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optional log base for ticks functions #233

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4 changes: 2 additions & 2 deletions src/nice.js
Original file line number Diff line number Diff line change
@@ -1,9 +1,9 @@
import {tickIncrement} from "./ticks.js";

export default function nice(start, stop, count) {
export default function nice(start, stop, count, log) {
let prestep;
while (true) {
const step = tickIncrement(start, stop, count);
const step = tickIncrement(start, stop, count, log);
if (step === prestep || step === 0 || !isFinite(step)) {
return [start, stop];
} else if (step > 0) {
Expand Down
38 changes: 24 additions & 14 deletions src/ticks.js
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@nickofthyme nickofthyme Dec 8, 2023

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Other implicit dependencies on base 10 (e.g., 2 and 5 are factors of 10, and 10 appears elsewhere in code)

Could you point me to the other parts of the code that would need to be addressed?

Original file line number Diff line number Diff line change
Expand Up @@ -2,35 +2,42 @@ const e10 = Math.sqrt(50),
e5 = Math.sqrt(10),
e2 = Math.sqrt(2);

function tickSpec(start, stop, count) {
const logParams = {
binary: [Math.log2, 2],
natural: [(n) => Math.log1p(n - 1), Math.E],
common: [Math.log10, 10],
Comment on lines +6 to +8
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In practice will probably only be used for base = 2 and base = e

Limits the log types to just common, natural and binary.

}
Comment on lines +5 to +9
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Tiny loss of precision and performance using Math.log(base) etc. instead of Math.LN10

Does this approach work for you to use the respective precise Math methods for each allowed log type?


function tickSpec(start, stop, count, log = 'common') {
const [logFn, base] = logParams[log] || logParams.common;
const step = (stop - start) / Math.max(0, count),
power = Math.floor(Math.log10(step)),
error = step / Math.pow(10, power),
factor = error >= e10 ? 10 : error >= e5 ? 5 : error >= e2 ? 2 : 1;
power = Math.floor(logFn(step)),
error = step / Math.pow(base, power),
factor = error >= e10 ? 10 : error >= e5 ? 5 : error >= e2 ? 2 : 1;
let i1, i2, inc;
if (power < 0) {
inc = Math.pow(10, -power) / factor;
inc = Math.pow(base, -power) / factor;
i1 = Math.round(start * inc);
i2 = Math.round(stop * inc);
if (i1 / inc < start) ++i1;
if (i2 / inc > stop) --i2;
inc = -inc;
} else {
inc = Math.pow(10, power) * factor;
inc = Math.pow(base, power) * factor;
i1 = Math.round(start / inc);
i2 = Math.round(stop / inc);
if (i1 * inc < start) ++i1;
if (i2 * inc > stop) --i2;
}
if (i2 < i1 && 0.5 <= count && count < 2) return tickSpec(start, stop, count * 2);
if (i2 < i1 && 0.5 <= count && count < 2) return tickSpec(start, stop, count * 2, log);
return [i1, i2, inc];
}

export default function ticks(start, stop, count) {
export default function ticks(start, stop, count, log) {
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@nickofthyme nickofthyme Dec 8, 2023

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Too many positional arguments (start, stop, count, base). Overall, I think I would prefer to keep the existing methods as-is and have base-specific variants of d3.ticks and d3.tickIncrement for base = 2 (binary) and base = e (“natural”).

I'm happy to separate these added methods into separate methods. But I'd like to avoid duplication of code. Would you be ok with having the log option on a base function then exporting a wrapped function for each log type with just start, stop and count args?

