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A1kmm on 03/01/09

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Difference of two numbers in log form

/ Published in: C

Given log(x) and log(y) compute log(x - y)

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/* Copyright (C) 2009 by Andrew Miller (ak.miller@auckland.ac.nz).
 * You may use this code under the GNU GPL version 3 (or at your option, any later version)
 *   See http://www.gnu.org/licenses/gpl-3.0.txt
 * You may alternatively elect to use this code under the GNU LGPL version 3  (or at your 
 *   option, any later version) at http://www.gnu.org/licenses/lgpl-3.0.txt .
 * You may alternatively elect to use this code under the Mozilla MPL version 1.1 or later
 *  (http://www.mozilla.org/MPL/MPL-1.1.html)
 *
 */
/* Given log(x) and log(y) compute log(x - y). */
double
log_form_subtract(double log_x, double log_y)
{
  if (log_x <= log_y)
    return 0.0/0.0;

double diff = log_x - log_y;

// If log(x) dominates, return it...
  if (diff > 708.0)
    return log_x;

/* We use the following trick:
   * log(x-y) = log(a(x/a - y/a)) = log(a) + log(x/a - y/a)
   *          = log(a) + log(exp(log(x)-log(a)) - exp(log(y)-log(a)))
   * We pick log(a) = (log(x) + log(y)) / 2. So
   * log(x-y) = (log(x) + log(y)) / 2 +
   *          = log(exp((log(x) - log(y)) / 2) - exp((log(y) - log(x)) / 2))
   */

diff /= 2.0;

return (log_x + log_y) / 2.0 + log(exp(diff) - exp(-diff));
}

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