I just did a rough calculation around the max size of an unsigned 64-bit integer, which is:
18,446,744,073,709,551,615
q5 q4 t b m t h
Looking at AWS's hardware specifications on their largest machines, it gets up to 3,904GB, which is:
3,904,000,000,000,000,000 bytes
5 q4 t b m t h
To me that means the pointers are stored as 64-bit integers. I am new to thinking about memory and pointers but just wanted to clarify that.
I'm a bit confused though still. A pointer is a "programming language construct". So technically, even on a 64-bit machine, if you are only using less than ~4 billion integers (32-bit max integer size), then I'm wondering why you can't just have the pointers be 32 bits. That way pointers are 32-bits until you run out of space, then you can start using 64-bit pointers. Then it would give you a bit more space to have more objects.
Still confused though. A pointer holds the location of an address in memory. It says the "address" is 64-bits. So if we were to have 32-bit pointers pointing to 32-bit chunks in the 64-bit memory, I'm not sure what that would look like or mean. It seems like it means you would have to do offsets (though I don't understand that too well).
Wondering if one could demonstrate in C, Assembly, or JavaScript, how it would look to store 32-bit pointers in a 64-bit address space. If C handles it for you automatically, then how Assembly does it.
I would like to know how I could use a large memory like above, but store 32-bit pointers, until the max is reached then use 64-bit pointers, and not sure what that would look like exactly. I will try to draw a diagram explaining how I'm thinking about it.
| The bars and . are like a ruler and mark the bit positions.
- Each row under a number (1, 2, 3, ...) means a memory address.
⬚ Means no data in memory address.
⬒ Means data of type 1 in memory address.
■ Means data of type 2 in memory address.
● Means a bit of integer pointer is plugged into memory address slot.
◌ Means no bit of integer pointer is plugged into memory address slot.
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| | | | | | | | | | | | | | | |
. | . | . | . | . | . | . | . | . | . | . | . | . | . | . | . | . | . | . | . | . | . | . | . | . | . | . | . | . | . | . | . |
1. Empty 64-bit memory.
◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌
⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚
◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ...
⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ⬚ ...
...
...
2. 64-bit memory filled with 32-bit pieces of data (type 1 ⬒, type 2 ■).
◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌
⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■
◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ...
⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ...
...
...
3. 64-bit memory filled with 64-bit pieces of data.
◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌
■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■
◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ...
⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ...
...
...
4. 64-bit memory filled with 4-bit pieces of data.
◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌
■ ■ ■ ■ ⬒ ⬒ ⬒ ⬒ ■ ■ ■ ■ ⬒ ⬒ ⬒ ⬒ ■ ■ ■ ■ ⬒ ⬒ ⬒ ⬒ ■ ■ ■ ■ ⬒ ⬒ ⬒ ⬒ ■ ■ ■ ■ ⬒ ⬒ ⬒ ⬒ ■ ■ ■ ■ ⬒ ⬒ ⬒ ⬒ ■ ■ ■ ■ ⬒ ⬒ ⬒ ⬒ ■ ■ ■ ■ ⬒ ⬒ ⬒ ⬒
◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ...
■ ■ ■ ■ ⬒ ⬒ ⬒ ⬒ ■ ■ ■ ■ ⬒ ⬒ ⬒ ⬒ ■ ■ ■ ■ ⬒ ⬒ ⬒ ⬒ ■ ■ ■ ■ ⬒ ⬒ ⬒ ⬒ ■ ■ ■ ■ ⬒ ⬒ ⬒ ⬒ ■ ■ ■ ■ ⬒ ⬒ ⬒ ⬒ ■ ■ ■ ■ ⬒ ⬒ ⬒ ⬒ ■ ■ ■ ■ ⬒ ⬒ ...
...
...
5. 64-bit memory filled with 32-bit pieces of data, with second 32-bits accessed by a 32-bit pointer.
◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒
◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ...
■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ...
...
...
6. 64-bit memory filled with 64-bit pieces of data, with second 64-bits accessed by a 64-bit pointer.
◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌
■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■
● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ...
⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ...
...
...
7. 64-bit memory filled with 4-bit pieces of data, with second piece of data accessed by a pointer.
◌ ◌ ◌ ◌ ● ● ● ● ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌
■ ■ ■ ■ ⬒ ⬒ ⬒ ⬒ ■ ■ ■ ■ ⬒ ⬒ ⬒ ⬒ ■ ■ ■ ■ ⬒ ⬒ ⬒ ⬒ ■ ■ ■ ■ ⬒ ⬒ ⬒ ⬒ ■ ■ ■ ■ ⬒ ⬒ ⬒ ⬒ ■ ■ ■ ■ ⬒ ⬒ ⬒ ⬒ ■ ■ ■ ■ ⬒ ⬒ ⬒ ⬒ ■ ■ ■ ■ ⬒ ⬒ ⬒ ⬒
◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ...
