package org.checkerframework.common.value.util;

import java.math.BigInteger;
import java.util.Arrays;
import java.util.Collection;
import java.util.Collections;
import java.util.List;
import java.util.Objects;
import javax.lang.model.type.TypeKind;
import org.checkerframework.checker.interning.qual.InternedDistinct;
import org.checkerframework.checker.nullness.qual.Nullable;

/**
 * The Range class models a 64-bit two's-complement integral interval, such as all integers between
 * 1 and 10, inclusive.
 *
 * <p>{@code Range} is immutable.
 */
public class Range {

  /** The lower bound of the interval, inclusive. */
  public final long from;

  /** The upper bound of the interval, inclusive. */
  public final long to;

  /**
   * Should ranges take overflow into account or ignore it?
   *
   * <ul>
   *   <li>If {@code ignoreOverflow} is true, then operations that would result in more than the max
   *       value are clipped to the max value (and similarly for the min).
   *   <li>If {@code ignoreOverflow} is false, then operations that would result in more than the
   *       max wrap around according to the rules of twos-complement arithmetic and produce a
   *       smaller value (and similarly for the min).
   * </ul>
   *
   * <p>Any checker that uses this library should set this field. By default, this field is set to
   * false (meaning overflow is taken into account), but a previous checker might have set it to
   * true.
   *
   * <p>A static field is used because passing an instance field throughout the class bloats the
   * code.
   */
  public static boolean ignoreOverflow = false;

  /** A range containing all possible 64-bit values. */
  public static final Range LONG_EVERYTHING = create(Long.MIN_VALUE, Long.MAX_VALUE);

  /** A range containing all possible 32-bit values. */
  public static final Range INT_EVERYTHING = create(Integer.MIN_VALUE, Integer.MAX_VALUE);

  /** A range containing all possible 16-bit values. */
  public static final Range SHORT_EVERYTHING = create(Short.MIN_VALUE, Short.MAX_VALUE);

  /** A range containing all possible char values. */
  public static final Range CHAR_EVERYTHING = create(Character.MIN_VALUE, Character.MAX_VALUE);

  /** A range containing all possible 8-bit values. */
  public static final Range BYTE_EVERYTHING = create(Byte.MIN_VALUE, Byte.MAX_VALUE);

  /** The empty range. This is the only Range object that contains nothing */
  @SuppressWarnings("interning:assignment") // no other constructor call makes this
  public static final @InternedDistinct Range NOTHING = new Range(Long.MAX_VALUE, Long.MIN_VALUE);

  /** An alias to the range containing all possible 64-bit values. */
  public static final Range EVERYTHING = LONG_EVERYTHING;

  /**
   * Constructs a range with its bounds specified by two parameters, {@code from} and {@code to}.
   *
   * <p>This is a private constructor that does no validation of arguments, so special instances
   * (e.g., {@link #NOTHING}) can be created through it.
   *
   * @param from the lower bound (inclusive)
   * @param to the upper bound (inclusive)
   */
  private Range(long from, long to) {
    this.from = from;
    this.to = to;
  }

  /**
   * Constructs a range with its bounds specified by two parameters, {@code from} and {@code to}.
   * Requires {@code from <= to}.
   *
   * @param from the lower bound (inclusive)
   * @param to the upper bound (inclusive)
   * @return the Range [from..to]
   */
  public static Range create(long from, long to) {
    if (!(from <= to)) {
      throw new IllegalArgumentException(String.format("Invalid Range: %s %s", from, to));
    }
    return new Range(from, to);
  }

  /**
   * Create a Range from a collection of Numbers.
   *
   * @param values collection whose min and max values will be used as the range's from and to
   *     values
   * @return a range that encompasses all the argument's values ({@link #NOTHING} if the argument is
   *     an empty collection)
   */
  public static Range create(Collection<? extends Number> values) {
    if (values.isEmpty()) {
      return NOTHING;
    }
    long min = values.iterator().next().longValue();
    long max = min;
    for (Number value : values) {
      long current = value.longValue();
      if (min > current) min = current;
      if (max < current) max = current;
    }
    return create(min, max);
  }

  /**
   * Returns a Range representing all possible values for the given primitive type.
   *
   * @param typeKind one of INT, SHORT, BYTE, CHAR, or LONG
   * @return the range for the given primitive type
   */
  public static Range create(TypeKind typeKind) {
    switch (typeKind) {
      case INT:
        return INT_EVERYTHING;
      case SHORT:
        return SHORT_EVERYTHING;
      case BYTE:
        return BYTE_EVERYTHING;
      case CHAR:
        return CHAR_EVERYTHING;
      case LONG:
        return LONG_EVERYTHING;
      default:
        throw new IllegalArgumentException(
            "Invalid TypeKind for Range: expected INT, SHORT, BYTE, CHAR, or LONG, got "
                + typeKind);
    }
  }

  /** Long.MIN_VALUE, as a BigInteger. */
  private static final BigInteger BIG_LONG_MIN_VALUE = BigInteger.valueOf(Long.MIN_VALUE);
  /** Long.MAX_VALUE, as a BigInteger. */
  private static final BigInteger BIG_LONG_MAX_VALUE = BigInteger.valueOf(Long.MAX_VALUE);
  /** The number of Long values, as a BigInteger. */
  private static final BigInteger BIG_LONG_WIDTH =
      BIG_LONG_MAX_VALUE.subtract(BIG_LONG_MIN_VALUE).add(BigInteger.ONE);

