nashorn/src/jdk/nashorn/internal/codegen/types/Range.java - platform/libcore - Git at Google

 /*
  * Copyright (c) 2010, 2013, Oracle and/or its affiliates. All rights reserved.
  * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
  *
  * This code is free software; you can redistribute it and/or modify it
  * under the terms of the GNU General Public License version 2 only, as
  * published by the Free Software Foundation.  Oracle designates this
  * particular file as subject to the "Classpath" exception as provided
  * by Oracle in the LICENSE file that accompanied this code.
  *
  * This code is distributed in the hope that it will be useful, but WITHOUT
  * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
  * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
  * version 2 for more details (a copy is included in the LICENSE file that
  * accompanied this code).
  *
  * You should have received a copy of the GNU General Public License version
  * 2 along with this work; if not, write to the Free Software Foundation,
  * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
  *
  * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
  * or visit www.oracle.com if you need additional information or have any
  * questions.
  */

 package jdk.nashorn.internal.codegen.types;

 import java.util.Arrays;
 import java.util.Collections;
 import java.util.List;

 import jdk.nashorn.internal.runtime.DebugLogger;
 import jdk.nashorn.internal.runtime.JSType;

 /**
  * Represents the value range of a symbol.
  */
 public abstract class Range {

     private static final Range GENERIC_RANGE = new Range() {
         @Override
         public Type getType() {
             return Type.OBJECT;
         }
     };

     private static final Range NUMBER_RANGE = new Range() {
         @Override
         public Type getType() {
             return Type.NUMBER;
         }
     };

     private static final Range UNKNOWN_RANGE = new Range() {
         @Override
         public Type getType() {
             return Type.UNKNOWN;
         }

         @Override
         public boolean isUnknown() {
             return true;
         }
     };

     private static class IntegerRange extends Range {
         private final long min;
         private final long max;
         private final Type type;

         private IntegerRange(final long min, final long max) {
             assert min <= max;
             this.min  = min;
             this.max  = max;
             this.type = typeFromRange(min, max);
         }

         private static Type typeFromRange(final long from, final long to) {
             if (from >= Integer.MIN_VALUE && to <= Integer.MAX_VALUE) {
                 return Type.INT;
             }
             return Type.LONG;
         }

         @Override
         public Type getType() {
             return type;
         }

         public long getMin() {
             return min;
         }

         public long getMax() {
             return max;
         }

         @Override
         public boolean isIntegerConst() {
             return getMin() == getMax();
         }

         private long getBitMask() {
             if (min == max) {
                 return min;
             }

             if (min < 0) {
                 return ~0L;
             }

             long mask = 1;
             while (mask < max) {
                 mask = (mask << 1) | 1;
             }
             return mask;
         }

         @Override
         public boolean equals(final Object obj) {
             if (obj instanceof IntegerRange) {
                 final IntegerRange other = (IntegerRange)obj;
                 return this.type == other.type && this.min == other.min && this.max == other.max;
             }
             return false;
         }

         @Override
         public int hashCode() {
             return Long.hashCode(min) ^ Long.hashCode(max);
         }

         @Override
         public String toString() {
             return super.toString() + "[" + min +", " + max + "]";
         }
     }

     /**
      * Get narrowest type for this range
      * @return type
      */
     public abstract Type getType();

     /**
      * Is this range unknown
      * @return true if unknown
      */
     public boolean isUnknown() {
         return false;
     }

     /**
      * Check if an integer is enough to span this range
      * @return true if integer is enough
      */
     public boolean isIntegerType() {
         return this instanceof IntegerRange;
     }

     /**
      * Check if an integer is enough to span this range
      * @return true if integer is enough
      */
     public boolean isIntegerConst() {
         return false;
     }

     /**
      * Create an unknown range - this is most likely a singleton object
      * and it represents "we have no known range information"
      * @return the range
      */
     public static Range createUnknownRange() {
         return UNKNOWN_RANGE;
     }

     /**
      * Create a constant range: [value, value]
      * @param value value
      * @return the range
      */
     public static Range createRange(final int value) {
         return createIntegerRange(value, value);
     }

     /**
      * Create a constant range: [value, value]
      * @param value value
      * @return the range
      */
     public static Range createRange(final long value) {
         return createIntegerRange(value, value);
     }

     /**
      * Create a constant range: [value, value]
      * @param value value
      * @return the range
      */
     public static Range createRange(final double value) {
         if (isRepresentableAsLong(value)) {
             return createIntegerRange((long) value, (long) value);
         }
         return createNumberRange();
     }

     /**
      * Create a constant range: [value, value]
      * @param value value
      * @return the range
      */
     public static Range createRange(final Object value) {
         if (value instanceof Integer) {
             return createRange((int)value);
         } else if (value instanceof Long) {
             return createRange((long)value);
         } else if (value instanceof Double) {
             return createRange((double)value);
         }

         return createGenericRange();
     }

     /**
      * Create a generic range - object symbol that carries no range
      * information
      * @return the range
      */
     public static Range createGenericRange() {
         return GENERIC_RANGE;
     }

