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CHAPTER 5

Conversions and Promotions

Every Java expression has a type that can be deduced from the structure of the expression and the types of the literals, variables, and methods mentioned in the expression. It is possible, however, to write an expression in a context where the type of the expression is not appropriate. In some cases, this leads to an error at compile time; for example, if the expression in an if statement (§14.8) has any type other than boolean, a compile-time error occurs. In other cases, the context may be able to accept a type that is related to the type of the expression; as a convenience, rather than requiring the programmer to indicate a type conversion explicitly, the Java language performs an implicit conversion from the type of the expression to a type acceptable for its surrounding context.

A specific conversion from type S to type T allows an expression of type S to be treated at compile time as if it had type T instead. In some cases this will require a corresponding action at run time to check the validity of the conversion or to translate the run-time value of the expression into a form appropriate for the new type T. For example:

In every conversion context, only certain specific conversions are permitted. The specific conversions that are possible in Java are grouped for convenience of description into several broad categories:

There are five conversion contexts in which conversion of Java expressions may occur. Each context allows conversions in some of the categories named above but not others. The term "conversion" is also used to describe the process of choosing a specific conversion for such a context. For example, we say that an expression that is an actual argument in a method invocation is subject to "method invocation conversion," meaning that a specific conversion will be implicitly chosen for that expression according to the rules for the method invocation argument context.

One conversion context is the operand of a numeric operator such as + or *. The conversion process for such operands is called numeric promotion. Promotion is special in that, in the case of binary operators, the conversion chosen for one operand may depend in part on the type of the other operand expression.

This chapter first describes the six categories of conversions (§5.1), including the special conversions to String allowed for the string concatenation operator +. Then the five conversion contexts are described:

Here are some examples of the various contexts for conversion:


class Test {			

	public static void main(String[] args) {

		// Casting conversion (§5.4) of a float literal to
		// type int. Without the cast operator, this would
		// be a compile-time error, because this is a
		// narrowing conversion (§5.1.3):
		int i = (int)12.5f;


		// String conversion (§5.4) of i's int value:
		System.out.println("(int)12.5f==" + i);


		// Assignment conversion (§5.2) of i's value to type
		// float. This is a widening conversion (§5.1.2):
		float f = i;


		// String conversion of f's float value:
		System.out.println("after float widening: " + f);


		// Numeric promotion (§5.6) of i's value to type
		// float. This is a binary numeric promotion.
		// After promotion, the operation is float*float:
		System.out.print(f);
		f = f * i;


		// Two string conversions of i and f:
		System.out.println("*" + i + "==" + f);


		// Method invocation conversion (§5.3) of f's value
		// to type double, needed because the method Math.sin
		// accepts only a double argument:
		double d = Math.sin(f);


		// Two string conversions of f and d:
		System.out.println("Math.sin(" + f + ")==" + d);

	}

}
which produces the output: 


(int)12.5f==12
after float widening: 12.0
12.0*12==144.0
Math.sin(144.0)==-0.49102159389846934

5.1 Kinds of Conversion

Specific type conversions in Java are divided into six categories.

5.1.1 Identity Conversions

A conversion from a type to that same type is permitted for any type. This may seem trivial, but it has two practical consequences. First, it is always permitted for an expression to have the desired type to begin with, thus allowing the simply stated rule that every expression is subject to conversion, if only a trivial identity conversion. Second, it implies that it is permitted for a program to include redundant cast operators for the sake of clarity.

The only permitted conversion that involves the type boolean is the identity conversion from boolean to boolean.

5.1.2 Widening Primitive Conversions

The following 19 specific conversions on primitive types are called the widening primitive conversions:

Widening primitive conversions do not lose information about the overall magnitude of a numeric value. Indeed, conversions widening from an integral type to another integral type and from float to double do not lose any information at all; the numeric value is preserved exactly. Conversion of an int or a long value to float, or of a long value to double, may result in loss of precision-that is, the result may lose some of the least significant bits of the value. In this case, the resulting floating-point value will be a correctly rounded version of the integer value, using IEEE 754 round-to-nearest mode (§4.2.4).