  /**
   * Creates a range using BigInteger type bounds.
   *
   * <p>If the BigInteger range is wider than the full range of the Long class, return EVERYTHING.
   *
   * <p>If one of the BigInteger bounds is out of Long's range and {@link #ignoreOverflow} is false,
   * convert the bounds to Long type in accordance with Java twos-complement overflow rules, e.g.,
   * Long.MAX_VALUE + 1 is converted to Long.MIN_VALUE.
   *
   * <p>If one of the BigInteger bounds is out of Long's range and {@link #ignoreOverflow} is true,
   * convert the bound that is outside Long's range to max/min value of a Long.
   *
   * @param bigFrom the lower bound of the BigInteger range
   * @param bigTo the upper bound of the BigInteger range
   * @return a range with Long type bounds converted from the BigInteger range
   */
  private static Range create(BigInteger bigFrom, BigInteger bigTo) {
    if (ignoreOverflow) {
      bigFrom = bigFrom.max(BIG_LONG_MIN_VALUE);
      bigTo = bigTo.min(BIG_LONG_MAX_VALUE);
    } else {
      BigInteger bigWidth = bigTo.subtract(bigFrom).add(BigInteger.ONE);
      if (bigWidth.compareTo(BIG_LONG_WIDTH) > 0) {
        return EVERYTHING;
      }
    }
    long longFrom = bigFrom.longValue();
    long longTo = bigTo.longValue();
    return createOrElse(longFrom, longTo, EVERYTHING);
  }

  /**
   * Creates a Range if {@code from<=to}; otherwise returns the given Range value.
   *
   * @param from lower bound for the range
   * @param to upper bound for the range
   * @param alternate what to return if {@code from > to}
   * @return a new Range [from..to], or {@code alternate}
   */
  private static Range createOrElse(long from, long to, Range alternate) {
    if (from <= to) {
      return new Range(from, to);
    } else {
      return alternate;
    }
  }

  /**
   * Returns a range with its bounds specified by two parameters, {@code from} and {@code to}. If
   * {@code from} is greater than {@code to}, returns {@link #NOTHING}.
   *
   * @param from the lower bound (inclusive)
   * @param to the upper bound (inclusive)
   * @return newly-created Range or NOTHING
   */
  private static Range createOrNothing(long from, long to) {
    return createOrElse(from, to, NOTHING);
  }

  /**
   * Returns the number of values in this range.
   *
   * @return how many values are in the range
   */
  private long width() {
    return to - from + 1;
  }

  @Override
  public String toString() {
    if (this.isNothing()) {
      return "[]";
    } else {
      return String.format("[%s..%s]", from, to);
    }
  }

  @Override
  public boolean equals(@Nullable Object obj) {
    if (this == obj) {
      return true;
    }
    if (obj instanceof Range) {
      return equalsRange((Range) obj);
    }
    return false;
  }

  @Override
  public int hashCode() {
    return Objects.hash(from, to);
  }

  /**
   * Compare two ranges in a type safe manner for equality without incurring the cost of an
   * instanceof check such as equals(Object) does.
   *
   * @param range to compare against
   * @return true for ranges that match from and to respectively
   */
  private boolean equalsRange(Range range) {
    return from == range.from && to == range.to;
  }

  /** Return true if this range contains every {@code long} value. */
  public boolean isLongEverything() {
    return equalsRange(LONG_EVERYTHING);
  }

  /** Return true if this range contains every {@code int} value. */
  public boolean isIntEverything() {
    return equalsRange(INT_EVERYTHING);
  }

  /** Return true if this range contains every {@code short} value. */
  public boolean isShortEverything() {
    return equalsRange(SHORT_EVERYTHING);
  }

  /** Return true if this range contains every {@code char} value. */
  public boolean isCharEverything() {
    return equalsRange(CHAR_EVERYTHING);
  }

  /** Return true if this range contains every {@code byte} value. */
  public boolean isByteEverything() {
    return equalsRange(BYTE_EVERYTHING);
  }

  /** Return true if this range contains no values. */
  public boolean isNothing() {
    return this == NOTHING;
  }

  /** The number of values representable in 32 bits: 2^32 or {@code 1<<32}. */
  private static final long INT_WIDTH = INT_EVERYTHING.width();

  /**
   * Converts this range to a 32-bit integral range.
   *
   * <p>If {@link #ignoreOverflow} is true and one of the bounds is outside the Integer range, then
   * that bound is set to the bound of the Integer range.
   *
   * <p>If {@link #ignoreOverflow} is false and this range is too wide, i.e., wider than the full
   * range of the Integer class, return INT_EVERYTHING.
   *
   * <p>If {@link #ignoreOverflow} is false and the bounds of this range are not representable as
   * 32-bit integers, convert the bounds to Integer type in accordance with Java twos-complement
   * overflow rules, e.g., Integer.MAX_VALUE + 1 is converted to Integer.MIN_VALUE.
   */
  public Range intRange() {
    if (this.isNothing()) {
      return this;
    }
    if (INT_EVERYTHING.contains(this)) {
      return this;
    }
    if (ignoreOverflow) {
      return create(clipToRange(from, INT_EVERYTHING), clipToRange(to, INT_EVERYTHING));
    }
    if (this.isWiderThan(INT_WIDTH)) {
      return INT_EVERYTHING;
    }
    return createOrElse((int) this.from, (int) this.to, INT_EVERYTHING);
  }

