/*							log.c
 *
 *	Natural logarithm
 *
 *
 *
 * SYNOPSIS:
 *
 * double x, y, log();
 *
 * y = log( x );
 *
 *
 *
 * DESCRIPTION:
 *
 * Returns the base e (2.718...) logarithm of x.
 *
 * The argument is separated into its exponent and fractional
 * parts.  If the exponent is between -1 and +1, the logarithm
 * of the fraction is approximated by
 *
 *     log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x).
 *
 * Otherwise, setting  z = 2(x-1)/x+1),
 * 
 *     log(x) = z + z**3 P(z)/Q(z).
 *
 *
 *
 * ACCURACY:
 *
 *                      Relative error:
 * arithmetic   domain     # trials      peak         rms
 *    IEEE      0.5, 2.0    150000      1.44e-16    5.06e-17
 *    IEEE      +-MAXNUM    30000       1.20e-16    4.78e-17
 *    DEC       0, 10       170000      1.8e-17     6.3e-18
 *
 * In the tests over the interval [+-MAXNUM], the logarithms
 * of the random arguments were uniformly distributed over
 * [0, MAXLOG].
 *
 * ERROR MESSAGES:
 *
 * log singularity:  x = 0; returns -INFINITY
 * log domain:       x < 0; returns NAN
 */

/*
Cephes Math Library Release 2.8:  June, 2000
Copyright 1984, 1995, 2000 by Stephen L. Moshier

Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:

1. Redistributions of source code must retain the above copyright notice,
   this list of conditions and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright
   notice, this list of conditions and the following disclaimer in the
   documentation and/or other materials provided with the distribution.
3. Neither the name of the <ORGANIZATION> nor the names of its
   contributors may be used to endorse or promote products derived from
   this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
POSSIBILITY OF SUCH DAMAGE.
*/

#include "mconf.h"
static char fname[] = {"log"};

/* Coefficients for log(1+x) = x - x**2/2 + x**3 P(x)/Q(x)
 * 1/sqrt(2) <= x < sqrt(2)
 */
#ifdef UNK
static double P[] = {
 1.01875663804580931796E-4,
 4.97494994976747001425E-1,
 4.70579119878881725854E0,
 1.44989225341610930846E1,
 1.79368678507819816313E1,
 7.70838733755885391666E0,
};
static double Q[] = {
/* 1.00000000000000000000E0, */
 1.12873587189167450590E1,
 4.52279145837532221105E1,
 8.29875266912776603211E1,
 7.11544750618563894466E1,
 2.31251620126765340583E1,
};
#endif

#ifdef DEC
static unsigned short P[] = {
0037777,0127270,0162547,0057274,
0041001,0054665,0164317,0005341,
0041451,0034104,0031640,0105773,
0041677,0011276,0123617,0160135,
0041701,0126603,0053215,0117250,
0041420,0115777,0135206,0030232,
};
static unsigned short Q[] = {
/*0040200,0000000,0000000,0000000,*/
0041220,0144332,0045272,0174241,
0041742,0164566,0035720,0130431,
0042246,0126327,0166065,0116357,
0042372,0033420,0157525,0124560,
0042271,0167002,0066537,0172303,
0041730,0164777,0113711,0044407,
};
#endif

#ifdef IBMPC
static unsigned short P[] = {
0x1bb0,0x93c3,0xb4c2,0x3f1a,
0x52f2,0x3f56,0xd6f5,0x3fdf,
0x6911,0xed92,0xd2ba,0x4012,
0xeb2e,0xc63e,0xff72,0x402c,
0xc84d,0x924b,0xefd6,0x4031,
0xdcf8,0x7d7e,0xd563,0x401e,
};
static unsigned short Q[] = {
/*0x0000,0x0000,0x0000,0x3ff0,*/
0xef8e,0xae97,0x9320,0x4026,
0xc033,0x4e19,0x9d2c,0x4046,
0xbdbd,0xa326,0xbf33,0x4054,
0xae21,0xeb5e,0xc9e2,0x4051,
0x25b2,0x9e1f,0x200a,0x4037,
};
#endif

#ifdef MIEEE
static unsigned short P[] = {
0x3f1a,0xb4c2,0x93c3,0x1bb0,
0x3fdf,0xd6f5,0x3f56,0x52f2,
0x4012,0xd2ba,0xed92,0x6911,
0x402c,0xff72,0xc63e,0xeb2e,
0x4031,0xefd6,0x924b,0xc84d,
0x401e,0xd563,0x7d7e,0xdcf8,
};
static unsigned short Q[] = {
/*0x3ff0,0x0000,0x0000,0x0000,*/
0x4026,0x9320,0xae97,0xef8e,
0x4046,0x9d2c,0x4e19,0xc033,
0x4054,0xbf33,0xa326,0xbdbd,
0x4051,0xc9e2,0xeb5e,0xae21,
0x4037,0x200a,0x9e1f,0x25b2,
};
#endif

/* Coefficients for log(x) = z + z**3 P(z)/Q(z),
 * where z = 2(x-1)/(x+1)
 * 1/sqrt(2) <= x < sqrt(2)
 */

