Fun with Macros: Gathering
Posted on May 21st, 2018.
I haven't written anything in a while. But after seeing the metaprogramming video on Computerphile the other day I felt the urge to write about Lisp again, so I decided to do a small series of posts on fun/useful little Common Lisp macros I've made over the past couple of years.
The Macro
The first macro we'll look at is gathering:
(defmacro gathering (&body body)
"Run `body` to gather some things and return a fresh list of them.
`body` will be executed with the symbol `gather` bound to a
function of one argument. Once `body` has finished, a list of
everything `gather` was called on will be returned.
It's handy for pulling results out of code that executes
procedurally and doesn't return anything, like `maphash` or
Alexandria's `map-permutations`.
The `gather` function can be passed to other functions, but should
not be retained once the `gathering` form has returned (it would
be useless to do so anyway).
Examples:
(gathering
(dotimes (i 5)
(gather i))
=>
(0 1 2 3 4)
(gathering
(mapc #'gather '(1 2 3))
(mapc #'gather '(a b)))
=>
(1 2 3 a b)
"
(alexandria:with-gensyms (result)
`(let ((,result nil))
(flet ((gather (item)
(push item ,result)
item))
,@body)
(nreverse ,result))))Notes
As the docstring mentions, sometimes you'll encounter procedural code that
iterates over things but doesn't return any results (CL's maphash and
Alexandria's map-permutations are two examples). The gathering macro
provides an easy way to plug into the guts of the iteration and get a list back.
The docstring describes how to use the macro, but there's a couple of extra
things to note before we move on.
Default LET Bindings
I'm aware that the (let ((,result nil)) ...) in the macro could be simplified
to (let (,result) ...) because bindings without an initial value default to
nil. I just personally dislike that style and prefer to be explicit about the
initial values, even when they're nil.
Hygiene
The fleted function that actually does the gathering is named as the symbol
gather, not a gensym. Some folks will dislike that because it captures the
function name. I don't mind it. I consider that behavior part of the
intended/documented API of the macro, and because the symbol gather is coming
from the macro's package you'll need to import it (or package qualify it) to
access it.
If you want to provide a bit more safety here you could potentially define
a vanilla function for gather like this:
(defun gather (value)
"Gather `value` into the result. Must be called from inside `gathering`."
(error "GATHER be called from within a GATHERING macro."))Doing this would mean calling gather outside a gathering block would signal
an error, and someone defining their own gather function (which could
accidentally get shadowed by the macro's flet later) would get a warning about
redefining the function, which would hopefully make them realize the potential
conflict earlier.
Of course you could also write your own version of gathering that takes in
a symbol to use for the function, if you prefer. That would avoid all of these
issues, at the cost of making every (gathering ...) slightly more verbose.
Data Structures
My actual implementation of this macro uses a simple queue data structure instead of a list to avoid having to reverse the result at the end, but I didn't want to include an extra dependency just for this blog post.
Dynamic Extent
Feel free to skip this section. It gets a little bit into the weeds.
One potential optimization we could make is to declare the gather function to
have dynamic extent. This means that some implementations (e.g. SBCL) can
stack allocate the closure and save a heap allocation.
(defmacro gathering-dynamic-extent (&body body)
(alexandria:with-gensyms (result)
`(let ((,result nil))
(flet ((gather (item)
(push item ,result)
item))
(declare (dynamic-extent #'gather)) ; NEW
,@body)
(nreverse ,result))))Whether this matters much depends on the usage patterns. If you use gathering
with some code that typically gathers no elements (and only occasionally gathers
a few), you won't have to heap allocate anything for the common cases, and
things will be a little more efficient. If you typically gather a bunch of
things then you're heap allocating all the cons cells anyway, so allocating the
closure wouldn't be a big deal.
