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optional log base for ticks functions #233

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optional log base for ticks functions #233

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a8ac7f9
feat: add optional base to ticks functions
nickofthyme Sep 21, 2021
73a4b62
add better tests around base e and 2
nickofthyme Oct 28, 2021
e983ad4
add base to nice function
nickofthyme Oct 28, 2021
4ecda5f
update docs to reflect addition of new base argument
nickofthyme Oct 28, 2021
13793c9
add more tests for tick with different bases
nickofthyme Oct 28, 2021
a764258
remove it.only in tests
nickofthyme Oct 28, 2021
f700c34
Merge branch 'main' into tick-with-base
nickofthyme Oct 28, 2021
79c5d11
Cleanup markdown styles
nickofthyme Nov 23, 2021
28d1a03
Merge branch 'main' into tick-with-base
nickofthyme Dec 8, 2023
c6ae425
merge with changes to main and use high precision Math methods
nickofthyme Dec 8, 2023
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14 changes: 7 additions & 7 deletions README.md
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Expand Up @@ -632,23 +632,23 @@ const shuffle = d3.shuffler(random);
shuffle([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]); // returns [7, 4, 5, 3, 9, 0, 6, 1, 2, 8]
```

<a name="ticks" href="#ticks">#</a> d3.<b>ticks</b>(<i>start</i>, <i>stop</i>, <i>count</i>) · [Source](https://github.com/d3/d3-array/blob/main/src/ticks.js), [Examples](https://observablehq.com/@d3/d3-ticks)
<a name="ticks" href="#ticks">#</a> d3.<b>ticks</b>(<i>start</i>, <i>stop</i>, <i>count</i>, <i>base</i>) · [Source](https://github.com/d3/d3-array/blob/main/src/ticks.js), [Examples](https://observablehq.com/@d3/d3-ticks)

Returns an array of approximately *count* + 1 uniformly-spaced, nicely-rounded values between *start* and *stop* (inclusive). Each value is a power of ten multiplied by 1, 2 or 5. See also [d3.tickIncrement](#tickIncrement), [d3.tickStep](#tickStep) and [*linear*.ticks](https://github.com/d3/d3-scale/blob/main/README.md#linear_ticks).
Returns an array of approximately *count* + 1 uniformly-spaced, nicely-rounded values between *start* and *stop* (inclusive). Each value is a power of the *base* (default is 10) multiplied by 1, 2 or 5. See also [d3.tickIncrement](#tickIncrement), [d3.tickStep](#tickStep) and [*linear*.ticks](https://github.com/d3/d3-scale/blob/main/README.md#linear_ticks).

Ticks are inclusive in the sense that they may include the specified *start* and *stop* values if (and only if) they are exact, nicely-rounded values consistent with the inferred [step](#tickStep). More formally, each returned tick *t* satisfies *start* ≤ *t* and *t* ≤ *stop*.

<a name="tickIncrement" href="#tickIncrement">#</a> d3.<b>tickIncrement</b>(<i>start</i>, <i>stop</i>, <i>count</i>) · [Source](https://github.com/d3/d3-array/blob/main/src/ticks.js), [Examples](https://observablehq.com/@d3/d3-ticks)
<a name="tickIncrement" href="#tickIncrement">#</a> d3.<b>tickIncrement</b>(<i>start</i>, <i>stop</i>, <i>count</i>, <i>base</i>) · [Source](https://github.com/d3/d3-array/blob/main/src/ticks.js), [Examples](https://observablehq.com/@d3/d3-ticks)

Like [d3.tickStep](#tickStep), except requires that *start* is always less than or equal to *stop*, and if the tick step for the given *start*, *stop* and *count* would be less than one, returns the negative inverse tick step instead. This method is always guaranteed to return an integer, and is used by [d3.ticks](#ticks) to guarantee that the returned tick values are represented as precisely as possible in IEEE 754 floating point.

<a name="tickStep" href="#tickStep">#</a> d3.<b>tickStep</b>(<i>start</i>, <i>stop</i>, <i>count</i>) · [Source](https://github.com/d3/d3-array/blob/main/src/ticks.js), [Examples](https://observablehq.com/@d3/d3-ticks)
<a name="tickStep" href="#tickStep">#</a> d3.<b>tickStep</b>(<i>start</i>, <i>stop</i>, <i>count</i>, <i>base</i>) · [Source](https://github.com/d3/d3-array/blob/main/src/ticks.js), [Examples](https://observablehq.com/@d3/d3-ticks)

Returns the difference between adjacent tick values if the same arguments were passed to [d3.ticks](#ticks): a nicely-rounded value that is a power of ten multiplied by 1, 2 or 5. Note that due to the limited precision of IEEE 754 floating point, the returned value may not be exact decimals; use [d3-format](https://github.com/d3/d3-format) to format numbers for human consumption.
