16 bits hex range for mips assembly instruction beq and bne

Question

I have implemented beq instruction for mips assembly language. As my understanding for beq instruction ( beq $s, $t, i ), i can take on integer values or hex values. I have establish a bound for 16 bits integer value. I was wondering what is the bound for 16 bits hex values, so when i is too large (or too small?) it would output error before executing it. Following is beq instruction in binary.

Branch On Equal
beq $s, $t, i
0001 00ss ssst tttt iiii iiii iiii iiii

I tried (i > 0xffff) but it seems not cover all the cases. What should i do here? Thanks.

Answer 1

It should be in between 0 and 2^16 - 1 for hex(0 <= i <= 65535);
It should be in between -2^15 and 2^15 - 1 for int(-32768<=i<=32767)

Answer 2

When you need to conditionally branch farther than +- 2^15 instructions (byte offset = two's complement 16 bits << 2), you can conditionally jump over a non-conditional jump that can reach the target.

beq $s, $t,  target      # short jump, approx +- 2^17 bytes

vs. j uses pseudo-direct addressing , keeping the top 4 bits of PC and replacing the rest with a 26-bit << 2 immediate. This lets you reach any target address in the same aligned 1/16th of address space as your code.

bne $s, $t,  .nojump
j   target               # anywhere with the same top 4 bits
.nojump:

vs. putting the address in a register and using jr to reach any 32-bit address:

bne $s, $t,  .nojump
lui  $t0,      %hi(target)
ori  $t0, $t0, %lo(target)      # this is what  la $t0, target does.  It might use addui, but whatever
jr   $t0
.nojump: