Add bitwise shifts to Quil

[antalsz]

This PR adds bitwise shifts to Quil:

SHIFT-LEFT n b
SHIFT-RIGHT n b
ARITHMETIC-SHIFT-RIGHT n b

These allow expressing the remainder of the bitwise operations besides & (AND), | (IOR), and ^ (XOR) that round out typical bitwise support:

• SHIFT-LEFT n b shifts the value in n left by b bits, filling in zeros. The equivalent to n <<= b.
• SHIFT-RIGHT n b shifts the value in n right by b bits, filling in zeros. The equivalent to n >>= b for unsigned n (or Java's >>=).
• ARITHMETIC-SHIFT-RIGHT n b shifts the value in n right by b bits, preserving the high bit. The equivalent to n >>= b for signed n (or Java's >>>=).

[jselig-rigetti]

This threw me off - "shift the bits of a left", took me a second to read it as "shift the bits of a left".

So to check my understanding, is this what the result is?

SHIFT-LEFT              0b10101 2   # 0b10100

SHIFT-RIGHT             0b10101 2   # 0b00101

ARITHMETIC-SHIFT-RIGHT  0b10101 2   # 0b10101

# overshifting

SHIFT-LEFT              0b10101 9   # 0b00000

SHIFT-RIGHT             0b10101 9   # 0b00000

ARITHMETIC-SHIFT-RIGHT  0b10101 9   # 0b10000

Also, why is there no corresponding ARITHMETIC-SHIFT-LEFT? Is there no need to preserve the high bit in that case, or is it achieved through other means (e.g. with an OR)?

[antalsz]

Your SHIFT-LEFT and SHIFT-RIGHT are correct, ARITHMETIC-SHIFT-RIGHT is not. Assuming 6-bit words, you'd get:

ARITHMETIC-SHIFT-RIGHT  0b10101 2   # 0b11101
ARITHMETIC-SHIFT-RIGHT  0b10101 9   # 0b11111

This makes arithmetic right shift signed division by 2 in 2's complement. There's not typically, AFAIK, a need for arithmetic left shift; the low bit doesn't have the same special semantics that the high bit does.

[stylewarning]

Any opposition to having ASH n k (Arithmetic SHift) with a positive or negative argument (for left and right arithmetic shifting) being defined as something like n * 2^k, alongside the usual interpretation for octets? Given Quil doesn't have a notion of signedness explicitly, I'm not sure arithmetic vs logical is very useful.

[antalsz]

@stylewarning I'm open to redefining ASHR if it's useful, as long as it corresponds naturally to a shift. The logical shifts are more immediately relevant for us, at any rate.

For ARITHMETIC-SHIFT-RIGHT n k, are you considering negative n or negative k? If you mean negative n, yeah, n / 2^k is a good definition; I would still want to include a descriptive statement that this is the same as bit-shifting for 2's complement words so that it's clear why this is called ARITHMETIC-SHIFT-RIGHT. You make a good point that while we have a notion of words we don't commit to their representation, and ARITHMETIC-SHIFT-RIGHT does assume some sort of 1 or 2's complement representation (or something else that uses a sign bit).

[mingyoungjeng]

x-posting this comment here.

To be consistent with the existing bitwise operations, is there a preferred abbreviated form of the new bitwise shift instructions?
Should they be written as:

1. SHL, SHR, ASHR
2. LSH, RSH, ARSH
3. some other variant?

[antalsz]

@mingyoungjeng Good call, thank you! Since @stylewarning wrote ASH and I wrote ASHR without thinking about it, it seems like SHL, SHR, and ASHR are the way to go, and a Google indicates that they're common. I also updated the wording around ASHR to include the arithmetic definition that @stylewarning requested.

[antalsz]

@stylewarning Does this look good to you? If you have no serious objections, maybe we try to get this in by the end of the week