  /** The number of values representable in 16 bits: 2^16 or 1&lt;&lt;16. */
  private static final long SHORT_WIDTH = SHORT_EVERYTHING.width();

  /**
   * Converts a this range to a 16-bit short range.
   *
   * <p>If {@link #ignoreOverflow} is true and one of the bounds is outside the Short range, then
   * that bound is set to the bound of the Short range.
   *
   * <p>If {@link #ignoreOverflow} is false and this range is too wide, i.e., wider than the full
   * range of the Short class, return SHORT_EVERYTHING.
   *
   * <p>If {@link #ignoreOverflow} is false and the bounds of this range are not representable as
   * 16-bit integers, convert the bounds to Short type in accordance with Java twos-complement
   * overflow rules, e.g., Short.MAX_VALUE + 1 is converted to Short.MIN_VALUE.
   */
  public Range shortRange() {
    if (this.isNothing()) {
      return this;
    }
    if (SHORT_EVERYTHING.contains(this)) {
      return this;
    }
    if (ignoreOverflow) {
      return create(clipToRange(from, SHORT_EVERYTHING), clipToRange(to, SHORT_EVERYTHING));
    }
    if (this.isWiderThan(SHORT_WIDTH)) {
      // short is promoted to int before the operation so no need for explicit casting
      return SHORT_EVERYTHING;
    }
    return createOrElse((short) this.from, (short) this.to, SHORT_EVERYTHING);
  }

  /** The number of values representable in char: */
  private static final long CHAR_WIDTH = CHAR_EVERYTHING.width();

  /**
   * Converts this range to a char range.
   *
   * <p>If {@link #ignoreOverflow} is true and one of the bounds is outside the Character range,
   * then that bound is set to the bound of the Character range.
   *
   * <p>If {@link #ignoreOverflow} is false and this range is too wide, i.e., wider than the full
   * range of the Character class, return CHAR_EVERYTHING.
   *
   * <p>If {@link #ignoreOverflow} is false and the bounds of this range are not representable as
   * 8-bit integers, convert the bounds to Character type in accordance with Java overflow rules
   * (twos-complement), e.g., Character.MAX_VALUE + 1 is converted to Character.MIN_VALUE.
   */
  public Range charRange() {
    if (this.isNothing()) {
      return this;
    }
    if (CHAR_EVERYTHING.contains(this)) {
      return this;
    }
    if (ignoreOverflow) {
      return create(clipToRange(from, CHAR_EVERYTHING), clipToRange(to, CHAR_EVERYTHING));
    }
    if (this.isWiderThan(CHAR_WIDTH)) {
      // char is promoted to int before the operation so no need for explicit casting
      return CHAR_EVERYTHING;
    }
    return createOrElse((char) this.from, (char) this.to, CHAR_EVERYTHING);
  }

  /** The number of values representable in 8 bits: 2^8 or 1&lt;&lt;8. */
  private static final long BYTE_WIDTH = BYTE_EVERYTHING.width();

  /**
   * Converts this range to a 8-bit byte range.
   *
   * <p>If {@link #ignoreOverflow} is true and one of the bounds is outside the Byte range, then
   * that bound is set to the bound of the Byte range.
   *
   * <p>If {@link #ignoreOverflow} is false and this range is too wide, i.e., wider than the full
   * range of the Byte class, return BYTE_EVERYTHING.
   *
   * <p>If {@link #ignoreOverflow} is false and the bounds of this range are not representable as
   * 8-bit integers, convert the bounds to Byte type in accordance with Java twos-complement
   * overflow rules, e.g., Byte.MAX_VALUE + 1 is converted to Byte.MIN_VALUE.
   */
  public Range byteRange() {
    if (this.isNothing()) {
      return this;
    }
    if (BYTE_EVERYTHING.contains(this)) {
      return this;
    }
    if (ignoreOverflow) {
      return create(clipToRange(from, BYTE_EVERYTHING), clipToRange(to, BYTE_EVERYTHING));
    }
    if (this.isWiderThan(BYTE_WIDTH)) {
      // byte is promoted to int before the operation so no need for explicit casting
      return BYTE_EVERYTHING;
    }
    return createOrElse((byte) this.from, (byte) this.to, BYTE_EVERYTHING);
  }

  /**
   * Return x clipped to the given range; out-of-range values become extremal values. Appropriate
   * only when {@link #ignoreOverflow} is true.
   *
   * @param x a value
   * @param r a range
   * @return a value within the range; if x is outside r, returns the min or max of r
   */
  private long clipToRange(long x, Range r) {
    if (x < r.from) {
      return r.from;
    } else if (x > r.to) {
      return r.to;
    } else {
      return x;
    }
  }

  /**
   * Returns true if the element is contained in this range.
   *
   * @param element the value to seek
   * @return true if {@code element} is in this range
   */
  public boolean contains(long element) {
    return from <= element && element <= to;
  }

  /**
   * Returns true if the other range is contained in this range.
   *
   * @param other the range that might be within this one
   * @return true if {@code other} is within this range
   */
  public boolean contains(Range other) {
    return other.isWithin(from, to);
  }

  /**
   * Returns the smallest range that includes all values contained in either of the two ranges. We
   * call this the union of two ranges.
   *
   * @param right a range to union with this range
   * @return a range resulting from the union of the specified range and this range
   */
  public Range union(Range right) {
    if (this.isNothing()) {
      return right;
    } else if (right.isNothing()) {
      return this;
    }

    long resultFrom = Math.min(from, right.from);
    long resultTo = Math.max(to, right.to);
    return create(resultFrom, resultTo);
  }

