Accumulator.java

/**
 * Implementation of the net.sf.geographiclib.Accumulator class
 *
 * Copyright (c) Charles Karney (2013-2019) <charles@karney.com> and licensed
 * under the MIT/X11 License.  For more information, see
 * https://geographiclib.sourceforge.io/
 **********************************************************************/
package net.sf.geographiclib;

/**
 * An accumulator for sums.
 * <p>
 * This allow many double precision numbers to be added together with twice the
 * normal precision.  Thus the effective precision of the sum is 106 bits or
 * about 32 decimal places.
 * <p>
 * The implementation follows J. R. Shewchuk,
 * <a href="https://doi.org/10.1007/PL00009321"> Adaptive Precision
 * Floating-Point Arithmetic and Fast Robust Geometric Predicates</a>,
 * Discrete &amp; Computational Geometry 18(3) 305&ndash;363 (1997).
 * <p>
 * In the documentation of the member functions, <i>sum</i> stands for the
 * value currently held in the accumulator.
 ***********************************************************************/
public  class Accumulator {
  // _s + _t accumulators for the sum.
  private double _s, _t;
  /**
   * Construct from a double.
   * <p>
   * @param y set <i>sum</i> = <i>y</i>.
   **********************************************************************/
  public Accumulator(double y) { _s = y; _t = 0; }
  /**
   * Construct from another Accumulator.
   * <p>
   * @param a set <i>sum</i> = <i>a</i>.
   **********************************************************************/
  public Accumulator(Accumulator a) { _s = a._s; _t = a._t; }
  /**
   * Set the value to a double.
   * <p>
   * @param y set <i>sum</i> = <i>y</i>.
   **********************************************************************/
  public void Set(double y) { _s = y; _t = 0; }
  /**
   * Return the value held in the accumulator.
   * <p>
   * @return <i>sum</i>.
   **********************************************************************/
  public double Sum() { return _s; }
  /**
   * Return the result of adding a number to <i>sum</i> (but don't change
   * <i>sum</i>).
   * <p>
   * @param y the number to be added to the sum.
   * @return <i>sum</i> + <i>y</i>.
   **********************************************************************/
  public double Sum(double y) {
    Accumulator a = new Accumulator(this);
    a.Add(y);
    return a._s;
  }
  /**
   * Add a number to the accumulator.
   * <p>
   * @param y set <i>sum</i> += <i>y</i>.
   **********************************************************************/
  public void Add(double y) {
    // Here's Shewchuk's solution...
    double u;                       // hold exact sum as [s, t, u]
    // Accumulate starting at least significant end
    { Pair r = GeoMath.sum(y, _t); y = r.first; u = r.second; }
    { Pair r = GeoMath.sum(y, _s); _s = r.first; _t = r.second; }
    // Start is _s, _t decreasing and non-adjacent.  Sum is now (s + t + u)
    // exactly with s, t, u non-adjacent and in decreasing order (except for
    // possible zeros).  The following code tries to normalize the result.
    // Ideally, we want _s = round(s+t+u) and _u = round(s+t+u - _s).  The
    // following does an approximate job (and maintains the decreasing
    // non-adjacent property).  Here are two "failures" using 3-bit floats:
    //
    // Case 1: _s is not equal to round(s+t+u) -- off by 1 ulp
    // [12, -1] - 8 -> [4, 0, -1] -> [4, -1] = 3 should be [3, 0] = 3
    //
    // Case 2: _s+_t is not as close to s+t+u as it shold be
    // [64, 5] + 4 -> [64, 8, 1] -> [64,  8] = 72 (off by 1)
    //                    should be [80, -7] = 73 (exact)
    //
    // "Fixing" these problems is probably not worth the expense.  The
    // representation inevitably leads to small errors in the accumulated
    // values.  The additional errors illustrated here amount to 1 ulp of the
    // less significant word during each addition to the Accumulator and an
    // additional possible error of 1 ulp in the reported sum.
    //
    // Incidentally, the "ideal" representation described above is not
    // canonical, because _s = round(_s + _t) may not be true.  For example,
    // with 3-bit floats:
    //
    // [128, 16] + 1 -> [160, -16] -- 160 = round(145).
    // But [160, 0] - 16 -> [128, 16] -- 128 = round(144).
    //
    if (_s == 0)              // This implies t == 0,
      _s = u;                 // so result is u
    else
      _t += u;                // otherwise just accumulate u to t.
  }
  /**
   * Negate an accumulator.
   * <p>
   * Set <i>sum</i> = &minus;<i>sum</i>.
   **********************************************************************/
  public void Negate() { _s = -_s; _t = -_t; }
  /**
   * Take the remainder.
   * <p>
   * @param y the modulus
   * <p>
   * Put <i>sum</i> in the rangle [&minus;<i>y</i>, <i>y</i>].
   **********************************************************************/
  public void Remainder(double y) {
    _s = GeoMath.remainder(_s, y);
    Add(0.0);                   // renormalize
  }
}