So exporting ticks, ticksNatural and ticksBinary, along with their respective tickIncrement functions.

stop = +stop, start = +start, count = +count;
if (!(count > 0)) return [];
if (start === stop) return [start];
const reverse = stop < start, [i1, i2, inc] = reverse ? tickSpec(stop, start, count) : tickSpec(start, stop, count);
const reverse = stop < start, [i1, i2, inc] = reverse ? tickSpec(stop, start, count, log) : tickSpec(start, stop, count, log);
if (!(i2 >= i1)) return [];
const n = i2 - i1 + 1, ticks = new Array(n);
if (reverse) {
Expand All @@ -43,13 +50,16 @@ export default function ticks(start, stop, count) {
return ticks;
}

export function tickIncrement(start, stop, count) {
stop = +stop, start = +start, count = +count;
return tickSpec(start, stop, count)[2];
export function tickIncrement(start, stop, count, log) {
(stop = +stop), (start = +start), (count = +count);
return tickSpec(start, stop, count, log)[2];
}

export function tickStep(start, stop, count) {
export function tickStep(start, stop, count, log) {
stop = +stop, start = +start, count = +count;
const reverse = stop < start, inc = reverse ? tickIncrement(stop, start, count) : tickIncrement(start, stop, count);
const reverse = stop < start,
inc = reverse
? tickIncrement(stop, start, count, log)
: tickIncrement(start, stop, count, log);
return (reverse ? -1 : 1) * (inc < 0 ? 1 / -inc : inc);
}
21 changes: 21 additions & 0 deletions test/nice-test.js
Original file line number Diff line number Diff line change
Expand Up @@ -44,3 +44,24 @@ it("nice(start, stop, count) returns the expected values", () => {
assert.deepStrictEqual(nice(132, 876, 5), [0, 1000]);
assert.deepStrictEqual(nice(132, 876, 1), [0, 1000]);
});

it("nice(start, stop, count, base) returns the expected values for binary log", () => {
assert.deepStrictEqual(nice(0.126, 0.51, 32, 'binary'), [0.125, 0.515625]);
assert.deepStrictEqual(nice(0.126, 0.48, 10, 'binary'), [0.125, 0.5]);
assert.deepStrictEqual(nice(0.126, 0.48, 6, 'binary'), [0.125, 0.5]);
assert.deepStrictEqual(nice(0.126, 0.48, 5, 'binary'), [0.125, 0.5]);
assert.deepStrictEqual(nice(0.126, 0.48, 1, 'binary'), [0, 0.5]);
assert.deepStrictEqual(nice(129, 876, 1000, 'binary'), [129, 876]);
assert.deepStrictEqual(nice(129, 876, 100, 'binary'), [128, 880]);
assert.deepStrictEqual(nice(129, 876, 30, 'binary'), [128, 896]);
assert.deepStrictEqual(nice(129, 876, 10, 'binary'), [128, 896]);
assert.deepStrictEqual(nice(129, 876, 6, 'binary'), [128, 896]);
assert.deepStrictEqual(nice(129, 876, 5, 'binary'), [128, 896]);
assert.deepStrictEqual(nice(129, 876, 1, 'binary'), [0, 1024]);
});

it("nice(start, stop, count, base) returns the expected values for natural log", () => {
assert.deepStrictEqual(nice(Math.E + 0.1, Math.E * 3 + 0.1, 2, 'natural'), [0, Math.E * 4]);
assert.deepStrictEqual(nice(-Math.E - 0.1, Math.E + 0.1, 2, 'natural'), [-Math.E * 2, Math.E * 2]);
assert.deepStrictEqual(nice(-Math.E * 10 - 0.5, Math.E * 20 - 0.5, 30, 'natural'), [-Math.E * 11, Math.E * 20]);
});
95 changes: 95 additions & 0 deletions test/tickIncrement-test.js
Original file line number Diff line number Diff line change
Expand Up @@ -60,3 +60,98 @@ it("tickIncrement(start, stop, count) returns approximately count + 1 tickIncrem
assert.strictEqual(tickIncrement(-10, 10, 2), 10);
assert.strictEqual(tickIncrement(-10, 10, 1), 20);
});