If you want to actually see the stack allocation in action, it might be a little
trickier than you think. SBCL is pretty smart about inlining things, so it
might not allocate the closure at runtime at all, even without the
dynamic-extent declaration:
(disassemble (lambda ()
(gathering
(mapc #'gather '(1 2 3)))))
; disassembly for (LAMBDA ())
; Size: 149 bytes. Origin: #x10040B8340
; 40: 498B4C2460 MOV RCX, [R12+96] ; no-arg-parsing entry point
; thread.binding-stack-pointer
; 45: 48894DF8 MOV [RBP-8], RCX
; 49: BB17001020 MOV EBX, #x20100017 ; NIL
; 4E: 488B0D9BFFFFFF MOV RCX, [RIP-101] ; '(1 2 3)
; 55: EB4D JMP L3
; 57: 660F1F840000000000 NOP
; 60: L0: 4881FA17001020 CMP RDX, #x20100017 ; NIL
; 67: 744A JEQ L4
; 69: 488B71F9 MOV RSI, [RCX-7]
; 6D: 49896C2440 MOV [R12+64], RBP ; thread.pseudo-atomic-bits
; 72: 4D8B5C2418 MOV R11, [R12+24] ; thread.alloc-region
; 77: 498D5310 LEA RDX, [R11+16]
; 7B: 493B542420 CMP RDX, [R12+32]
; 80: 7746 JNBE L5
; 82: 4989542418 MOV [R12+24], RDX ; thread.alloc-region
; 87: L1: 498D5307 LEA RDX, [R11+7]
; 8B: 49316C2440 XOR [R12+64], RBP ; thread.pseudo-atomic-bits
; 90: 7403 JEQ L2
; 92: 0F0B09 BREAK 9 ; pending interrupt trap
; 95: L2: 488972F9 MOV [RDX-7], RSI
; 99: 48895A01 MOV [RDX+1], RBX
; 9D: 488BDA MOV RBX, RDX
; A0: 488B4901 MOV RCX, [RCX+1]
; A4: L3: 488BD1 MOV RDX, RCX
; A7: 8D41F9 LEA EAX, [RCX-7]
; AA: A80F TEST AL, 15
; AC: 74B2 JEQ L0
; AE: 0F0B0A BREAK 10 ; error trap
; B1: 2F BYTE #X2F ; OBJECT-NOT-LIST-ERROR
; B2: 10 BYTE #X10 ; RDX
; B3: L4: 488BD3 MOV RDX, RBX
; B6: B902000000 MOV ECX, 2
; BB: FF7508 PUSH QWORD PTR [RBP+8]
; BE: B8B8733120 MOV EAX, #x203173B8 ; #<FDEFN SB-IMPL::LIST-NREVERSE>
; C3: FFE0 JMP RAX
; C5: 0F0B10 BREAK 16 ; Invalid argument count trap
; C8: L5: 6A10 PUSH 16
; CA: 41BB3000B021 MOV R11D, #x21B00030 ; ALLOC-TO-R11
; D0: 41FFD3 CALL R11
; D3: EBB2 JMP L1
NILHere SBCL knows what mapc is and expands it inline (notice how
there's no function call to mapc). It then realizes it never needs to
allocate a closure for gather at all, it can just inline that too! All the
allocation stuff in that disassembly is for the pushing of new cons cells (to
convince yourself of this, run (disassemble (lambda (&aux result) (push
1 result) result)) and compare the assembly).
But if we make our own version of mapc:
(defun my-mapc (function list)
(mapc function list))Now we can see a difference, because SBCL won't necessarily know it can
stack allocate the closure unless we tell it. Here's what the disassembly
looks like without the dynamic-extent inside gathering:
(disassemble (lambda ()
(gathering
(my-mapc #'gather '(1 2 3)))))
; disassembly for (LAMBDA ())
; Size: 212 bytes. Origin: #x1004331A20
; 20: 498B4C2460 MOV RCX, [R12+96] ; no-arg-parsing entry point
; thread.binding-stack-pointer
; 25: 48894DF8 MOV [RBP-8], RCX
; 29: B817001020 MOV EAX, #x20100017 ; NIL
; 2E: 49896C2440 MOV [R12+64], RBP ; thread.pseudo-atomic-bits
; 33: 4D8B5C2418 MOV R11, [R12+24] ; thread.alloc-region
; 38: 498D5B10 LEA RBX, [R11+16]
; 3C: 493B5C2420 CMP RBX, [R12+32]
; 41: 0F874D010000 JNBE #x1004331B94
