Category : C Source Code
Archive   : CEPHES22.ZIP
Filename : LOGL.C

 
Output of file : LOGL.C contained in archive : CEPHES22.ZIP
/* logl.c
*
* Natural logarithm, long double precision
*
*
*
* SYNOPSIS:
*
* long double x, y, logl();
*
* y = logl( 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 8.71e-20 2.75e-20
* IEEE exp(+-10000) 100000 5.39e-20 2.34e-20
*
* In the tests over the interval exp(+-10000), the logarithms
* of the random arguments were uniformly distributed over
* [-10000, +10000].
*
* ERROR MESSAGES:
*
* log singularity: x = 0; returns MINLOG
* log domain: x < 0; returns MINLOG
*/

/*
Cephes Math Library Release 2.2: December, 1990
Copyright 1984, 1990 by Stephen L. Moshier
Direct inquiries to 30 Frost Street, Cambridge, MA 02140
*/

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

/* Coefficients for log(1+x) = x - x**2/2 + x**3 P(x)/Q(x)
* 1/sqrt(2) <= x < sqrt(2)
* Theoretical peak relative error = 2.32e-20
*/
#ifdef UNK
static long double P[] = {
4.5270000862445199635215E-5,
4.9854102823193375972212E-1,
6.5787325942061044846969E0,
2.9911919328553073277375E1,
6.0949667980987787057556E1,
5.7112963590585538103336E1,
2.0039553499201281259648E1,
};
static long double Q[] = {
/* 1.0000000000000000000000E0,*/
1.5062909083469192043167E1,
8.3047565967967209469434E1,
2.2176239823732856465394E2,
3.0909872225312059774938E2,
2.1642788614495947685003E2,
6.0118660497603843919306E1,
};
#endif

#ifdef IBMPC
static short P[] = {
0x51b9,0x9cae,0x4b15,0xbde0,0x3ff0,
0x19cf,0xf0d4,0xc507,0xff40,0x3ffd,
0x9942,0xa7d2,0xfa37,0xd284,0x4001,
0x4add,0x65ce,0x9c5c,0xef4b,0x4003,
0x8445,0x619a,0x75c3,0xf3cc,0x4004,
0x81ab,0x3cd0,0xacba,0xe473,0x4004,
0x4cbf,0xcc18,0x016c,0xa051,0x4003,
};
static short Q[] = {
/*0x0000,0x0000,0x0000,0x8000,0x3fff,*/
0xb8b7,0x81f1,0xacf4,0xf101,0x4002,
0xbc31,0x09a4,0x5a91,0xa618,0x4005,
0xaeec,0xe7da,0x2c87,0xddc3,0x4006,
0x2bde,0x4845,0xa2ee,0x9a8c,0x4007,
0x3120,0x4703,0x89f2,0xd86d,0x4006,
0x7347,0x3224,0x8223,0xf079,0x4004,
};
#endif

#ifdef MIEEE
static long P[] = {
0x3ff00000,0xbde04b15,0x9cae51b9,
0x3ffd0000,0xff40c507,0xf0d419cf,
0x40010000,0xd284fa37,0xa7d29942,
0x40030000,0xef4b9c5c,0x65ce4add,
0x40040000,0xf3cc75c3,0x619a8445,
0x40040000,0xe473acba,0x3cd081ab,
0x40030000,0xa051016c,0xcc184cbf,
};
static long Q[] = {
/*0x3fff0000,0x80000000,0x00000000,*/
0x40020000,0xf101acf4,0x81f1b8b7,
0x40050000,0xa6185a91,0x09a4bc31,
0x40060000,0xddc32c87,0xe7daaeec,
0x40070000,0x9a8ca2ee,0x48452bde,
0x40060000,0xd86d89f2,0x47033120,
0x40040000,0xf0798223,0x32247347,
};
#endif

/* Coefficients for log(x) = z + z^3 P(z^2)/Q(z^2),
* where z = 2(x-1)/(x+1)
* 1/sqrt(2) <= x < sqrt(2)
* Theoretical peak relative error = 6.16e-22
*/

