src/math/log10l.c

   1 /* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_log10l.c */
   2 /*
   3  * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
   4  *
   5  * Permission to use, copy, modify, and distribute this software for any
   6  * purpose with or without fee is hereby granted, provided that the above
   7  * copyright notice and this permission notice appear in all copies.
   8  *
   9  * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
  10  * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
  11  * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
  12  * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
  13  * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
  14  * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
  15  * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
  16  */
  17 /*
  18  *      Common logarithm, long double precision
  19  *
  20  *
  21  * SYNOPSIS:
  22  *
  23  * long double x, y, log10l();
  24  *
  25  * y = log10l( x );
  26  *
  27  *
  28  * DESCRIPTION:
  29  *
  30  * Returns the base 10 logarithm of x.
  31  *
  32  * The argument is separated into its exponent and fractional
  33  * parts.  If the exponent is between -1 and +1, the logarithm
  34  * of the fraction is approximated by
  35  *
  36  *     log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x).
  37  *
  38  * Otherwise, setting  z = 2(x-1)/x+1),
  39  *
  40  *     log(x) = z + z**3 P(z)/Q(z).
  41  *
  42  *
  43  * ACCURACY:
  44  *
  45  *                      Relative error:
  46  * arithmetic   domain     # trials      peak         rms
  47  *    IEEE      0.5, 2.0     30000      9.0e-20     2.6e-20
  48  *    IEEE     exp(+-10000)  30000      6.0e-20     2.3e-20
  49  *
  50  * In the tests over the interval exp(+-10000), the logarithms
  51  * of the random arguments were uniformly distributed over
  52  * [-10000, +10000].
  53  *
  54  * ERROR MESSAGES:
  55  *
  56  * log singularity:  x = 0; returns MINLOG
  57  * log domain:       x < 0; returns MINLOG
  58  */
  59
  60 #include "libm.h"
  61
  62 #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
  63 long double log10l(long double x)
  64 {
  65         return log10(x);
  66 }
  67 #elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
  68 /* Coefficients for log(1+x) = x - x**2/2 + x**3 P(x)/Q(x)
  69  * 1/sqrt(2) <= x < sqrt(2)
  70  * Theoretical peak relative error = 6.2e-22
  71  */
  72 static const long double P[] = {
  73  4.9962495940332550844739E-1L,
  74  1.0767376367209449010438E1L,
  75  7.7671073698359539859595E1L,
  76  2.5620629828144409632571E2L,
  77  4.2401812743503691187826E2L,
  78  3.4258224542413922935104E2L,
  79  1.0747524399916215149070E2L,
  80 };
  81 static const long double Q[] = {
  82 /* 1.0000000000000000000000E0,*/
  83  2.3479774160285863271658E1L,
  84  1.9444210022760132894510E2L,
  85  7.7952888181207260646090E2L,
  86  1.6911722418503949084863E3L,
  87  2.0307734695595183428202E3L,
  88  1.2695660352705325274404E3L,
  89  3.2242573199748645407652E2L,
  90 };
  91
  92 /* Coefficients for log(x) = z + z^3 P(z^2)/Q(z^2),
  93  * where z = 2(x-1)/(x+1)
  94  * 1/sqrt(2) <= x < sqrt(2)
  95  * Theoretical peak relative error = 6.16e-22
  96  */
  97 static const long double R[4] = {
  98  1.9757429581415468984296E-3L,
  99 -7.1990767473014147232598E-1L,
 100  1.0777257190312272158094E1L,
 101 -3.5717684488096787370998E1L,
 102 };
 103 static const long double S[4] = {
 104 /* 1.00000000000000000000E0L,*/
 105 -2.6201045551331104417768E1L,
 106  1.9361891836232102174846E2L,
 107 -4.2861221385716144629696E2L,
 108 };
 109 /* log10(2) */
 110 #define L102A 0.3125L
 111 #define L102B -1.1470004336018804786261e-2L
 112 /* log10(e) */
 113 #define L10EA 0.5L
 114 #define L10EB -6.5705518096748172348871e-2L
 115
 116 #define SQRTH 0.70710678118654752440L
 117
 118 long double log10l(long double x)
 119 {
 120         long double y, z;
 121         int e;
 122
 123         if (isnan(x))
 124                 return x;
 125         if(x <= 0.0) {
 126                 if(x == 0.0)
 127                         return -1.0 / (x*x);
 128                 return (x - x) / 0.0;
 129         }
 130         if (x == INFINITY)
 131                 return INFINITY;
 132         /* separate mantissa from exponent */
 133         /* Note, frexp is used so that denormal numbers
 134          * will be handled properly.
 135          */
 136         x = frexpl(x, &e);
 137
 138         /* logarithm using log(x) = z + z**3 P(z)/Q(z),
 139          * where z = 2(x-1)/x+1)
 140          */
 141         if (e > 2 || e < -2) {
 142                 if (x < SQRTH) {  /* 2(2x-1)/(2x+1) */
 143                         e -= 1;
 144                         z = x - 0.5;
 145                         y = 0.5 * z + 0.5;
 146                 } else {  /*  2 (x-1)/(x+1)   */
 147                         z = x - 0.5;
 148                         z -= 0.5;
 149                         y = 0.5 * x  + 0.5;
 150                 }
 151                 x = z / y;
 152                 z = x*x;
 153                 y = x * (z * __polevll(z, R, 3) / __p1evll(z, S, 3));
 154                 goto done;
 155         }
 156
 157         /* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */
 158         if (x < SQRTH) {
 159                 e -= 1;
 160                 x = 2.0*x - 1.0;
 161         } else {
 162                 x = x - 1.0;
 163         }
 164         z = x*x;
 165         y = x * (z * __polevll(x, P, 6) / __p1evll(x, Q, 7));
 166         y = y - 0.5*z;
 167
 168 done:
 169         /* Multiply log of fraction by log10(e)
 170          * and base 2 exponent by log10(2).
 171          *
 172          * ***CAUTION***
 173          *
 174          * This sequence of operations is critical and it may
 175          * be horribly defeated by some compiler optimizers.
 176          */
 177         z = y * (L10EB);
 178         z += x * (L10EB);
 179         z += e * (L102B);
 180         z += y * (L10EA);
 181         z += x * (L10EA);
 182         z += e * (L102A);
 183         return z;
 184 }
 185 #elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384
 186 // TODO: broken implementation to make things compile
 187 long double log10l(long double x)
 188 {
 189         return log10(x);
 190 }
 191 #endif