describe("tickIncrement(start, stop, count, base) returns approximately count + 1 tickIncrement when start < stop", () => {
it("common", () => {
assert.strictEqual(tickIncrement( 0, 1, 10), -10);
assert.strictEqual(tickIncrement( 0, 1, 9), -10);
assert.strictEqual(tickIncrement( 0, 1, 8), -10);
assert.strictEqual(tickIncrement( 0, 1, 7), -5);
assert.strictEqual(tickIncrement( 0, 1, 6), -5);
assert.strictEqual(tickIncrement( 0, 1, 5), -5);
assert.strictEqual(tickIncrement( 0, 1, 4), -5);
assert.strictEqual(tickIncrement( 0, 1, 3), -2);
assert.strictEqual(tickIncrement( 0, 1, 2), -2);
assert.strictEqual(tickIncrement( 0, 1, 1), 1);
assert.strictEqual(tickIncrement( 0, 10, 10), 1);
assert.strictEqual(tickIncrement( 0, 10, 9), 1);
assert.strictEqual(tickIncrement( 0, 10, 8), 1);
assert.strictEqual(tickIncrement( 0, 10, 7), 2);
assert.strictEqual(tickIncrement( 0, 10, 6), 2);
assert.strictEqual(tickIncrement( 0, 10, 5), 2);
assert.strictEqual(tickIncrement( 0, 10, 4), 2);
assert.strictEqual(tickIncrement( 0, 10, 3), 5);
assert.strictEqual(tickIncrement( 0, 10, 2), 5);
assert.strictEqual(tickIncrement( 0, 10, 1), 10);
assert.strictEqual(tickIncrement(-10, 10, 10), 2);
assert.strictEqual(tickIncrement(-10, 10, 9), 2);
assert.strictEqual(tickIncrement(-10, 10, 8), 2);
assert.strictEqual(tickIncrement(-10, 10, 7), 2);
assert.strictEqual(tickIncrement(-10, 10, 6), 5);
assert.strictEqual(tickIncrement(-10, 10, 5), 5);
assert.strictEqual(tickIncrement(-10, 10, 4), 5);
assert.strictEqual(tickIncrement(-10, 10, 3), 5);
assert.strictEqual(tickIncrement(-10, 10, 2), 10);
assert.strictEqual(tickIncrement(-10, 10, 1), 20);
});

it("binary", () => {
assert.strictEqual(tickIncrement(0, 1, 10, "binary"), -8);
assert.strictEqual(tickIncrement(0, 1, 9, "binary"), -8);
assert.strictEqual(tickIncrement(0, 1, 8, "binary"), -8);
assert.strictEqual(tickIncrement(0, 1, 7, "binary"), -8);
assert.strictEqual(tickIncrement(0, 1, 6, "binary"), -8);
assert.strictEqual(tickIncrement(0, 1, 5, "binary"), -4);
assert.strictEqual(tickIncrement(0, 1, 4, "binary"), -4);
assert.strictEqual(tickIncrement(0, 1, 3, "binary"), -4);
assert.strictEqual(tickIncrement(0, 1, 2, "binary"), -2);
assert.strictEqual(tickIncrement(0, 1, 1, "binary"), 1);
assert.strictEqual(tickIncrement(0, 10, 10, "binary"), 1);
assert.strictEqual(tickIncrement(0, 10, 9, "binary"), 1);
assert.strictEqual(tickIncrement(0, 10, 8, "binary"), 1);
assert.strictEqual(tickIncrement(0, 10, 7, "binary"), 2);
assert.strictEqual(tickIncrement(0, 10, 6, "binary"), 2);
assert.strictEqual(tickIncrement(0, 10, 5, "binary"), 2);
assert.strictEqual(tickIncrement(0, 10, 4, "binary"), 2);
assert.strictEqual(tickIncrement(0, 10, 3, "binary"), 4);
assert.strictEqual(tickIncrement(0, 10, 2, "binary"), 4);
assert.strictEqual(tickIncrement(0, 10, 1, "binary"), 8);
assert.strictEqual(tickIncrement(-10, 10, 10, "binary"), 2);
assert.strictEqual(tickIncrement(-10, 10, 9, "binary"), 2);
assert.strictEqual(tickIncrement(-10, 10, 8, "binary"), 2);
assert.strictEqual(tickIncrement(-10, 10, 7, "binary"), 4);
assert.strictEqual(tickIncrement(-10, 10, 6, "binary"), 4);
assert.strictEqual(tickIncrement(-10, 10, 5, "binary"), 4);
assert.strictEqual(tickIncrement(-10, 10, 4, "binary"), 4);
assert.strictEqual(tickIncrement(-10, 10, 3, "binary"), 8);
assert.strictEqual(tickIncrement(-10, 10, 2, "binary"), 8);
assert.strictEqual(tickIncrement(-10, 10, 1, "binary"), 16);
});