A widening conversion of a signed integer value to an integral type T simply sign-extends the two's-complement representation of the integer value to fill the wider format. A widening conversion of a character to an integral type T zero-extends the representation of the character value to fill the wider format.

Despite the fact that loss of precision may occur, widening conversions among primitive types never result in a run-time exception (§11).

Here is an example of a widening conversion that loses precision:


class Test {
	public static void main(String[] args) {
		int big = 1234567890;
		float approx = big;
		System.out.println(big - (int)approx);
	}
}
which prints: 

-46
thus indicating that information was lost during the conversion from type int to type float because values of type float are not precise to nine significant digits.

5.1.3 Narrowing Primitive Conversions

The following 23 specific conversions on primitive types are called the narrowing primitive conversions:

Narrowing conversions may lose information about the overall magnitude of a numeric value and may also lose precision.

A narrowing conversion of a signed integer to an integral type T simply discards all but the n lowest order bits, where n is the number of bits used to represent type T. In addition to a possible loss of information about the magnitude of the numeric value, this may cause the sign of the resulting value to differ from the sign of the input value.

A narrowing conversion of a character to an integral type T likewise simply discards all but the n lowest order bits, where n is the number of bits used to represent type T. In addition to a possible loss of information about the magnitude of the numeric value, this may cause the resulting value to be a negative number, even though characters represent 16-bit unsigned integer values.

A narrowing conversion of a floating-point number to an integral type T takes two steps:

  1. In the first step, the floating-point number is converted either to a long, if T is long, or to an int, if T is byte, short, char, or int, as follows:
  2. In the second step:
The example: 


class Test {
	public static void main(String[] args) {
		float fmin = Float.NEGATIVE_INFINITY;
		float fmax = Float.POSITIVE_INFINITY;
		System.out.println("long: " + (long)fmin +
								".." + (long)fmax);
		System.out.println("int: " + (int)fmin +
								".." + (int)fmax);
		System.out.println("short: " + (short)fmin +
								".." + (short)fmax);
		System.out.println("char: " + (int)(char)fmin +
								".." + (int)(char)fmax);
		System.out.println("byte: " + (byte)fmin +
								".." + (byte)fmax);
	}
}
produces the output: 


long: -9223372036854775808..9223372036854775807
int: -2147483648..2147483647
short: 0..-1
char: 0..65535
byte: 0..-1
The results for char, int, and long are unsurprising, producing the minimum and maximum representable values of the type.

The results for byte and short lose information about the sign and magnitude of the numeric values and also lose precision. The results can be understood by examining the low order bits of the minimum and maximum int. The minimum int is, in hexadecimal, 0x80000000, and the maximum int is 0x7fffffff. This explains the short results, which are the low 16 bits of these values, namely, 0x0000 and 0xffff; it explains the char results, which also are the low 16 bits of these values, namely, '\u0000' and '\uffff'; and it explains the byte results, which are the low 8 bits of these values, namely, 0x00 and 0xff.

A narrowing conversion from double to float behaves in accordance with IEEE 754. The result is correctly rounded using IEEE 754 round-to-nearest mode. A value too small to be represented as a float is converted to positive or negative zero; a value too large to be represented as a float is converted to a (positive or negative) infinity. A double NaN is always converted to a float NaN.

Despite the fact that overflow, underflow, or other loss of information may occur, narrowing conversions among primitive types never result in a run-time exception (§11).

