byte
, short
, int
, long
, char
, boolean
, float
, and double
are the types that store most raw numerical data in Java programs.
int aInt = 8; // The defining (number) part of this int declaration is called a literal.
int hexInt = 0x1a; // = 26; You can define literals with hex values prefixed with 0x.
int binInt = 0b11010; // = 26; You can also define binary literals; prefixed with 0b.
long goodLong = 10000000000L; // By default, integer literals are of type int. By adding the L at the end of the literal you are telling the compiler that the literal is a long. Without this the compiler would throw an "Integer number too large" error.
double aDouble = 3.14; // Floating-Point Literals are of type double by default.
float aFloat = 3.14F; // By default this literal would have been a double (and caused an "Incompatible Types" error), but by adding an F we tell the compiler it is a float.
Java has 8 primitive data types, namely boolean
, byte
, short
, char
, int
, long
, float
and double
. (All other types are reference types. This includes all array types, and built-in object types / classes that have special significance in the Java language; e.g. String
, Class
and Throwable
and its subclasses.)
The result of all operations (addition, subtraction, multiplication, etc) on a primitive type is at least an int
, thus adding a short
to a short
produces an int
, as does adding a byte
to a byte
, or a char
to a char
. If you want to assign the result of that back to a value of the same type, you must cast it. e.g.
byte a = 1;
byte b = 2;
byte c = (byte) (a + b);
Not casting the operation will result in a compile error.
This is due to the following part of the Java Language Spec, §2.11.1:
A compiler encodes loads of literal values of types
byte
andshort
using Java Virtual Machine instructions that sign-extend those values to values of typeint
at compile-time or run-time. Loads of literal values of typesboolean
andchar
are encoded using instructions that zero-extend the literal to a value of typeint
at compile-time or run-time. [..]. Thus, most operations on values of actual typesboolean
,byte
,char
, andshort
are correctly performed by instructions operating on values of computational typeint
.
The reason behind this is also specified in that section:
Given the Java Virtual Machine's one-byte opcode size, encoding types into opcodes places pressure on the design of its instruction set. If each typed instruction supported all of the Java Virtual Machine's run-time data types, there would be more instructions than could be represented in a
byte
. [...] Separate instructions can be used to convert between unsupported and supported data types as necessary.
A primitive data type such as int
holds values directly into the variable that is using it, meanwhile a variable that was declared using Integer
holds a reference to the value.
According to java API: "The Integer class wraps a value of the primitive type int in an object. An object of type Integer contains a single field whose type is int."
By default, int
is a 32-bit signed integer. It can store a minimum value of -2^{31}, and a maximum value of 2^{31} - 1.
int example = -42;
int myInt = 284;
int anotherInt = 73;
int addedInts = myInt + anotherInt; // 284 + 73 = 357
int subtractedInts = myInt - anotherInt; // 284 - 73 = 211
If you need to store a number outside of this range, long
should be used instead. Exceeding the value range of int
leads to an integer overflow, causing the value exceeding the range to be added to the opposite site of the range (positive becomes negative and vise versa). The value is ((value - MIN_VALUE) % RANGE) + MIN_VALUE
, or ((value + 2147483648) % 4294967296) - 2147483648
int demo = 2147483647; //maximum positive integer
System.out.println(demo); //prints 2147483647
demo = demo + 1; //leads to an integer overflow
System.out.println(demo); // prints -2147483648
The maximum and minimum values of int
can be found at:
int high = Integer.MAX_VALUE; // high == 2147483647
int low = Integer.MIN_VALUE; // low == -2147483648
The default value of an int
is 0
int defaultInt; // defaultInt == 0
A short
is a 16-bit signed integer. It has a minimum value of -2^{15} (-32,768), and a maximum value of 2^{15} ‑1 (32,767)
short example = -48;
short myShort = 987;
short anotherShort = 17;
short addedShorts = (short) (myShort + anotherShort); // 1,004
short subtractedShorts = (short) (myShort - anotherShort); // 970
The maximum and minimum values of short
can be found at:
short high = Short.MAX_VALUE; // high == 32767
short low = Short.MIN_VALUE; // low == -32768
The default value of a short
is 0
short defaultShort; // defaultShort == 0
By default, long
is a 64-bit signed integer (in Java 8, it can be either signed or unsigned). Signed, it can store a minimum value of -2^{63}, and a maximum value of 2^{63} - 1, and unsigned it can store a minimum value of 0 and a maximum value of 2^{64} - 1
long example = -42;
long myLong = 284;
long anotherLong = 73;
//an "L" must be appended to the end of the number, because by default,
//numbers are assumed to be the int type. Appending an "L" makes it a long
//as 549755813888 (2 ^ 39) is larger than the maximum value of an int (2^31 - 1),
//"L" must be appended
long bigNumber = 549755813888L;
long addedLongs = myLong + anotherLong; // 284 + 73 = 357
long subtractedLongs = myLong - anotherLong; // 284 - 73 = 211
The maximum and minimum values of long
can be found at:
long high = Long.MAX_VALUE; // high == 9223372036854775807L
long low = Long.MIN_VALUE; // low == -9223372036854775808L
The default value of a long
is 0L
long defaultLong; // defaultLong == 0L
Note: letter "L" appended at the end of long
literal is case insensitive, however it is good practice to use capital as it is easier to distinct from digit one:
2L == 2l; // true
Warning: Java caches Integer objects instances from the range -128 to 127. The reasoning is explained here: https://blogs.oracle.com/darcy/entry/boxing_and_caches_integer_valueof
The following results can be found:
Long val1 = 127L;
Long val2 = 127L;
System.out.println(val1 == val2); // true
Long val3 = 128L;
Long val4 = 128L;
System.out.println(val3 == val4); // false
To properly compare 2 Object Long values, use the following code(From Java 1.7 onward):
Long val3 = 128L;
Long val4 = 128L;
System.out.println(Objects.equal(val3, val4)); // true
Comparing a primitive long to an Object long will not result in a false negative like comparing 2 objects with == does.
