Output of file : LOG10L.C contained in archive : CEPHES22.ZIP
/* log10l.c
*
* Common logarithm, long double precision
*
*
*
* SYNOPSIS:
*
* long double x, y, log10l();
*
* y = log10l( x );
*
*
*
* DESCRIPTION:
*
* Returns the base 10 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 30000 9.0e-20 2.6e-20
* IEEE exp(+-10000) 30000 6.0e-20 2.3e-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: January, 1991
Copyright 1984, 1991 by Stephen L. Moshier
Direct inquiries to 30 Frost Street, Cambridge, MA 02140
*/

#include "mconf.h"
static char fname[] = {"log10l"};

/* 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 = 6.2e-22
*/
#ifdef UNK
static long double P[] = {
4.9962495940332550844739E-1L,
1.0767376367209449010438E1L,
7.7671073698359539859595E1L,
2.5620629828144409632571E2L,
4.2401812743503691187826E2L,
3.4258224542413922935104E2L,
1.0747524399916215149070E2L,
};
static long double Q[] = {
/* 1.0000000000000000000000E0,*/
2.3479774160285863271658E1L,
1.9444210022760132894510E2L,
7.7952888181207260646090E2L,
1.6911722418503949084863E3L,
2.0307734695595183428202E3L,
1.2695660352705325274404E3L,
3.2242573199748645407652E2L,
};
#endif

#ifdef IBMPC
static short P[] = {
0xfe72,0xce22,0xd7b9,0xffce,0x3ffd,
0xb778,0x0e34,0x2c71,0xac47,0x4002,
0xea8b,0xc751,0x96f8,0x9b57,0x4005,
0xfeaf,0x6a02,0x67fb,0x801a,0x4007,
0x6b5a,0xf252,0x51ff,0xd402,0x4007,
0x39ce,0x9f76,0x8704,0xab4a,0x4007,
0x1b39,0x740b,0x532e,0xd6f3,0x4005,
};
static short Q[] = {
/*0x0000,0x0000,0x0000,0x8000,0x3fff,*/
0x2f3a,0xbf26,0x93d5,0xbbd6,0x4003,
0x13c8,0x031a,0x2d7b,0xc271,0x4006,
0x449d,0x1993,0xd933,0xc2e1,0x4008,
0x5b65,0x574e,0x8301,0xd365,0x4009,
0xa65d,0x3bd2,0xc043,0xfdd8,0x4009,
0x3b21,0xffea,0x1cf5,0x9eb2,0x4009,
0x545c,0xd708,0x7e62,0xa136,0x4007,
};
#endif

#ifdef MIEEE
static long P[] = {
0x3ffd0000,0xffced7b9,0xce22fe72,
0x40020000,0xac472c71,0x0e34b778,
0x40050000,0x9b5796f8,0xc751ea8b,
0x40070000,0x801a67fb,0x6a02feaf,
0x40070000,0xd40251ff,0xf2526b5a,
0x40070000,0xab4a8704,0x9f7639ce,
0x40050000,0xd6f3532e,0x740b1b39,
};
static long Q[] = {
/*0x3fff0000,0x80000000,0x00000000,*/
0x40030000,0xbbd693d5,0xbf262f3a,
0x40060000,0xc2712d7b,0x031a13c8,
0x40080000,0xc2e1d933,0x1993449d,
0x40090000,0xd3658301,0x574e5b65,
0x40090000,0xfdd8c043,0x3bd2a65d,
0x40090000,0x9eb21cf5,0xffea3b21,
0x40070000,0xa1367e62,0xd708545c,
};
#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,
};
/* log10(2) */
#define L102A 0.3125L
#define L102B -1.1470004336018804786261e-2L
/* log10(e) */
#define L10EA 0.5L
#define L10EB -6.5705518096748172348871e-2L
#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 LG102A[] = {0x0000,0x0000,0x0000,0xa000,0x3ffd};
#define L102A *(long double *)LG102A
static short LG102B[] = {0x0cee,0x8601,0xaf60,0xbbec,0xbff8};
#define L102B *(long double *)LG102B
static short LG10EA[] = {0x0000,0x0000,0x0000,0x8000,0x3ffe};
#define L10EA *(long double *)LG10EA
static short LG10EB[] = {0x39ab,0x235e,0x9d5b,0x8690,0xbffb};
#define L10EB *(long double *)LG10EB
#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 LG102A[] = {0x3ffd0000,0xa0000000,0x00000000};
#define L102A *(long double *)LG102A
static long LG102B[] = {0xbff80000,0xbbecaf60,0x86010cee};
#define L102B *(long double *)LG102B
static long LG10EA[] = {0x3ffe8000,0x00000000,0x00000000};
#define L10EA *(long double *)LG10EA
static long LG10EB[] = {0xbffb0000,0x86909d5b,0x235e39ab};
#define L10EB *(long double *)LG10EB
#endif

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

long double log10l(x)
long double x;
{
long double y;
VOLATILE long double z;
int e;

/* Test for domain */
if( x <= 0.0L )
{
if( x == 0.0L )
mtherr( fname, SING );
else
mtherr( fname, DOMAIN );
return( -4.9314733889673399399914e3L );
}

/* 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;
y = x * ( z * polevll( z, R, 3 ) / p1evll( z, S, 3 ) );
goto done;
}

/* 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, 7 ) );
y = y - ldexpl( z, -1 ); /* -0.5x^2 + ... */

done:

/* Multiply log of fraction by log10(e)
* and base 2 exponent by log10(2).
*
* ***CAUTION***
*
* This sequence of operations is critical and it may
* be horribly defeated by some compiler optimizers.
*/
z = y * (L10EB);
z += x * (L10EB);
z += e * (L102B);
z += y * (L10EA);
z += x * (L10EA);
z += e * (L102A);

return( z );
}

### 3 Responses to “Category : C Source CodeArchive   : CEPHES22.ZIPFilename : LOG10L.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/