Here is a small test program that demonstrates a number of narrowing conversions that lose information:


class Test {

	public static void main(String[] args) {

		// A narrowing of int to short loses high bits:
		System.out.println("(short)0x12345678==0x" +
					Integer.toHexString((short)0x12345678));


		// A int value not fitting in byte changes sign and magnitude:
		System.out.println("(byte)255==" + (byte)255);


		// A float value too big to fit gives largest int value:
		System.out.println("(int)1e20f==" + (int)1e20f);


		// A NaN converted to int yields zero:
		System.out.println("(int)NaN==" + (int)Float.NaN);


		// A double value too large for float yields infinity:
		System.out.println("(float)-1e100==" + (float)-1e100);


		// A double value too small for float underflows to zero:
		System.out.println("(float)1e-50==" + (float)1e-50);

	}

}
This test program produces the following output: 


(short)0x12345678==0x5678
(byte)255==-1
(int)1e20f==2147483647
(int)NaN==0
(float)-1e100==-Infinity
(float)1e-50==0.0

5.1.4 Widening Reference Conversions

The following conversions are called the widening reference conversions:

Such conversions never require a special action at run time and therefore never throw an exception at run time. They consist simply in regarding a reference as having some other type in a manner that can be proved correct at compile time.

See §8 for the detailed specifications for classes, §9 for interfaces, and §10 for arrays.

5.1.5 Narrowing Reference Conversions

The following conversions are called the narrowing reference conversions:

Such conversions require a test at run time to find out whether the actual reference value is a legitimate value of the new type. If not, then a ClassCastException is thrown.

5.1.6 String Conversions

There is a string conversion to type String from every other type, including the null type.

5.1.7 Forbidden Conversions

5.2 Assignment Conversion

Assignment conversion occurs when the value of an expression is assigned (§15.25) to a variable: the type of the expression must be converted to the type of the variable. Assignment contexts allow the use of an identity conversion (§5.1.1), a widening primitive conversion (§5.1.2), or a widening reference conversion (§5.1.4). In addition, a narrowing primitive conversion may be used if all of the following conditions are satisfied:

If the type of the expression cannot be converted to the type of the variable by a conversion permitted in an assignment context, then a compile-time error occurs.

If the type of an expression can be converted to the type a variable by assignment conversion, we say the expression (or its value) is assignable to the variable or, equivalently, that the type of the expression is assignment compatible with the type of the variable.

An assignment conversion never causes an exception. (Note, however, that an assignment may result in an exception in a special case involving array elements -see §10.10 and §15.25.1.)

The compile-time narrowing of constants means that code such as:

byte theAnswer = 42;
is allowed. Without the narrowing, the fact that the integer literal 42 has type int would mean that a cast to byte would be required: 

byte theAnswer = (byte)42;									// cast is permitted but not required
A value of primitive type must not be assigned to a variable of reference type; an attempt to do so will result in a compile-time error. A value of type boolean can be assigned only to a variable of type boolean.

The following test program contains examples of assignment conversion of primitive values:


class Test {
	public static void main(String[] args) {
		short s = 12;							// narrow 12 to short
		float f = s;							// widen short to float
		System.out.println("f=" + f);

		char c = '\u0123';
		long l = c;							// widen char to long
		System.out.println("l=0x" + Long.toString(l,16));

		f = 1.23f;
		double d = f;							// widen float to double
		System.out.println("d=" + d);
	}
}
It produces the following output: 


f=12.0	
i=0x123
d=1.2300000190734863
The following test, however, produces compile-time errors: 


class Test {
	public static void main(String[] args) {
		short s = 123;
		char c = s;							// error: would require cast
		s = c;							// error: would require cast
	}
}
because not all short values are char values, and neither are all char values short values.

A value of reference type must not be assigned to a variable of primitive type; an attempt to do so will result in a compile-time error.

A value of the null type (the null reference is the only such value) may be assigned to any reference type, resulting in a null reference of that type.