; 47: 49895C2418 MOV [R12+24], RBX ; thread.alloc-region
; 4C: 498D5B0F LEA RBX, [R11+15]
; 50: 66C743F14101 MOV WORD PTR [RBX-15], 321
; 56: 488943F9 MOV [RBX-7], RAX
; 5A: 49316C2440 XOR [R12+64], RBP ; thread.pseudo-atomic-bits
; 5F: 7403 JEQ L0
; 61: 0F0B09 BREAK 9 ; pending interrupt trap
; 64: L0: 48895DE8 MOV [RBP-24], RBX
; 68: 49896C2440 MOV [R12+64], RBP ; thread.pseudo-atomic-bits
; 6D: 4D8B5C2418 MOV R11, [R12+24] ; thread.alloc-region
; 72: 498D4B20 LEA RCX, [R11+32]
; 76: 493B4C2420 CMP RCX, [R12+32]
; 7B: 0F8723010000 JNBE #x1004331BA4
; 81: 49894C2418 MOV [R12+24], RCX ; thread.alloc-region
; 86: 498D4B0B LEA RCX, [R11+11]
; 8A: B835020000 MOV EAX, 565
; 8F: 480B042508011020 OR RAX, [#x20100108] ; SB-VM:FUNCTION-LAYOUT
; 97: 488941F5 MOV [RCX-11], RAX
; 9B: 488D058E000000 LEA RAX, [RIP+142] ; = #x1004331B30
; A2: 488941FD MOV [RCX-3], RAX
; A6: 49316C2440 XOR [R12+64], RBP ; thread.pseudo-atomic-bits
; AB: 7403 JEQ L1
; AD: 0F0B09 BREAK 9 ; pending interrupt trap
; B0: L1: 48895905 MOV [RCX+5], RBX
; B4: 488BD1 MOV RDX, RCX
; B7: 488D4424F0 LEA RAX, [RSP-16]
; BC: 4883EC10 SUB RSP, 16
; C0: 488B3DE9FEFFFF MOV RDI, [RIP-279] ; '(1 2 3)
; C7: B904000000 MOV ECX, 4
; CC: 488928 MOV [RAX], RBP
; CF: 488BE8 MOV RBP, RAX
; D2: B838734F20 MOV EAX, #x204F7338 ; #<FDEFN MY-MAPC>
; D7: FFD0 CALL RAX
; D9: 480F42E3 CMOVB RSP, RBX
; DD: 488B5DE8 MOV RBX, [RBP-24]
; E1: 488B53F9 MOV RDX, [RBX-7]
; E5: B902000000 MOV ECX, 2
; EA: FF7508 PUSH QWORD PTR [RBP+8]
; ED: B8B8733120 MOV EAX, #x203173B8 ; #<FDEFN SB-IMPL::LIST-NREVERSE>
; F2: FFE0 JMP RAX
NILNow we can see it's allocating the closure on the heap (note the
SB-VM:FUNCTION-LAYOUT).
If we add the dynamic-extent back into gathering:
(disassemble (lambda ()
(gathering-dynamic-extent
(my-mapc #'gather '(1 2 3)))))
; disassembly for (LAMBDA ())
; Size: 136 bytes. Origin: #x10043F46E0
; 6E0: 498B4C2460 MOV RCX, [R12+96] ; no-arg-parsing entry point
; thread.binding-stack-pointer
; 6E5: 48894DF8 MOV [RBP-8], RCX
; 6E9: 48C745E817001020 MOV QWORD PTR [RBP-24], #x20100017 ; NIL
; 6F1: 488BDC MOV RBX, RSP
; 6F4: 48895DE0 MOV [RBP-32], RBX
; 6F8: 4883EC20 SUB RSP, 32
; 6FC: 4883E4F0 AND RSP, -16
; 700: 488D4C240B LEA RCX, [RSP+11]
; 705: B835020000 MOV EAX, 565
; 70A: 480B042508011020 OR RAX, [#x20100108] ; SB-VM:FUNCTION-LAYOUT
; 712: 488941F5 MOV [RCX-11], RAX
; 716: 488D0583000000 LEA RAX, [RIP+131] ; = #x10043F47A0
; 71D: 488941FD MOV [RCX-3], RAX
; 721: 48896905 MOV [RCX+5], RBP
; 725: 488BD1 MOV RDX, RCX
; 728: 488D4424F0 LEA RAX, [RSP-16]
; 72D: 4883EC10 SUB RSP, 16
; 731: 488B3D38FFFFFF MOV RDI, [RIP-200] ; '(1 2 3)
; 738: B904000000 MOV ECX, 4
; 73D: 488928 MOV [RAX], RBP
; 740: 488BE8 MOV RBP, RAX
; 743: B838734F20 MOV EAX, #x204F7338 ; #<FDEFN MY-MAPC>
; 748: FFD0 CALL RAX
; 74A: 480F42E3 CMOVB RSP, RBX
; 74E: 488B5DE0 MOV RBX, [RBP-32]
; 752: 488BE3 MOV RSP, RBX
; 755: 488B55E8 MOV RDX, [RBP-24]
; 759: B902000000 MOV ECX, 2
; 75E: FF7508 PUSH QWORD PTR [RBP+8]
; 761: B8B8733120 MOV EAX, #x203173B8 ; #<FDEFN SB-IMPL::LIST-NREVERSE>
; 766: FFE0 JMP RAX
NILMuch nicer. However, this optimization comes with a price: safety.
