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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.
*
* {@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?
*
*
* - 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).
*
- 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).
*
*
* 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.
*
*
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);
/** 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);
/** A range containing all possible 32-bit values. */
public static final Range INT_EVERYTHING = create(Integer.MIN_VALUE, Integer.MAX_VALUE);
/** The number of values representable in 32 bits: 2^32 or {@code 1<<32}. */
private static final long INT_WIDTH = INT_EVERYTHING.width();
/** A range containing all possible 16-bit values. */
public static final Range SHORT_EVERYTHING = create(Short.MIN_VALUE, Short.MAX_VALUE);
/** The number of values representable in 16 bits: 2^16 or 1<<16. */
private static final long SHORT_WIDTH = SHORT_EVERYTHING.width();
/** A range containing all possible char values. */
public static final Range CHAR_EVERYTHING = create(Character.MIN_VALUE, Character.MAX_VALUE);
/** The number of values representable in char: */
private static final long CHAR_WIDTH = CHAR_EVERYTHING.width();
/** A range containing all possible 8-bit values. */
public static final Range BYTE_EVERYTHING = create(Byte.MIN_VALUE, Byte.MAX_VALUE);
/** The number of values representable in 8 bits: 2^8 or 1<<8. */
private static final long BYTE_WIDTH = BYTE_EVERYTHING.width();
/** 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}.
*
*
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 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);
}
}
/**
* Creates a range using BigInteger type bounds.
*
*
If the BigInteger range is wider than the full range of the Long class, return EVERYTHING.
*
*
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.
*
*
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;
}
/**
* Converts this range to a 32-bit integral range.
*
*
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.
*
*
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.
*
*
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.
*
* @return this range, converted to a 32-bit integral range
*/
@SuppressWarnings("UnnecessaryLongToIntConversion")
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);
}
/**
* Converts a this range to a 16-bit short range.
*
*
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.
*
*
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.
*
*
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.
*
* @return this range, converted to a 16-bit short range
*/
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);
}
/**
* Converts this range to a char range.
*
*
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.
*
*
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.
*
*
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);
}
/**
* Converts this range to an 8-bit byte range.
*
*
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.
*
*
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.
*
*
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.
*
* @return this range, converted to an 8-bit byte range
*/
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 possibleValues =
Arrays.asList(from * right.from, from * right.to, to * right.from, to * right.to);
return create(possibleValues);
} else {
BigInteger bigLeftFrom = BigInteger.valueOf(from);
BigInteger bigRightFrom = BigInteger.valueOf(right.from);
BigInteger bigRightTo = BigInteger.valueOf(right.to);
BigInteger bigLeftTo = BigInteger.valueOf(to);
List 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.
*
* 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/se17/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.
*
*
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 < operator. For
* example:
*
*
*
* {@literal @}IntRange(from = 0, to = 10) int a;
* {@literal @}IntRange(from = 3, to = 7) int b;
* ...
* if (a < b) {
* // range of a is now refined to [0, 6] because a value in range [7, 10]
* // cannot be smaller than variable b with range [3, 7].
* ...
* }
*
*
*
* 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 <=
* operator. For example:
*
*
*
* {@literal @}IntRange(from = 0, to = 10) int a;
* {@literal @}IntRange(from = 3, to = 7) int b;
* ...
* if (a <= b) {
* // range of a is now refined to [0, 7] because a value in range [8, 10]
* // cannot be less than or equal to variable b with range [3, 7].
* ...
* }
*
*
*
* 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 > operator. For
* example:
*
*
*
* {@literal @}IntRange(from = 0, to = 10) int a;
* {@literal @}IntRange(from = 3, to = 7) int b;
* ...
* if (a > b) {
* // range of a is now refined to [4, 10] because a value in range [0, 3]
* // cannot be greater than variable b with range [3, 7].
* ...
* }
*
*
*
* 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 >=
* operator. For example:
*
*
*
* {@literal @}IntRange(from = 0, to = 10) int a;
* {@literal @}IntRange(from = 3, to = 7) int b;
* ...
* if (a >= b) {
* // range of a is now refined to [3, 10] because a value in range [0, 2]
* // cannot be greater than or equal to variable b with range [3, 7].
* ...
* }
*
*
*
* 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:
*
*
*
* {@literal @}IntRange(from = 0, to = 10) int a;
* {@literal @}IntRange(from = 3, to = 15) int b;
* ...
* if (a == b) {
* // range of a is now refined to [3, 10] because a value in range [0, 2]
* // cannot be equal to variable b with range [3, 15].
* ...
* }
*
*
*
* @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:
*
*
*
* {@literal @}IntRange(from = 0, to = 10) int a;
* {@literal @}IntRange(from = 0, to = 0) int b;
* ...
* if (a != b) {
* // range of a is now refined to [1, 10] because it cannot
* // be zero.
* ...
* }
*
*
*
* @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;
}
/**
* Returns true 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;
}
}
/**
* Returns true if this range represents a constant value.
*
* @return true if this range represents a constant value
*/
public boolean isConstant() {
return from == to;
}
/**
* Returns true 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;
}
/**
* Returns true 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);
}
/**
* Returns true 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);
}
}