123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167 |
- /* acosh.c
- *
- * Inverse hyperbolic cosine
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, acosh();
- *
- * y = acosh( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns inverse hyperbolic cosine of argument.
- *
- * If 1 <= x < 1.5, a rational approximation
- *
- * sqrt(z) * 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
- * DEC 1,3 30000 4.2e-17 1.1e-17
- * IEEE 1,3 30000 4.6e-16 8.7e-17
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * acosh domain |x| < 1 NAN
- *
- */
- /* acosh.c */
- /*
- Cephes Math Library Release 2.8: June, 2000
- Copyright 1984, 1995, 2000 by Stephen L. Moshier
- */
- /* acosh(z) = sqrt(x) * R(x), z = x + 1, interval 0 < x < 0.5 */
- #include <math.h>
- #ifdef UNK
- static double P[] = {
- 1.18801130533544501356E2,
- 3.94726656571334401102E3,
- 3.43989375926195455866E4,
- 1.08102874834699867335E5,
- 1.10855947270161294369E5
- };
- static double Q[] = {
- /* 1.00000000000000000000E0,*/
- 1.86145380837903397292E2,
- 4.15352677227719831579E3,
- 2.97683430363289370382E4,
- 8.29725251988426222434E4,
- 7.83869920495893927727E4
- };
- #endif
- #ifdef DEC
- static unsigned short P[] = {
- 0041755,0115055,0144002,0146444,
- 0043166,0132103,0155150,0150302,
- 0044006,0057360,0003021,0162753,
- 0044323,0021557,0175225,0056253,
- 0044330,0101771,0040046,0006636
- };
- static unsigned short Q[] = {
- /*0040200,0000000,0000000,0000000,*/
- 0042072,0022467,0126670,0041232,
- 0043201,0146066,0152142,0034015,
- 0043750,0110257,0121165,0026100,
- 0044242,0007103,0034667,0033173,
- 0044231,0014576,0175573,0017472
- };
- #endif
- #ifdef IBMPC
- static unsigned short P[] = {
- 0x59a4,0xb900,0xb345,0x405d,
- 0x1a18,0x7b4d,0xd688,0x40ae,
- 0x3cbd,0x00c2,0xcbde,0x40e0,
- 0xab95,0xff52,0x646d,0x40fa,
- 0xc1b4,0x2804,0x107f,0x40fb
- };
- static unsigned short Q[] = {
- /*0x0000,0x0000,0x0000,0x3ff0,*/
- 0x0853,0xf5b7,0x44a6,0x4067,
- 0x4702,0xda8c,0x3986,0x40b0,
- 0xa588,0xf44e,0x1215,0x40dd,
- 0xe6cf,0x6736,0x41c8,0x40f4,
- 0x63e7,0xdf6f,0x232f,0x40f3
- };
- #endif
- #ifdef MIEEE
- static unsigned short P[] = {
- 0x405d,0xb345,0xb900,0x59a4,
- 0x40ae,0xd688,0x7b4d,0x1a18,
- 0x40e0,0xcbde,0x00c2,0x3cbd,
- 0x40fa,0x646d,0xff52,0xab95,
- 0x40fb,0x107f,0x2804,0xc1b4
- };
- static unsigned short Q[] = {
- 0x4067,0x44a6,0xf5b7,0x0853,
- 0x40b0,0x3986,0xda8c,0x4702,
- 0x40dd,0x1215,0xf44e,0xa588,
- 0x40f4,0x41c8,0x6736,0xe6cf,
- 0x40f3,0x232f,0xdf6f,0x63e7,
- };
- #endif
- #ifdef ANSIPROT
- extern double polevl ( double, void *, int );
- extern double p1evl ( double, void *, int );
- extern double log ( double );
- extern double sqrt ( double );
- #else
- double log(), sqrt(), polevl(), p1evl();
- #endif
- extern double LOGE2, INFINITY, NAN;
- double acosh(x)
- double x;
- {
- double a, z;
- if( x < 1.0 )
- {
- mtherr( "acosh", DOMAIN );
- return(NAN);
- }
- if( x > 1.0e8 )
- {
- #ifdef INFINITIES
- if( x == INFINITY )
- return( INFINITY );
- #endif
- return( log(x) + LOGE2 );
- }
- z = x - 1.0;
- if( z < 0.5 )
- {
- a = sqrt(z) * (polevl(z, P, 4) / p1evl(z, Q, 5) );
- return( a );
- }
- a = sqrt( z*(x+1.0) );
- return( log(x + a) );
- }
|