■ ■ ■ ■ ⬒ ⬒ ⬒ ⬒ ■ ■ ■ ■ ⬒ ⬒ ⬒ ⬒ ■ ■ ■ ■ ⬒ ⬒ ⬒ ⬒ ■ ■ ■ ■ ⬒ ⬒ ⬒ ⬒ ■ ■ ■ ■ ⬒ ⬒ ⬒ ⬒ ■ ■ ■ ■ ⬒ ⬒ ⬒ ⬒ ■ ■ ■ ■ ⬒ ⬒ ⬒ ⬒ ■ ■ ■ ■ ⬒ ⬒ ...
...
...
8. 64-bit memory filled with 8-bit pieces of data, with second piece of data accessed by a pointer.
◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ● ● ● ● ● ● ● ● ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌
■ ■ ■ ■ ■ ■ ■ ■ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ■ ■ ■ ■ ■ ■ ■ ■ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ■ ■ ■ ■ ■ ■ ■ ■ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ■ ■ ■ ■ ■ ■ ■ ■ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒
◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ◌ ...
■ ■ ■ ■ ■ ■ ■ ■ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ■ ■ ■ ■ ■ ■ ■ ■ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ■ ■ ■ ■ ■ ■ ■ ■ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ■ ■ ■ ■ ■ ■ ■ ■ ⬒ ⬒ ⬒ ⬒ ⬒ ⬒ ...
...
...
What I'm imagining is that the integers are like keys to a lock (which is the memory address). An empty key hole looks like the 64 ◌'s in a row in (1). A full key hole for a 64-bit address looks like the 64 ●'s in a row in (6). If I give the 64-bit memory address space a 32-bit key, it's like it would look like (5). So it wouldn't fully fill in the 64-bit long (64-◌ long) key hole, it would only fill (in this case) the second half of it. And so it seems like it wouldn't match the address. But I'm trying to point to the 32-bits of data right there in the second half! In order to match the address, it seems you'd have to fill in the key holes in the full 64-bit row, as in (6). I am wondering if my understanding is messed up here, please let me know where I'm off.
In case that wasn't clear, the first numbers 1-4 in the chart show data that lays in memory (with 1 being an empty memory). The second numbers 5-8 show us trying to access the data using a pointer (the black circles ● in a row being the pointer/key to the memory address lock).
Finally, I have one last issue. I wonder if you can take it further and store data at even smaller chunks. Such as storing 4-bits of data, as in (7). This just goes to demonstrate how the pointer / address system works in a bit more detail. I don't know if you can have a 4-bit pointer point to a 4-bit chunk of memory. This seems like, because of alignment requirements, you would end up fetching at least 8-bits at a time. But that's okay. I just want to make sure it is or isn't possible to use an n-bit pointer to access n-bits of data in a 64-bit memory space.
And if so, how that would look, either in C or Assembly, or JavaScript would also work.
I would like to know this to know how you are supposed to store data in a 64-bit memory, and what you are allowed to do with the pointers given the "memory addresses are 64-bits". That is, if I can do memory.get(a32BitPointer) and have it return 32 bits of data, from a 32-bit aligned memory slot. (Or equivalently, a 4, 8, 16, etc. bit piece of data or sized pointer).
Answer
A pointer points to contains an absolute address.
If you need to add a value before you use the pointer, what you have is an offset, not a real pointer.
In C, a void pointer can be a function pointer, e.g. you can call a function through it. For that to work you need all 64 bits if the CPU is in 64-bit mode.
If your CPU supports 64 address lines (it may physically have less), then it has an address space of 2^64, which is 0x1 0000 0000 0000 0000 - ranging from 0x0000 0000 0000 0000 to 0xFFFF FFFF FFFF FFFF.
If you want your pointer to be useable by CPU instructions without needing additional CPU instructions to find out what you really mean (native CPU code can deal with pointers directly), then it must be as wide as the CPU's address space.
Offsets are slower because the CPU must add to get the address you want, though CPUs have native instructions that do that too.
I'm not a super expert with the x86-64 ISA, but there's probably CPU instructions that treat 32-bit values as 64-bit values with the first 32 bits assumed to be 0. CPU still has to internally "extend" the real value to 64 bits.
In x86 and x86-64 you certainly can use 8, 16, 32, and 64 bit offsets (no x86/x86 CPU instructions work with just 4-bit values)
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