Unsigned int considered harmful for Java
Introduction
Every now and then, a developer comes along and complains about the lack of unsigned integer types in Java, demanding that they be implemented in the language. Oftentimes it’s a novice coming from C/C++ or C# who has worked with unsigned types before, or one who wants to guarantee no negative numbers in certain situations. Said novice C/C++/C# programmer typically does not fully understand the semantics and ramifications of unsigned integers in C/C++/C# to begin with.
While on the surface this feature request seems reasonable – extra types will be added but one can choose to ignore them if not explicitly needed – it would actually cause deep problems for all Java developers whether they like it or not. Moreover, arithmetic operations on unsigned integers can already be quite easily and efficiently emulated using signed integers, as proven in practice in numerous lowlevel libraries. Here I will argue why Java supporting unsigned integer types would be not only unnecessary but also harmful.
Emulating unsigned arithmetic
Let’s assume that for whatever reason, you must perform unsigned integer arithmetic in Java. Maybe you’re writing a cryptographic algorithm, decoding a multimedia stream, or implementing a file format / network protocol where data fields are specified as unsigned.
Straightforward emulation
The conceptually simple way to emulate unsigned arithmetic using only Java’s signed integer types is to widen the number while masking off the new high bits, perform the arithmetic, and narrow down the result.
Suppose we have this C/C++ code:
uint16_t a = (...); // Input uint16_t b = (...); // Input uint16_t c = a + b; // Output
Then this is one way to make it work in Java:
short a = (...); // Treat bits as unsigned value short b = (...); // Treat bits as unsigned value int wideA = a & 0xFFFF; // This value is now correct int wideB = b & 0xFFFF; // This value is now correct int temp = wideA + wideB; // Wide result short c = (short)temp; // Discard top bits; treat bits as unsigned value
Or more compactly (Java):
short a = (...); // Input short b = (...); // Input short c = (short)((a & 0xFFFF) + (b & 0xFFFF));
Notes:
In a compound expression like
(a + b) / (c * d)
, the widenings and narrowings must be performed per operation, otherwise the result may be incorrect.To operate on two
uint32_t
values, we need to widen them to Javalong
usingval & 0xFFFFFFFFL
. Unfortunately this technique does not allow us to operate on twouint64_t
values because there is no wider signed type in Java; we’d need to step up to the clumsyBigInteger
library.
When we say “treat bits as unsigned value”, it refers to the fact that we can put a fixedwidth sequence of n bits into an integer variable without caring about the meaning of its value. At least, this usage is acceptable for unsigned and two’s complement integers.
(This assumption of an integer being a plain sequence of bits may not be true in signmagnitude, ones’ complement, and floatingpoint because of problems like negative zero, trap values, collapsed NaN values, and flushing subnormals to zero.)
Efficient emulation
The Java language specification requires its signed integers to be represented in two’s complement format. Because of this, many basic operations are exactly the same whether the integer type is signed or unsigned. For example, the sum of two 8bit integers giving an 8bit result will have the same bit pattern whether all three of these values are treated as signed or unsigned. The same goes for subtraction, multiplication, left shift, equality, and of course bitwise AND/OR/XOR/NOT operations. The only ones that are signednesssensitive are division, remainder, right shift, inequalities, casting, and string conversion. To summarize:
These operations are the same:
+
,
,*
,~
,&
,
,^
,<<
,==
,!=
, downcasting.These operations are different:
/
,%
,>>
,<
,<=
,>
,>=
, upcasting,parseInt()
,toString()
.
Java’s advantage of having mostly unified signed/unsigned arithmetic operations (from a bitlevel standpoint) is not enjoyed by C/C++ users. This is because signed integers can be implemented on the machine in two’s complement, ones’ complement, or signmagnitude, and the C/C++ standards allow the lowlevel detail of the bit format to be exposed to the programmer. Furthermore, while signed overflow is silent and welldefined in Java, it is undefined behavior in C/C++ and leads to all sorts of nasty problems. (In fact, if you stretch the argument you could say that if you wanted safe and reliable two’s complement signed overflow in C/C++, you should emulate the signed arithmetic using unsigned arithmetic – the reverse situation of what’s being argued here for Java.)
Continuing the previous example, this is the efficient Java translation:
short a = (...); // Input, treat bits as unsigned value short b = (...); // Input, treat bits as unsigned value short c = (short)(a + b); // Output, treat bits as unsigned value
We can ignore the mandatory widening from 16 bits to 32 bits (promotion from short
to int
with sign extension), and we can ignore the arithmetic that occurs in the high 16 bits because it has no effect at all on the low 16 bits.
This technique is even easier for 32 and 64bit unsigned arithmetic because no narrowing in Java is needed. C/C++ example:
uint32_t a = (...); // Input uint32_t b = (...); // Input uint32_t c = a * b; // Output
Java translation (look ma, no extra effort!):
int a = (...); // Input, treat bits as unsigned value int b = (...); // Input, treat bits as unsigned value int c = a * b; // Output, treat bits as unsigned value
As for the operations that behave differently for signed versus unsigned types, let’s discuss how to emulate them without resorting to widening:

The Java language already defines signed (
>>
) and unsigned (>>>
) right shift operators. The rationale behind these operators is that for unsigned integers, right shifting is equivalent to flooring division by a power of 2. To emulate this behavior for signed integers, copies of the sign bit (instead of zero) are shifted in from the left side. 
Unsigned division/remainder has no easy solution. You can either cast to a wider type like
long
to do the arithmetic, useBigInteger
, or implement the grade school division algorithm from scratch. Luckily, Java SE 8 adds standard library functions to take care of this:Integer.divideUnsigned()
,remainderUnsigned()
.Otherwise, here is some nontrivial code I wrote for unsigned 32bit division:
int unsignedDivide(int x, int y) { if (y >= 0) { if (x >= 0) return x / y; // Easy case else { // x >= 2^31 int i = Integer.numberOfLeadingZeros(y); // At least 1 if ((x >>> i) < y) i; // Perform one step of long division and offload the rest return (1 << i) + (x  (y << i)) / y; } } else // y >= 2^31 return unsignedLessThan(x, y) ? 0 : 1; }

Unsigned inequalities are also covered by Java SE 8 functions. Otherwise, they can be emulated with a clever trick: Flip the top bits of both operands and proceed with the same inequality operator. For example:
// x and y are treated as uint32 boolean unsignedLessThan(int x, int y) { return (x ^ 0x80000000) < (y ^ 0x80000000); }
(The mathematical proof is left as an exercise for the reader.)

To cast down (narrowing) to an unsigned type, nothing special needs to be done. To cast up (widening) from a pseudounsigned type to native Java signed type, the upper bits need to be masked off to suppress sign extension. For example:
byte a = (...); // Input, treat as uint8 short b = (...); // Input, treat as uint16 int c = (...); // Input, treat as uint32 long d = (...); // Input, treat as uint64 int aInt = a & 0xFF; // Correct value int bInt = b & 0xFFFF; // Correct value long cLong = c & 0xFFFFFFFFL; // Correct value int cIntWrong = c & 0xFFFFFFFF; // Wrong, does absolutely nothing! long cLongWrong = c & 0xFFFFFFFF; // Wrong, does not suppress sign extension! long dLongWrong = d & 0xFFFFFFFFFFFFFFFFL; // Wrong, does nothing!

To convert a uint32 to a string, this algorithm can be used:
String unsignedToString(int x) { if (x >= 0) // Easy case return Integer.toString(x); else { int temp = (x >>> 1) / 5; // Unsigned division by 10 // Extract the last digit and offload the prefix return Integer.toString(temp) + Integer.toString(x  temp * 10); } }
The algorithm above is readily adaptable to uint64/
long
.
Notes
This discussion of emulating basic arithmetic operations does not cover special operations like signed/unsigned saturating arithmetic, vector operations, etc.
Fancy functions such as these in
java.lang.Integer
only care about the bits, not signedness:reverse()
,reverseBytes()
,rotateLeft()
,bitCount()
,highestOneBit()
,numberOfLeadingZeros()
, etc.
Mixedtype arithmetic pitfalls
Type conversion rules
When a programming language has both signed and unsigned integer types, it means that they will interact with each other in some way or another. At the very least, there must exist explicit conversions between types and rules that govern these conversions. The rules tend to become complicated when implicit conversions are implemented in the language specification. For example, this is what C has to say about mixedtype integer arithmetic (C11 standard draft, page 71):
If both operands have the same type, then no further conversion is needed.
Otherwise, if both operands have signed integer types or both have unsigned integer types, the operand with the type of lesser integer conversion rank is converted to the type of the operand with greater rank.
Otherwise, if the operand that has unsigned integer type has rank greater than or equal to the rank of the type of the other operand, then the operand with signed integer type is converted to the type of the operand with unsigned integer type.
Otherwise, if the type of the operand with signed integer type can represent all of the values of the type of the operand with unsigned integer type, then the operand with unsigned integer type is converted to the type of the operand with signed integer type.
Otherwise, both operands are converted to the unsigned integer type corresponding to the type of the operand with signed integer type.
Examples:
(
long
OPint
) → (long
OPlong
). (Rule 2)(
int
OPunsigned int
) → (unsigned int
OPunsigned int
). (Rule 3)(
unsigned long long
OPshort
) → (unsigned long long
OPunsigned long long
). (Rule 3)If the compiler implements
sizeof(int) < sizeof(long)
, then:
(unsigned int
OPlong
) → (long
OPlong
). (Rule 4)Else the compiler implements
sizeof(int) == sizeof(long)
, then:
(unsigned int
OPlong
) → (unsigned long
OPunsigned long
). (Rule 5)
(Note: These examples avoid showing the promotion of char
and short
to int
.)
Usage examples

