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/* round2n.c (round floating-point number to nearest power of two) */
/***********************************************************************
* This code is part of GLPK (GNU Linear Programming Kit).
* Copyright (C) 2000 Free Software Foundation, Inc.
* Written by Andrew Makhorin <mao@gnu.org>.
*
* GLPK is free software: you can redistribute it and/or modify it
* under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* GLPK is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
* or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
* License for more details.
*
* You should have received a copy of the GNU General Public License
* along with GLPK. If not, see <http://www.gnu.org/licenses/>.
***********************************************************************/
#include "env.h"
#include "misc.h"
/***********************************************************************
* NAME
*
* round2n - round floating-point number to nearest power of two
*
* SYNOPSIS
*
* #include "misc.h"
* double round2n(double x);
*
* RETURNS
*
* Given a positive floating-point value x the routine round2n returns
* 2^n such that |x - 2^n| is minimal.
*
* EXAMPLES
*
* round2n(10.1) = 2^3 = 8
* round2n(15.3) = 2^4 = 16
* round2n(0.01) = 2^(-7) = 0.0078125
*
* BACKGROUND
*
* Let x = f * 2^e, where 0.5 <= f < 1 is a normalized fractional part,
* e is an integer exponent. Then, obviously, 0.5 * 2^e <= x < 2^e, so
* if x - 0.5 * 2^e <= 2^e - x, we choose 0.5 * 2^e = 2^(e-1), and 2^e
* otherwise. The latter condition can be written as 2 * x <= 1.5 * 2^e
* or 2 * f * 2^e <= 1.5 * 2^e or, finally, f <= 0.75. */
double round2n(double x)
{ int e;
double f;
xassert(x > 0.0);
f = frexp(x, &e);
return ldexp(1.0, f <= 0.75 ? e-1 : e);
}
/* eof */
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