/****************************************************************************
Copyright (c) 2003, Landmark Graphics and others. All rights reserved.
This program and accompanying materials are made available under the terms of
the Common Public License - v1.0, which accompanies this distribution, and is
available at http://www.eclipse.org/legal/cpl-v10.html
****************************************************************************/
package com.lgc.wsh.util;

import java.io.Serializable;
import java.util.Comparator;
import java.util.logging.Logger;

import static com.lgc.wsh.util.MathPlus.DBL_EPSILON;
import static com.lgc.wsh.util.MathPlus.FLT_EPSILON;

/** This class allows safe comparisons of floating point numbers
    with limited precision.
    The Comparator interface should be used for instances of
    java.lang.Number.
    @author W.S. Harlan
*/
public class Almost implements Serializable, Comparator<Number> {
  static final long serialVersionUID = 1;
    private static final Logger LOG
    = Logger.getLogger(Almost.class.getName());

  /** Default epsilon assumes math has destroyed one digit of accuracy.*/
  private double _epsilon = 10.*FLT_EPSILON;

  /** This default minValue may be too small.
      If subtraction is involved, to same value as epsilon */
  private double _minValue = 100.*Float.MIN_VALUE;

  /** This instance uses default float precision */
  public static final Almost FLOAT = new Almost();

  /** This instance uses default double precision */
  public static final Almost DOUBLE = new Almost(true);

  /** Accept default precision, appropriate for arithmetic on floats.
   */
  public Almost() {}

  /** Specify precision to be used for operations.
      @param epsilon The smallest positive number that can be added to 1
      before the number is considered different from 1.
      For double precision, use a multiple of MathPlus.DBL_EPSILON.
      For float precision use a multiple of MathPlus.FLT_EPSILON.
      I recommend multiplying these values by at least 10
      to allow for errors introduced by arithmetic.
      @param minValue The smallest positive value that should be
      distinguished from zero. Use a multiple (say 100) of
      Double.MIN_VALUE or Float.MIN_VALUE.
   */
  public Almost(double epsilon, double minValue) {
    _epsilon = Math.abs(epsilon);
    _minValue = Math.abs(minValue);
  }

  /** Specify precision to be used for operations.
      MinValue defaults to 100.*Float.MIN_VALUE;
      @param epsilon The smallest positive number that can be added to 1
      before the number is considered different from 1.
      For float precision use a multiple of 1.192092896e-07.
      For double precision, use a multiple of 2.2204460492503131e-016;
      I recommend multiplying these values by at least 10
      to allow for errors introduced by arithmetic.
      Should be much less than 1.
   */
  public Almost(double epsilon) {
    if (epsilon > 0.1) {
      throw new IllegalArgumentException
        ("Epsilon should be a small number: "+epsilon);
    }
    _epsilon = Math.abs(epsilon);
  }

  /** Specify precision to be used for operations.
      Epsilon will be 0.1 to this power.
      MinValue defaults to 100.*Float.MIN_VALUE;
      @param significantDigits the number of significant digits, should be
      positive.
   */
  public Almost(int significantDigits) {
    if (significantDigits < 1) {
      throw new IllegalArgumentException
        ("The number of significant digits should be positive.");
    }
    significantDigits = Math.abs(significantDigits);
    _epsilon = 1.;
    while (significantDigits >0) {
      _epsilon *= 0.1;
      --significantDigits;
    }
  }

  /** Constructor that allows either double or float precision.
      @param isDouble If true, the precision will be appropriate
      for a double; if false, a float.
  */
  public Almost(boolean isDouble) {
    if (isDouble) {
      _epsilon = 10.*DBL_EPSILON;
      _minValue = 100.*Double.MIN_VALUE;
    } // else already have correct defaults
  }

  /** Get the smallest positive number that can be added to 1
      before the number is considered different from 1.
      @return epsilon
  */
  public double getEpsilon() { return _epsilon; }