Returns the difference between adjacent tick values if the same arguments were passed to [d3.ticks](#ticks): a nicely-rounded value that is a power of the *base* (default is 10) multiplied by 1, 2 or 5. Note that due to the limited precision of IEEE 754 floating point, the returned value may not be exact decimals; use [d3-format](https://github.com/d3/d3-format) to format numbers for human consumption.

<a name="nice" href="#nice">#</a> d3.<b>nice</b>(<i>start</i>, <i>stop</i>, <i>count</i>) · [Source](https://github.com/d3/d3-array/blob/main/src/nice.js)
<a name="nice" href="#nice">#</a> d3.<b>nice</b>(<i>start</i>, <i>stop</i>, <i>count</i>, <i>base</i>) · [Source](https://github.com/d3/d3-array/blob/main/src/nice.js)

Returns a new interval [*niceStart*, *niceStop*] covering the given interval [*start*, *stop*] and where *niceStart* and *niceStop* are guaranteed to align with the corresponding [tick step](#tickStep). Like [d3.tickIncrement](#tickIncrement), this requires that *start* is less than or equal to *stop*.
Returns a new interval [*niceStart*, *niceStop*] covering the given interval [*start*, *stop*] and where *niceStart* and *niceStop* are guaranteed to align with the corresponding [tick step](#tickStep) given the provided *base* (default is 10). Like [d3.tickIncrement](#tickIncrement), this requires that *start* is less than or equal to *stop*.

<a name="range" href="#range">#</a> d3.<b>range</b>([<i>start</i>, ]<i>stop</i>[, <i>step</i>]) · [Source](https://github.com/d3/d3-array/blob/main/src/range.js), [Examples](https://observablehq.com/@d3/d3-range)

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

export default function nice(start, stop, count) {
export default function nice(start, stop, count, base) {
let prestep;
while (true) {
const step = tickIncrement(start, stop, count);
const step = tickIncrement(start, stop, count, base);
if (step === prestep || step === 0 || !isFinite(step)) {
return [start, stop];
} else if (step > 0) {
Expand Down
18 changes: 9 additions & 9 deletions src/ticks.js
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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?

Expand Up @@ -2,7 +2,7 @@ var e10 = Math.sqrt(50),
e5 = Math.sqrt(10),
e2 = Math.sqrt(2);

export default function ticks(start, stop, count) {
export default function ticks(start, stop, count, base = 10) {
var reverse,
i = -1,
n,
Expand All @@ -12,7 +12,7 @@ export default function ticks(start, stop, count) {
stop = +stop, start = +start, count = +count;
if (start === stop && count > 0) return [start];
if (reverse = stop < start) n = start, start = stop, stop = n;
if ((step = tickIncrement(start, stop, count)) === 0 || !isFinite(step)) return [];
if ((step = tickIncrement(start, stop, count, base)) === 0 || !isFinite(step)) return [];

if (step > 0) {
let r0 = Math.round(start / step), r1 = Math.round(stop / step);
Expand All @@ -34,18 +34,18 @@ export default function ticks(start, stop, count) {
return ticks;
}

export function tickIncrement(start, stop, count) {
export function tickIncrement(start, stop, count, base = 10) {
var step = (stop - start) / Math.max(0, count),
power = Math.floor(Math.log(step) / Math.LN10),
error = step / Math.pow(10, power);
power = Math.floor(Math.log(step) / Math.log(base) + Number.EPSILON),
error = step / Math.pow(base, power);
return power >= 0
? (error >= e10 ? 10 : error >= e5 ? 5 : error >= e2 ? 2 : 1) * Math.pow(10, power)
: -Math.pow(10, -power) / (error >= e10 ? 10 : error >= e5 ? 5 : error >= e2 ? 2 : 1);