Here is a sample program illustrating assignments of references:


public class Point { int x, y; }

public class Point3D extends Point { int z; }


public interface Colorable {
	void setColor(int color);
}


public class ColoredPoint extends Point implements Colorable 
{
	int color;
	public void setColor(int color) { this.color = color; }
}







class Test {

	public static void main(String[] args) {

		// Assignments to variables of class type:
		Point p = new Point();
		p = new Point3D();							// ok: because Point3d is a
									// subclass of Point
		
		Point3D p3d = p;							// error: will require a cast because a 
									// Point might not be a Point3D
									// (even though it is, dynamically,
									// in this example.)

		// Assignments to variables of type Object:
		Object o = p;							// ok: any object to Object
		int[] a = new int[3];
		Object o2 = a;							// ok: an array to Object


		// Assignments to variables of interface type:
		ColoredPoint cp = new ColoredPoint();
		Colorable c = cp;							// ok: ColoredPoint implements
									// Colorable


		// Assignments to variables of array type:
		byte[] b = new byte[4];
		a = b;							// error: these are not arrays
									// of the same primitive type
		Point3D[] p3da = new Point3D[3];
		Point[] pa = p3da;							// ok: since we can assign a
									// Point3D to a Point
		p3da = pa;							// error: (cast needed) since a Point
									// can't be assigned to a Point3D

	}

}
Assignment of a value of compile-time reference type S (source) to a variable of compile-time reference type T (target) is checked as follows:

See §8 for the detailed specifications of classes, §9 for interfaces, and §10 for arrays.

The following test program illustrates assignment conversions on reference values, but fails to compile because it violates the preceding rules, as described in its comments. This example should be compared to the preceding one.


public class Point { int x, y; }

public interface Colorable { void setColor(int color); }


public class ColoredPoint extends Point implements Colorable 
{
	int color;
	public void setColor(int color) { this.color = color; }
}


class Test {

	public static void main(String[] args) {

		Point p = new Point();

		ColoredPoint cp = new ColoredPoint();

		// Okay because ColoredPoint is a subclass of Point:
		p = cp;


		// Okay because ColoredPoint implements Colorable:
		Colorable c = cp;


		// The following cause compile-time errors because
		// we cannot be sure they will succeed, depending on
		// the run-time type of p; a run-time check will be
		// necessary for the needed narrowing conversion and
		// must be indicated by including a cast:
		cp = p;				// p might be neither a ColoredPoint
						// nor a subclass of ColoredPoint
		c = p;				// p might not implement Colorable

	}

}
Here is another example involving assignment of array objects: 


class Point { int x, y; }

class ColoredPoint extends Point { int color; }


class Test {
	public static void main(String[] args) {
		long[] veclong = new long[100];
		Object o = veclong;									// okay
		Long l = veclong;									// compile-time error
		short[] vecshort = veclong;									// compile-time error
		Point[] pvec = new Point[100];
		ColoredPoint[] cpvec = new ColoredPoint[100];
		pvec = cpvec;									// okay
		pvec[0] = new Point();									// okay at compile time,
											// but would throw an
											// exception at run time
		cpvec = pvec;									// compile-time error
	}
}
In this example: 


		cpvec = (ColoredPoint[])pvec;										// okay, but may throw an
												// exception at run time

5.3 Method Invocation Conversion

Method invocation conversion is applied to each argument value in a method or constructor invocation (§15.8, §15.11): the type of the argument expression must be converted to the type of the corresponding parameter. Method invocation contexts allow the use of an identity conversion (§5.1.1), a widening primitive conversion (§5.1.2), or a widening reference conversion (§5.1.4).

Method invocation conversions specifically do not include the implicit narrowing of integer constants which is part of assignment conversion (§5.2). The Java designers felt that including these implicit narrowing conversions would add additional complexity to the overloaded method matching resolution process (§15.11.2). Thus, the example:


class Test {

	static int m(byte a, int b) { return a+b; }


	static int m(short a, short b) { return a-b; }

	public static void main(String[] args) {
		System.out.println(m(12, 2));										// compile-time error
	}

}
causes a compile-time error because the integer literals 12 and 2 have type int, so neither method m matches under the rules of (§15.11.2). A language that included implicit narrowing of integer constants would need additional rules to resolve cases like this example.