  /** Get the smallest positive value that should be distinguished from
      zero.
      @return minValue
  */
  public double getMinValue() { return _minValue; }

  /** See if value is between two other values, including almost equality
      @param x Value to check
      @param x1 Value at one end of interval.
      @param x2 Value at other end of interval.
      @return true if x is between x1 and x2.
   */
  public boolean between (double x, double x1, double x2) {
    return ((cmp (x, x1) * cmp (x, x2)) <= 0);
  }

  /** See if value is outside two other values.
      @param x Value to check
      @param x1 Value at one end of interval.
      @param x2 Value at other end of interval.
      @return Return 0 if x is between x1 and x2,
      -1 if outside and closer to x1, 1 if outside and closer to x2.
   */
  public int outside (double x, double x1, double x2) {
    int i=0;
    if (between (x, x1, x2)) i = 0;
    else if (between (x1, x, x2)) i = -1;
    else if (between (x2, x, x1)) i = 1;
    return i;
  }

  /** See if the number is almost zero
      @param r A number to check
      @return true if the r is almost zero.
  */
  public boolean zero (double r) {
    if (r < 0.) r = -r;
    return (r < _minValue);
  }

  /** See if two numbers are almost equal.
      @param r1 First number to check
      @param r2 Second number to check
      @return True if r1 and r2 are almost equal
  */
  public boolean equal (double r1, double r2) {
    return (cmp (r1, r2) == 0);
  }

  /** Check whether first number is strictly less than second.
      @param r1 First number to check
      @param r2 Second number to check
      @return true if r1&lt;r2
  */
  public boolean lt (double r1, double r2) {return cmp(r1,r2) < 0;}

  /** Check whether first number is less than or equal to second.
      @param r1 First number to check
      @param r2 Second number to check
      @return true if r1&lt;=r2
  */
  public boolean le (double r1, double r2) {return cmp(r1,r2) <= 0;}

  /** Check whether first number is strictly greater than second.
      @param r1 First number to check
      @param r2 Second number to check
      @return true if r1&gt;r2
  */
  public boolean gt (double r1, double r2) {return cmp(r1,r2) > 0;}

  /** Check whether first number is greater than or equal to second.
      @param r1 First number to check
      @param r2 Second number to check
      @return true if r1&gt;=r2
  */
  public boolean ge (double r1, double r2) {return cmp(r1,r2) >= 0;}

  /** Check order of two numbers, within precision.
      @param r1 First number to check
      @param r2 Second number to check
      @return 1 if r1>r2; -1 if r1 &lt; r2; 0 if r1==r2, within precision.
  */
  public int cmp (double r1, double r2) {
    if (r1 == r2) return 0; // no need for more careful test

    // if (zero (r1) && zero (r2)) return 0; // optimized by following
    double ar1 = r1;
    double ar2 = r2;
    if (ar1 < 0.) ar1 = -ar1;
    if (ar2 < 0.) ar2 = -ar2;
    if (ar1 < _minValue && ar2 < _minValue) return 0;

    if (0*r1*r2 != 0)
      throw new IllegalArgumentException("Comparing a NaN");

    double er1 = _epsilon * ar1;
    double er2 = _epsilon * ar2;
    if (r1 - er1 > r2 + er2 )
      return 1;
    else if (r1 + er1 < r2 - er2 )
      return -1;
    else
      return 0;
  }

