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<!DOCTYPE html>
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<title>Optimizing an Advent of Code solution in assembly</title>
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<span>Philippe Gaultier</span>
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<p><a href="/blog"> ⏴ Back to all articles</a></p>
<p class="publication-date">Published on 2023-10-05</p>
</div>
<div class="article-title">
<h1>Optimizing an Advent of Code solution in assembly</h1>
<div class="tags"> <a href="/blog/articles-by-tag.html#x86-64" class="tag">x86_64</a> <a href="/blog/articles-by-tag.html#advent-of-code" class="tag">Advent of Code</a> <a href="/blog/articles-by-tag.html#optimization" class="tag">Optimization</a> <a href="/blog/articles-by-tag.html#algorithm" class="tag">Algorithm</a> <a href="/blog/articles-by-tag.html#c" class="tag">C</a> <a href="/blog/articles-by-tag.html#lisp" class="tag">Lisp</a> <a href="/blog/articles-by-tag.html#scheme" class="tag">Scheme</a></div>
</div>
<strong>Table of contents</strong>
<ul>
<li>
<a href="#the-new-solution">The new solution</a>
</li>
<li>
<a href="#the-x86-64-implementation">The x86_64 implementation</a>
</li>
<li>
<a href="#benchmarking">Benchmarking</a>
</li>
<li>
<a href="#learnings">Learnings</a>
</li>
<li>
<a href="#appendix-the-full-code">Appendix: The full code</a>
<ul>
<li>
<a href="#the-old-c-implementation">The old C implementation</a>
</li>
<li>
<a href="#the-x64-implementation">The x64 implementation</a>
</li>
</ul>
</li>
</ul>
<p>A few days ago I was tweaking the appearance of this blog and I stumbled upon my <a href="/blog/advent_of_code_2018_5">first article</a> which is about solving a simple problem from Advent of Code. Here it is again:</p>
<blockquote>
<p>We have a string looking like this: <code>AabcdZZqQ</code> which represents a chain of
chemical units. Adjacent units of the same type (i.e letter) and opposite
polarity (i.e casing) react together and disappear.
It means we want to remove adjacent characters which are the same letter and have opposite casing, e.g
<code>Aa</code> and <code>qQ</code> disappear while <code>bc</code> and <code>ZZ</code> remain. Once we are finished, we have: <code>bcdZZ</code>.</p>
<p>The final output is the number of characters in the final string, i.e, <code>5</code>.</p>
</blockquote>
<p>Immediately, I thought I could do better than my past self:</p>
<ul>
<li>In the Lisp solution, there are lots of allocations and the code is not straightforward.</li>
<li>In the Lisp solution, we use multiple external dependencies, which usually turn out to be problematic in the long run.</li>
<li>In the C solution, there is no allocation apart from the input but we do a lot of unnecessary work.</li>
<li>In the C solution, we use <code>abs(x) == 32</code> which we could avoid by doing <code>x*x == 32*32</code>.</li>
</ul>
<p>This coincided with me listening to an interview from the VLC developers saying they wrote hundred of thousand of lines of (multi platform!) Assembly code by hand in their new AV1 decoder. I thought that was intriguing, who still writes assembly by hand in 2023? Well these guys are no idiots so I should try it as well.</p>
<h2 id="the-new-solution">
<a class="title" href="#the-new-solution">The new solution</a>
<a class="hash-anchor" href="#the-new-solution" aria-hidden="true" onclick="navigator.clipboard.writeText(this.href);"></a>
</h2>
<p>I came up with a new algorithm, which on paper does less work. It's one linear pass on the input, and does not allocate.</p>
<p>Since the result we care about is the number of remaining characters, we simply keep track of the count as we sift through the input.</p>
<p>We maintain two pointers, <code>current</code> and <code>next</code>, which we compare to decide whether we should merge the characters they point to. 'Merging' means setting the two characters to <code>0</code> (it's basically a tombstone) and lower the count.</p>
<p><code>next</code> is always incremented by one in each loop iteration, that's the easy one.</p>
<p><code>current</code> is always pointing to a character before <code>current</code>, but not always directly adjacent, because there may be tombstones, i.e. zeroes, in-between.</p>
<p>In pseudo-code:</p>
<pre><code>remaining_count = len(input)
end = input + len(input)
current = &input[0]
next = &input[1]
while next != end:
diff = *next - *current
if diff*diff == 32*32:
*current = 0
*next = 0
remaining_count -= 2
current -= 1
while current == 0:
current -= 1
endwhile
else:
current = next
endif
next += 1
endwhile
print(remaining_count)
</code></pre>
<p>The easy case is when there is no need to merge: <code>current</code> simply becomes <code>next</code> (and <code>next</code> is incremented at the end of the loop iteration).</p>
<p>The 'hard' case is merging: we set the two tombstones, lower the count, and now we are in a pickle: <code>current</code> needs to go backwards, but we do not know to where. There might be an arbitrary number of zeroes preceding the character <code>current</code> points to: the data on the left of <code>next</code> is sparse, the data on the right of <code>next</code> is not.</p>
<pre><code>[...] 0 0 A 0 0 0 0 B 0 0 0 0 C D E F [...]
