github.com/afumu/libc@v0.0.6/musl/src/math/log2l.c (about)

     1  /* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_log2l.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   *      Base 2 logarithm, long double precision
    19   *
    20   *
    21   * SYNOPSIS:
    22   *
    23   * long double x, y, log2l();
    24   *
    25   * y = log2l( x );
    26   *
    27   *
    28   * DESCRIPTION:
    29   *
    30   * Returns the base 2 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 (natural)
    34   * logarithm 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      9.8e-20     2.7e-20
    48   *    IEEE     exp(+-10000)  70000      5.4e-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  
    55  #include "libm.h"
    56  
    57  #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
    58  long double log2l(long double x)
    59  {
    60  	return log2(x);
    61  }
    62  #elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
    63  /* Coefficients for ln(1+x) = x - x**2/2 + x**3 P(x)/Q(x)
    64   * 1/sqrt(2) <= x < sqrt(2)
    65   * Theoretical peak relative error = 6.2e-22
    66   */
    67  static const long double P[] = {
    68   4.9962495940332550844739E-1L,
    69   1.0767376367209449010438E1L,
    70   7.7671073698359539859595E1L,
    71   2.5620629828144409632571E2L,
    72   4.2401812743503691187826E2L,
    73   3.4258224542413922935104E2L,
    74   1.0747524399916215149070E2L,
    75  };
    76  static const long double Q[] = {
    77  /* 1.0000000000000000000000E0,*/
    78   2.3479774160285863271658E1L,
    79   1.9444210022760132894510E2L,
    80   7.7952888181207260646090E2L,
    81   1.6911722418503949084863E3L,
    82   2.0307734695595183428202E3L,
    83   1.2695660352705325274404E3L,
    84   3.2242573199748645407652E2L,
    85  };
    86  
    87  /* Coefficients for log(x) = z + z^3 P(z^2)/Q(z^2),
    88   * where z = 2(x-1)/(x+1)
    89   * 1/sqrt(2) <= x < sqrt(2)
    90   * Theoretical peak relative error = 6.16e-22
    91   */
    92  static const long double R[4] = {
    93   1.9757429581415468984296E-3L,
    94  -7.1990767473014147232598E-1L,
    95   1.0777257190312272158094E1L,
    96  -3.5717684488096787370998E1L,
    97  };
    98  static const long double S[4] = {
    99  /* 1.00000000000000000000E0L,*/
   100  -2.6201045551331104417768E1L,
   101   1.9361891836232102174846E2L,
   102  -4.2861221385716144629696E2L,
   103  };
   104  /* log2(e) - 1 */
   105  #define LOG2EA 4.4269504088896340735992e-1L
   106  
   107  #define SQRTH 0.70710678118654752440L
   108  
   109  long double log2l(long double x)
   110  {
   111  	long double y, z;
   112  	int e;
   113  
   114  	if (isnan(x))
   115  		return x;
   116  	if (x == INFINITY)
   117  		return x;
   118  	if (x <= 0.0) {
   119  		if (x == 0.0)
   120  			return -1/(x*x); /* -inf with divbyzero */
   121  		return 0/0.0f; /* nan with invalid */
   122  	}
   123  
   124  	/* separate mantissa from exponent */
   125  	/* Note, frexp is used so that denormal numbers
   126  	 * will be handled properly.
   127  	 */
   128  	x = frexpl(x, &e);
   129  
   130  	/* logarithm using log(x) = z + z**3 P(z)/Q(z),
   131  	 * where z = 2(x-1)/x+1)
   132  	 */
   133  	if (e > 2 || e < -2) {
   134  		if (x < SQRTH) {  /* 2(2x-1)/(2x+1) */
   135  			e -= 1;
   136  			z = x - 0.5;
   137  			y = 0.5 * z + 0.5;
   138  		} else {  /*  2 (x-1)/(x+1)   */
   139  			z = x - 0.5;
   140  			z -= 0.5;
   141  			y = 0.5 * x + 0.5;
   142  		}
   143  		x = z / y;
   144  		z = x*x;
   145  		y = x * (z * __polevll(z, R, 3) / __p1evll(z, S, 3));
   146  		goto done;
   147  	}
   148  
   149  	/* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */
   150  	if (x < SQRTH) {
   151  		e -= 1;
   152  		x = 2.0*x - 1.0;
   153  	} else {
   154  		x = x - 1.0;
   155  	}
   156  	z = x*x;
   157  	y = x * (z * __polevll(x, P, 6) / __p1evll(x, Q, 7));
   158  	y = y - 0.5*z;
   159  
   160  done:
   161  	/* Multiply log of fraction by log2(e)
   162  	 * and base 2 exponent by 1
   163  	 *
   164  	 * ***CAUTION***
   165  	 *
   166  	 * This sequence of operations is critical and it may
   167  	 * be horribly defeated by some compiler optimizers.
   168  	 */
   169  	z = y * LOG2EA;
   170  	z += x * LOG2EA;
   171  	z += y;
   172  	z += x;
   173  	z += e;
   174  	return z;
   175  }
   176  #elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384
   177  // TODO: broken implementation to make things compile
   178  long double log2l(long double x)
   179  {
   180  	return log2(x);
   181  }
   182  #endif