# The PowerPC 600 series, part 4: Bitwise operations and constants

The PowerPC 600 series includes the following bitwise logical operations:

```    and     rd, ra, rb      ; rd =   ra &  rb
or      rd, ra, rb      ; rd =   ra |  rb
xor     rd, ra, rb      ; rd =   ra ^  rb
nand    rd, ra, rb      ; rd = ~(ra &  rb)
nor     rd, ra, rb      ; rd = ~(ra |  rb)
eqv     rd, ra, rb      ; rd = ~(ra ^  rb)
andc    rd, ra, rb      ; rd =   ra & ~rb "and complement"
orc     rd, ra, rb      ; rd =   ra | ~rb "or complement"
; also "." versions
```

Each of these instructions also comes with a dot variant that updates cr0 based on the result.

There are also versions that take immediates or sometimes shifted immediates, and sometimes they update flags, and sometimes they don't. There isn't much orthogonality here. It's all case-by-case.

```    andi.   rd, ra, imm16   ; rd =   ra &  (uint16_t)imm16, update cr0
andis.  rd, ra, imm16   ; rd =   ra & ((uint16_t)imm16 << 16), update cr0
ori     rd, ra, imm16   ; rd =   ra |  (uint16_t)imm16
oris    rd, ra, imm16   ; rd =   ra | ((uint16_t)imm16 << 16)
xori    rd, ra, imm16   ; rd =   ra ^  (uint16_t)imm16
xoris   rd, ra, imm16   ; rd =   ra ^ ((uint16_t)imm16 << 16)
```

Immediates are allowed only on three of the bitwise operations, and the `and` version always updates flags, whereas the `or` and `xor` versions never update flags.

For some reason, sign extension is placed in the logical operations group.

```    extsb   rd, ra          ; rd = (int8_t)ra
extsb.  rd, ra          ; rd = (int8_t)ra, update cr0
extsh   rd, ra          ; rd = (int16_t)ra
extsh.  rd, ra          ; rd = (int16_t)ra, update cr0
```

We now have enough instructions to load constants.

If the constant is in the range `0xFFFF8000` to `0x00007FFF`, it can be loaded in one instruction:

```    ; load immediate: rd = (int16_t)imm16
addi    rd, 0, imm16     ; li   rd, imm16
```

It can also be done in one instruction if the constant is an exact multiple of 65536.

```    ; load immediate shifted: rd = imm16 << 16
addis   rd, 0, imm16     ; lis  rd, imm16
```

These take advantage of the fact that the `addi` and `addis` instructions treat r0 as if it were zero. They are the only non-memory instructions that have this special behavior with respect to r0.

If the constant you want to load doesn't fall into either of the two categories above, then you'll have to load it in two steps:

```    addis   rd, 0, imm16a    ; rd =  imm16a << 16
ori     rd, rd, imm16b   ; rd = (imm16a << 16) | (uint16_t)imm16b
```

This sequence takes advantage of the fact that the `ori` instruction treats its 16-bit immediate as an unsigned value. That way, we don't have to play funny games with the most significant 16 bits if the least-significant 16 bits happen to form a negative integer when interpreted as a signed 16-bit value.

While I'm here I may as well mention a third synthetic instruction based on `addi`:

```    ; load address: rd = effective address of imm16(ra)
addi    rd, ra, imm16    ; la   rd, imm16(ra)
```

A commonly-used synthetic instruction is "move register":

```    or      rd, ra, ra       ; mr  rd, ra
or.     rd, ra, ra       ; mr. rd, ra
```

Moving a register to itself is functionally a nop, but the processor overloads it to signal information about priority.

```    or      r1, r1, r1       ; low priority
or      r6, r6, r6       ; medium-low priority
or      r2, r2, r2       ; normal priority
```

A program can voluntarily set itself to low priority if it is waiting for a spin lock. There are other priority levels which are available only to kernel mode and are ignored in user mode.

Finally, everybody's favorite instruction:

```    ori     r0, r0, 0        ; nop
```

This is the official `nop` instruction recognized by the processor. There are other instructions that have no visible effect, but they might not be optimized efficiently. For example, `rlwinm ra, ra, 0, 0, 31` has no visible effect, but it will probably introduce a register dependency. And as we saw above, sometimes instructions with no visible effect become overloaded as signals to the processor, so your best bet is to avoid them.

Wait, you don't know what the `rlwinm` instruction does? We'll dig into that next time, when we enter the crazy world of rotating and shifting, and you'll be formally introduced to the `rlwinm` instruction, the Swiss army knife instruction of the PowerPC instruction set.

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1. How does that priority signalling actually work? Is it something that the CPU itself uses to e.g. go into a lower power mode? Or is it something used by the OS software (by decoding the instructions?) to make decisions about thread priorities?

Having had to debug a lot of optimized PPC assembly on the Xbox 360, I can tell you that the rotate and shift family of instructions are absolutely bonkers, and I was constantly having to refer to the PPC ISA manuals to understand what the code I was stepping through was doing.

1. StackOverflow says that it adjusts the relative priorities of execution units within a single core. So it’s to adjust how aggressively the execution unit competes for resources with other execution units.

1. Fabian Giesen says:

It’s not really about execution unit priority; it’s about which hardware thread gets how many issue slots. Assuming you have multiple hardware threads running on the same CPU core that is.

If either 0 or 1 hardware threads are currently in a runnable state (i.e. not waiting on say a cache miss or otherwise stalling), it doesn’t matter. You just issue instructions from the one thread you can, if any.

But if you have at least 2 HW threads in runnable state (say thread A and thread B), the way HW multithreading works is that on some cycles thread A gets to feed new instructions into the pipe, and on some cycles thread B does. There is only one frontend that decodes instructions, and it’s time-sliced between the threads. The priority adjustments control how many time slices each thread gets. (This is time-slicing at the individual cycle level, mind, much finer-grained than OS-level threading is.)

2. poizan42 says:

There are 8 bitwise operators out of 16 logical connectives, so I was curious about which ones are missing.

Contradiction and tautology (constant false and true) are obviously missing since they are independent of input. Then there are “Proposition P” and “Proposition Q” – the ones that just gives the first or second input back – as well as their negations. So that takes away 6 of the operators as not using both inputs. The last 2 remaining are andc and orc with swapped arguments (or alternatively the negation of them). Since you can just swap the arguments around it would seem that all 16 logical connectives are actually accessible in at most one instruction.