  /**
   * Returns the smallest range that includes all values contained in both of the two ranges. We
   * call this the intersection of two ranges. If there is no overlap between the two ranges,
   * returns an empty range.
   *
   * @param right the range to intersect with this range
   * @return a range resulting from the intersection of the specified range and this range
   */
  public Range intersect(Range right) {
    if (this.isNothing() || right.isNothing()) {
      return NOTHING;
    }

    long resultFrom = Math.max(from, right.from);
    long resultTo = Math.min(to, right.to);
    return createOrNothing(resultFrom, resultTo);
  }

  /**
   * Returns the range with the lowest to and from values of this range and the passed range.
   *
   * @param other the range to compare
   * @return the range with the lowest to and from values of this range and the passed range
   */
  public Range min(Range other) {
    return create(Math.min(this.from, other.from), Math.min(this.to, other.to));
  }

  /**
   * Returns the range with the highest to and from values of this range and the passed range.
   *
   * @param other the range to compare
   * @return the range with the highest to and from values of this range and the passed range
   */
  public Range max(Range other) {
    return create(Math.max(this.from, other.from), Math.max(this.to, other.to));
  }

  /**
   * Returns the smallest range that includes all possible values resulting from adding an arbitrary
   * value in the specified range to an arbitrary value in this range. We call this the addition of
   * two ranges.
   *
   * @param right a range to be added to this range
   * @return the range resulting from the addition of the specified range and this range
   */
  public Range plus(Range right) {
    if (this.isNothing() || right.isNothing()) {
      return NOTHING;
    }

    if (this.isWithinHalfLong() && right.isWithinHalfLong()) {
      // This bound is adequate to guarantee no overflow when using long to evaluate
      long resultFrom = from + right.from;
      long resultTo = to + right.to;
      if (from > to) {
        return Range.EVERYTHING;
      } else {
        return create(resultFrom, resultTo);
      }
    } else {
      BigInteger bigFrom = BigInteger.valueOf(from).add(BigInteger.valueOf(right.from));
      BigInteger bigTo = BigInteger.valueOf(to).add(BigInteger.valueOf(right.to));
      return create(bigFrom, bigTo);
    }
  }

  /**
   * Returns the smallest range that includes all possible values resulting from subtracting an
   * arbitrary value in the specified range from an arbitrary value in this range. We call this the
   * subtraction of two ranges.
   *
   * @param right the range to be subtracted from this range
   * @return the range resulting from subtracting the specified range from this range
   */
  public Range minus(Range right) {
    if (this.isNothing() || right.isNothing()) {
      return NOTHING;
    }

    if (this.isWithinHalfLong() && right.isWithinHalfLong()) {
      // This bound is adequate to guarantee no overflow when using long to evaluate
      long resultFrom = from - right.to;
      long resultTo = to - right.from;
      return create(resultFrom, resultTo);
    } else {
      BigInteger bigFrom = BigInteger.valueOf(from).subtract(BigInteger.valueOf(right.to));
      BigInteger bigTo = BigInteger.valueOf(to).subtract(BigInteger.valueOf(right.from));
      return create(bigFrom, bigTo);
    }
  }

  /**
   * Returns the smallest range that includes all possible values resulting from multiplying an
   * arbitrary value in the specified range by an arbitrary value in this range. We call this the
   * multiplication of two ranges.
   *
   * @param right the specified range to be multiplied by this range
   * @return the range resulting from multiplying the specified range by this range
   */
  public Range times(Range right) {
    if (this.isNothing() || right.isNothing()) {
      return NOTHING;
    }

    // These bounds are adequate:  Integer.MAX_VALUE^2 is still a bit less than Long.MAX_VALUE.
    if (this.isWithinInteger() && right.isWithinInteger()) {
      List<Long> possibleValues =
          Arrays.asList(from * right.from, from * right.to, to * right.from, to * right.to);
      return create(possibleValues);
    } else {
      final BigInteger bigLeftFrom = BigInteger.valueOf(from);
      final BigInteger bigRightFrom = BigInteger.valueOf(right.from);
      final BigInteger bigRightTo = BigInteger.valueOf(right.to);
      final BigInteger bigLeftTo = BigInteger.valueOf(to);
      List<BigInteger> bigPossibleValues =
          Arrays.asList(
              bigLeftFrom.multiply(bigRightFrom),
              bigLeftFrom.multiply(bigRightTo),
              bigLeftTo.multiply(bigRightFrom),
              bigLeftTo.multiply(bigRightTo));
      return create(Collections.min(bigPossibleValues), Collections.max(bigPossibleValues));
    }
  }