? (error >= e10 ? 10 : error >= e5 ? 5 : error >= e2 ? 2 : 1) * Math.pow(base, power)
: -Math.pow(base, -power) / (error >= e10 ? 10 : error >= e5 ? 5 : error >= e2 ? 2 : 1);
}

export function tickStep(start, stop, count) {
export function tickStep(start, stop, count, base = 10) {
var step0 = Math.abs(stop - start) / Math.max(0, count),
step1 = Math.pow(10, Math.floor(Math.log(step0) / Math.LN10)),
step1 = Math.pow(base, Math.floor(Math.log(step0) / Math.log(base) + Number.EPSILON)),
error = step0 / step1;
if (error >= e10) step1 *= 10;
else if (error >= e5) step1 *= 5;
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21 changes: 21 additions & 0 deletions test/nice-test.js
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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 with base 2", () => {
assert.deepStrictEqual(nice(0.126, 0.51, 32, 2), [0.125, 0.515625]);
assert.deepStrictEqual(nice(0.126, 0.48, 10, 2), [0.125, 0.5]);
assert.deepStrictEqual(nice(0.126, 0.48, 6, 2), [0.125, 0.5]);
assert.deepStrictEqual(nice(0.126, 0.48, 5, 2), [0.125, 0.5]);
assert.deepStrictEqual(nice(0.126, 0.48, 1, 2), [0, 0.5]);
assert.deepStrictEqual(nice(129, 876, 1000, 2), [129, 876]);
assert.deepStrictEqual(nice(129, 876, 100, 2), [128, 880]);
assert.deepStrictEqual(nice(129, 876, 30, 2), [128, 896]);
assert.deepStrictEqual(nice(129, 876, 10, 2), [128, 896]);
assert.deepStrictEqual(nice(129, 876, 6, 2), [128, 896]);
assert.deepStrictEqual(nice(129, 876, 5, 2), [128, 896]);
assert.deepStrictEqual(nice(129, 876, 1, 2), [0, 1024]);
});

it("nice(start, stop, count, base) returns the expected values with base e", () => {
assert.deepStrictEqual(nice(Math.E + 0.1, Math.E * 3 + 0.1, 2, Math.E), [0, Math.E * 4]);
assert.deepStrictEqual(nice(-Math.E - 0.1, Math.E + 0.1, 2, Math.E), [-Math.E * 2, Math.E * 2]);
assert.deepStrictEqual(nice(-Math.E * 10 - 0.5, Math.E * 20 - 0.5, 30, Math.E), [-Math.E * 11, Math.E * 20]);
});
128 changes: 128 additions & 0 deletions test/tickIncrement-test.js
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Expand Up @@ -60,3 +60,131 @@ 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("base 2", () => {
assert.strictEqual(tickIncrement( 0, 1, 10, 2), -8);
assert.strictEqual(tickIncrement( 0, 1, 9, 2), -8);
assert.strictEqual(tickIncrement( 0, 1, 8, 2), -8);
assert.strictEqual(tickIncrement( 0, 1, 7, 2), -8);
assert.strictEqual(tickIncrement( 0, 1, 6, 2), -8);
assert.strictEqual(tickIncrement( 0, 1, 5, 2), -4);
assert.strictEqual(tickIncrement( 0, 1, 4, 2), -4);
assert.strictEqual(tickIncrement( 0, 1, 3, 2), -4);
assert.strictEqual(tickIncrement( 0, 1, 2, 2), -2);
assert.strictEqual(tickIncrement( 0, 1, 1, 2), 1);
assert.strictEqual(tickIncrement( 0, 10, 10, 2), 1);
assert.strictEqual(tickIncrement( 0, 10, 9, 2), 1);
assert.strictEqual(tickIncrement( 0, 10, 8, 2), 1);
assert.strictEqual(tickIncrement( 0, 10, 7, 2), 2);
assert.strictEqual(tickIncrement( 0, 10, 6, 2), 2);
assert.strictEqual(tickIncrement( 0, 10, 5, 2), 2);
assert.strictEqual(tickIncrement( 0, 10, 4, 2), 2);
assert.strictEqual(tickIncrement( 0, 10, 3, 2), 4);
assert.strictEqual(tickIncrement( 0, 10, 2, 2), 4);
assert.strictEqual(tickIncrement( 0, 10, 1, 2), 8);
assert.strictEqual(tickIncrement(-10, 10, 10, 2), 2);
assert.strictEqual(tickIncrement(-10, 10, 9, 2), 2);
assert.strictEqual(tickIncrement(-10, 10, 8, 2), 2);
assert.strictEqual(tickIncrement(-10, 10, 7, 2), 4);
assert.strictEqual(tickIncrement(-10, 10, 6, 2), 4);
assert.strictEqual(tickIncrement(-10, 10, 5, 2), 4);
