make bins faster by quantization (#220)

* make bins faster by quantization

ref. observablehq/plot#454

* better fractional step

* fix quantization for custom domains

Co-authored-by: Mike Bostock <mbostock@gmail.com>

src/bin.js

@@ -18,6 +18,7 @@ export default function bin() {
     var i,
         n = data.length,
         x,
+        step,
         values = new Array(n);
 
     for (i = 0; i < n; ++i) {
@@ -36,6 +37,11 @@ export default function bin() {
       if (domain === extent) [x0, x1] = nice(x0, x1, tn);
       tz = ticks(x0, x1, tn);
 
+      // If the domain is aligned with the first tick (which it will by
+      // default), then we can use quantization rather than bisection to bin
+      // values, which is substantially faster.
+      if (tz[0] <= x0) step = tickIncrement(x0, x1, tn);
+
       // If the last threshold is coincident with the domain’s upper bound, the
       // last bin will be zero-width. If the default domain is used, and this
       // last threshold is coincident with the maximum input value, we can
@@ -75,10 +81,25 @@ export default function bin() {
     }
 
     // Assign data to bins by value, ignoring any outside the domain.
-    for (i = 0; i < n; ++i) {
-      x = values[i];
-      if (x != null && x0 <= x && x <= x1) {
-        bins[bisect(tz, x, 0, m)].push(data[i]);
+    if (isFinite(step)) {
+      if (step > 0) {
+        for (i = 0; i < n; ++i) {
+          if ((x = values[i]) != null && x0 <= x && x <= x1) {
+            bins[Math.floor((x - x0) / step)].push(data[i]);
+          }
+        }
+      } else if (step < 0) {
+        for (i = 0; i < n; ++i) {
+          if ((x = values[i]) != null && x0 <= x && x <= x1) {
+            bins[Math.floor((x0 - x) * step)].push(data[i]);
+          }
+        }
+      }
+    } else {
+      for (i = 0; i < n; ++i) {
+        if ((x = values[i]) != null && x0 <= x && x <= x1) {
+          bins[bisect(tz, x, 0, m)].push(data[i]);
+        }
       }
     }
 

test/bin-test.js

@@ -164,6 +164,48 @@ it("bin()() returns bins whose rightmost bin is not too wide", () => {
   ]);
 });
 
+it("bin(data) handles fractional step correctly", () => {
+  const h = bin().thresholds(10);
+  assert.deepStrictEqual(h([9.8, 10, 11, 12, 13, 13.2]), [
+    box([9.8], 9.5, 10),
+    box([10], 10, 10.5),
+    box([], 10.5, 11),
+    box([11], 11, 11.5),
+    box([], 11.5, 12),
+    box([12], 12, 12.5),
+    box([], 12.5, 13),
+    box([13, 13.2], 13, 13.5)
+  ]);
+});
+
+it("bin(data) handles fractional step correctly with a custom, non-aligned domain", () => {
+  const h = bin().thresholds(10).domain([9.7, 13.3]);
+  assert.deepStrictEqual(h([9.8, 10, 11, 12, 13, 13.2]), [
+    box([9.8], 9.7, 10),
+    box([10], 10, 10.5),
+    box([], 10.5, 11),
+    box([11], 11, 11.5),
+    box([], 11.5, 12),
+    box([12], 12, 12.5),
+    box([], 12.5, 13),
+    box([13, 13.2], 13, 13.3)
+  ]);
+});
+
+it("bin(data) handles fractional step correctly with a custom, aligned domain", () => {
+  const h = bin().thresholds(10).domain([9.5, 13.5]);
+  assert.deepStrictEqual(h([9.8, 10, 11, 12, 13, 13.2]), [
+    box([9.8], 9.5, 10),
+    box([10], 10, 10.5),
+    box([], 10.5, 11),
+    box([11], 11, 11.5),
+    box([], 11.5, 12),
+    box([12], 12, 12.5),
+    box([], 12.5, 13),
+    box([13, 13.2], 13, 13.5)
+  ]);
+});
+
 it("bin(data) coerces values to numbers as expected", () => {
   const h = bin().thresholds(10);
   assert.deepStrictEqual(h(["1", "2", "3", "4", "5"]), [