The gather closure should never be called outside of the gathering block
that defines it. As the docstring says: it would be useless to do so anyway,
because the result has already been returned. But what would happen if the user
accidentally calls the closure? Let's try it out, first on the original
version without the dynamic-extent declaration:
(defparameter *f* nil)
(defun leak (function)
(setf *f* function))
(gathering (leak #'gather))
(funcall *f* 1)
; => 1Here the closure is heap-allocated, so calling it later is fine (if useless). But what happens if we try our optimized version?
(gathering-dynamic-extent (leak #'gather))
(funcall *f*)
; CORRUPTION WARNING in SBCL pid 19575(tid 0x7fffb6814380):
; Memory fault at 0xffffffff849ff8e7 (pc=0x19ff8df, sp=0x19ff890)
; The integrity of this image is possibly compromised.
; Continuing with fingers crossed.
;
; debugger invoked on a SB-SYS:MEMORY-FAULT-ERROR in thread
; #<THREAD "main thread" RUNNING {1001936BF3}>:
; Unhandled memory fault at #xFFFFFFFF849FF8E7.
;
; restarts (invokable by number or by possibly-abbreviated name):
; 0: [ABORT] Exit debugger, returning to top level.
;
; (SB-SYS:MEMORY-FAULT-ERROR)
; 0]Things get even worse if you're brave (foolish) enough to be running with
(declaim (safety 0)):
(gathering-dynamic-extent (leak #'gather))
(funcall *f*)
; debugger invoked on a SB-KERNEL:FLOATING-POINT-EXCEPTION in thread
; #<THREAD "main thread" RUNNING {1001936BF3}>:
; An arithmetic error SB-KERNEL:FLOATING-POINT-EXCEPTION was signalled.
; No traps are enabled? How can this be?
;
;
; restarts (invokable by number or by possibly-abbreviated name):
; 0: [ABORT] Exit debugger, returning to top level.
;
; ("bogus stack frame")
; 0]The moral of this story is that although we can optimize for a little bit of speed, it comes at a price that might not be worth paying.
Here's an exercise for you: make the original heap-allocated version signal an
error (with a nice error message) when called outside of its gathering block,
instead of silently doing something useless.
Examples
Let's finish up by looking at some places where I've found this macro to be handy. I won't go into too much depth about the individual pieces of code, but feel free to ask if you have questions.
Pandigitals
First up, an example from my Project Euler utils.lisp file:
(defun pandigitals (&optional (start 1) (end 9))
"Return a list of all `start` to `end` (inclusive) pandigital numbers."
(gathering
(map-permutations
(lambda (digits)
;; 0-to-n pandigitals are annoying because we don't want
;; to include those with a 0 first.
(unless (zerop (first digits))
(gather (digits-to-number digits))))
(irange start end)
:copy nil)))This is a prime example of where Alexandria's map-permutations not returning
anything is annoying, but also shows how gathering provides you a little more
flexibility. Even if map-permutations returned a list of results, we'd still
need to filter out the ones that start with zero. With gathering we can avoid
collecting the unneeded results at all by simply not calling gather on them.
Hash Table Contents
Next is an easy way to convert a hash table to lists of (key value):
(defun hash-table-contents (hash-table)
"Return a fresh list of `(key value)` elements of `hash-table`."
(gathering (maphash (compose #'gather #'list) hash-table)))Because gather is a fleted function we can use it like any other function.
Here we compose it with list and pass it off to maphash (which, for some
reason, doesn't return its results).
Triangle Generation
We'll end with a triangle-generation function from my procedural art bot:
(defun generate-universe-balancing (depth)
(gathering
(labels ((should-stop-p (iteration)
(or (= depth iteration)
(and (> iteration 6)
(randomp (map-range 0 depth
0.0 0.05
iteration)
#'rand))))
(recur (triangle &optional (iteration 0))
(if (should-stop-p iteration)
(gather triangle)
(map nil (rcurry #'recur (1+ iteration))
(split-triangle-self-balancing triangle)))))
(map nil #'recur (initial-triangles)))))This is used to generate the triangles for images like this:
Using gathering lets me write the recursive generation algorithm in a natural
way, and just plug in a simple (gather triangle) when we finally bottom out at
the base case.