A boolean
can store one of two values, either true
or false
boolean foo = true;
System.out.println("foo = " + foo); // foo = true
boolean bar = false;
System.out.println("bar = " + bar); // bar = false
boolean notFoo = !foo;
System.out.println("notFoo = " + notFoo); // notFoo = false
boolean fooAndBar = foo && bar;
System.out.println("fooAndBar = " + fooAndBar); // fooAndBar = false
boolean fooOrBar = foo || bar;
System.out.println("fooOrBar = " + fooOrBar); // fooOrBar = true
boolean fooXorBar = foo ^ bar;
System.out.println("fooXorBar = " + fooXorBar); // fooXorBar = true
The default value of a boolean
is false
boolean defaultBoolean; // defaultBoolean == false
A byte
is a 8-bit signed integer. It can store a minimum value of -2^{7} (-128), and a maximum value of 2^{7} - 1 (127)
byte example = -36;
byte myByte = 96;
byte anotherByte = 7;
byte addedBytes = (byte) (myByte + anotherByte); // 103
byte subtractedBytes = (byte) (myBytes - anotherByte); // 89
The maximum and minimum values of byte
can be found at:
byte high = Byte.MAX_VALUE; // high == 127
byte low = Byte.MIN_VALUE; // low == -128
The default value of a byte
is 0
byte defaultByte; // defaultByte == 0
A float
is a single-precision 32-bit IEEE 754 floating point number. By default, decimals are interpreted as doubles. To create a float
, simply append an f
to the decimal literal.
double doubleExample = 0.5; // without 'f' after digits = double
float floatExample = 0.5f; // with 'f' after digits = float
float myFloat = 92.7f; // this is a float...
float positiveFloat = 89.3f; // it can be positive,
float negativeFloat = -89.3f; // or negative
float integerFloat = 43.0f; // it can be a whole number (not an int)
float underZeroFloat = 0.0549f; // it can be a fractional value less than 0
Floats handle the five common arithmetical operations: addition, subtraction, multiplication, division, and modulus.
Note: The following may vary slightly as a result of floating point errors. Some results have been rounded for clarity and readability purposes (i.e. the printed result of the addition example was actually 34.600002).
// addition
float result = 37.2f + -2.6f; // result: 34.6
// subtraction
float result = 45.1f - 10.3f; // result: 34.8
// multiplication
float result = 26.3f * 1.7f; // result: 44.71
// division
float result = 37.1f / 4.8f; // result: 7.729166
// modulus
float result = 37.1f % 4.8f; // result: 3.4999971
Because of the way floating point numbers are stored (i.e. in binary form), many numbers don't have an exact representation.
float notExact = 3.1415926f;
System.out.println(notExact); // 3.1415925
While using float
is fine for most applications, neither float
nor double
should be used to store exact representations of decimal numbers (like monetary amounts), or numbers where higher precision is required. Instead, the BigDecimal
class should be used.
The default value of a float
is 0.0f.
float defaultFloat; // defaultFloat == 0.0f
A float
is precise to roughly an error of 1 in 10 million.