5.4 String Conversion

String conversion applies only to the operands of the binary + operator when one of the arguments is a String. In this single special case, the other argument to the + is converted to a String, and a new String which is the concatenation of the two strings is the result of the +. String conversion is specified in detail within the description of the string concatenation + operator (§15.17.1).

5.5 Casting Conversion

Casting conversion is applied to the operand of a cast operator (§15.15): the type of the operand expression must be converted to the type explicitly named by the cast operator. Casting contexts allow the use of an identity conversion (§5.1.1), a widening primitive conversion (§5.1.2), a narrowing primitive conversion (§5.1.3), a widening reference conversion (§5.1.4), or a narrowing reference conversion (§5.1.5). Thus casting conversions are more inclusive than assignment or method invocation conversions: a cast can do any permitted conversion other than a string conversion.

Some casts can be proven incorrect at compile time; such casts result in a compile-time error.

A value of a primitive type can be cast to another primitive type by identity conversion, if the types are the same, or by a widening primitive conversion or a narrowing primitive conversion.

A value of a primitive type cannot be cast to a reference type by casting conversion, nor can a value of a reference type be cast to a primitive type.

The remaining cases involve conversion between reference types. The detailed rules for compile-time correctness checking of a casting conversion of a value of compile-time reference type S (source) to a compile-time reference type T (target) are as follows:

See §8 for the detailed specifications of classes, §9 for interfaces, and §10 for arrays.

If a cast to a reference type is not a compile-time error, there are two cases:

If a run-time exception is thrown, it is a ClassCastException (§11.5.1.1, §20.22).

Here are some examples of casting conversions of reference types, similar to the example in §5.2:


public class Point { int x, y; }

public interface Colorable { void setColor(int color); }


public class ColoredPoint extends Point implements Colorable 
{
	int color;
	public void setColor(int color) { this.color = color; }
}


final class EndPoint extends Point { }


class Test {

	public static void main(String[] args) {
		Point p = new Point();
		ColoredPoint cp = new ColoredPoint();
		Colorable c;


		// The following may cause errors at run time because
		// we cannot be sure they will succeed; this possibility
		// is suggested by the casts:
		cp = (ColoredPoint)p;							// p might not reference an
									// object which is a ColoredPoint
									// or a subclass of ColoredPoint
		c = (Colorable)p;							// p might not be Colorable


		// The following are incorrect at compile time because
		// they can never succeed as explained in the text:
		Long l = (Long)p;							// compile-time error #1
		EndPoint e = new EndPoint();
		c = (Colorable)e;							// compile-time error #2

	}

}
Here the first compile-time error occurs because the class types Long and Point are unrelated (that is, they are not the same, and neither is a subclass of the other), so a cast between them will always fail.

The second compile-time error occurs because a variable of type EndPoint can never reference a value that implements the interface Colorable. This is because EndPoint is a final type, and a variable of a final type always holds a value of the same run-time type as its compile-time type. Therefore, the run-time type of variable e must be exactly the type EndPoint, and type EndPoint does not implement Colorable.

Here is an example involving arrays (§10): 


class Point {

	int x, y;

	Point(int x, int y) { this.x = x; this.y = y; }

	public String toString() { return "("+x+","+y+")"; }

}

public interface Colorable { void setColor(int color); }


public class ColoredPoint extends Point implements Colorable 
{

	int color;

	ColoredPoint(int x, int y, int color) {
		super(x, y); setColor(color);
	}


	public void setColor(int color) { this.color = color; }

	public String toString() {
		return super.toString() + "@" + color;
	}

}


class Test {

	public static void main(String[] args) {
		Point[] pa = new ColoredPoint[4];
		pa[0] = new ColoredPoint(2, 2, 12);
		pa[1] = new ColoredPoint(4, 5, 24);
		ColoredPoint[] cpa = (ColoredPoint[])pa;
		System.out.print("cpa: {");
		for (int i = 0; i < cpa.length; i++)
			System.out.print((i == 0 ? " " : ", ") + cpa[i]);
		System.out.println(" }");
	}