#ifdef UNK
static long double R[4] = {
1.9757429581415468984296E-3L,
-7.1990767473014147232598E-1L,
1.0777257190312272158094E1L,
-3.5717684488096787370998E1L,
};
static long double S[4] = {
/* 1.00000000000000000000E0L,*/
-2.6201045551331104417768E1L,
1.9361891836232102174846E2L,
-4.2861221385716144629696E2L,
};
static long double C1 = 6.9314575195312500000000E-1;
static long double C2 = 1.4286068203094172321215E-6;
#endif
#ifdef IBMPC
static short R[20] = {
0x6ef4,0xf922,0x7763,0x817b,0x3ff6,
0x15fd,0x1af9,0xde8f,0xb84b,0xbffe,
0x8b96,0x4f8d,0xa53c,0xac6f,0x4002,
0x8932,0xb4e3,0xe8ae,0x8ede,0xc004,
};
static short S[15] = {
/*0x0000,0x0000,0x0000,0x8000,0x3fff,*/
0x7ce4,0x1fc9,0xbdc5,0xd19b,0xc003,
0x0af3,0x0d10,0x716f,0xc19e,0x4006,
0x4d7d,0x0f55,0x5d06,0xd64e,0xc007,
};
static short sc1[] = {0x0000,0x0000,0x0000,0xb172,0x3ffe};
#define C1 (*(long double *)sc1)
static short sc2[] = {0x4f1e,0xcd5e,0x8e7b,0xbfbe,0x3feb};
#define C2 (*(long double *)sc2)
#endif
#ifdef MIEEE
static long R[12] = {
0x3ff60000,0x817b7763,0xf9226ef4,
0xbffe0000,0xb84bde8f,0x1af915fd,
0x40020000,0xac6fa53c,0x4f8d8b96,
0xc0040000,0x8edee8ae,0xb4e38932,
};
static long S[9] = {
/*0x3fff0000,0x80000000,0x00000000,*/
0xc0030000,0xd19bbdc5,0x1fc97ce4,
0x40060000,0xc19e716f,0x0d100af3,
0xc0070000,0xd64e5d06,0x0f554d7d,
};
static long sc1[] = {0x3ffe0000,0xb1720000,0x00000000};
#define C1 (*(long double *)sc1)
static long sc2[] = {0x3feb0000,0xbfbe8e7b,0xcd5e4f1e};
#define C2 (*(long double *)sc2)
#endif


#define SQRTH 0.70710678118654752440
extern long double MINLOGL;
long double frexpl(), ldexpl(), polevll(), p1evll();


long double logl(x)
long double x;
{
long double y, z;
int e;

/* Test for domain */
if( x <= 0.0L )
{
if( x == 0.0L )
mtherr( fname, SING );
else
mtherr( fname, DOMAIN );
return( MINLOGL );
}

/* separate mantissa from exponent */

/* Note, frexp is used so that denormal numbers
* will be handled properly.
*/
x = frexpl( x, &e );


/* 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 - 0.5L;
y = 0.5L * z + 0.5L;
}
else
{ /* 2 (x-1)/(x+1) */
z = x - 0.5L;
z -= 0.5L;
y = 0.5L * x + 0.5L;
}
x = z / y;
z = x*x;
z = x * ( z * polevll( z, R, 3 ) / p1evll( z, S, 3 ) );
z = z + e * C2;
z = z + x;
z = z + e * C1;
return( z );
}


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

if( x < SQRTH )
{
e -= 1;
x = ldexpl( x, 1 ) - 1.0L; /* 2x - 1 */
}
else
{
x = x - 1.0L;
}
z = x*x;
y = x * ( z * polevll( x, P, 6 ) / p1evll( x, Q, 6 ) );
y = y + e * C2;
z = y - ldexpl( z, -1 ); /* y - 0.5 * z */
/* Note, the sum of above terms does not exceed x/4,
* so it contributes at most about 1/4 lsb to the error.
*/
z = z + x;
z = z + e * C1; /* This sum has an error of 1/2 lsb. */
return( z );
}


  3 Responses to “Category : C Source Code
Archive   : CEPHES22.ZIP
Filename : LOGL.C

  1. Very nice! Thank you for this wonderful archive. I wonder why I found it only now. Long live the BBS file archives!

  2. This is so awesome! 😀 I’d be cool if you could download an entire archive of this at once, though.

  3. But one thing that puzzles me is the “mtswslnkmcjklsdlsbdmMICROSOFT” string. There is an article about it here. It is definitely worth a read: http://www.os2museum.com/wp/mtswslnk/