assert.strictEqual(tickIncrement(-10, 10, 4, 2), 4);
assert.strictEqual(tickIncrement(-10, 10, 3, 2), 8);
assert.strictEqual(tickIncrement(-10, 10, 2, 2), 8);
assert.strictEqual(tickIncrement(-10, 10, 1, 2), 16);
});

it("base 5", () => {
assert.strictEqual(tickIncrement( 0, 1, 10, 5), -12.5);
assert.strictEqual(tickIncrement( 0, 1, 9, 5), -12.5);
assert.strictEqual(tickIncrement( 0, 1, 8, 5), -12.5);
assert.strictEqual(tickIncrement( 0, 1, 7, 5), -5);
assert.strictEqual(tickIncrement( 0, 1, 6, 5), -5);
assert.strictEqual(tickIncrement( 0, 1, 5, 5), -5);
assert.strictEqual(tickIncrement( 0, 1, 4, 5), -5);
assert.strictEqual(tickIncrement( 0, 1, 3, 5), -2.5);
assert.strictEqual(tickIncrement( 0, 1, 2, 5), -2.5);
assert.strictEqual(tickIncrement( 0, 1, 1, 5), 1);
assert.strictEqual(tickIncrement( 0, 10, 10, 5), 1);
assert.strictEqual(tickIncrement( 0, 10, 9, 5), 1);
assert.strictEqual(tickIncrement( 0, 10, 8, 5), 1);
assert.strictEqual(tickIncrement( 0, 10, 7, 5), 2);
assert.strictEqual(tickIncrement( 0, 10, 6, 5), 2);
assert.strictEqual(tickIncrement( 0, 10, 5, 5), 2);
assert.strictEqual(tickIncrement( 0, 10, 4, 5), 2);
assert.strictEqual(tickIncrement( 0, 10, 3, 5), 5);
assert.strictEqual(tickIncrement( 0, 10, 2, 5), 5);
assert.strictEqual(tickIncrement( 0, 10, 1, 5), 10);
assert.strictEqual(tickIncrement(-10, 10, 10, 5), 2);
assert.strictEqual(tickIncrement(-10, 10, 9, 5), 2);
assert.strictEqual(tickIncrement(-10, 10, 8, 5), 2);
assert.strictEqual(tickIncrement(-10, 10, 7, 5), 2);
assert.strictEqual(tickIncrement(-10, 10, 6, 5), 5);
assert.strictEqual(tickIncrement(-10, 10, 5, 5), 5);
assert.strictEqual(tickIncrement(-10, 10, 4, 5), 5);
assert.strictEqual(tickIncrement(-10, 10, 3, 5), 5);
assert.strictEqual(tickIncrement(-10, 10, 2, 5), 10);
assert.strictEqual(tickIncrement(-10, 10, 1, 5), 25);
});

it("base 10", () => {
assert.strictEqual(tickIncrement( 0, 1, 10, 10), -10);
assert.strictEqual(tickIncrement( 0, 1, 9, 10), -10);
assert.strictEqual(tickIncrement( 0, 1, 8, 10), -10);
assert.strictEqual(tickIncrement( 0, 1, 7, 10), -5);
assert.strictEqual(tickIncrement( 0, 1, 6, 10), -5);
assert.strictEqual(tickIncrement( 0, 1, 5, 10), -5);
assert.strictEqual(tickIncrement( 0, 1, 4, 10), -5);
assert.strictEqual(tickIncrement( 0, 1, 3, 10), -2);
assert.strictEqual(tickIncrement( 0, 1, 2, 10), -2);
assert.strictEqual(tickIncrement( 0, 1, 1, 10), 1);
assert.strictEqual(tickIncrement( 0, 10, 10, 10), 1);
assert.strictEqual(tickIncrement( 0, 10, 9, 10), 1);
assert.strictEqual(tickIncrement( 0, 10, 8, 10), 1);
assert.strictEqual(tickIncrement( 0, 10, 7, 10), 2);
assert.strictEqual(tickIncrement( 0, 10, 6, 10), 2);
assert.strictEqual(tickIncrement( 0, 10, 5, 10), 2);
assert.strictEqual(tickIncrement( 0, 10, 4, 10), 2);
assert.strictEqual(tickIncrement( 0, 10, 3, 10), 5);
assert.strictEqual(tickIncrement( 0, 10, 2, 10), 5);
assert.strictEqual(tickIncrement( 0, 10, 1, 10), 10);
assert.strictEqual(tickIncrement(-10, 10, 10, 10), 2);
assert.strictEqual(tickIncrement(-10, 10, 9, 10), 2);
assert.strictEqual(tickIncrement(-10, 10, 8, 10), 2);
assert.strictEqual(tickIncrement(-10, 10, 7, 10), 2);
assert.strictEqual(tickIncrement(-10, 10, 6, 10), 5);
assert.strictEqual(tickIncrement(-10, 10, 5, 10), 5);
assert.strictEqual(tickIncrement(-10, 10, 4, 10), 5);
assert.strictEqual(tickIncrement(-10, 10, 3, 10), 5);
assert.strictEqual(tickIncrement(-10, 10, 2, 10), 10);
assert.strictEqual(tickIncrement(-10, 10, 1, 10), 20);
});

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