Inconsistent Operation Widen Rules in Java

When you perform a unary or binary operation in Java the standard behaviour is to use the widest operand (or a wider one for byte, short and char).  This is simple to understand but can be confusing if you consider what the optimal type is likely to be.

Multiplication

When you perform multiplication, you often get a much large number than either of the individual numbers in magnitude. i.e. |a*b| >> |a| and |a*b| >> |b| is often the case.  And for small types this works as expected

Consider this program

public static void main(String[] args) throws IOException {
    System.out.println(is(Byte.MAX_VALUE * Byte.MAX_VALUE));
    System.out.println(is(Short.MAX_VALUE * Short.MAX_VALUE));
    System.out.println(is(Character.MAX_VALUE * Character.MAX_VALUE));
    System.out.println(is(Integer.MAX_VALUE * Integer.MAX_VALUE));
    System.out.println(is(Long.MAX_VALUE * Long.MAX_VALUE));
}
static String is(byte b) {
    return "byte: " + b;
}
static String is(char ch) {
    return "char: " + ch;
}
static String is(short i) {
    return "short: " + i;
}
static String is(int i) {
    return "int: " + i;
}
static String is(long l) {
    return "long: " + l;
}

int: 16129
int: 1073676289
int: -131071
int: 1
long: 1

Only byte * byte and short * short doesn't overflow as these have been widened.  char * char isn't a meaningful operation even though it is allowed. But int * int does overflow even though we have a long type which could store this value without an overflow.  Both byte and short are widened implicitly but not int. longshould really be widened but we don't have a wider primitive type, which would have made sense once upon a time however a 64-bit primitive doesn't seem so long these days.

Division

System.out.println(is(Byte.MAX_VALUE / (byte) 1));
System.out.println(is(Byte.MAX_VALUE / (short) 1));
System.out.println(is(Byte.MAX_VALUE / (char) 1));
System.out.println(is(Byte.MAX_VALUE / (int) 1));
System.out.println(is(Byte.MAX_VALUE/ (long) 1));

prints

int: 127
int: 127
int: 127
int: 127
long: 127

Modulus

System.out.println(is(Byte.MAX_VALUE % Byte.MAX_VALUE));
System.out.println(is(Byte.MAX_VALUE % Short.MAX_VALUE));
System.out.println(is(Byte.MAX_VALUE % Character.MAX_VALUE));
System.out.println(is(Byte.MAX_VALUE % Integer.MAX_VALUE));
System.out.println(is(Byte.MAX_VALUE % Long.MAX_VALUE));
   
System.out.println(is(Byte.MAX_VALUE % (byte) 2));
System.out.println(is(Short.MAX_VALUE % (byte) 2));
System.out.println(is(Character.MAX_VALUE % (byte) 2));
System.out.println(is(Integer.MAX_VALUE % (byte) 2));
System.out.println(is(Long.MAX_VALUE % (byte) 2));

int: 0
int: 127
int: 127
int: 127
long: 127
int: 1
int: 1
int: 1
int: 1
long: 1

Negation

System.out.println(is(-Byte.MIN_VALUE));
System.out.println(is(-Short.MIN_VALUE));
System.out.println(is(-Character.MIN_VALUE));
System.out.println(is(-Integer.MIN_VALUE));
System.out.println(is(-Long.MIN_VALUE));

int: 128
int: 32768
int: 0
int: -2147483648
long: -9223372036854775808

System.out.println(is(+Byte.MIN_VALUE));
System.out.println(is(+Short.MIN_VALUE));
System.out.println(is(+Character.MIN_VALUE));
System.out.println(is(+Integer.MIN_VALUE));
System.out.println(is(+Long.MIN_VALUE));

int: -128
int: -32768
int: 0
int: -2147483648
long: -9223372036854775808

long i = ...
byte b = ...
long l = i % b + Integer.MAX_VALUE;