package org.checkerframework.common.value.util;
import java.math.BigInteger;
import java.util.Arrays;
import java.util.Collections;
import java.util.List;
import org.checkerframework.dataflow.util.HashCodeUtils;
/**
* The Range class models a 64-bit two's-complement integral interval, such as all integers between
* 1 and 10, inclusive. Ranges are immutable.
*
* @author JasonMrX
*/
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;
/** A range containing all possible 64-bit values. */
public static final Range EVERYTHING = new Range(Long.MIN_VALUE, Long.MAX_VALUE);
/** A range containing all possible 32-bit values. */
public static final Range INT_EVERYTHING = new Range(Integer.MIN_VALUE, Integer.MAX_VALUE);
/** A range containing all possible 16-bit values. */
public static final Range SHORT_EVERYTHING = new Range(Short.MIN_VALUE, Short.MAX_VALUE);
/** A range containing all possible 8-bit values. */
public static final Range BYTE_EVERYTHING = new Range(Byte.MIN_VALUE, Byte.MAX_VALUE);
/** The empty range. */
public static final Range NOTHING = new Range();
/**
* Constructs a range with its bounds specified by two parameters, {@code from} and {@code to}.
*
* @param from the lower bound (inclusive)
* @param to the upper bound (inclusive)
*/
public Range(long from, long to) {
if (!(from <= to)) {
throw new IllegalArgumentException(String.format("Invalid Range: %s %s", from, to));
}
this.from = from;
this.to = to;
}
/** Creates the singleton empty range. */
private Range() {
this.from = Long.MAX_VALUE;
this.to = Long.MIN_VALUE;
}
/**
* 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)
*/
private Range createRangeOrNothing(long from, long to) {
if (from <= to) {
return new Range(from, to);
} else {
return NOTHING;
}
}
@Override
public String toString() {
if (this.isNothing()) {
return "[]";
} else {
return String.format("[%s..%s]", from, to);
}
}
@Override
public boolean equals(Object obj) {
if (obj instanceof Range) {
Range range = (Range) obj;
return from == range.from && to == range.to;
}
return false;
}
@Override
public int hashCode() {
return HashCodeUtils.hash(from, to);
}
/** Return true if this range contains every {@code long} value. */
public boolean isEverything() {
return from == Long.MIN_VALUE && to == Long.MAX_VALUE;
}
/** 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 1<<32. */
private static long integerWidth = (long) Integer.MAX_VALUE - (long) Integer.MIN_VALUE + 1;
/**
* Converts a this range to a 32-bit integral range.
*
* <p>If this range is too wide, i.e., wider than the full range of the Integer class, return
* INT_EVERYTHING.
*
* <p>If the bounds of this range are not representable as 32-bit integers, convert the bounds
* to Integer type in accordance with Java overflow rules, e.g., Integer.MAX_VALUE + 1 is
* converted to Integer.MIN_VALUE.
*/
public Range intRange() {
if (this.isNothing()) {
return this;
}
if (this.isWiderThan(integerWidth)) {
return INT_EVERYTHING;
} else {
int intFrom = (int) this.from;
int intTo = (int) this.to;
if (intFrom <= intTo) {
return new Range(intFrom, intTo);
} else {
return INT_EVERYTHING;
}
}
}
/** The number of values representable in 16 bits: 2^16 or 1<<16. */
private static long shortWidth = Short.MAX_VALUE - Short.MIN_VALUE + 1;
/**
* Converts a this range to a 16-bit short range.
*
* <p>If this range is too wide, i.e., wider than the full range of the Short class, return
* SHORT_EVERYTHING.
*
* <p>If the bounds of this range are not representable as 16-bit integers, convert the bounds
* to Integer type in accordance with Java overflow rules, e.g., Short.MAX_VALUE + 1 is
* converted to Short.MIN_VALUE.
*/
public Range shortRange() {
if (this.isNothing()) {
return this;
}
if (this.isWiderThan(shortWidth)) {
// short is be promoted to int before the operation so no need for explicit casting
return SHORT_EVERYTHING;
} else {
short shortFrom = (short) this.from;
short shortTo = (short) this.to;
if (shortFrom <= shortTo) {
return new Range(shortFrom, shortTo);
} else {
return SHORT_EVERYTHING;
}
}
}
/** The number of values representable in 8 bits: 2^8 or 1<<8. */
private static long byteWidth = Byte.MAX_VALUE - Byte.MIN_VALUE + 1;
/**
* Converts a this range to a 8-bit byte range.
*
* <p>If this range is too wide, i.e., wider than the full range of the Byte class, return
* BYTE_EVERYTHING.
*
* <p>If the bounds of this range are not representable as 8-bit integers, convert the bounds to
* Integer type in accordance with Java overflow rules, e.g., Byte.MAX_VALUE + 1 is converted to
* Byte.MIN_VALUE.