it("natural", () => {
assert.strictEqual(normalizeLn(tickIncrement( 0, Math.E / 100, 10, 'natural')), -1);
assert.strictEqual(normalizeLn(tickIncrement( 0, Math.E / 10, 10, 'natural')), -0.5);
assert.strictEqual(normalizeLn(tickIncrement( 0, Math.E / 10, 1, 'natural')), -0.5);
assert.strictEqual(normalizeLn(tickIncrement( 0, Math.E, 3, 'natural')), -0.5);
assert.strictEqual(normalizeLn(tickIncrement( -Math.E, Math.E, 2, 'natural')), 1);
assert.strictEqual(normalizeLn(tickIncrement( 0, Math.E * 10, 10, 'natural')), 1);
assert.strictEqual(normalizeLn(tickIncrement( 1, Math.E * 10, 10, 'natural')), 2);
assert.strictEqual(normalizeLn(tickIncrement( -Math.E * 10, Math.E * 10, 10, 'natural')), 2);
assert.strictEqual(normalizeLn(tickIncrement( Math.E, Math.E * 100, 10, 'natural')), 1);
assert.strictEqual(normalizeLn(tickIncrement( -Math.E * 100, Math.E * 100, 10, 'natural')), 2);
assert.strictEqual(normalizeLn(tickIncrement( 0, Math.E * 100, 10, 'natural')), 1);
assert.strictEqual(tickIncrement( 0, 10, 10, 'natural'), 1);
assert.strictEqual(tickIncrement( -10, 10, 10, 'natural'), 2);
});
})

export function normalizeLn(value) {
let tries = 0, normValue = value;
while (tries++ < 10 && normValue % 0.5 !== 0) normValue *= Math.E;
if (tries > 10) {
tries = 0, normValue = value
while (tries++ < 10 && normValue % 0.5 !== 0) normValue /= Math.E;
}
return tries > 10 ? NaN : normValue;
}
116 changes: 116 additions & 0 deletions test/tickStep-test.js
Original file line number Diff line number Diff line change
@@ -1,4 +1,5 @@
import assert from "assert";
import {normalizeLn} from "./tickIncrement-test.js";
import {tickStep} from "../src/index.js";

it("tickStep(start, stop, count) returns NaN if any argument is NaN", () => {
Expand Down Expand Up @@ -93,3 +94,118 @@ it("tickStep(start, stop, count) returns -tickStep(stop, start, count)", () => {
assert.strictEqual(tickStep(-10, 10, 2), -tickStep(10, -10, 2));
assert.strictEqual(tickStep(-10, 10, 1), -tickStep(10, -10, 1));
});