     /**
      * Create a number range - number symbol that carries no range
      * information
      * @return the range
      */
     public static Range createNumberRange() {
         return NUMBER_RANGE;
     }

     /**
      * Create an integer range [min, max]
      * @param min minimum value, inclusive
      * @param max maximum value, inclusive
      * @return the range
      */
     public static IntegerRange createIntegerRange(final long min, final long max) {
         return new IntegerRange(min, max);
     }

     /**
      * Create an integer range of maximum type width for the given type
      * @param type the type
      * @return the range
      */
     public static IntegerRange createIntegerRange(final Type type) {
         assert type.isNumeric() && !type.isNumber();
         final long min;
         final long max;
         if (type.isInteger()) {
             min = Integer.MIN_VALUE;
             max = Integer.MAX_VALUE;
         } else if (type.isLong()) {
             min = Long.MIN_VALUE;
             max = Long.MAX_VALUE;
         } else {
             throw new AssertionError(); //type incompatible with integer range
         }
         return new IntegerRange(min, max);
     }

     /**
      * Create an range of maximum type width for the given type
      * @param type the type
      * @return the range
      */
     public static Range createTypeRange(final Type type) {
         if (type.isNumber()) {
             return createNumberRange();
         } else if (type.isNumeric()) {
             return createIntegerRange(type);
         } else {
             return createGenericRange();
         }
     }

     // check that add doesn't overflow
     private static boolean checkAdd(final long a, final long b) {
         final long result = a + b;
         return ((a ^ result) & (b ^ result)) >= 0;
     }

     // check that sub doesn't overflow
     private static boolean checkSub(final long a, final long b) {
         final long result = a - b;
         return ((a ^ result) & (b ^ result)) >= 0;
     }

     private static boolean checkMul(final long a, final long b) {
         // TODO correct overflow check
         return a >= Integer.MIN_VALUE && a <= Integer.MAX_VALUE && b >= Integer.MIN_VALUE && b <= Integer.MAX_VALUE;
     }

     /**
      * The range functionality class responsible for merging ranges and drawing
      * range conclusions from operations executed
      */
     public static class Functionality {
         /** logger */
         protected final DebugLogger log;

         /**
          * Constructor
          * @param log logger
          */
         public Functionality(final DebugLogger log) {
             this.log = log;
         }

         /**
          * Join two ranges
          * @param a first range
          * @param b second range
          * @return the joined range
          */
         public Range join(final Range a, final Range b) {
             if (a.equals(b)) {
                 return a;
             }

             Type joinedType = a.getType();
             if (a.getType() != b.getType()) {
                 if (a.isUnknown()) {
                     return b;
                 }
                 if (b.isUnknown()) {
                     return a;
                 }

                 joinedType = Type.widest(a.getType(), b.getType());
             }

             if (joinedType.isInteger() || joinedType.isLong()) {
                 return createIntegerRange(
                         Math.min(((IntegerRange) a).getMin(), ((IntegerRange) b).getMin()),
                         Math.max(((IntegerRange) a).getMax(), ((IntegerRange) b).getMax()));
             }

             return createTypeRange(joinedType);
         }

         /**
          * Add operation
          * @param a range of first symbol to be added
          * @param b range of second symbol to be added
          * @return resulting range representing the value range after add
          */
         public Range add(final Range a, final Range b) {
             if (a.isIntegerType() && b.isIntegerType()) {
                 final IntegerRange lhs = (IntegerRange)a;
                 final IntegerRange rhs = (IntegerRange)b;
                 if (checkAdd(lhs.getMin(), rhs.getMin()) && checkAdd(lhs.getMax(), rhs.getMax())) {
                     return createIntegerRange(lhs.getMin() + rhs.getMin(), lhs.getMax() + rhs.getMax());
                 }
             }

             if (a.getType().isNumeric() && b.getType().isNumeric()) {
                 return createNumberRange();
             }

             return createGenericRange();
         }

         /**
          * Sub operation
          * @param a range of first symbol to be subtracted
          * @param b range of second symbol to be subtracted
          * @return resulting range representing the value range after subtraction
          */
         public Range sub(final Range a, final Range b) {
             if (a.isIntegerType() && b.isIntegerType()) {
                 final IntegerRange lhs = (IntegerRange)a;
                 final IntegerRange rhs = (IntegerRange)b;
                 if (checkSub(lhs.getMin(), rhs.getMax()) && checkSub(lhs.getMax(), rhs.getMin())) {
                     return createIntegerRange(lhs.getMin() - rhs.getMax(), lhs.getMax() - rhs.getMin());
                 }
             }

             if (a.getType().isNumeric() && b.getType().isNumeric()) {
                 return createNumberRange();
             }

             return createGenericRange();
         }

         /**
          * Mul operation
          * @param a range of first symbol to be multiplied
          * @param b range of second symbol to be multiplied
          * @return resulting range representing the value range after multiplication
          */
         public Range mul(final Range a, final Range b) {
             if (a.isIntegerType() && b.isIntegerType()) {
                 final IntegerRange lhs = (IntegerRange)a;
                 final IntegerRange rhs = (IntegerRange)b;

