,0x341f,0x8118,0x3ffb, XPD 0x0fd5,0x937f,0x0515,0xd4ed,0x3ffd, XPD 0x2364,0xc41b,0x1891,0x8cab,0x3fff, XPD 0x0000,0x0000,0x0000,0x8000,0x3fff, XPD }; static short Q[] = { 0x1e7c,0x4f16,0xe98c,0xdb03,0x3ff1, XPD 0xc319,0xc272,0xa90a,0xc4e3,0x3ff7, XPD 0x2f83,0x9e5e,0x80af,0xb3b6,0x3ffb, XPD 0xe1e0,0xc97c,0x573a,0xfdc5,0x3ffd, XPD 0xcdf2,0x6ec5,0xc33c,0x9755,0x3fff, XPD 0x0000,0x0000,0x0000,0x8000,0x3fff, XPD }; #endif #ifdef MIEEE static long P[] = { 0x3fef0000,0xf3df9f55,0x4dba4536, 0x3ff60000,0xd7a7289c,0xf9aa23a5, 0x3ffb0000,0x8118341f,0x86457e8b, 0x3ffd0000,0xd4ed0515,0x937f0fd5, 0x3fff0000,0x8cab1891,0xc41b2364, 0x3fff0000,0x80000000,0x00000000, }; static long Q[] = { 0x3ff10000,0xdb03e98c,0x4f161e7c, 0x3ff70000,0xc4e3a90a,0xc272c319, 0x3ffb0000,0xb3b680af,0x9e5e2f83, 0x3ffd0000,0xfdc5573a,0xc97ce1e0, 0x3fff0000,0x9755c33c,0x6ec5cdf2, 0x3fff0000,0x80000000,0x00000000, }; #endif extern long double LOGE2L; #ifdef INFINITIES extern long double INFINITYL; #endif #ifdef NANS extern long double NANL; #endif #ifdef ANSIPROT extern long double logl ( long double ); extern long double sqrtl ( long double ); extern long double polevll ( long double, void *, int ); extern int isnanl ( long double ); #else long double logl(), sqrtl(), polevll(), isnanl(); #endif long double acoshl(x) long double x; { long double a, z; #ifdef NANS if( isnanl(x) ) return(x); #endif if( x < 1.0L ) { mtherr( "acoshl", DOMAIN ); #ifdef NANS return(NANL); #else return(0.0L); #endif } if( x > 1.0e10 ) { #ifdef INFINITIES if( x == INFINITYL ) return( INFINITYL ); #endif return( logl(x) + LOGE2L ); } z = x - 1.0L; if( z < 0.5L ) { a = sqrtl(2.0L*z) * (polevll(z, P, 5) / polevll(z, Q, 5) ); return( a ); } a = sqrtl( z*(x+1.0L) ); return( logl(x + a) ); }