Mixedtype computations easily lead to subtle problems. For example:
unsigned int size = (...); for (int i = 0; i < size; i++) { ... }
If
size > INT_MAX
, theni
will eventually have a signed overflow (undefined behavior). Furthermore, indexing an array withi
being negative is also undefined behavior (assuming that the array pointer doesn’t have a positive offset). However by dumb luck, this loop idiom will probably work for large sizes – because even afteri
overflows, it gets converted tounsigned int
for the comparison operation, and afteri
is incremented sufficiently many times the comparison will eventually yieldfalse
and terminate the loop.I admit that I’m tempted to declare my loop counters as
int
instead ofunsigned int
because it saves typing, most programming tutorials useint
for simplicity, and most data sizes are small enough that it doesn’t matter. But when the upper bound isunsigned int
, I have to choose either the laziness of usingint
or the correctness of usingunsigned int
.And speaking of loops, the decreasing loop idiom
for (int i = n  1; i >= 0; i)
does not work ifi
is an unsigned type. 
The PVSStudio C/C++ linter has caught many, many examples of code containing
if (x < 0)
wherex
is an unsigned type, in real opensource projects. (This pointless check always yieldsfalse
, of course.) This gives evidence that programmers make mistakes in carefully distinguishing signed and unsigned integer types in practice. 
In Java’s number system, there is almost no good reason to perform two casts consecutively. In C/C++ however, there are legitimate examples of this ugly construct emerging from signed vs. unsigned types:
// 'char' type may be signed or unsigned, implementationdefined char *array = (...); // First force each byte to be unsigned, then widen to do packing uint32_t packed = (uint32_t)(uint8_t)array[0] << 24  (uint32_t)(uint8_t)array[1] << 16  (uint32_t)(uint8_t)array[2] << 8  (uint32_t)(uint8_t)array[3] << 0;
(Alternatively we could write
array[0] & UINT32_C(0xFF)
, but this involves mixedtype arithmetic which is harder to reason about.) 
When you interact with someone else’s API that uses unsigned integer types, it forces you to use unsigned integer types in your own code as well. For example:
struct Image { uint8_t *pixels; uint32_t width; uint32_t height; };
Now if you want to write loops to perform signal processing on the pixels, you must use unsigned variables to count the ranges [0, width) and [0, height). In other words, you must write:
for (uint32_t i = 0; i < img.width; i++)
, notfor (int i = 0; i < img.width; i++)
.This syndrome of unsigned sizes is pervasive in C/C++, appearing in places like
sizeof
,malloc(size_t)
,vector.size()
, and many others.
Other considerations

A wider signed type can always represent narrower unsigned types. For example, int32 can represent all uint31 values. But the reverse is not true; no unsigned type can represent all the values of a signed type (namely the negative ones are always left out). Thus if we have access to sufficiently wide signed types, we don’t need any unsigned types at all. (This is more or less the situation in Java.)
People have made the observation that programming primarily involves unsigned numbers (starting from 0), which is indeed true. However, one needs to make use of negative numbers occasionally (such as when subtracting two unsigned indexes), so signed types must exist in a programming language too. Unsigned and signed types are both useful, but signed types have strictly more functionality than unsigned types. Thus it is clear that if language simplicity is desired, then unsigned types are the ones that can be safely omitted.

Bytes are a different story however. I argue that signed bytes make programming needlessly annoying, and that only unsigned bytes should have been implemented in the first place: Java’s signed byte type is a mistake. And the fact that C/C++ specify
char
to be signed or unsigned depending on the implementation is even more annoying, because now you need to ensure that your code handles both alternatives correctly. 
It’s true that using unsigned types gains you 1 bit of extra indexing headroom, i.e. doubling the range. For example, Java array lengths go up to 2^{31} − 1 (~2 billion) because
int
is signed. If insteadunsigned int
is used for sizes and indexes, then up to 2^{32} − 1 (~4 billion) elements can be addressed.However in light of this small gain, there are some serious drawbacks. First, negative numbers can be used to signal error conditions, such as
String.indexOf()
returning −1 if not found. They also provide headroom to detect some instances of accidental overflows, such asNegativeArraySizeException
when creating a negativesized array orArrayIndexOutOfBoundsException
when accessing a negative array index. Second, it detracts from the more important longterm goal of upgrading to fully 64bit addressing.(There are some examples of small addressing gains outside of Java. x86 CPUs originally had 32bit memory addressing, but added PAE to extend to 36 bits. Then this small step was made useless when AMD’s x8664 implementation was introduced. Another example is that in the 32bit editions of the Windows NT family of operating systems, you can change the user/kernel address space split so that user programs can use up to 3 GiB of memory instead of the default 2 GiB. But again this is a small gain compared to switching to a fully 64bit kernel and user processes.)