                 //ensure that nothing ever overflows or underflows
                 if (checkMul(lhs.getMin(), rhs.getMin()) &&
                     checkMul(lhs.getMax(), rhs.getMax()) &&
                     checkMul(lhs.getMin(), rhs.getMax()) &&
                     checkMul(lhs.getMax(), rhs.getMin())) {

                     final List<Long> results =
                         Arrays.asList(
                             lhs.getMin() * rhs.getMin(),
                             lhs.getMin() * rhs.getMax(),
                             lhs.getMax() * rhs.getMin(),
                             lhs.getMax() * rhs.getMax());
                     return createIntegerRange(Collections.min(results), Collections.max(results));
                 }
             }

             if (a.getType().isNumeric() && b.getType().isNumeric()) {
                 return createNumberRange();
             }

             return createGenericRange();
         }

         /**
          * Neg operation
          * @param a range of value symbol to be negated
          * @return resulting range representing the value range after neg
          */
         public Range neg(final Range a) {
             if (a.isIntegerType()) {
                 final IntegerRange rhs = (IntegerRange)a;
                 if (rhs.getMin() != Long.MIN_VALUE && rhs.getMax() != Long.MIN_VALUE) {
                     return createIntegerRange(-rhs.getMax(), -rhs.getMin());
                 }
             }

             if (a.getType().isNumeric()) {
                 return createNumberRange();
             }

             return createGenericRange();
         }

         /**
          * Bitwise and operation
          * @param a range of first symbol to be and:ed
          * @param b range of second symbol to be and:ed
          * @return resulting range representing the value range after and
          */
         public Range and(final Range a, final Range b) {
             if (a.isIntegerType() && b.isIntegerType()) {
                 final int resultMask = (int) (((IntegerRange)a).getBitMask() & ((IntegerRange)b).getBitMask());
                 if (resultMask >= 0) {
                     return createIntegerRange(0, resultMask);
                 }
             } else if (a.isUnknown() && b.isIntegerType()) {
                 final long operandMask = ((IntegerRange)b).getBitMask();
                 if (operandMask >= 0) {
                     return createIntegerRange(0, operandMask);
                 }
             } else if (a.isIntegerType() && b.isUnknown()) {
                 final long operandMask = ((IntegerRange)a).getBitMask();
                 if (operandMask >= 0) {
                     return createIntegerRange(0, operandMask);
                 }
             }

             return createTypeRange(Type.INT);
         }

         /**
          * Bitwise or operation
          * @param a range of first symbol to be or:ed
          * @param b range of second symbol to be or:ed
          * @return resulting range representing the value range after or
          */
         public Range or(final Range a, final Range b) {
             if (a.isIntegerType() && b.isIntegerType()) {
                 final int resultMask = (int)(((IntegerRange)a).getBitMask() | ((IntegerRange)b).getBitMask());
                 if (resultMask >= 0) {
                     return createIntegerRange(0, resultMask);
                 }
             }

             return createTypeRange(Type.INT);
         }

         /**
          * Bitwise xor operation
          * @param a range of first symbol to be xor:ed
          * @param b range of second symbol to be xor:ed
          * @return resulting range representing the value range after and
          */
         public Range xor(final Range a, final Range b) {
             if (a.isIntegerConst() && b.isIntegerConst()) {
                 return createRange(((IntegerRange)a).getMin() ^ ((IntegerRange)b).getMin());
             }

             if (a.isIntegerType() && b.isIntegerType()) {
                 final int resultMask = (int)(((IntegerRange)a).getBitMask() | ((IntegerRange)b).getBitMask());
                 if (resultMask >= 0) {
                     return createIntegerRange(0, createIntegerRange(0, resultMask).getBitMask());
                 }
             }
             return createTypeRange(Type.INT);
         }

         /**
          * Bitwise shl operation
          * @param a range of first symbol to be shl:ed
          * @param b range of second symbol to be shl:ed
          * @return resulting range representing the value range after shl
          */
         public Range shl(final Range a, final Range b) {
             if (b.isIntegerType() && b.isIntegerConst()) {
                 final IntegerRange left  = (IntegerRange)(a.isIntegerType() ? a : createTypeRange(Type.INT));
                 final int          shift = (int)((IntegerRange) b).getMin() & 0x1f;
                 final int          min   = (int)left.getMin() << shift;
                 final int          max   = (int)left.getMax() << shift;
                 if (min >> shift == left.getMin() && max >> shift == left.getMax()) {
                     return createIntegerRange(min, max);
                 }
             }