Note: Float.POSITIVE_INFINITY
, Float.NEGATIVE_INFINITY
, Float.NaN
are float
values. NaN
stands for results of operations that cannot be determined, such as dividing 2 infinite values. Furthermore 0f
and -0f
are different, but ==
yields true:
float f1 = 0f;
float f2 = -0f;
System.out.println(f1 == f2); // true
System.out.println(1f / f1); // Infinity
System.out.println(1f / f2); // -Infinity
System.out.println(Float.POSITIVE_INFINITY / Float.POSITIVE_INFINITY); // NaN
A double
is a double-precision 64-bit IEEE 754 floating point number.
double example = -7162.37;
double myDouble = 974.21;
double anotherDouble = 658.7;
double addedDoubles = myDouble + anotherDouble; // 315.51
double subtractedDoubles = myDouble - anotherDouble; // 1632.91
double scientificNotationDouble = 1.2e-3; // 0.0012
Because of the way floating point numbers are stored, many numbers don't have an exact representation.
double notExact = 1.32 - 0.42; // result should be 0.9
System.out.println(notExact); // 0.9000000000000001
While using double
is fine for most applications, neither float
nor double
should be used to store precise numbers such as currency. Instead, the BigDecimal
class should be used
The default value of a double
is 0.0d
public double defaultDouble; // defaultDouble == 0.0
Note: Double.POSITIVE_INFINITY
, Double.NEGATIVE_INFINITY
, Double.NaN
are double
values. NaN
stands for results of operations that cannot be determined, such as dividing 2 infinite values. Furthermore 0d
and -0d
are different, but ==
yields true:
double d1 = 0d;
double d2 = -0d;
System.out.println(d1 == d2); // true
System.out.println(1d / d1); // Infinity
System.out.println(1d / d2); // -Infinity
System.out.println(Double.POSITIVE_INFINITY / Double.POSITIVE_INFINITY); // NaN
A char
can store a single 16-bit Unicode character. A character literal is enclosed in single quotes
char myChar = 'u';
char myChar2 = '5';
char myChar3 = 65; // myChar3 == 'A'
It has a minimum value of \u0000
(0 in the decimal representation, also called the null character) and a maximum value of \uffff
(65,535).
The default value of a char
is \u0000
.
char defaultChar; // defaultChar == \u0000
In order to define a char of '
value an escape sequence (character preceded by a backslash) has to be used:
char singleQuote = '\'';
There are also other escape sequences:
char tab = '\t';
char backspace = '\b';
char newline = '\n';
char carriageReturn = '\r';
char formfeed = '\f';
char singleQuote = '\'';
char doubleQuote = '\"'; // escaping redundant here; '"' would be the same; however still allowed
char backslash = '\\';
char unicodeChar = '\uXXXX' // XXXX represents the Unicode-value of the character you want to display
You can declare a char
of any Unicode character.
char heart = '\u2764';
System.out.println(Character.toString(heart)); // Prints a line containing "❤".
It is also possible to add to a char
. e.g. to iterate through every lower-case letter, you could do to the following:
for (int i = 0; i <= 26; i++) {
char letter = (char) ('a' + i);
System.out.println(letter);
}
Java and most other languages store negative integral numbers in a representation called 2's complement notation.
For a unique binary representation of a data type using n
bits, values are encoded like this:
The least significant n-1
bits store a positive integral number x
in integral representation. Most significant value stores a bit vith value s
. The value repesented by those bits is
x - s * 2^{n-1}
i.e. if the most significant bit is 1, then a value that is just by 1 larger than the number you could represent with the other bits (2^{n-2} + 2^{n-3} + ... + 2^{1} + 2^{0} = 2^{n-1} - 1
) is subtracted allowing a unique binary representation for each value from - 2^{n-1} (s = 1; x = 0) to 2^{n-1} - 1 (s = 0; x = 2^{n-1} - 1).
This also has the nice side effect, that you can add the binary representations as if they were positive binary numbers:
v1 = x1 - s1 * 2^{n-1} v2 = x2 - s2 * 2^{n-1}
s1 | s2 | x1 + x2 overflow | addition result |
---|---|---|---|
0 | 0 | No | x1 + x2 = v1 + v2 |
0 | 0 | Yes | too large to be represented with data type (overflow) |
0 | 1 | No | x1 + x2 - 2^{n-1} = x1 + x2 - s2 * 2^{n-1} |
0 | 1 | Yes | (x1 + x2) mod 2^{n-1} = x1 + x2 - 2^{n-1} |
1 | 0 | * | see above (swap summands) |
1 | 1 | No | too small to be represented with data type (x1 + x2 - 2^{n} < -2^{n-1} ; underflow) |
1 | 1 | Yes | (x1 + x2) mod 2^{n-1} - 2^{n-1} = (x1 + x2 - 2^{n-1}) - 2^{n-1} |
Note that this fact makes finding binary representation of the additive inverse (i.e. the negative value) easy:
Observe that adding the bitwise complement to the number results in all bits being 1. Now add 1 to make value overflow and you get the neutral element 0 (all bits 0).