#ifdef UNK
static double R[3] = {
-7.89580278884799154124E-1,
 1.63866645699558079767E1,
-6.41409952958715622951E1,
};
static double S[3] = {
/* 1.00000000000000000000E0,*/
-3.56722798256324312549E1,
 3.12093766372244180303E2,
-7.69691943550460008604E2,
};
#endif
#ifdef DEC
static unsigned short R[12] = {
0140112,0020756,0161540,0072035,
0041203,0013743,0114023,0155527,
0141600,0044060,0104421,0050400,
};
static unsigned short S[12] = {
/*0040200,0000000,0000000,0000000,*/
0141416,0130152,0017543,0064122,
0042234,0006000,0104527,0020155,
0142500,0066110,0146631,0174731,
};
#endif
#ifdef IBMPC
static unsigned short R[12] = {
0x0e84,0xdc6c,0x443d,0xbfe9,
0x7b6b,0x7302,0x62fc,0x4030,
0x2a20,0x1122,0x0906,0xc050,
};
static unsigned short S[12] = {
/*0x0000,0x0000,0x0000,0x3ff0,*/
0x6d0a,0x43ec,0xd60d,0xc041,
0xe40e,0x112a,0x8180,0x4073,
0x3f3b,0x19b3,0x0d89,0xc088,
};
#endif
#ifdef MIEEE
static unsigned short R[12] = {
0xbfe9,0x443d,0xdc6c,0x0e84,
0x4030,0x62fc,0x7302,0x7b6b,
0xc050,0x0906,0x1122,0x2a20,
};
static unsigned short S[12] = {
/*0x3ff0,0x0000,0x0000,0x0000,*/
0xc041,0xd60d,0x43ec,0x6d0a,
0x4073,0x8180,0x112a,0xe40e,
0xc088,0x0d89,0x19b3,0x3f3b,
};
#endif

#ifdef ANSIPROT
extern double frexp ( double, int * );
extern double ldexp ( double, int );
extern double polevl ( double, void *, int );
extern double p1evl ( double, void *, int );
extern int isnan ( double );
extern int isfinite ( double );
#else
double frexp(), ldexp(), polevl(), p1evl();
int isnan(), isfinite();
#endif
#define SQRTH 0.70710678118654752440
extern double INFINITY, NAN;

double c_log(double x)
{
int e;
#ifdef DEC
short *q;
#endif
double y, z;

#ifdef NANS
if( isnan(x) )
	return(x);
#endif
#ifdef INFINITIES
if( x == INFINITY )
	return(x);
#endif
/* Test for domain */
if( x <= 0.0 )
	{
	if( x == 0.0 )
	        {
		mtherr( fname, SING );
		return( -INFINITY );
	        }
	else
	        {
		mtherr( fname, DOMAIN );
		return( NAN );
	        }
	}

/* separate mantissa from exponent */

#ifdef DEC
q = (short *)&x;
e = *q;			/* short containing exponent */
e = ((e >> 7) & 0377) - 0200;	/* the exponent */
*q &= 0177;	/* strip exponent from x */
*q |= 040000;	/* x now between 0.5 and 1 */
#endif

/* Note, frexp is used so that denormal numbers
 * will be handled properly.
 */
#ifdef IBMPC
x = frexp( x, &e );
/*
q = (short *)&x;
q += 3;
e = *q;
e = ((e >> 4) & 0x0fff) - 0x3fe;
*q &= 0x0f;
*q |= 0x3fe0;
*/
#endif

/* Equivalent C language standard library function: */
#ifdef UNK
x = frexp( x, &e );
#endif

#ifdef MIEEE
x = frexp( x, &e );
#endif



/* logarithm using log(x) = z + z**3 P(z)/Q(z),
 * where z = 2(x-1)/x+1)
 */

if( (e > 2) || (e < -2) )
{
if( x < SQRTH )
	{ /* 2( 2x-1 )/( 2x+1 ) */
	e -= 1;
	z = x - 0.5;
	y = 0.5 * z + 0.5;
	}	
else
	{ /*  2 (x-1)/(x+1)   */
	z = x - 0.5;
	z -= 0.5;
	y = 0.5 * x  + 0.5;
	}

x = z / y;


/* rational form */
z = x*x;
z = x * ( z * polevl( z, R, 2 ) / p1evl( z, S, 3 ) );
y = e;
z = z - y * 2.121944400546905827679e-4;
z = z + x;
z = z + e * 0.693359375;
goto ldone;
}



/* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */

if( x < SQRTH )
	{
	e -= 1;
	x = ldexp( x, 1 ) - 1.0; /*  2x - 1  */
	}	
else
	{
	x = x - 1.0;
	}


/* rational form */
z = x*x;
#if DEC
y = x * ( z * polevl( x, P, 5 ) / p1evl( x, Q, 6 ) );
#else
y = x * ( z * polevl( x, P, 5 ) / p1evl( x, Q, 5 ) );
#endif
if( e )
	y = y - e * 2.121944400546905827679e-4;
y = y - ldexp( z, -1 );   /*  y - 0.5 * z  */
z = x + y;
if( e )
	z = z + e * 0.693359375;

ldone:

return( z );
}
