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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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1. /* Copyright (C) 2009 by Andrew Miller ([email protected]).
2.  * You may use this code under the GNU GPL version 3 (or at your option, any later version)
4.  * You may alternatively elect to use this code under the GNU LGPL version 3 (or at your
5.  * option, any later version) at http://www.gnu.org/licenses/lgpl-3.0.txt .
6.  * You may alternatively elect to use this code under the Mozilla MPL version 1.1 or later
7.  * (http://www.mozilla.org/MPL/MPL-1.1.html)
8.  *
9.  */
10. /* Given log(x) and log(y) compute log(x - y). */
11. double
12. log_form_subtract(double log_x, double log_y)
13. {
14. if (log_x <= log_y)
15. return 0.0/0.0;
16.
17. double diff = log_x - log_y;
18.
19. // If log(x) dominates, return it...
20. if (diff > 708.0)
21. return log_x;
22.
23. /* We use the following trick:
24.   * log(x-y) = log(a(x/a - y/a)) = log(a) + log(x/a - y/a)
25.   * = log(a) + log(exp(log(x)-log(a)) - exp(log(y)-log(a)))
26.   * We pick log(a) = (log(x) + log(y)) / 2. So
27.   * log(x-y) = (log(x) + log(y)) / 2 +
28.   * = log(exp((log(x) - log(y)) / 2) - exp((log(y) - log(x)) / 2))
29.   */
30.
31. diff /= 2.0;
32.
33. return (log_x + log_y) / 2.0 + log(exp(diff) - exp(-diff));
34. } Subscribe to comments