In risc-v, beq instruction has 12bits of imm[12:1].
And PC-relative addressing is Target address = PC immediate x 2
It says the reason of the multiply with 2 is for the half word instruction.
So, I think the immediate value can represent the range of [-2^12 ~ 2^12-2],
because of the hidden bit in imm[0] == 0.
And multiplying with 2 makes the range as [-2^13 ~ 2^13-2].
So, when we think in 2 byte increments instruction, the branch can reach in range of
-2^12 ~ 2^12-2
and in 4 byte increments instruction, the branch can reach in range of
-2^11 ~ 2^11-2.
But in risc-v org page 29 https://riscv.org/wp-content/uploads/2017/05/riscv-spec-v2.2.pdf,
it says the conditional branch range is -4KiB ~ 4KiB,
which means -2^10 ~ 2^10 in 32-bit instructions.
Q1. In PC relative addressing, Is it right we use 13bits result (with hidden 0bit) in calculation?
Q2. If it is right, how can I calculate the range of the branch instruction?
CodePudding user response：
Q1. In PC relative addressing, Is it right we use 13bits result (with hidden 0bit) in calculation?
Yes, as you note, the formula that the processor uses is
Target address = PC of the branch instruction immediate x 2
The x2 reintroduces that 13th bit that is known to be zero and hence stripped away during encoding.
Q2. If it is right, how can I calculate the range of the branch instruction?
You have the right idea.
The encoded immediate value is 12 bits wide, so the value added to the PC is 13 bits wide (immediate x 2). The immediate is a signed field.
The maximum immediate is positive, and is a 0 bit followed by 11 bits of 1's, which is 2047 (aka 0x7FF or 2^11-1), and the minimum immediate is negative, and is a 1 bit (sign) followed by 11 bits of 0's, which is -2048 (aka 0x800 or -2^11).
Therefore the maximum forward range is a 0 bit followed by 11 bits of 1's followed by 1 bit of 0, which is 4094 (aka 0xFFE or 2^12-2).
While the maximum backward range is a 1 bit followed by 12 bits of 0's, which is -4096 (aka is 0x1000 (in 13 bits) or -2^12).
Let's note, that it is common to speak of range in terms of bytes on byte-addressable machines. Instruction addresses are byte addresses (even, for example, if all the instructions are the same 32-bit size). so the (byte) range is -4096 .. 4094 — these are the instruction addresses that can be reached.
However, if you want to consider how many 16-bit instructions can be reached, we would divide that byte range in half, so -2048 .. 2047, and if considering how many 32-bit instructions can be reached, we would divide that byte range in quarter, so -1024 .. 1023.5 .