^ ^ ^
| | |
target | |
current |
next
</code></pre>
<p>So we have to do a backwards search to find the first non zero character.
We could memoize this location, but that would basically come down to the Scheme solution, having an output array of the same size as the input.</p>
<p>Astute readers might have noticed a potential issue with the backwards search: We may underflow the <code>input</code> and go out of bounds! To avoid that, we could clamp <code>current</code>, but the branch misprediction is costly (an earlier implementation of mine did this and that was almost twice as slow!), and we can simplify the code as well as improve the performance by simply prefixing the <code>input</code> with a non-zero value that has no chance of being merged with the rest of the input, say, <code>1</code>.</p>
<p>Let's implement it in x86_64 assembly!</p>
<h2 id="the-x86-64-implementation">
<a class="title" href="#the-x86-64-implementation">The x86_64 implementation</a>
<a class="hash-anchor" href="#the-x86-64-implementation" aria-hidden="true" onclick="navigator.clipboard.writeText(this.href);"></a>
</h2>
<p><em>For a gentle introduction to x64 assembly, go read an <a href="/blog/x11_x64.html">earlier article</a> of mine.</em></p>
<pre><code class="language-x86asm">BITS 64
CPU X64
%define SYSCALL_EXIT 60
%define SYSCALL_WRITE 1
section .data
prefix: db 1
input: db "xPGgpXlvVLLP..." ; Truncated for readability
static input:data
%define input_len 50000
section .text
exit:
static exit:function
mov rax, SYSCALL_EXIT
mov rdi, 0
syscall
solve:
static solve:function
push rbp
mov rbp, rsp
; TODO
pop rbp
ret
global _start
_start:
call solve
call exit
</code></pre>
<p>We circumvent reading the input from a file and embed it directly in our code, something many people having their hand at Advent of Code challenges do. It is in the <code>data</code> section and not in the <code>.rodata</code> section because we are going to mutate it in place with the tombstones.</p>
<p>We also have to exit the program by ourselves since there is no libc, and we create a <code>solve</code> function which will have our logic.</p>
<p>We compile and run it so (on Linux, other OSes will be similar but slightly different):</p>
<pre><code class="language-shell">$ nasm -f elf64 -g aoc2018_5.asm && ld.lld aoc2018_5.o -static -g -o aoc2018_5
$ ./aoc2020_5
</code></pre>
<p>Which outputs nothing for now, of course.</p>
<hr />
<p>We will need to print the <code>remaining_count</code> to <code>stdout</code> at the end so we add a function to do so:</p>
<pre><code class="language-x86asm">write_int_to_stdout:
static write_int:function
push rbp
mov rbp, rsp
sub rsp, 32
%define ARG0 rdi
%define N rax
%define BUF rsi
%define BUF_LEN r10
%define BUF_END r9
lea BUF, [rsp+32]
mov BUF_LEN, 0
lea BUF_END, [rsp]
mov N, ARG0
.loop:
mov rcx, 10 ; Divisor.
mov rdx, 0 ; Reset rem.
div rcx ; rax /= rcx
add rdx, '0' ; Convert to ascii.
; *(end--) = rem
dec BUF_END
mov [BUF_END], dl
inc BUF_LEN
cmp N, 0
jnz .loop
mov rax, SYSCALL_WRITE
mov rdi, 1
mov rsi, BUF_END
mov rdx, BUF_LEN
syscall
%undef ARG0
%undef N
%undef BUF
%undef BUF_LEN
%undef BUF_END
add rsp, 32
pop rbp
ret
</code></pre>
<p>I am trying a new style of writing assembly which I saw notably the Go developers use: Since the biggest problem is that we have no named variables, we leverage the macro system from <code>nasm</code> to name the registers we work with in a human readable fashion.</p>
<p>Our <code>solve</code> function can now return a dummy number and we can print it out by passing the return value (in <code>rax</code>) of <code>solve</code> as the first argument (in <code>rdi</code>) of <code>write_int_to_stdout</code>:</p>
<pre><code class="language-x86asm">solve:
static solve:function
push rbp
mov rbp, rsp
mov rax, 123
pop rbp
ret
global _start
_start:
call solve
mov rdi, rax
call write_int_to_stdout
call exit
</code></pre>
<hr />
<p>We now can focus on implementing <code>solve</code>. It's a one to one translation of the pseudo-code. We just have to judiciously choose which registers to use based on the x64 System V ABI to avoid bookkeeping work of saving and restoring registers. For example, we use <code>rax</code> to store <code>remaining_count</code> since this will be the return value, so that we do not have to do anything special at the end of the function.</p>
<p>Another pitfall to be aware of is that since we are dealing with ASCII characters, we could use the 8 bit form of the registers. However, some opcode such as <code>imul</code> are not usable with these. We have to use the 16, 32, or 64 bit form. This does not compile:</p>