}
This example compiles without errors and produces the output: 

cpa: { (2,2)@12, (4,5)@24, null, null }
The following example uses casts to compile, but it throws exceptions at run time, because the types are incompatible:


public class Point { int x, y; }

public interface Colorable { void setColor(int color); }


public class ColoredPoint extends Point implements Colorable 
{

	int color;


	public void setColor(int color) { this.color = color; }

}


class Test {

	public static void main(String[] args) {

		Point[] pa = new Point[100];


		// The following line will throw a ClassCastException:
		ColoredPoint[] cpa = (ColoredPoint[])pa;


		System.out.println(cpa[0]);


		int[] shortvec = new int[2];


		Object o = shortvec;


		// The following line will throw a ClassCastException:
		Colorable c = (Colorable)o;


		c.setColor(0);

	}

}

5.6 Numeric Promotions

Numeric promotion is applied to the operands of an arithmetic operator. Numeric promotion contexts allow the use of an identity conversion (§5.1.1) or a widening primitive conversion (§5.1.2).

Numeric promotions are used to convert the operands of a numeric operator to a common type so that an operation can be performed. The two kinds of numeric promotion are unary numeric promotion (§5.6.1) and binary numeric promotion (§5.6.2). The analogous conversions in C are called "the usual unary conversions" and "the usual binary conversions."

Numeric promotion is not a general feature of Java, but rather a property of the specific definitions of the built-in operations.

5.6.1 Unary Numeric Promotion

Some operators apply unary numeric promotion to a single operand, which must produce a value of a numeric type:

Unary numeric promotion is performed on expressions in the following situations:

Here is a test program that includes examples of unary numeric promotion: 


class Test {
	public static void main(String[] args) {
		byte b = 2;
		int a[] = new int[b];							// dimension expression promotion
		char c = '\u0001';
		a[c] = 1;							// index expression promotion
		a[0] = -c;							// unary - promotion
		System.out.println("a: " + a[0] + "," + a[1]);

		b = -1;
		int i = ~b;							// bitwise complement promotion
		System.out.println("~0x" + Integer.toHexString(b)
							+ "==0x" + Integer.toHexString(i));

		i = b << 4L;							// shift promotion (left operand)
		System.out.println("0x" + Integer.toHexString(b)
					 + "<<4L==0x" + Integer.toHexString(i));
	}
}
This test program produces the output: 


a: -1,1
~0xffffffff==0x0
0xffffffff<<4L==0xfffffff0

5.6.2 Binary Numeric Promotion

When an operator applies binary numeric promotion to a pair of operands, each of which must denote a value of a numeric type, the following rules apply, in order, using widening conversion (§5.1.2) to convert operands as necessary:

Binary numeric promotion is performed on the operands of certain operators:

An example of binary numeric promotion appears above in §5.1. Here is another: 


class Test {
	public static void main(String[] args) {
		int i = 0;
		float f = 1.0f;
		double d = 2.0;


		// First i*f promoted to float*float, then
		// float==double is promoted to double==double:
		if (i * f == d)
			System.out.println("oops");


		// A char&byte is promoted to int&int:
		byte b = 0x1f;
		char c = 'G';
		int control = c & b;
		System.out.println(Integer.toHexString(control));


		// A int:float promoted to float:float:
		f = (b==0) ? f : 4.0f;
		System.out.println(1.0/f);

	}

}
which produces the output: 


7
0.25
The example converts the ASCII character G to the ASCII control-G (BEL), by masking off all but the low 5 bits of the character. The 7 is the numeric value of this control character.

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