it("tickStep(start, stop, count, base) with binary log returns approximately count + 1 tickStep when start < stop", () => {
assert.strictEqual(tickStep( 0, 1, 10, 'binary'), 0.125);
assert.strictEqual(tickStep( 0, 1, 9, 'binary'), 0.125);
assert.strictEqual(tickStep( 0, 1, 8, 'binary'), 0.125);
assert.strictEqual(tickStep( 0, 1, 7, 'binary'), 0.125);
assert.strictEqual(tickStep( 0, 1, 6, 'binary'), 0.125);
assert.strictEqual(tickStep( 0, 1, 5, 'binary'), 0.25);
assert.strictEqual(tickStep( 0, 1, 4, 'binary'), 0.25);
assert.strictEqual(tickStep( 0, 1, 3, 'binary'), 0.25);
assert.strictEqual(tickStep( 0, 1, 2, 'binary'), 0.5);
assert.strictEqual(tickStep( 0, 1, 1, 'binary'), 1);
assert.strictEqual(tickStep( 0, 10, 10, 'binary'), 1);
assert.strictEqual(tickStep( 0, 10, 9, 'binary'), 1);
assert.strictEqual(tickStep( 0, 10, 8, 'binary'), 1);
assert.strictEqual(tickStep( 0, 10, 7, 'binary'), 2);
assert.strictEqual(tickStep( 0, 10, 6, 'binary'), 2);
assert.strictEqual(tickStep( 0, 10, 5, 'binary'), 2);
assert.strictEqual(tickStep( 0, 10, 4, 'binary'), 2);
assert.strictEqual(tickStep( 0, 10, 3, 'binary'), 4);
assert.strictEqual(tickStep( 0, 10, 2, 'binary'), 4);
assert.strictEqual(tickStep( 0, 10, 1, 'binary'), 8);
assert.strictEqual(tickStep(-10, 10, 10, 'binary'), 2);
assert.strictEqual(tickStep(-10, 10, 9, 'binary'), 2);
assert.strictEqual(tickStep(-10, 10, 8, 'binary'), 2);
assert.strictEqual(tickStep(-10, 10, 7, 'binary'), 4);
assert.strictEqual(tickStep(-10, 10, 6, 'binary'), 4);
assert.strictEqual(tickStep(-10, 10, 5, 'binary'), 4);
assert.strictEqual(tickStep(-10, 10, 4, 'binary'), 4);
assert.strictEqual(tickStep(-10, 10, 3, 'binary'), 8);
assert.strictEqual(tickStep(-10, 10, 2, 'binary'), 8);
assert.strictEqual(tickStep(-10, 10, 1, 'binary'), 16);
});

it("tickStep(start, stop, count, base) with natural log returns approximately count + 1 tickStep when start < stop", () => {
assert.strictEqual(normalizeLn(tickStep( 0, Math.E / 100, 10, 'natural')), 1);
assert.strictEqual(normalizeLn(tickStep( 0, Math.E / 10, 10, 'natural')), 2);
assert.strictEqual(normalizeLn(tickStep( 0, Math.E / 10, 1, 'natural')), 2);
assert.strictEqual(normalizeLn(tickStep( 0, Math.E, 3, 'natural')), 2);
assert.strictEqual(normalizeLn(tickStep( -Math.E, Math.E, 2, 'natural')), 1);
assert.strictEqual(normalizeLn(tickStep( 0, Math.E * 10, 10, 'natural')), 1);
assert.strictEqual(normalizeLn(tickStep( 1, Math.E * 10, 10, 'natural')), 2);
assert.strictEqual(normalizeLn(tickStep( -Math.E * 10, Math.E * 10, 10, 'natural')), 2);
assert.strictEqual(normalizeLn(tickStep( Math.E, Math.E * 100, 10, 'natural')), 1);
assert.strictEqual(normalizeLn(tickStep( -Math.E * 100, Math.E * 100, 10, 'natural')), 2);
assert.strictEqual(normalizeLn(tickStep( 0, Math.E * 100, 10, 'natural')), 1);
assert.strictEqual(tickStep( 0, 10, 10, 'natural'), 1);
assert.strictEqual(tickStep( -10, 10, 10, 'natural'), 2);
});

