commit d216bfc20ae501461780777a8169bc7c2c62abd9
Author: Spencer Tipping <spencer.tipping@gmail.com>
Date:   Wed Mar 8 10:57:07 2017 -0700

    Simple interpreter

diff --git a/README.md b/README.md
new file mode 100644
index 0000000..03beaa5
--- /dev/null
+++ b/README.md
@@ -0,0 +1,100 @@
+# How to write a JIT compiler
+First up, you probably don't want to. JIT, or more accurately "dynamic code
+generation," is typically not the most effective way to optimize a project, and
+common techniques end up trading away a lot of portability and require fairly
+detailed knowledge about processor-level optimization.
+
+That said, though, writing JIT compiler is a lot of fun and a great way to
+learn stuff. The first thing to do is to write an interpreter.
+
+## MandelASM
+GPUs are fine for machine learning, but serious fractal enthusiasts design
+their own processors to generate Mandelbrot sets. And the first step in
+processor design, of course, is to write an emulator for it. Our emulator will
+interpret the machine code we want to run and emit an image to stdout.
+
+To keep it simple, our processor has four complex-valued registers called `a`,
+`b`, `c`, and `d`, and it supports three in-place operations:
+
+- `=ab`: assign register `a` to register `b`
+- `+ab`: add register `a` to register `b`
+- `*ab`: multiply register `b` by register `a`
+
+For each pixel, the interpreter will zero all of the registers and then set `a`
+to the current pixel's coordinates. It then iterates the machine code for up to
+255 iterations waiting for register `b` to "overflow" (i.e. for its complex
+absolute value to exceed 2).
+
+### Simple interpreter
+The first thing to do is write up a bare-bones interpreter in C. It would be
+simpler to use `complex.h` here, but I'm going to write it in terms of
+individual numbers because the JIT compiler will end up generating the longhand
+logic. In production code we'd include bounds-checks and stuff, but I'm
+omitting those here for simplicity.
+
+```c
+// simple.c
+#include <stdio.h>
+#include <stdlib.h>
+
+#define sqr(x) ((x) * (x))
+
+typedef struct { double r; double i; } complex;
+
+void interpret(complex *registers, char const *code) {
+  complex *src, *dst;
+  double r, i;
+  for (; *code; code += 3) {
+    dst = &registers[code[2] - 'a'];
+    src = &registers[code[1] - 'a'];
+    switch (*code) {
+      case '=':
+        dst->r = src->r;
+        dst->i = src->i;
+        break;
+      case '+':
+        dst->r += src->r;
+        dst->i += src->i;
+        break;
+      case '*':
+        r = dst->r * src->r - dst->i * src->i;
+        i = dst->r * src->i + dst->i * src->r;
+        dst->r = r;
+        dst->i = i;
+        break;
+      default:
+        fprintf(stderr, "undefined instruction %s (ASCII %x)\n", code, *code);
+        exit(1);
+    }
+  }
+}
+
+int main(int argc, char **argv) {
+  complex registers[4];
+  int i, x, y;
+  printf("P2\n%d %d\n%d\n", 800, 800, 255);
+  for (y = 0; y < 800; ++y) {
+    for (x = 0; x < 800; ++x) {
+      registers[0].r = -2 + 4 * (x / 800.0);
+      registers[0].i = -2 + 4 * (y / 800.0);
+      for (i = 1; i < 4; ++i) registers[i].r = registers[i].i = 0;
+      for (i = 0; i < 255 && sqr(registers[1].r) + sqr(registers[1].i) < 4; ++i)
+        interpret(registers, argv[1]);
+      printf(" %d", 255 - i);
+    }
+    printf("\n");
+  }
+  return 0;
+}
+```
+
+Now we can see the results by using `display` from ImageMagick
+(`apt-get install imagemagick`), or by saving to a file:
+
+```sh
+$ gcc simple.c -o simple
+$ ./simple *bb+ab | display -           # imagemagick version
+$ ./simple *bb+ab > output.ppm          # save a grayscale PPM image
+```
+
+![image](http://storage8.static.itmages.com/i/17/0308/h_1488995804_6848135_3dd0ab2cdf.jpeg)
diff --git a/simple.c b/simple.c
new file mode 100644
index 0000000..04c5ebe
--- /dev/null
+++ b/simple.c
@@ -0,0 +1,53 @@
+// simple.c
+#include <stdio.h>
+#include <stdlib.h>
+
+#define sqr(x) ((x) * (x))
+
+typedef struct { double r; double i; } complex;
+
+void interpret(complex *registers, char const *code) {
+  complex *src, *dst;
+  double r, i;
+  for (; *code; code += 3) {
+    dst = &registers[code[2] - 'a'];
+    src = &registers[code[1] - 'a'];
+    switch (*code) {
+      case '=':
+        dst->r = src->r;
+        dst->i = src->i;
+        break;
+      case '+':
+        dst->r += src->r;
+        dst->i += src->i;
+        break;
+      case '*':
+        r = dst->r * src->r - dst->i * src->i;
+        i = dst->r * src->i + dst->i * src->r;
+        dst->r = r;
+        dst->i = i;
+        break;
+      default:
+        fprintf(stderr, "undefined instruction %s (ASCII %x)\n", code, *code);
+        exit(1);
+    }
+  }
+}
+
+int main(int argc, char **argv) {
+  complex registers[4];
+  int i, x, y;
+  printf("P2\n%d %d\n%d\n", 800, 800, 255);
+  for (y = 0; y < 800; ++y) {
+    for (x = 0; x < 800; ++x) {
+      registers[0].r = -2 + 4 * (x / 800.0);
+      registers[0].i = -2 + 4 * (y / 800.0);
+      for (i = 1; i < 4; ++i) registers[i].r = registers[i].i = 0;
+      for (i = 0; i < 255 && sqr(registers[1].r) + sqr(registers[1].i) < 4; ++i)
+        interpret(registers, argv[1]);
+      printf(" %d", 255 - i);
+    }
+    printf("\n");
+  }
+  return 0;
+}