168 lines
3.1 KiB
C
168 lines
3.1 KiB
C
/* acosh.c
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*
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* Inverse hyperbolic cosine
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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, acosh();
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*
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* y = acosh( 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 inverse hyperbolic cosine of argument.
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*
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* If 1 <= x < 1.5, a rational approximation
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*
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* sqrt(z) * P(z)/Q(z)
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*
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* where z = x-1, is used. Otherwise,
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*
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* acosh(x) = log( x + sqrt( (x-1)(x+1) ).
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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 1,3 30000 4.2e-17 1.1e-17
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* IEEE 1,3 30000 4.6e-16 8.7e-17
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*
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*
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* ERROR MESSAGES:
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*
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* message condition value returned
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* acosh domain |x| < 1 NAN
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*
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*/
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/* acosh.c */
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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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*/
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/* acosh(z) = sqrt(x) * R(x), z = x + 1, interval 0 < x < 0.5 */
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#include "mconf.h"
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#ifdef UNK
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const static double P[] = {
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1.18801130533544501356E2,
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3.94726656571334401102E3,
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3.43989375926195455866E4,
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1.08102874834699867335E5,
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1.10855947270161294369E5
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};
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const static double Q[] = {
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/* 1.00000000000000000000E0,*/
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1.86145380837903397292E2,
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4.15352677227719831579E3,
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2.97683430363289370382E4,
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8.29725251988426222434E4,
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7.83869920495893927727E4
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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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0041755,0115055,0144002,0146444,
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0043166,0132103,0155150,0150302,
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0044006,0057360,0003021,0162753,
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0044323,0021557,0175225,0056253,
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0044330,0101771,0040046,0006636
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};
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static unsigned short Q[] = {
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/*0040200,0000000,0000000,0000000,*/
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0042072,0022467,0126670,0041232,
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0043201,0146066,0152142,0034015,
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0043750,0110257,0121165,0026100,
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0044242,0007103,0034667,0033173,
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0044231,0014576,0175573,0017472
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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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0x59a4,0xb900,0xb345,0x405d,
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0x1a18,0x7b4d,0xd688,0x40ae,
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0x3cbd,0x00c2,0xcbde,0x40e0,
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0xab95,0xff52,0x646d,0x40fa,
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0xc1b4,0x2804,0x107f,0x40fb
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};
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static unsigned short Q[] = {
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/*0x0000,0x0000,0x0000,0x3ff0,*/
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0x0853,0xf5b7,0x44a6,0x4067,
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0x4702,0xda8c,0x3986,0x40b0,
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0xa588,0xf44e,0x1215,0x40dd,
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0xe6cf,0x6736,0x41c8,0x40f4,
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0x63e7,0xdf6f,0x232f,0x40f3
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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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0x405d,0xb345,0xb900,0x59a4,
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0x40ae,0xd688,0x7b4d,0x1a18,
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0x40e0,0xcbde,0x00c2,0x3cbd,
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0x40fa,0x646d,0xff52,0xab95,
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0x40fb,0x107f,0x2804,0xc1b4
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};
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static unsigned short Q[] = {
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0x4067,0x44a6,0xf5b7,0x0853,
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0x40b0,0x3986,0xda8c,0x4702,
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0x40dd,0x1215,0xf44e,0xa588,
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0x40f4,0x41c8,0x6736,0xe6cf,
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0x40f3,0x232f,0xdf6f,0x63e7,
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};
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#endif
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#ifdef ANSIPROT
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extern double polevl ( double, void *, int );
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extern double p1evl ( double, void *, int );
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extern double log ( double );
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extern double sqrt ( double );
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#else
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double log(), sqrt(), polevl(), p1evl();
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#endif
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extern double LOGE2, INFINITY, NAN;
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double acosh(x)
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double x;
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{
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double a, z;
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if( x < 1.0 )
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{
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mtherr( "acosh", DOMAIN );
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return(NAN);
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}
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if( x > 1.0e8 )
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{
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#ifdef INFINITIES
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if( x == INFINITY )
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return( INFINITY );
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#endif
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return( log(x) + LOGE2 );
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}
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z = x - 1.0;
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if( z < 0.5 )
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{
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a = sqrt(z) * (polevl(z, P, 4) / p1evl(z, Q, 5) );
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return( a );
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}
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a = sqrt( z*(x+1.0) );
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return( log(x + a) );
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}
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