Being able to outlaw negative values can be useful in certain cases. For example, data sizes are never negative, so when putting these values in signed types it takes extra effort to explicitly check that the values are are not negative. Also, bounds checking on unsigned types only needs to check the upper bound, whereas signed types also need to check nonnegativity. However, I do not believe these small benefits are worth the huge risks of the programmer doing mixedtype arithmetic/comparisons/conversions incorrectly. It’s better to be just a little more verbose than to have subtle bugs hiding implicitly in the code.

One legitimate concern is when a file/network format specifies an unsigned data field – how should we represent it in Java? Let’s suppose that the Foo image file format defines unsigned 32bit fields for width and height. There are a couple of reasonable ways to implement a Foo library in Java:
class FooImageFileChoice0 { // Make it the user's responsibility // to treat these fields as uint32 int width; int height; } class FooImageFileChoice1 { // Values shall be uint32 only. // Values outside [0,0xFFFFFFFF] considered illegal. long width; long height; } class FooImageFileChoice2 { // Design a custom type with its own // arithmetic and conversion methods Uint32 width; Uint32 height; } class FooImageFileChoice3 { // To hell with fixedwidth integer types! BigInteger width; BigInteger height; }
None of these alternatives is as correct as using
uint32_t
in C/C++, but I don’t think this situation comes up often enough to matter. And it’s not like C/C++ is perfect either, because it’s difficult to express more esoteric value constraints like: uint24, range [10, 99], 4k + 3, must be a prime number, etc. 
Adding unsigned types would increase the alreadycluttered Java standard library API. Because Java has method overloading (like C++) but not templates (unlike C++) or unified types (unlike C#), certain library functions must define a separate method for each primitive type. For example,
java.util.Arrays
defines these method variants for filling an entire array:void fill(byte[] arr, byte val) void fill(short[] arr, short val) void fill(int[] arr, int val) void fill(long[] arr, long val) void fill(char[] arr, char val) void fill(float[] arr, float val) void fill(double[] arr, double val) void fill(Object[] arr, Object val)
The set of methods above is already a mouthful. If we hypothetically add unsigned types, we boost the list by 50%:
void fill(byte[] arr, byte val) void fill(ubyte[] arr, ubyte val) void fill(short[] arr, short val) void fill(ushort[] arr, ushort val) void fill(int[] arr, int val) void fill(uint[] arr, uint val) void fill(long[] arr, long val) void fill(ulong[] arr, ulong val) void fill(char[] arr, char val) void fill(float[] arr, float val) void fill(double[] arr, double val) void fill(Object[] arr, Object val)
Other parts of Java that must change include the reflection library, the JVM specification, the Java Native Interface specification, etc.

I have successfully implemented in Java numerous lowlevel libraries that conceptually require unsigned arithmetic. These libraries include cryptographic ciphers and hash functions, random number generators, big integer operations, and data compression. Even though these situations require uint32 arithmetic or something like it, I had no problem whatsoever expressing these operations in terms of Java’s signed integer types. Based on this experience, I expect that a competent programmer (who understands two’s complement binary representation) will have no trouble doing unsigned arithmetic in Java (which only superficially seems to not support unsigned math).
Examples:
 Forcing a file’s CRC to any value (CRC32)
 NotepadCrypt format decrypter (SHA256, AES)
 Native hash functions for Java (MD5, SHA1, Whirlpool, etc.)
Conclusion
Unsigned integer types do not belong in the Java programming language. They add considerable complexity to the type system, type conversion rules, library APIs, and the language and virtual machine specifications. Yet for developers who truly need unsigned arithmetic, this functionality can already be achieved effectively using signed integer types with only a small amount of knowledge and effort. Hence unsigned ints would add almost no expressive power but considerable pain – a rather unwise tradeoff, isn’t it?
More info
 Javamex: Unsigned arithmetic in Java
 Joseph D. Darcy’s Oracle Weblog: Unsigned Integer Arithmetic API now in JDK 8
 CERT Secure Coding Standards: INT02C. Understand integer conversion rules
 Java and unsigned int [...]  Why no unsigned types?
 Stack Overflow: Why doesn’t Java support unsigned ints?
 Bug ID JDK4186775: request unsigned integer types, esp. unsigned byte
 Canadian Mind Products: Java glossary  unsigned