  /**
   * Returns the smallest range that includes all possible values resulting from dividing (integer
   * division) an arbitrary value in this range by an arbitrary value in the specified range. We
   * call this the division of two ranges.
   *
   * @param right the specified range by which this range is divided
   * @return the range resulting from dividing this range by the specified range
   */
  public Range divide(Range right) {
    if (this.isNothing() || right.isNothing()) {
      return NOTHING;
    }
    if (right.from == 0 && right.to == 0) {
      return NOTHING;
    }
    // Special cases that involve overflow.
    // The only overflow in integer division is Long.MIN_VALUE / -1 == Long.MIN_VALUE.
    if (from == Long.MIN_VALUE && right.contains(-1)) {
      // The values in the right range are all negative because right does not contain 0 but does
      // contain 1.
      if (from != to) {
        // Special case 1:
        // This range contains Long.MIN_VALUE and Long.MIN_VALUE + 1, which makes the
        // result range EVERYTHING.
        return EVERYTHING;
      } else if (right.from != right.to) {
        // Special case 2:
        // This range contains only Long.MIN_VALUE, and the right range contains at least -1
        // and -2. The result range is from Long.MIN_VALUE to Long.MIN_VALUE / -2.
        return create(Long.MIN_VALUE, Long.MIN_VALUE / -2);
      } else {
        // Special case 3:
        // This range contains only Long.MIN_VALUE, and right contains only -1.
        return create(Long.MIN_VALUE, Long.MIN_VALUE);
      }
    }
    // We needn't worry about the overflow issue starting from here.

    // There are 9 different cases:
    // (note: pos=positive, neg=negative, unk=unknown sign, np=non-positive, nn=non-negative)
    long resultFrom;
    long resultTo;
    if (from > 0) { // this range is positive
      if (right.from >= 0) {
        // 1. right: nn
        resultFrom = from / Math.max(right.to, 1);
        resultTo = to / Math.max(right.from, 1);
      } else if (right.to <= 0) {
        // 2. right: np
        resultFrom = to / Math.min(right.to, -1);
        resultTo = from / Math.min(right.from, -1);
      } else {
        // 3. right: unk; values include -1 and 1
        resultFrom = -to;
        resultTo = to;
      }
    } else if (to < 0) { // this range is negative
      if (right.from >= 0) {
        // 4. right: nn
        resultFrom = from / Math.max(right.from, 1);
        resultTo = to / Math.max(right.to, 1);
      } else if (right.to <= 0) {
        // 5. right: np
        resultFrom = to / Math.min(right.from, -1);
        resultTo = from / Math.min(right.to, -1);
      } else {
        // 6. right: unk; values include -1 and 1
        resultFrom = from;
        resultTo = -from;
      }
    } else { // this range spans both signs
      if (right.from >= 0) {
        // 7. right: nn
        resultFrom = from / Math.max(right.from, 1);
        resultTo = to / Math.max(right.from, 1);
      } else if (right.to <= 0) {
        // 8. right: np
        resultFrom = to / Math.min(right.to, -1);
        resultTo = from / Math.min(right.to, -1);
      } else {
        // 9. right: unk; values include -1 and 1
        resultFrom = Math.min(from, -to);
        resultTo = Math.max(-from, to);
      }
    }
    return create(resultFrom, resultTo);
  }

  /**
   * Returns a range that includes all possible values of the remainder of dividing an arbitrary
   * value in this range by an arbitrary value in the specified range.
   *
   * <p>In the current implementation, the result might not be the smallest range that includes all
   * the possible values.
   *
   * @param right the specified range by which this range is divided
   * @return the range of the remainder of dividing this range by the specified range
   */
  public Range remainder(Range right) {
    if (this.isNothing() || right.isNothing()) {
      return NOTHING;
    }
    if (right.from == 0 && right.to == 0) {
      return NOTHING;
    }
    // Special cases that would cause overflow if we use the general method below
    if (right.from == Long.MIN_VALUE) {
      Range range;
      // The value Long.MIN_VALUE as a divisor needs special handling as follows:
      if (from == Long.MIN_VALUE) {
        if (to == Long.MIN_VALUE) {
          // This range only contains Long.MIN_VALUE, so the result range is {0}.
          range = create(0, 0);
        } else { // (to > Long.MIN_VALUE)
          // When this range contains Long.MIN_VALUE, which would have a remainder of 0 if
          // divided by Long.MIN_VALUE, the result range is {0} unioned with [from + 1, to].
          range = create(from + 1, to).union(create(0, 0));
        }
      } else { // (from > Long.MIN_VALUE)
        // When this range doesn't contain Long.MIN_VALUE, the remainder of each value
        // in this range divided by Long.MIN_VALUE is this value itself. Therefore the
        // result range is this range itself.
        range = this;
      }
      // If right.to > Long.MIN_VALUE, union the previous result with the result of range
      // [right.from + 1, right.to] divided by this range, which can be calculated using
      // the general method (see below)
      if (right.to > Long.MIN_VALUE) {
        Range rangeAdditional = this.remainder(create(right.from + 1, right.to));
        range = range.union(rangeAdditional);
      }
      return range;
    }
    // General method:
    // Calculate range1: the result range of this range divided by EVERYTHING. For example,
    // if this range is [3, 5], then the result range would be [0, 5]. If this range is [-3, 4],
    // then the result range would be [-3, 4]. In general, the result range is {0} union with
    // this range excluding the value Long.MIN_VALUE.
    Range range1 =
        create(Math.max(Long.MIN_VALUE + 1, from), Math.max(Long.MIN_VALUE + 1, to))
            .union(create(0, 0));
    // Calculate range2: the result range of range EVERYTHING divided by the right range. For
    // example, if the right range is [-5, 3], then the result range would be [-4, 4]. If the
    // right range is [3, 6], then the result range would be [-5, 5]. In general, the result
    // range is calculated as following:
    long maxAbsolute = Math.max(Math.abs(right.from), Math.abs(right.to));
    Range range2 = create(-maxAbsolute + 1, maxAbsolute - 1);
    // Since range1 and range2 are both super sets of the minimal result range, we return the
    // intersection of range1 and range2, which is correct (super set) and precise enough.
    return range1.intersect(range2);
  }

  /**
   * Returns a range that includes all possible values resulting from left shifting an arbitrary
   * value in this range by an arbitrary number of bits in the specified range. We call this the
   * left shift of a range.
   *
   * @param right the range of bits by which this range is left shifted
   * @return the range resulting from left shifting this range by the specified range
   */
  public Range shiftLeft(Range right) {
    if (this.isNothing() || right.isNothing()) {
      return NOTHING;
    }

    // Shifting operations in Java are depending on the type of the left-hand operand:
    // If the left-hand operand is int  type, only the 5 lowest-order bits of the right-hand
    // operand are used.
    // If the left-hand operand is long type, only the 6 lowest-order bits of the right-hand
    // operand are used.
    // For example, while 1 << -1== 1 << 31, 1L << -1 == 1L << 63.
    // For ths reason, we restrict the shift-bits to analyze in [0. 31] and give up the analysis
    // when out of this range.
    //
    // Other possible solutions:
    // 1. create different methods for int type and long type and use them accordingly
    // 2. add an additional boolean parameter to indicate the type of the left-hand operand
    //
    // see https://docs.oracle.com/javase/specs/jls/se11/html/jls-15.html#jls-15.19 for more
    // detail.
    if (right.isWithin(0, 31)) {
      if (this.isWithinInteger()) {
        // This bound is adequate to guarantee no overflow when using long to evaluate
        long resultFrom = from << (from >= 0 ? right.from : right.to);
        long resultTo = to << (to >= 0 ? right.to : right.from);
        return create(resultFrom, resultTo);
      } else {
        BigInteger bigFrom =
            BigInteger.valueOf(from).shiftLeft(from >= 0 ? (int) right.from : (int) right.to);
        BigInteger bigTo =
            BigInteger.valueOf(to).shiftLeft(to >= 0 ? (int) right.to : (int) right.from);
        return create(bigFrom, bigTo);
      }
    } else {
      // In other cases, we give up on the calculation and return EVERYTHING (rare in practice).
      return EVERYTHING;
    }
  }

  /**
   * Returns a range that includes all possible values resulting from signed right shifting an
   * arbitrary value in this range by an arbitrary number of bits in the specified range. We call
   * this the signed right shift operation of a range.
   *
   * @param right the range of bits by which this range is signed right shifted
   * @return the range resulting from signed right shifting this range by the specified range
   */
  public Range signedShiftRight(Range right) {
    if (this.isNothing() || right.isNothing()) {
      return NOTHING;
    }

    if (this.isWithinInteger() && right.isWithin(0, 31)) {
      // This bound is adequate to guarantee no overflow when using long to evaluate
      long resultFrom = from >> (from >= 0 ? right.to : right.from);
      long resultTo = to >> (to >= 0 ? right.from : right.to);
      return create(resultFrom, resultTo);
    } else {
      // Signed shift right operation for long type cannot be simulated with BigInteger.
      // Give up on the calculation and return EVERYTHING instead.
      return EVERYTHING;
    }
  }

  /**
   * When this range only contains non-negative values, the refined result should be the same as
   * {@link #signedShiftRight(Range)}. We give up the analysis when this range contains negative
   * value(s).
   */
  public Range unsignedShiftRight(Range right) {
    if (this.from >= 0) {
      return signedShiftRight(right);
    }

    if (this.isNothing() || right.isNothing()) {
      return NOTHING;
    }

    return EVERYTHING;
  }

  /**
   * Returns a range that includes all possible values resulting from performing the bitwise and
   * operation on a value in this range by a mask in the specified range. We call this the bitwise
   * and operation of a range.
   *
   * <p>The current implementation is conservative: it only refines the cases where the range of
   * mask represents a constant. In other cases, it gives up on the refinement and returns {@code
   * EVERYTHING} instead.
   *
   * @param right the range of mask of the bitwise and operation
   * @return the range resulting from the bitwise and operation of this range and the specified
   *     range of mask
   */
  public Range bitwiseAnd(Range right) {
    if (this.isNothing() || right.isNothing()) {
      return NOTHING;
    }

    // We only refine the cases where the range of mask represent a constant.
    // Recall these two's-complement facts:
    //   11111111  represents  -1
    //   10000000  represents  MIN_VALUE

    Range constant = null;
    Range variable = null;
    if (right.isConstant()) {
      constant = right;
      variable = this;
    } else if (this.isConstant()) {
      constant = this;
      variable = right;
    }