             return createTypeRange(Type.INT);
         }

         /**
          * Bitwise shr operation
          * @param a range of first symbol to be shr:ed
          * @param b range of second symbol to be shr:ed
          * @return resulting range representing the value range after shr
          */
         public Range shr(final Range a, final Range b) {
             if (b.isIntegerType() && b.isIntegerConst()) {
                 final long         shift = ((IntegerRange) b).getMin() & 0x1f;
                 final IntegerRange left  = (IntegerRange)(a.isIntegerType() ? a : createTypeRange(Type.INT));
                 if (left.getMin() >= 0) {
                     long min = left.getMin() >>> shift;
                     long max = left.getMax() >>> shift;
                     return createIntegerRange(min, max);
                 } else if (shift >= 1) {
                     return createIntegerRange(0, JSType.MAX_UINT >>> shift);
                 }
             }

             return createTypeRange(Type.INT);
         }

         /**
          * Bitwise sar operation
          * @param a range of first symbol to be sar:ed
          * @param b range of second symbol to be sar:ed
          * @return resulting range representing the value range after sar
          */
         public Range sar(final Range a, final Range b) {
             if (b.isIntegerType() && b.isIntegerConst()) {
                 final IntegerRange left  = (IntegerRange)(a.isIntegerType() ? a : createTypeRange(Type.INT));
                 final long         shift = ((IntegerRange) b).getMin() & 0x1f;
                 final long         min   = left.getMin() >> shift;
                 final long         max   = left.getMax() >> shift;
                 return createIntegerRange(min, max);
             }

             return createTypeRange(Type.INT);
         }

         /**
          * Modulo operation
          * @param a range of first symbol to the mod operation
          * @param b range of second symbol to be mod operation
          * @return resulting range representing the value range after mod
          */
         public Range mod(final Range a, final Range b) {
             if (a.isIntegerType() && b.isIntegerType()) {
                 final IntegerRange rhs = (IntegerRange) b;
                 if (rhs.getMin() > 0 || rhs.getMax() < 0) { // divisor range must not include 0
                     final long absmax = Math.max(Math.abs(rhs.getMin()), Math.abs(rhs.getMax())) - 1;
                     return createIntegerRange(rhs.getMin() > 0 ? 0 : -absmax, rhs.getMax() < 0 ? 0 : +absmax);
                 }
             }
             return createTypeRange(Type.NUMBER);
         }

         /**
          * Division operation
          * @param a range of first symbol to the division
          * @param b range of second symbol to be division
          * @return resulting range representing the value range after division
          */
         public Range div(final Range a, final Range b) {
             // TODO
             return createTypeRange(Type.NUMBER);
         }
     }

     /**
      * Simple trace functionality that will log range creation
      */
     public static class TraceFunctionality extends Functionality {
         TraceFunctionality(final DebugLogger log) {
             super(log);
         }

         private Range trace(final Range result, final String operation, final Range... operands) {
             log.fine("range::" + operation + Arrays.toString(operands) + " => " + result);
             return result;
         }

         @Override
         public Range join(final Range a, final Range b) {
             final Range result = super.join(a, b);
             if (!a.equals(b)) {
                 trace(result, "join", a, b);
             }
             return result;
         }

         @Override
         public Range add(final Range a, final Range b) {
             return trace(super.add(a, b), "add", a, b);
         }

         @Override
         public Range sub(final Range a, final Range b) {
             return trace(super.sub(a, b), "sub", a, b);
         }

         @Override
         public Range mul(final Range a, final Range b) {
             return trace(super.mul(a, b), "mul", a, b);
         }

         @Override
         public Range neg(final Range a) {
             return trace(super.neg(a), "neg", a);
         }

         @Override
         public Range and(final Range a, final Range b) {
             return trace(super.and(a, b), "and", a, b);
         }

         @Override
         public Range or(final Range a, final Range b) {
             return trace(super.or(a, b), "or", a, b);
         }

         @Override
         public Range xor(final Range a, final Range b) {
             return trace(super.xor(a, b), "xor", a, b);
         }

         @Override
         public Range shl(final Range a, final Range b) {
             return trace(super.shl(a, b), "shl", a, b);
         }

         @Override
         public Range shr(final Range a, final Range b) {
             return trace(super.shr(a, b), "shr", a, b);
         }

         @Override
         public Range sar(final Range a, final Range b) {
             return trace(super.sar(a, b), "sar", a, b);
         }

         @Override
         public Range mod(final Range a, final Range b) {
             return trace(super.mod(a, b), "mod", a, b);
         }

         @Override
         public Range div(final Range a, final Range b) {
             return trace(super.div(a, b), "div", a, b);
         }
     }

     @Override
     public String toString() {
         return String.valueOf(getType());
     }