it("tickStep(start, stop, count, base) with binary log returns -tickStep(stop, start, count)", () => {
assert.strictEqual(tickStep( 0, 1, 10, 'binary'), -tickStep( 1, 0, 10, 'binary'));
assert.strictEqual(tickStep( 0, 1, 9, 'binary'), -tickStep( 1, 0, 9, 'binary'));
assert.strictEqual(tickStep( 0, 1, 8, 'binary'), -tickStep( 1, 0, 8, 'binary'));
assert.strictEqual(tickStep( 0, 1, 7, 'binary'), -tickStep( 1, 0, 7, 'binary'));
assert.strictEqual(tickStep( 0, 1, 6, 'binary'), -tickStep( 1, 0, 6, 'binary'));
assert.strictEqual(tickStep( 0, 1, 5, 'binary'), -tickStep( 1, 0, 5, 'binary'));
assert.strictEqual(tickStep( 0, 1, 4, 'binary'), -tickStep( 1, 0, 4, 'binary'));
assert.strictEqual(tickStep( 0, 1, 3, 'binary'), -tickStep( 1, 0, 3, 'binary'));
assert.strictEqual(tickStep( 0, 1, 2, 'binary'), -tickStep( 1, 0, 2, 'binary'));
assert.strictEqual(tickStep( 0, 1, 1, 'binary'), -tickStep( 1, 0, 1, 'binary'));
assert.strictEqual(tickStep( 0, 10, 10, 'binary'), -tickStep(10, 0, 10, 'binary'));
assert.strictEqual(tickStep( 0, 10, 9, 'binary'), -tickStep(10, 0, 9, 'binary'));
assert.strictEqual(tickStep( 0, 10, 8, 'binary'), -tickStep(10, 0, 8, 'binary'));
assert.strictEqual(tickStep( 0, 10, 7, 'binary'), -tickStep(10, 0, 7, 'binary'));
assert.strictEqual(tickStep( 0, 10, 6, 'binary'), -tickStep(10, 0, 6, 'binary'));
assert.strictEqual(tickStep( 0, 10, 5, 'binary'), -tickStep(10, 0, 5, 'binary'));
assert.strictEqual(tickStep( 0, 10, 4, 'binary'), -tickStep(10, 0, 4, 'binary'));
assert.strictEqual(tickStep( 0, 10, 3, 'binary'), -tickStep(10, 0, 3, 'binary'));
assert.strictEqual(tickStep( 0, 10, 2, 'binary'), -tickStep(10, 0, 2, 'binary'));
assert.strictEqual(tickStep( 0, 10, 1, 'binary'), -tickStep(10, 0, 1, 'binary'));
assert.strictEqual(tickStep(-10, 10, 10, 'binary'), -tickStep(10, -10, 10, 'binary'));
assert.strictEqual(tickStep(-10, 10, 9, 'binary'), -tickStep(10, -10, 9, 'binary'));
assert.strictEqual(tickStep(-10, 10, 8, 'binary'), -tickStep(10, -10, 8, 'binary'));
assert.strictEqual(tickStep(-10, 10, 7, 'binary'), -tickStep(10, -10, 7, 'binary'));
assert.strictEqual(tickStep(-10, 10, 6, 'binary'), -tickStep(10, -10, 6, 'binary'));
assert.strictEqual(tickStep(-10, 10, 5, 'binary'), -tickStep(10, -10, 5, 'binary'));
assert.strictEqual(tickStep(-10, 10, 4, 'binary'), -tickStep(10, -10, 4, 'binary'));
assert.strictEqual(tickStep(-10, 10, 3, 'binary'), -tickStep(10, -10, 3, 'binary'));
assert.strictEqual(tickStep(-10, 10, 2, 'binary'), -tickStep(10, -10, 2, 'binary'));
assert.strictEqual(tickStep(-10, 10, 1, 'binary'), -tickStep(10, -10, 1, 'binary'));
});