<pre><code class="language-x86asm"> mov dl, 2
imul dl, dl
</code></pre>
<p>But this does:</p>
<pre><code class="language-x86asm"> mov dx, 2
imul dx, dx
</code></pre>
<p>And so we need to zero extend the 16 bit registers in some locations with <code>movzx</code> to fill the remainder of the register with zeroes. Forgetting to do so will lead to very nasty, obscure bugs.</p>
<p>Finally, we always write loops in the form of <code>do { ... } while(condition)</code>. This is easier in our case; we assume (and know) the input is not empty, for example.</p>
<p>Here we go. Note that this function does not need any stack space, since we modify the input in place, and the standard registers are enough to store the few values we keep track of:</p>
<pre><code class="language-x86asm">solve:
static solve:function
push rbp
mov rbp, rsp
%define INPUT_LEN r10
%define CURRENT r9
%define NEXT r11
%define REMAINING_COUNT rax
%define END r8
lea CURRENT, [input]
lea NEXT, [input + 1]
mov INPUT_LEN, input_len
mov REMAINING_COUNT, INPUT_LEN
lea END, [input]
add END, INPUT_LEN
.loop:
movzx dx, BYTE [CURRENT]
movzx cx, BYTE [NEXT]
sub dx, cx
imul dx, dx
mov rcx, 32*32
cmp rdx, rcx
jnz .else
.then:
mov BYTE [CURRENT], 0
mov BYTE [NEXT], 0
sub REMAINING_COUNT, 2
.reverse_search:
dec CURRENT
mov dl, [CURRENT]
cmp dl, 0
jz .reverse_search
jmp .endif
.else:
mov CURRENT, NEXT
.endif:
inc NEXT
cmp NEXT, END
jl .loop
%undef INPUT_LEN
%undef CURRENT
%undef NEXT
%undef REMAINING_COUNT
%undef END
pop rbp
ret
</code></pre>
<h2 id="benchmarking">
<a class="title" href="#benchmarking">Benchmarking</a>
<a class="hash-anchor" href="#benchmarking" aria-hidden="true" onclick="navigator.clipboard.writeText(this.href);"></a>
</h2>
<p>So, did it work? Is it fast? Let's compare the old C solution (also embedding the input data for a fair comparison) with our new Assembly one:</p>
<pre><code class="language-sh">$ clang -Ofast -g3 -march=native aoc2018_5.c -o aoc2018_5-c
$ hyperfine --warmup 3 --shell=none ./aoc2018_5 ./aoc2018_5-c
Benchmark 1: ./aoc2018_5
Time (mean ± σ): 2.7 ms ± 1.0 ms [User: 2.4 ms, System: 0.1 ms]
Range (min … max): 1.2 ms … 4.6 ms 1174 runs
Benchmark 2: ./aoc2018_5-c
Time (mean ± σ): 5.3 ms ± 1.4 ms [User: 5.0 ms, System: 0.2 ms]
Range (min … max): 4.1 ms … 10.4 ms 442 runs
Summary
'./aoc2018_5' ran
1.95 ± 0.86 times faster than './aoc2018_5-c'
</code></pre>
<p>Yes, indeed, almost twice as fast!</p>
<h2 id="learnings">
<a class="title" href="#learnings">Learnings</a>
<a class="hash-anchor" href="#learnings" aria-hidden="true" onclick="navigator.clipboard.writeText(this.href);"></a>
</h2>
<ul>
<li>Assembly can absolutely be written by hand, although with (much) more effort and a harder time troubleshooting what goes wrong.</li>
<li>Some tools (profilers, reverse-engineering tools) expect that the assembly they consume came from a C source file and will be confused when it's not the case.</li>
<li>There is no need to reach for esoteric, vendor specific instructions (such as SIMD or Intel string opcodes) to go fast and even beat a C implementation that does a bit more work than necessary.</li>
<li>Doing less work is the most important thing when optimizing.</li>
<li>At the same time, doing a bit of work instead of memoizing can be fast(er), even though it seems counter-intuitive, due to memory latency and cache misses.</li>
<li>Having a clear idea in pseudo-code of the solution will simplify the implementation in any language.</li>
<li>Naive assembly is very fast (your CPU is crazy fast when you do not abuse it with badly written interpreted languages, seriously!), but a good compiler will emit better assembly than you if you write C or similar. Unless you are an expert like the VLC guys.</li>
</ul>
<h2 id="appendix-the-full-code">
<a class="title" href="#appendix-the-full-code">Appendix: The full code</a>
<a class="hash-anchor" href="#appendix-the-full-code" aria-hidden="true" onclick="navigator.clipboard.writeText(this.href);"></a>
</h2>
<h3 id="the-old-c-implementation">
<a class="title" href="#the-old-c-implementation">The old C implementation</a>
<a class="hash-anchor" href="#the-old-c-implementation" aria-hidden="true" onclick="navigator.clipboard.writeText(this.href);"></a>
</h3>
<details>
<summary>The full code</summary>
<pre><code class="language-c">#include <stdint.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
static char input[] =
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