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perf(morton): precompute wipe masks, minor other refactoring
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@postspectacular
postspectacular committed Dec 20, 2019
1 parent a78d07a commit 4b79950
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Showing 2 changed files with 120 additions and 56 deletions.
116 changes: 60 additions & 56 deletions packages/morton/src/zcurve.ts
View file
Original file line number Diff line number Diff line change
Expand Up @@ -11,8 +11,8 @@ type Range2_64 = Exclude<Range1_64, 1>;

/**
* Z-Curve encoder/decoder and optimized bbox range extraction for
* arbitrary dimensions. Supports max. 32bit per-component value range
* and resulting Morton codes encoded as `BigInt`.
* arbitrary dimensions (>= 2). Supports max. 32bit per-component value
* range and resulting Morton codes encoded as `BigInt`.
*/
export class ZCurve<T extends Range2_64> {
/**
Expand Down Expand Up @@ -64,39 +64,26 @@ export class ZCurve<T extends Range2_64> {

dim: T;
bits: number;
pattern: ArrayLike<number>;
masks: bigint[];
fullMask: bigint;
order: ArrayLike<number>;
masks!: bigint[];
wipeMasks!: bigint[];

/**
* @param dim - dimensions
* @param bits - number of bits per component
* @param pattern - component order
* @param order - component ordering
*/
constructor(
dim: T,
bits: Range1_32,
pattern?: ArrayLike<RangeValueMap[T]>
) {
assert(dim >= 1, `unsupported dimensions`);
constructor(dim: T, bits: Range1_32, order?: ArrayLike<RangeValueMap[T]>) {
assert(dim >= 2, `unsupported dimensions`);
assert(bits >= 1 && bits <= 32, `unsupported bits per component`);
this.dim = dim;
this.bits = bits;
if (!pattern) {
pattern = [];
for (let i = 0; i < dim; i++) (<any>pattern)[i] = <any>i;
}
this.pattern = pattern;
this.masks = [];
this.fullMask = (1n << BigInt(dim * bits)) - 1n;
for (let i = dim; --i >= 0; ) {
this.masks[i] = ZCurve.encodeComponent(
MASKS[bits],
bits,
dim,
pattern[i]
);
if (!order) {
order = [];
for (let i = 0; i < dim; i++) (<any>order)[i] = <any>i;
}
this.order = order;
this.initMasks();
}

/**
Expand All @@ -106,9 +93,9 @@ export class ZCurve<T extends Range2_64> {
*/
encode(p: ArrayLike<number>) {
let res = 0n;
const { dim, bits, pattern } = this;
const { dim, bits, order } = this;
for (let i = dim; --i >= 0; ) {
res = ZCurve.encodeComponent(p[i], bits, dim, pattern[i], res);
res = ZCurve.encodeComponent(p[i], bits, dim, order[i], res);
}
return res;
}
Expand All @@ -120,9 +107,9 @@ export class ZCurve<T extends Range2_64> {
* @param out - optional result array
*/
decode(z: bigint, out: NumericArray = []) {
const { dim, bits, pattern } = this;
const { dim, bits, order } = this;
for (let i = dim; --i >= 0; ) {
out[i] = ZCurve.decodeComponent(z, bits, dim, pattern[i]);
out[i] = ZCurve.decodeComponent(z, bits, dim, order[i]);
}
return out;
}
Expand Down Expand Up @@ -206,22 +193,25 @@ export class ZCurve<T extends Range2_64> {
const zmaxBit = zmax & mask;
const currBit = zcurr & mask;
const bitMask = 1 << ((bitPos / dim) | 0);
const offset = bitPos % dim;
if (!currBit) {
if (!zminBit && zmaxBit) {
bigmin = this.loadBits(bitMask, bitPos, zmin, offset);
zmax = this.loadBits(bitMask - 1, bitPos, zmax, offset);
} else if (zminBit && zmaxBit) {
return zmin;
} else if (zminBit && !zmaxBit) {
throw new Error("illegal BIGMIN state");
bigmin = this.loadBits(bitMask, bitPos, zmin);
zmax = this.loadBits(bitMask - 1, bitPos, zmax);
} else if (zminBit) {
if (zmaxBit) {
return zmin;
} else {
throw new Error("illegal BIGMIN state");
}
}
} else {
if (!zminBit && !zmaxBit) {
return bigmin;
} else if (!zminBit && zmaxBit) {
zmin = this.loadBits(bitMask, bitPos, zmin, offset);
} else if (zminBit && !zmaxBit) {
if (!zminBit) {
if (zmaxBit) {
zmin = this.loadBits(bitMask, bitPos, zmin);
} else {
return bigmin;
}
} else if (!zmaxBit) {
throw new Error("illegal BIGMIN state");
}
}
Expand All @@ -243,21 +233,35 @@ export class ZCurve<T extends Range2_64> {
return true;
}