    if (constant != null) {
      long mask = constant.from;
      if (mask >= 0) {
        // Sign bit of mask is 0.  The elements in the result range must be positive, and
        // the result range is upper-bounded by the mask.
        if (variable.from >= 0) {
          // Case 1.1: The result range is upper-bounded by the upper bound of this range.
          return create(0, Math.min(mask, variable.to));
        } else if (variable.to < 0) {
          // Case 1.2: The result range is upper-bounded by the upper bound of this range
          // after ignoring the sign bit. The upper bound of this range has the most bits
          // (of the highest place values) set to 1.
          return create(0, Math.min(mask, noSignBit(variable.to)));
        } else {
          // Case 1.3:  Since this range contains -1, the upper bound of this range after ignoring
          // the sign bit is Long.MAX_VALUE and thus doesn't contribute to further refinement.
          return create(0, mask);
        }
      } else {
        // Sign bit of mask is 1.
        if (variable.from >= 0) {
          // Case 2.1: Similar to case 1.1 except that the sign bit of the mask can be ignored.
          return create(0, Math.min(noSignBit(mask), variable.to));
        } else if (variable.to < 0) {
          // Case 2.2: The sign bit of the elements in the result range must be 1.  Therefore the
          // lower bound of the result range is Long.MIN_VALUE (when all 1-bits are mismatched
          // between the mask and the element in this range). The result range is also upper-bounded
          // by this mask itself and the upper bound of this range.  (Because more set bits means a
          // larger number -- still negative, but closer to 0.)
          return create(Long.MIN_VALUE, Math.min(mask, variable.to));
        } else {
          // Case 2.3: Similar to case 2.2 except that the elements in this range could
          // be positive, and thus the result range is upper-bounded by the upper bound
          // of this range and the mask after ignoring the sign bit.
          return create(Long.MIN_VALUE, Math.min(noSignBit(mask), variable.to));
        }
      }
    }

    return EVERYTHING;
  }

  /** Return the argument, with its sign bit zeroed out. */
  private long noSignBit(Long mask) {
    return mask & (-1L >>> 1);
  }

  /** We give up the analysis for bitwise OR operation. */
  public Range bitwiseOr(Range right) {
    if (this.isNothing() || right.isNothing()) {
      return NOTHING;
    }

    return EVERYTHING;
  }

  /** We give up the analysis for bitwise XOR operation. */
  public Range bitwiseXor(Range right) {
    if (this.isNothing() || right.isNothing()) {
      return NOTHING;
    }

    return EVERYTHING;
  }

  /**
   * Returns the range of a variable that falls within this range after applying the unary plus
   * operation (which is a no-op).
   *
   * @return this range
   */
  public Range unaryPlus() {
    return this;
  }

  /**
   * Returns the range of a variable that falls within this range after applying the unary minus
   * operation.
   *
   * @return the resulted range of applying unary minus on an arbitrary value in this range
   */
  public Range unaryMinus() {
    if (this.isNothing()) {
      return NOTHING;
    }

    if (from == Long.MIN_VALUE && from != to) {
      // the only case that needs special handling because of overflow
      return EVERYTHING;
    }

    return create(-to, -from);
  }

  /**
   * Returns the range of a variable that falls within this range after applying the bitwise
   * complement operation.
   *
   * @return the resulting range of applying bitwise complement on an arbitrary value in this range
   */
  public Range bitwiseComplement() {
    if (this.isNothing()) {
      return NOTHING;
    }

    return create(~to, ~from);
  }

  /**
   * Refines this range to reflect that some value in it can be less than a value in the given
   * range. This is used for calculating the control-flow-refined result of the &lt; operator. For
   * example:
   *
   * <pre>
   * <code>
   *    {@literal @}IntRange(from = 0, to = 10) int a;
   *    {@literal @}IntRange(from = 3, to = 7) int b;
   *     ...
   *     if (a &lt; b) {
   *         // range of <i>a</i> is now refined to [0, 6] because a value in range [7, 10]
   *         // cannot be smaller than variable <i>b</i> with range [3, 7].
   *         ...
   *     }
   * </code>
   * </pre>
   *
   * Use the {@link #refineGreaterThanEq(Range)} method if you are also interested in refining the
   * range of {@code b} in the code above.
   *
   * @param right the specified {@code Range} to compare with
   * @return the refined {@code Range}
   */
  public Range refineLessThan(Range right) {
    if (this.isNothing() || right.isNothing()) {
      return NOTHING;
    }

    if (right.to == Long.MIN_VALUE) {
      return NOTHING;
    }

    long resultTo = Math.min(to, right.to - 1);
    return createOrNothing(from, resultTo);
  }

  /**
   * Refines this range to reflect that some value in it can be less than or equal to a value in the
   * given range. This is used for calculating the control-flow-refined result of the &lt;=
   * operator. For example:
   *
   * <pre>
   * <code>
   *    {@literal @}IntRange(from = 0, to = 10) int a;
   *    {@literal @}IntRange(from = 3, to = 7) int b;
   *     ...
   *     if (a &lt;= b) {
   *         // range of <i>a</i> is now refined to [0, 7] because a value in range [8, 10]
   *         // cannot be less than or equal to variable <i>b</i> with range [3, 7].
   *         ...
   *     }
   * </code>
   * </pre>
   *
   * Use the {@link #refineGreaterThan(Range)} method if you are also interested in refining the
   * range of {@code b} in the code above.
   *
   * @param right the specified {@code Range} to compare with
   * @return the refined {@code Range}
   */
  public Range refineLessThanEq(Range right) {
    if (this.isNothing() || right.isNothing()) {
      return NOTHING;
    }

    long resultTo = Math.min(to, right.to);
    return createOrNothing(from, resultTo);
  }

  /**
   * Refines this range to reflect that some value in it can be greater than a value in the given
   * range. This is used for calculating the control-flow-refined result of the &gt; operator. For
   * example:
   *
   * <pre>
   * <code>
   *    {@literal @}IntRange(from = 0, to = 10) int a;
   *    {@literal @}IntRange(from = 3, to = 7) int b;
   *     ...
   *     if (a &gt; b) {
   *         // range of <i>a</i> is now refined to [4, 10] because a value in range [0, 3]
   *         // cannot be greater than variable <i>b</i> with range [3, 7].
   *         ...
   *     }
   * </code>
   * </pre>
   *
   * Use the {@link #refineLessThanEq(Range)} method if you are also interested in refining the
   * range of {@code b} in the code above.
   *
   * @param right the specified {@code Range} to compare with
   * @return the refined {@code Range}
   */
  public Range refineGreaterThan(Range right) {
    if (this.isNothing() || right.isNothing()) {
      return NOTHING;
    }

    if (right.from == Long.MAX_VALUE) {
      return NOTHING;
    }

    long resultFrom = Math.max(from, right.from + 1);
    return createOrNothing(resultFrom, to);
  }

