当一个长整数被转换成一个短整数时，会发生什么？

Question

I use java to copy one long integer y to a short integer x:

long y = 40002;
short x = (short) y;
System.out.println("x now equals " + x);

The result is: x now equals -25534.

I tried to figure out how 40002 was cast into -25534, but I failed. The 40002 corresponds to 1001 1100 0100 0010, the -25534 corresponds to 1110 0011 1011 1110. Can any friend tell me what happened in this process? Thanks a lot!

Answer 1

What you have done by casting a long to a short is a narrowing primitive conversion , which is covered by the JLS, Section 5.1.3 :

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.

The long value 40002 is the following 64 bits:

00000000 00000000 00000000 00000000 00000000 00000000 10011100 01000010

The conversion only retains the least significant 16 bits:

10011100 01000010

That leading 1 is interpreted in 2's complement notation to be -2^15, not +2^15. That explains why there is a difference of 2^16, of 65,536, in the long value and the short value.

Answer 2

Integer overflow happened.

A short is two signed bytes, which means that Short.MAX_VALUE is 2 ¹⁵ -1, which is 32,767. "Larger" values logically "wrap around" into the negative range.

In this case the excess amount is 40,002 - 2 ¹⁵ = 7234
Short.MIN_VALUE is -2 ¹⁵ = -32,768
-32,768 + 7234 = -25,534

which is the number you're wondering about.

Answer 3

Thank all of you guys. According to all of your answers, I summarize as follows: The long value 40002 is the following 64 bits:

00000000 00000000 00000000 00000000 00000000 00000000 10011100 01000010

The conversion only retains the least significant 16 bits:

10011100 01000010

When JVM regard 10011100 01000010 as a short integer, it will compute it like this:

-2^15 + 00011100 01000010 = -32768 + 7234 = -25534

This is it.

Answer 4

Basically, it's going to cycle through the values, when you reach the max and add 1 it's going to be the lowest value, so 32768 is going to be -32768, when you reach 65536 (32768*2) it's going to be 0 and when you reach 98303 (32768*2+32767) it's going to be 32767, if you add one you'll get to 98304 (32768*3) and it's going to be -32768 again.

So 40002 (which is higher than 32768 but lower than 32768*2) is clearly going to be a negative number when converted to short.