     @SuppressWarnings("unused")
     private static boolean isRepresentableAsInt(final double number) {
         return (int)number == number && !isNegativeZero(number);
     }

     private static boolean isRepresentableAsLong(final double number) {
         return (long)number == number && !isNegativeZero(number);
     }

     private static boolean isNegativeZero(final double number) {
         return Double.doubleToLongBits(number) == Double.doubleToLongBits(-0.0);
     }
 }
	/*
	* Copyright (c) 2010, 2013, Oracle and/or its affiliates. All rights reserved.
	* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
	*
	* This code is free software; you can redistribute it and/or modify it
	* under the terms of the GNU General Public License version 2 only, as
	* published by the Free Software Foundation. Oracle designates this
	* particular file as subject to the "Classpath" exception as provided
	* by Oracle in the LICENSE file that accompanied this code.
	*
	* This code is distributed in the hope that it will be useful, but WITHOUT
	* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
	* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
	* version 2 for more details (a copy is included in the LICENSE file that
	* accompanied this code).
	*
	* You should have received a copy of the GNU General Public License version
	* 2 along with this work; if not, write to the Free Software Foundation,
	* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
	*
	* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
	* or visit www.oracle.com if you need additional information or have any
	* questions.
	*/

	package jdk.nashorn.internal.codegen.types;

	import java.util.Arrays;
	import java.util.Collections;
	import java.util.List;

	import jdk.nashorn.internal.runtime.DebugLogger;
	import jdk.nashorn.internal.runtime.JSType;

	/**
	* Represents the value range of a symbol.
	*/
	public abstract class Range {

	private static final Range GENERIC_RANGE = new Range() {
	@Override
	public Type getType() {
	return Type.OBJECT;
	}
	};

	private static final Range NUMBER_RANGE = new Range() {
	@Override
	public Type getType() {
	return Type.NUMBER;
	}
	};

	private static final Range UNKNOWN_RANGE = new Range() {
	@Override
	public Type getType() {
	return Type.UNKNOWN;
	}

	@Override
	public boolean isUnknown() {
	return true;
	}
	};

	private static class IntegerRange extends Range {
	private final long min;
	private final long max;
	private final Type type;

	private IntegerRange(final long min, final long max) {
	assert min <= max;
	this.min = min;
	this.max = max;
	this.type = typeFromRange(min, max);
	}

	private static Type typeFromRange(final long from, final long to) {
	if (from >= Integer.MIN_VALUE && to <= Integer.MAX_VALUE) {
	return Type.INT;
	}
	return Type.LONG;
	}

	@Override
	public Type getType() {
	return type;
	}

	public long getMin() {
	return min;
	}

	public long getMax() {
	return max;
	}

	@Override
	public boolean isIntegerConst() {
	return getMin() == getMax();
	}

	private long getBitMask() {
	if (min == max) {
	return min;
	}

	if (min < 0) {
	return ~0L;
	}

	long mask = 1;
	while (mask < max) {
	mask = (mask << 1) \| 1;
	}
	return mask;
	}

	@Override
	public boolean equals(final Object obj) {
	if (obj instanceof IntegerRange) {
	final IntegerRange other = (IntegerRange)obj;
	return this.type == other.type && this.min == other.min && this.max == other.max;
	}
	return false;
	}

	@Override
	public int hashCode() {
	return Long.hashCode(min) ^ Long.hashCode(max);
	}

	@Override
	public String toString() {
	return super.toString() + "[" + min +", " + max + "]";
	}
	}

	/**
	* Get narrowest type for this range
	* @return type
	*/
	public abstract Type getType();

	/**
	* Is this range unknown
	* @return true if unknown
	*/
	public boolean isUnknown() {
	return false;
	}

	/**
	* Check if an integer is enough to span this range
	* @return true if integer is enough
	*/
	public boolean isIntegerType() {
	return this instanceof IntegerRange;
	}

	/**
	* Check if an integer is enough to span this range
	* @return true if integer is enough
	*/
	public boolean isIntegerConst() {
	return false;
	}

	/**
	* Create an unknown range - this is most likely a singleton object
	* and it represents "we have no known range information"
	* @return the range
	*/
	public static Range createUnknownRange() {
	return UNKNOWN_RANGE;
	}

	/**
	* Create a constant range: [value, value]
	* @param value value
	* @return the range
	*/
	public static Range createRange(final int value) {
	return createIntegerRange(value, value);
	}

	/**
	* Create a constant range: [value, value]
	* @param value value
	* @return the range
	*/
	public static Range createRange(final long value) {
	return createIntegerRange(value, value);
	}

	/**
	* Create a constant range: [value, value]
	* @param value value
	* @return the range
	*/
	public static Range createRange(final double value) {
	if (isRepresentableAsLong(value)) {
	return createIntegerRange((long) value, (long) value);
	}
	return createNumberRange();
	}

	/**
	* Create a constant range: [value, value]
	* @param value value
	* @return the range
	*/
	public static Range createRange(final Object value) {
	if (value instanceof Integer) {
	return createRange((int)value);
	} else if (value instanceof Long) {
	return createRange((long)value);
	} else if (value instanceof Double) {
	return createRange((double)value);
	}

	return createGenericRange();
	}

	/**
	* Create a generic range - object symbol that carries no range
	* information
	* @return the range
	*/
	public static Range createGenericRange() {
	return GENERIC_RANGE;
	}