  /**
   * Refines this range to reflect that some value in it can be greater than or equal to a value in
   * the given range. This is used for calculating the control-flow-refined result of the &gt;=
   * operator. For example:
   *
   * <pre>
   * <code>
   *    {@literal @}IntRange(from = 0, to = 10) int a;
   *    {@literal @}IntRange(from = 3, to = 7) int b;
   *     ...
   *     if (a &gt;= b) {
   *         // range of <i>a</i> is now refined to [3, 10] because a value in range [0, 2]
   *         // cannot be greater than or equal to variable <i>b</i> with range [3, 7].
   *         ...
   *     }
   * </code>
   * </pre>
   *
   * Use the {@link #refineLessThan(Range)} method if you are also interested in refining the range
   * of {@code b} in the code above.
   *
   * @param right the specified {@code Range} to compare with
   * @return the refined {@code Range}
   */
  public Range refineGreaterThanEq(Range right) {
    if (this.isNothing() || right.isNothing()) {
      return NOTHING;
    }

    long resultFrom = Math.max(from, right.from);
    return createOrNothing(resultFrom, to);
  }

  /**
   * Refines this range to reflect that some value in it can be equal to a value in the given range.
   * This is used for calculating the control-flow-refined result of the == operator. For example:
   *
   * <pre>
   * <code>
   *    {@literal @}IntRange(from = 0, to = 10) int a;
   *    {@literal @}IntRange(from = 3, to = 15) int b;
   *     ...
   *     if (a == b) {
   *         // range of <i>a</i> is now refined to [3, 10] because a value in range [0, 2]
   *         // cannot be equal to variable <i>b</i> with range [3, 15].
   *         ...
   *     }
   * </code>
   * </pre>
   *
   * @param right the specified {@code Range} to compare with
   * @return the refined {@code Range}
   */
  public Range refineEqualTo(Range right) {
    return this.intersect(right);
  }

  /**
   * Refines this range to reflect that some value in it must not be equal to a value in the given
   * range. This only changes the range if the given range (right) contains exactly one integer, and
   * that integer is one of the bounds of this range. This is used for calculating the
   * control-flow-refined result of the != operator. For example:
   *
   * <pre>
   * <code>
   *    {@literal @}IntRange(from = 0, to = 10) int a;
   *    {@literal @}IntRange(from = 0, to = 0) int b;
   *     ...
   *     if (a != b) {
   *         // range of <i>a</i> is now refined to [1, 10] because it cannot
   *         // be zero.
   *         ...
   *     }
   * </code>
   * </pre>
   *
   * @param right the specified {@code Range} to compare with
   * @return the refined {@code Range}
   */
  public Range refineNotEqualTo(Range right) {
    if (right.isConstant()) {
      if (this.to == right.to) {
        return create(this.from, this.to - 1);
      } else if (this.from == right.from) {
        return create(this.from + 1, this.to);
      }
    }
    return this;
  }

  /**
   * Determines if the range is wider than a given value, i.e., if the number of possible values
   * enclosed by this range is more than the given value.
   *
   * @param value the value to compare with
   * @return true if wider than the given value
   */
  public boolean isWiderThan(long value) {
    if (this.isWithin((Long.MIN_VALUE >> 1) + 1, Long.MAX_VALUE >> 1)) {
      // This bound is adequate to guarantee no overflow when using long to evaluate.
      // Long.MIN_VALUE >> 1 + 1 = -4611686018427387903
      // Long.MAX_VALUE >> 1 = 4611686018427387903
      return width() > value;
    } else {
      return BigInteger.valueOf(to)
              .subtract(BigInteger.valueOf(from))
              .add(BigInteger.ONE)
              .compareTo(BigInteger.valueOf(value))
          > 0;
    }
  }

  /** Determines if this range represents a constant value. */
  public boolean isConstant() {
    return from == to;
  }

  /**
   * Determines if this range is completely contained in the range specified by the given lower
   * bound inclusive and upper bound inclusive.
   *
   * @param lb lower bound for the range that might contain this one
   * @param ub upper bound for the range that might contain this one
   * @return true if this range is within the given bounds
   */
  public boolean isWithin(long lb, long ub) {
    assert lb <= ub;
    return lb <= from && to <= ub;
  }

  /**
   * Determines if this range is contained inclusively between Long.MIN_VALUE/2 and
   * Long.MAX_VALUE/2. Note: Long.MIN_VALUE/2 != -Long.MAX_VALUE/2
   */
  private boolean isWithinHalfLong() {
    return isWithin(Long.MIN_VALUE >> 1, Long.MAX_VALUE >> 1);
  }

  /**
   * Determines if this range is completely contained in the scope of the Integer type.
   *
   * @return true if the range is contained within the Integer range inclusive
   */
  public boolean isWithinInteger() {
    return isWithin(Integer.MIN_VALUE, Integer.MAX_VALUE);
  }
}