*/
public Range byteRange() {
if (this.isNothing()) {
return this;
}
if (this.isWiderThan(byteWidth)) {
// byte is be promoted to int before the operation so no need for explicit casting
return BYTE_EVERYTHING;
} else {
byte byteFrom = (byte) this.from;
byte byteTo = (byte) this.to;
if (byteFrom <= byteTo) {
return new Range(byteFrom, byteTo);
} else {
return BYTE_EVERYTHING;
}
}
}
/** Returns true if the element is contained in this range. */
public boolean contains(long element) {
return from <= element && element <= to;
}
/** Returns true if the element is contained in this range. */
public boolean contains(Range other) {
return from <= other.from && other.to <= 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 new Range(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 createRangeOrNothing(resultFrom, resultTo);
}
/**
* 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 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;
return new Range(resultFrom, resultTo);
} else {
BigInteger bigFrom = BigInteger.valueOf(from).add(BigInteger.valueOf(right.from));
BigInteger bigTo = BigInteger.valueOf(to).add(BigInteger.valueOf(right.to));
return bigRangeToLongRange(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 new Range(resultFrom, resultTo);
} else {
BigInteger bigFrom = BigInteger.valueOf(from).subtract(BigInteger.valueOf(right.to));
BigInteger bigTo = BigInteger.valueOf(to).subtract(BigInteger.valueOf(right.from));
return bigRangeToLongRange(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 new Range(Collections.min(possibleValues), Collections.max(possibleValues));
} else {
List<BigInteger> bigPossibleValues =
Arrays.asList(
BigInteger.valueOf(from).multiply(BigInteger.valueOf(right.from)),
BigInteger.valueOf(from).multiply(BigInteger.valueOf(right.to)),
BigInteger.valueOf(to).multiply(BigInteger.valueOf(right.from)),
BigInteger.valueOf(to).multiply(BigInteger.valueOf(right.to)));
BigInteger bigFrom = Collections.min(bigPossibleValues);
BigInteger bigTo = Collections.max(bigPossibleValues);
return bigRangeToLongRange(bigFrom, bigTo);
}
}
/**
* 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 new Range(Long.MIN_VALUE, Long.MIN_VALUE / -2);
} else {
// Special case 3:
// This range contains only Long.MIN_VALUE, and right contains only -1.
return new Range(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 new Range(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 = new Range(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 = (new Range(from + 1, to)).union(new Range(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(new Range(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 =
(new Range(Math.max(Long.MIN_VALUE + 1, from), Math.max(Long.MIN_VALUE + 1, to)))
.union(new Range(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 = new Range(-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 http://docs.oracle.com/javase/specs/jls/se7/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 new Range(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 bigRangeToLongRange(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 new Range(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;
}
}
/** We give up the analysis for unsigned shift right operation */
public Range unsignedShiftRight(Range right) {
return EVERYTHING;
}
/** We give up the analysis for bitwise AND operation */
public Range bitwiseAnd(Range right) {
return EVERYTHING;
}
/** We give up the analysis for bitwise OR operation */
public Range bitwiseOr(Range right) {
return EVERYTHING;
}
/** We give up the analysis for bitwise XOR operation */
public Range bitwiseXor(Range right) {
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 new Range(-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 new Range(~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:
*
* <pre>
* <code>
* {@literal @}IntRange(from = 0, to = 10) int a;
* {@literal @}IntRange(from = 3, to = 7) int b;
* ...
* if (a < 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 createRangeOrNothing(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:
*
* <pre>
* <code>
* {@literal @}IntRange(from = 0, to = 10) int a;
* {@literal @}IntRange(from = 3, to = 7) int b;
* ...
* if (a <= 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 createRangeOrNothing(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:
*
* <pre>
* <code>
* {@literal @}IntRange(from = 0, to = 10) int a;
* {@literal @}IntRange(from = 3, to = 7) int b;
* ...
* if (a > 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 createRangeOrNothing(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:
*
* <pre>
* <code>
* {@literal @}IntRange(from = 0, to = 10) int a;
* {@literal @}IntRange(from = 3, to = 7) 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 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 createRangeOrNothing(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.to == right.from) {
if (this.to == right.to) {
return new Range(this.from, this.to - 1);
} else if (this.from == right.from) {
return new Range(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 to - from + 1 > value;
} else {
return BigInteger.valueOf(to)
.subtract(BigInteger.valueOf(from))
.add(BigInteger.ONE)
.compareTo(BigInteger.valueOf(value))
== 1;
}
}
/**
* Determines if this range is completely contained in the range specified by the given lower
* bound and upper bound.
*/
public boolean isWithin(long lb, long ub) {
return from >= lb && to <= ub;
}
/**
* Determines if this range is completely contained in the range that is of half length of the
* Long type and centered with 0.
*/
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. */
private boolean isWithinInteger() {
return isWithin(Integer.MIN_VALUE, Integer.MAX_VALUE);
}
private static final BigInteger longWidth =
BigInteger.valueOf(Long.MAX_VALUE)
.subtract(BigInteger.valueOf(Long.MIN_VALUE))
.add(BigInteger.ONE);
/**
* Converts a range with BigInteger type bounds to a range with Long type bounds.
*
* <p>If the BigInteger range is too wide, i.e., wider than the full range of the Long class,
* return EVERYTHING.
*
* <p>If the BigInteger bounds are out of the Long type scope, convert the bounds to Long type
* in accordance with Java overflow rules, e.g., Long.MAX_VALUE + 1 is converted to
* Long.MIN_VALUE.
*
* @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 bigRangeToLongRange(BigInteger bigFrom, BigInteger bigTo) {
BigInteger numValues = bigTo.subtract(bigFrom).add(BigInteger.ONE);
if (numValues.compareTo(longWidth) == 1) {
return EVERYTHING;
} else {
long resultFrom = bigFrom.longValue();
long resultTo = bigTo.longValue();
if (resultFrom <= resultTo) {
return new Range(resultFrom, resultTo);
} else {
return EVERYTHING;
}
}
}
}