	/**
	* Create a number range - number symbol that carries no range
	* information
	* @return the range
	*/
	public static Range createNumberRange() {
	return NUMBER_RANGE;
	}

	/**
	* Create an integer range [min, max]
	* @param min minimum value, inclusive
	* @param max maximum value, inclusive
	* @return the range
	*/
	public static IntegerRange createIntegerRange(final long min, final long max) {
	return new IntegerRange(min, max);
	}

	/**
	* Create an integer range of maximum type width for the given type
	* @param type the type
	* @return the range
	*/
	public static IntegerRange createIntegerRange(final Type type) {
	assert type.isNumeric() && !type.isNumber();
	final long min;
	final long max;
	if (type.isInteger()) {
	min = Integer.MIN_VALUE;
	max = Integer.MAX_VALUE;
	} else if (type.isLong()) {
	min = Long.MIN_VALUE;
	max = Long.MAX_VALUE;
	} else {
	throw new AssertionError(); //type incompatible with integer range
	}
	return new IntegerRange(min, max);
	}

	/**
	* Create an range of maximum type width for the given type
	* @param type the type
	* @return the range
	*/
	public static Range createTypeRange(final Type type) {
	if (type.isNumber()) {
	return createNumberRange();
	} else if (type.isNumeric()) {
	return createIntegerRange(type);
	} else {
	return createGenericRange();
	}
	}

	// check that add doesn't overflow
	private static boolean checkAdd(final long a, final long b) {
	final long result = a + b;
	return ((a ^ result) & (b ^ result)) >= 0;
	}

	// check that sub doesn't overflow
	private static boolean checkSub(final long a, final long b) {
	final long result = a - b;
	return ((a ^ result) & (b ^ result)) >= 0;
	}

	private static boolean checkMul(final long a, final long b) {
	// TODO correct overflow check
	return a >= Integer.MIN_VALUE && a <= Integer.MAX_VALUE && b >= Integer.MIN_VALUE && b <= Integer.MAX_VALUE;
	}

	/**
	* The range functionality class responsible for merging ranges and drawing
	* range conclusions from operations executed
	*/
	public static class Functionality {
	/** logger */
	protected final DebugLogger log;

	/**
	* Constructor
	* @param log logger
	*/
	public Functionality(final DebugLogger log) {
	this.log = log;
	}

	/**
	* Join two ranges
	* @param a first range
	* @param b second range
	* @return the joined range
	*/
	public Range join(final Range a, final Range b) {
	if (a.equals(b)) {
	return a;
	}

	Type joinedType = a.getType();
	if (a.getType() != b.getType()) {
	if (a.isUnknown()) {
	return b;
	}
	if (b.isUnknown()) {
	return a;
	}

	joinedType = Type.widest(a.getType(), b.getType());
	}

	if (joinedType.isInteger() \|\| joinedType.isLong()) {
	return createIntegerRange(
	Math.min(((IntegerRange) a).getMin(), ((IntegerRange) b).getMin()),
	Math.max(((IntegerRange) a).getMax(), ((IntegerRange) b).getMax()));
	}

	return createTypeRange(joinedType);
	}

	/**
	* Add operation
	* @param a range of first symbol to be added
	* @param b range of second symbol to be added
	* @return resulting range representing the value range after add
	*/
	public Range add(final Range a, final Range b) {
	if (a.isIntegerType() && b.isIntegerType()) {
	final IntegerRange lhs = (IntegerRange)a;
	final IntegerRange rhs = (IntegerRange)b;
	if (checkAdd(lhs.getMin(), rhs.getMin()) && checkAdd(lhs.getMax(), rhs.getMax())) {
	return createIntegerRange(lhs.getMin() + rhs.getMin(), lhs.getMax() + rhs.getMax());
	}
	}

	if (a.getType().isNumeric() && b.getType().isNumeric()) {
	return createNumberRange();
	}

	return createGenericRange();
	}

	/**
	* Sub operation
	* @param a range of first symbol to be subtracted
	* @param b range of second symbol to be subtracted
	* @return resulting range representing the value range after subtraction
	*/
	public Range sub(final Range a, final Range b) {
	if (a.isIntegerType() && b.isIntegerType()) {
	final IntegerRange lhs = (IntegerRange)a;
	final IntegerRange rhs = (IntegerRange)b;
	if (checkSub(lhs.getMin(), rhs.getMax()) && checkSub(lhs.getMax(), rhs.getMin())) {
	return createIntegerRange(lhs.getMin() - rhs.getMax(), lhs.getMax() - rhs.getMin());
	}
	}

	if (a.getType().isNumeric() && b.getType().isNumeric()) {
	return createNumberRange();
	}

	return createGenericRange();
	}

	/**
	* Mul operation
	* @param a range of first symbol to be multiplied
	* @param b range of second symbol to be multiplied
	* @return resulting range representing the value range after multiplication
	*/
	public Range mul(final Range a, final Range b) {
	if (a.isIntegerType() && b.isIntegerType()) {
	final IntegerRange lhs = (IntegerRange)a;
	final IntegerRange rhs = (IntegerRange)b;