  /** Return a hashcode consistent with imprecise floating-point equality.
      Integers and Longs require exact equality.
      @param number Number to get hashcode of
      @param significantDigits
      Number of significant digits to honor in hashCode
      @return new hash code.
   */
  public int hashCodeOf(Number number, int significantDigits) {
    // Integers must be exactly equal
    if (number instanceof Long || number instanceof Integer) {
      return number.intValue();
    }
    double value = number.doubleValue();
    // zero is special
    if (this.zero(value)) return 0;
    // make value positive definite, and remember sign
    boolean flipSign = value<0.;
    if (flipSign) value = -value;
    int pow = 0;
    // Put value in range [0.1,1.0), and remember base 10 exponent
    while (value <0.1) {value *= 10.; ++pow;}
    while (value >1.) {value *= 0.1; --pow;}
    // If mantissa is 1, it is too easy to get wrong exponent.
    if (this.equal(value,1.) || this.equal(value,0.1)) return 1;
    // Now round to an integer with the correct number of significant digits
    for (int i=0; i< Math.abs(significantDigits); ++i) {value *= 10.;}
    int result = (new Long((long)(value + 0.5))).intValue();
    // Combine singificant info into a single hash code
    result = 100*result + pow;
    if (flipSign) result = -result;
    return result;
  }

  /** Return a hashcode consistent with imprecise floating-point equality.
      Integers and Longs require exact equality.
      The precision is consistent with the value of epsilon.
 * @param number number to get hashcode from
 * @return hashcode
   */
  public int hashCodeOf(Number number) {
    double epsilon = _epsilon;
    int digits = 0;
    while (epsilon < 0.99) {epsilon *= 10.; ++digits;}
    return hashCodeOf(number,digits);
  }

  /** Safely divide one number by another.  Handle zeros and infinity.
      Never throws floating point exceptions.
      @param top Numerator
      @param bottom Denominator
      @param limitIsOne If true, 0/0 returns 1.  If false, 0/0 returns 0.
      @return Regular value if arguments are okay.
      Return +/- 0.01*Float.MAX_VALUE, rather than infinity.
   */
  public double divide (double top, double bottom, boolean limitIsOne) {
    return divide(top, bottom, (limitIsOne)?1.:0.);
  }

  /** Safely take the reciprocal of a number.
      @param value Value to take reciprocal of.
      @return reciprocal of value
  */
  public double reciprocal(double value) {return divide(1., value, 0.);}

  /** Safely divide one number by another.  Handle zeros and infinity.
      Never throws floating point exceptions.
      @param top Numerator
      @param bottom Denominator
      @param limit This is the returned value for 0/0.
      @return Regular value if arguments are okay.
      Return +/- 0.01*Float.MAX_VALUE, rather than infinity.
   */
  public double divide (double top, double bottom, double limit) {
    // remember sign of result
    double sign = 1.;
    if ((top > 0. && bottom < 0.) || (top < 0. && bottom > 0.)) {sign = -1.;}
    // remove signs to simplify if's
    if (top<0)    top    = -top;
    if (bottom<0) bottom = -bottom;

    if (bottom >= 1.                      // Might underflow, but don't care.
        || top < bottom * 0.1*Float.MAX_VALUE) { // bottom<1 won't overflow
      return sign * top / bottom;                 // safe
    } else if (equal (top, bottom)) {
      if (zero (top)) {                           // define 0/0 = limit
        return limit;
      }
          return sign;                  // ratio is within precision of unity
    } else {                // clip overflow
      return sign * 0.01 *Float.MAX_VALUE;
    }
  }

  // Comparator
  public int compare(Number n1, Number n2) {
    return cmp(n1.doubleValue(),n2.doubleValue());
  }

  // Object
  @Override public boolean equals (Object object) {
    if (this == object ) {return true;}
    else if (object==null || getClass()!=object.getClass()) {return false;}
    else if (this.hashCode()!=object.hashCode()) {return false;}
    Almost other = (Almost) object;
    if (this._epsilon != other._epsilon) return false;
    if (this._minValue != other._minValue) return false;
    return true;
  }

  // Object
  @Override public int hashCode() {
    return new Long(Double.doubleToLongBits(_epsilon) ^
                    Double.doubleToLongBits(_minValue)).intValue();
  }

  // Object
  @Override public String toString() {
    return "Almost<eps="+_epsilon+",min="+_minValue+">";
  }
}