So the negative value of a number i
can be calculated using (ignoring possible promotion to int
here)
(~i) + 1
Example: taking the negative value of 0 (byte
):
The result of negating 0
, is 11111111
. Adding 1 gives a value of 100000000
(9 bits). Because a byte
can only store 8 bits, the leftmost value is truncated, and the result is 00000000
Original | Process | Result |
---|---|---|
0 (00000000) | Negate | -0 (11111111) |
11111111 | Add 1 to binary | 100000000 |
100000000 | Truncate to 8 bits | 00000000 (-0 equals 0) |
Primitive | Boxed Type | Memory Size of primitive / boxed |
---|---|---|
boolean | Boolean | 1 byte / 16 bytes |
byte | Byte | 1 byte / 16 bytes |
short | Short | 2 bytes / 16 bytes |
char | Char | 2 bytes / 16 bytes |
int | Integer | 4 bytes / 16 bytes |
long | Long | 8 bytes / 16 bytes |
float | Float | 4 bytes / 16 bytes |
double | Double | 8 bytes / 16 bytes |
Boxed objects always require 8 bytes for type and memory management, and because the size of objects is always a multiple of 8, boxed types all require 16 bytes total. In addition, each usage of a boxed object entails storing a reference which accounts for another 4 or 8 bytes, depending on the JVM and JVM options.
In data-intensive operations, memory consumption can have a major impact on performance. Memory consumption grows even more when using arrays: a float[5]
array will require only 32 bytes; whereas a Float[5]
storing 5 distinct non-null values will require 112 bytes total (on 64 bit without compressed pointers, this increases to 152 bytes).
The space overheads of the boxed types can be mitigated to a degree by the boxed value caches. Some of the boxed types implement a cache of instances. For example, by default, the Integer
class will cache instances to represent numbers in the range -128
to +127
. This does not, however, reduce the additional cost arising from the additional memory indirection.
If you create an instance of a boxed type either by autoboxing or by calling the static valueOf(primitive)
method, the runtime system will attempt to use a cached value. If your application uses a lot of values in the range that is cached, then this can substantially reduce the memory penalty of using boxed types. Certainly, if you are creating boxed value instances "by hand", it is better to use valueOf
rather than new
. (The new
operation always creates a new instance.) If, however, the majority of your values are not in the cached range, it can be faster to call new
and save the cache lookup.
In Java, we can convert between integer values and floating-point values. Also, since every character corresponds to a number in the Unicode encoding, char
types can be converted to and from the integer and floating-point types. boolean
is the only primitive datatype that cannot be converted to or from any other primitive datatype.
There are two types of conversions: widening conversion and narrowing conversion.
A widening conversion is when a value of one datatype is converted to a value of another datatype that occupies more bits than the former. There is no issue of data loss in this case.
Correspondingly, A narrowing conversion is when a value of one datatype is converted to a value of another datatype that occupies fewer bits than the former. Data loss can occur in this case.
Java performs widening conversions automatically. But if you want to perform a narrowing conversion (if you are sure that no data loss will occur), then you can force Java to perform the conversion using a language construct known as a cast
.
Widening Conversion:
int a = 1;
double d = a; // valid conversion to double, no cast needed (widening)
Narrowing Conversion:
double d = 18.96
int b = d; // invalid conversion to int, will throw a compile-time error
int b = (int) d; // valid conversion to int, but result is truncated (gets rounded down)
// This is type-casting
// Now, b = 18
Table showing size and values range of all primitive types:
data type | numeric representation | range of values | default value |
---|---|---|---|
boolean | n/a | false and true | false |
byte | 8-bit signed | -2^{7} to 2^{7} - 1 | 0 |
-128 to +127 | |||
short | 16-bit signed | -2^{15} to 2^{15} - 1 | 0 |
-32,768 to +32,767 | |||
int | 32-bit signed | -2^{31} to 2^{31} - 1 | 0 |
-2,147,483,648 to +2,147,483,647 | |||
long | 64-bit signed | -2^{63} to 2^{63} - 1 | 0L |
-9,223,372,036,854,775,808 to 9,223,372,036,854,775,807 | |||
float | 32-bit floating point | 1.401298464e-45 to 3.402823466e+38 (positive or negative) | 0.0F |
double | 64-bit floating point | 4.94065645841246544e-324d to 1.79769313486231570e+308d (positive or negative) | 0.0D |
char | 16-bit unsigned | 0 to 2^{16} - 1 | 0 |
0 to 65,535 |
Notes:
byte
through long
) use binary twos-complement representation, and the floating point types use standard IEE 754 binary floating point representations.int
and long
. While these methods allow a program to treat values of the respective types as unsigned, the types remain signed types.char
conventionally represents a Unicode / UTF-16 code unit.boolean
contains just one bit of information, its size in memory varies depending on the Java Virtual Machine implementation (see boolean type).