	//ensure that nothing ever overflows or underflows
	if (checkMul(lhs.getMin(), rhs.getMin()) &&
	checkMul(lhs.getMax(), rhs.getMax()) &&
	checkMul(lhs.getMin(), rhs.getMax()) &&
	checkMul(lhs.getMax(), rhs.getMin())) {

	final List<Long> results =
	Arrays.asList(
	lhs.getMin() * rhs.getMin(),
	lhs.getMin() * rhs.getMax(),
	lhs.getMax() * rhs.getMin(),
	lhs.getMax() * rhs.getMax());
	return createIntegerRange(Collections.min(results), Collections.max(results));
	}
	}

	if (a.getType().isNumeric() && b.getType().isNumeric()) {
	return createNumberRange();
	}

	return createGenericRange();
	}

	/**
	* Neg operation
	* @param a range of value symbol to be negated
	* @return resulting range representing the value range after neg
	*/
	public Range neg(final Range a) {
	if (a.isIntegerType()) {
	final IntegerRange rhs = (IntegerRange)a;
	if (rhs.getMin() != Long.MIN_VALUE && rhs.getMax() != Long.MIN_VALUE) {
	return createIntegerRange(-rhs.getMax(), -rhs.getMin());
	}
	}

	if (a.getType().isNumeric()) {
	return createNumberRange();
	}

	return createGenericRange();
	}

	/**
	* Bitwise and operation
	* @param a range of first symbol to be and:ed
	* @param b range of second symbol to be and:ed
	* @return resulting range representing the value range after and
	*/
	public Range and(final Range a, final Range b) {
	if (a.isIntegerType() && b.isIntegerType()) {
	final int resultMask = (int) (((IntegerRange)a).getBitMask() & ((IntegerRange)b).getBitMask());
	if (resultMask >= 0) {
	return createIntegerRange(0, resultMask);
	}
	} else if (a.isUnknown() && b.isIntegerType()) {
	final long operandMask = ((IntegerRange)b).getBitMask();
	if (operandMask >= 0) {
	return createIntegerRange(0, operandMask);
	}
	} else if (a.isIntegerType() && b.isUnknown()) {
	final long operandMask = ((IntegerRange)a).getBitMask();
	if (operandMask >= 0) {
	return createIntegerRange(0, operandMask);
	}
	}

	return createTypeRange(Type.INT);
	}

	/**
	* Bitwise or operation
	* @param a range of first symbol to be or:ed
	* @param b range of second symbol to be or:ed
	* @return resulting range representing the value range after or
	*/
	public Range or(final Range a, final Range b) {
	if (a.isIntegerType() && b.isIntegerType()) {
	final int resultMask = (int)(((IntegerRange)a).getBitMask() \| ((IntegerRange)b).getBitMask());
	if (resultMask >= 0) {
	return createIntegerRange(0, resultMask);
	}
	}

	return createTypeRange(Type.INT);
	}

	/**
	* Bitwise xor operation
	* @param a range of first symbol to be xor:ed
	* @param b range of second symbol to be xor:ed
	* @return resulting range representing the value range after and
	*/
	public Range xor(final Range a, final Range b) {
	if (a.isIntegerConst() && b.isIntegerConst()) {
	return createRange(((IntegerRange)a).getMin() ^ ((IntegerRange)b).getMin());
	}

	if (a.isIntegerType() && b.isIntegerType()) {
	final int resultMask = (int)(((IntegerRange)a).getBitMask() \| ((IntegerRange)b).getBitMask());
	if (resultMask >= 0) {
	return createIntegerRange(0, createIntegerRange(0, resultMask).getBitMask());
	}
	}
	return createTypeRange(Type.INT);
	}

	/**
	* Bitwise shl operation
	* @param a range of first symbol to be shl:ed
	* @param b range of second symbol to be shl:ed
	* @return resulting range representing the value range after shl
	*/
	public Range shl(final Range a, final Range b) {
	if (b.isIntegerType() && b.isIntegerConst()) {
	final IntegerRange left = (IntegerRange)(a.isIntegerType() ? a : createTypeRange(Type.INT));
	final int shift = (int)((IntegerRange) b).getMin() & 0x1f;
	final int min = (int)left.getMin() << shift;
	final int max = (int)left.getMax() << shift;
	if (min >> shift == left.getMin() && max >> shift == left.getMax()) {
	return createIntegerRange(min, max);
	}
	}