protected loadBits(
mask: number,
bitPos: number,
z: bigint,
offset: number
) {
const { bits, dim } = this;
const wipeMask =
ZCurve.encodeComponent(
MASKS[bits] >>> (bits - (((bitPos / dim) | 0) + 1)),
protected initMasks() {
const { bits, dim, order } = this;
this.masks = [];
for (let i = dim; --i >= 0; ) {
this.masks[i] = ZCurve.encodeComponent(
MASKS[bits],
bits,
dim,
offset
) ^ this.fullMask;
const bitPattern = ZCurve.encodeComponent(mask, bits, dim, offset);
return (z & wipeMask) | bitPattern;
order[i]
);
}
this.wipeMasks = [];
const fullMask = (1n << BigInt(dim * bits)) - 1n;
for (let i = dim * bits; --i >= 0; ) {
this.wipeMasks[i] =
ZCurve.encodeComponent(
MASKS[bits] >>> (bits - (((i / dim) | 0) + 1)),
bits,
dim,
i % dim
) ^ fullMask;
}
}

protected loadBits(mask: number, bitPos: number, z: bigint) {
const dim = this.dim;
return (
(z & this.wipeMasks[bitPos]) |
ZCurve.encodeComponent(mask, this.bits, dim, bitPos % dim)
);
}
}
60 changes: 60 additions & 0 deletions packages/morton/test/zcurve.ts
View file
Original file line number Diff line number Diff line change
Expand Up @@ -2,6 +2,12 @@ import * as assert from "assert";
import { ZCurve } from "../src";

describe("ZCurve", () => {
it("ctor", () => {
assert.throws(() => new ZCurve(<any>1, 8));
assert.throws(() => new ZCurve(2, <any>0));
assert.throws(() => new ZCurve(2, <any>33));
});

it("range 2d (1)", () => {
const z = new ZCurve(2, 8);
assert.deepEqual(
Expand Down Expand Up @@ -47,4 +53,58 @@ describe("ZCurve", () => {
]
);
});

it("range 3d (2)", () => {
const z = new ZCurve(3, 8);
assert.deepEqual(
[...z.range([3, 2, 0], [4, 6, 1])],
[
25n,
27n,
29n,
31n,
80n,
82n,
84n,
86n,
137n,
139n,
141n,
143n,
153n,
157n,
192n,
194n,
196n,
198n,
208n,
212n
]
);
assert.deepEqual(
[...z.range([3, 2, 0], [4, 6, 1])].map((i) => z.decode(i)),
[
[3, 2, 0],
[3, 3, 0],
[3, 2, 1],
[3, 3, 1],
[4, 2, 0],
[4, 3, 0],
[4, 2, 1],
[4, 3, 1],
[3, 4, 0],
[3, 5, 0],
[3, 4, 1],
[3, 5, 1],
[3, 6, 0],
[3, 6, 1],
[4, 4, 0],
[4, 5, 0],
[4, 4, 1],
[4, 5, 1],
[4, 6, 0],
[4, 6, 1]
]
);
});
});

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