it("tickStep(start, stop, count, base) with natural log returns -tickStep(stop, start, count)", () => {
assert.strictEqual(tickStep( 0, 1, 10, 'natural'), -tickStep( 1, 0, 10, 'natural'));
assert.strictEqual(tickStep( 0, 1, 9, 'natural'), -tickStep( 1, 0, 9, 'natural'));
assert.strictEqual(tickStep( 0, 1, 8, 'natural'), -tickStep( 1, 0, 8, 'natural'));
assert.strictEqual(tickStep( 0, 1, 7, 'natural'), -tickStep( 1, 0, 7, 'natural'));
assert.strictEqual(tickStep( 0, 1, 6, 'natural'), -tickStep( 1, 0, 6, 'natural'));
assert.strictEqual(tickStep( 0, 1, 5, 'natural'), -tickStep( 1, 0, 5, 'natural'));
assert.strictEqual(tickStep( 0, 1, 4, 'natural'), -tickStep( 1, 0, 4, 'natural'));
assert.strictEqual(tickStep( 0, 1, 3, 'natural'), -tickStep( 1, 0, 3, 'natural'));
assert.strictEqual(tickStep( 0, 1, 2, 'natural'), -tickStep( 1, 0, 2, 'natural'));
assert.strictEqual(tickStep( 0, 1, 1, 'natural'), -tickStep( 1, 0, 1, 'natural'));
assert.strictEqual(tickStep( 0, 10, 10, 'natural'), -tickStep(10, 0, 10, 'natural'));
assert.strictEqual(tickStep( 0, 10, 9, 'natural'), -tickStep(10, 0, 9, 'natural'));
assert.strictEqual(tickStep( 0, 10, 8, 'natural'), -tickStep(10, 0, 8, 'natural'));
assert.strictEqual(tickStep( 0, 10, 7, 'natural'), -tickStep(10, 0, 7, 'natural'));
assert.strictEqual(tickStep( 0, 10, 6, 'natural'), -tickStep(10, 0, 6, 'natural'));
assert.strictEqual(tickStep( 0, 10, 5, 'natural'), -tickStep(10, 0, 5, 'natural'));
assert.strictEqual(tickStep( 0, 10, 4, 'natural'), -tickStep(10, 0, 4, 'natural'));
assert.strictEqual(tickStep( 0, 10, 3, 'natural'), -tickStep(10, 0, 3, 'natural'));
assert.strictEqual(tickStep( 0, 10, 2, 'natural'), -tickStep(10, 0, 2, 'natural'));
assert.strictEqual(tickStep( 0, 10, 1, 'natural'), -tickStep(10, 0, 1, 'natural'));
assert.strictEqual(tickStep(-10, 10, 10, 'natural'), -tickStep(10, -10, 10, 'natural'));
assert.strictEqual(tickStep(-10, 10, 9, 'natural'), -tickStep(10, -10, 9, 'natural'));
assert.strictEqual(tickStep(-10, 10, 8, 'natural'), -tickStep(10, -10, 8, 'natural'));
assert.strictEqual(tickStep(-10, 10, 7, 'natural'), -tickStep(10, -10, 7, 'natural'));
assert.strictEqual(tickStep(-10, 10, 6, 'natural'), -tickStep(10, -10, 6, 'natural'));
assert.strictEqual(tickStep(-10, 10, 5, 'natural'), -tickStep(10, -10, 5, 'natural'));
assert.strictEqual(tickStep(-10, 10, 4, 'natural'), -tickStep(10, -10, 4, 'natural'));
assert.strictEqual(tickStep(-10, 10, 3, 'natural'), -tickStep(10, -10, 3, 'natural'));
assert.strictEqual(tickStep(-10, 10, 2, 'natural'), -tickStep(10, -10, 2, 'natural'));
assert.strictEqual(tickStep(-10, 10, 1, 'natural'), -tickStep(10, -10, 1, 'natural'));
});
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