	return createTypeRange(Type.INT);
	}

	/**
	* Bitwise shr operation
	* @param a range of first symbol to be shr:ed
	* @param b range of second symbol to be shr:ed
	* @return resulting range representing the value range after shr
	*/
	public Range shr(final Range a, final Range b) {
	if (b.isIntegerType() && b.isIntegerConst()) {
	final long shift = ((IntegerRange) b).getMin() & 0x1f;
	final IntegerRange left = (IntegerRange)(a.isIntegerType() ? a : createTypeRange(Type.INT));
	if (left.getMin() >= 0) {
	long min = left.getMin() >>> shift;
	long max = left.getMax() >>> shift;
	return createIntegerRange(min, max);
	} else if (shift >= 1) {
	return createIntegerRange(0, JSType.MAX_UINT >>> shift);
	}
	}

	return createTypeRange(Type.INT);
	}

	/**
	* Bitwise sar operation
	* @param a range of first symbol to be sar:ed
	* @param b range of second symbol to be sar:ed
	* @return resulting range representing the value range after sar
	*/
	public Range sar(final Range a, final Range b) {
	if (b.isIntegerType() && b.isIntegerConst()) {
	final IntegerRange left = (IntegerRange)(a.isIntegerType() ? a : createTypeRange(Type.INT));
	final long shift = ((IntegerRange) b).getMin() & 0x1f;
	final long min = left.getMin() >> shift;
	final long max = left.getMax() >> shift;
	return createIntegerRange(min, max);
	}

	return createTypeRange(Type.INT);
	}

	/**
	* Modulo operation
	* @param a range of first symbol to the mod operation
	* @param b range of second symbol to be mod operation
	* @return resulting range representing the value range after mod
	*/
	public Range mod(final Range a, final Range b) {
	if (a.isIntegerType() && b.isIntegerType()) {
	final IntegerRange rhs = (IntegerRange) b;
	if (rhs.getMin() > 0 \|\| rhs.getMax() < 0) { // divisor range must not include 0
	final long absmax = Math.max(Math.abs(rhs.getMin()), Math.abs(rhs.getMax())) - 1;
	return createIntegerRange(rhs.getMin() > 0 ? 0 : -absmax, rhs.getMax() < 0 ? 0 : +absmax);
	}
	}
	return createTypeRange(Type.NUMBER);
	}

	/**
	* Division operation
	* @param a range of first symbol to the division
	* @param b range of second symbol to be division
	* @return resulting range representing the value range after division
	*/
	public Range div(final Range a, final Range b) {
	// TODO
	return createTypeRange(Type.NUMBER);
	}
	}

	/**
	* Simple trace functionality that will log range creation
	*/
	public static class TraceFunctionality extends Functionality {
	TraceFunctionality(final DebugLogger log) {
	super(log);
	}

	private Range trace(final Range result, final String operation, final Range... operands) {
	log.fine("range::" + operation + Arrays.toString(operands) + " => " + result);
	return result;
	}

	@Override
	public Range join(final Range a, final Range b) {
	final Range result = super.join(a, b);
	if (!a.equals(b)) {
	trace(result, "join", a, b);
	}
	return result;
	}

	@Override
	public Range add(final Range a, final Range b) {
	return trace(super.add(a, b), "add", a, b);
	}

	@Override
	public Range sub(final Range a, final Range b) {
	return trace(super.sub(a, b), "sub", a, b);
	}

	@Override
	public Range mul(final Range a, final Range b) {
	return trace(super.mul(a, b), "mul", a, b);
	}

	@Override
	public Range neg(final Range a) {
	return trace(super.neg(a), "neg", a);
	}

	@Override
	public Range and(final Range a, final Range b) {
	return trace(super.and(a, b), "and", a, b);
	}

	@Override
	public Range or(final Range a, final Range b) {
	return trace(super.or(a, b), "or", a, b);
	}

	@Override
	public Range xor(final Range a, final Range b) {
	return trace(super.xor(a, b), "xor", a, b);
	}

	@Override
	public Range shl(final Range a, final Range b) {
	return trace(super.shl(a, b), "shl", a, b);
	}

	@Override
	public Range shr(final Range a, final Range b) {
	return trace(super.shr(a, b), "shr", a, b);
	}

	@Override
	public Range sar(final Range a, final Range b) {
	return trace(super.sar(a, b), "sar", a, b);
	}

	@Override
	public Range mod(final Range a, final Range b) {
	return trace(super.mod(a, b), "mod", a, b);
	}

	@Override
	public Range div(final Range a, final Range b) {
	return trace(super.div(a, b), "div", a, b);
	}
	}

	@Override
	public String toString() {
	return String.valueOf(getType());
	}

	@SuppressWarnings("unused")
	private static boolean isRepresentableAsInt(final double number) {
	return (int)number == number && !isNegativeZero(number);
	}

	private static boolean isRepresentableAsLong(final double number) {
	return (long)number == number && !isNegativeZero(number);
	}

	private static boolean isNegativeZero(final double number) {
	return Double.doubleToLongBits(number) == Double.doubleToLongBits(-0.0);
	}
	}