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charts.ticks

Axis ticks: a round step (1, 2 or 5 x 10^k), the ticks on it, and calendar ticks from days to years.

1.0.0 · published 2026-10-03 by charlie · Anterra

Pinned by 57 tests, run in TypeScript, Python and Rust.tickStep 16 · niceTicks 12 · timeTickInterval 12 · timeTicks 17

What it does

Where the ticks on an axis go. `niceTicks(0, 1, 10)` is `[0, 0.1, ..., 1]`, `timeTicks("2026-01-01", "2026-12-31", "month", 3)` is the four quarter starts, and `tickStep` and `timeTickInterval` say what spacing to use for about `count` ticks. This is a group: the four functions are the tick half of an axis, used with `charts.scale` and `charts.format`.

## Number ticks

The functions

A group: 4 functions that work together, each in its own file, each pinned by its own tests in TypeScript, Python and Rust. A project can install only the ones it calls.

  1. tick_step (start: float, stop: float, count: int) -> float
  2. nice_ticks (start: float, stop: float, count: int) -> float[]
  3. time_tick_interval (start: date, stop: date, count: int) -> TimeTickInterval
  4. time_ticks (start: date, stop: date, interval: TimeInterval, step: int) -> date[]

The types it declares, generated into your project

TimeInterval = Literal["day", "week", "month", "quarter", "year"]

@dataclass(frozen=True)
class TimeTickInterval:
    """A calendar interval and how many of it between ticks."""

    interval: TimeInterval
    #: 1 or more
    step: int

Once installed, your code imports each one from the group's module.

tick_step throws on bad input 16 tests

def tick_step(start: float, stop: float, count: int) -> float
startfloat
stopfloat
countintroughly how many ticks are wanted, at least 1
returnsfloat1, 2 or 5 times a power of ten, exactly the nearest double to it (0.1, not 0.1000000000000001); 0 when start equals stop

For example

  • tick_step(0, 10, 10) → 1 ten ticks over ten
  • tick_step(0, 100, 10) → 10 ten ticks over a hundred
  • tick_step(0, 1, 10) → 0.1 a tenth, exactly the double 0.1
from fune.charts.ticks import tick_step  # charts.ticks@^1
impl/python/tick_step.py · 45 lines · open · raw
import math
from typing import Tuple


def tick_step(start: float, stop: float, count: int) -> float:
    """The tick step for about count ticks: 1, 2 or 5 times a power of ten,
    as d3-array's tickIncrement chooses it, found without log10 and returned
    as one correctly rounded division so 0.2 is exactly the double 0.2."""
    mul, div = tick_spec(start, stop, count)
    return mul / div


# Exported for nice_ticks, which needs the step as a multiplier or a divisor.


def tick_spec(start: float, stop: float, count: int) -> Tuple[float, float]:
    """The step as (multiplier, divisor), one of which is 1; (0, 1) when start equals stop."""
    for v in (start, stop):
        if isinstance(v, bool) or not isinstance(v, (int, float)) or not math.isfinite(v):
            raise ValueError(f"start and stop must be finite numbers; got {start} and {stop}")
    if isinstance(count, bool) or not isinstance(count, int) or count < 1:
        raise ValueError(f"count must be a whole number of at least 1, got {count}")
    raw = abs(float(stop) - float(start)) / count
    if raw == 0:
        return 0.0, 1.0
    if raw >= 1:
        power = 1.0
        while power * 10 <= raw:
            power *= 10
        return _nice_factor(raw / power) * power, 1.0
    inverse = 1.0
    while raw * inverse < 1:
        inverse *= 10
    factor = _nice_factor(raw * inverse)
    return (1.0, 1.0) if factor == inverse else (1.0, inverse / factor)


def _nice_factor(error: float) -> float:
    if error >= math.sqrt(50):
        return 10.0
    if error >= math.sqrt(10):
        return 5.0
    if error >= math.sqrt(2):
        return 2.0
    return 1.0

nice_ticks throws on bad input 12 tests

def nice_ticks(start: float, stop: float, count: int) -> List[float]
startfloat
stopfloat
countintroughly how many ticks are wanted, at least 1
returnsfloat[]the multiples of tickStep between start and stop inclusive, running from start towards stop

For example

  • nice_ticks(0, 10, 5) → 0, 2, 4, 6, 8, 10 steps of two
  • nice_ticks(0, 1, 10) → 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1 tenths are exact: the fourth tick is 0.3, not 0.30000000000000004
  • nice_ticks(0.13, 0.87, 5) → 0.2, 0.4, 0.6, 0.8 ticks inside a messy extent
from fune.charts.ticks import nice_ticks  # charts.ticks@^1
impl/python/nice_ticks.py · 47 lines · open · raw

Imports name this capability’s declared dependencies, which fune builds next to it in your project; each one links to its page.

from typing import List, Tuple

from .charts_ticks_tick_step import tick_spec  ← tickStep, another function of this group · built into the same file, even by a slim install
from .math_round_float import round_float  ← from math.round-float ^1.0.0 · built alongside by fune


def nice_ticks(start: float, stop: float, count: int) -> List[float]:
    """Ticks at round values between start and stop, as d3.ticks, each one
    exact operation on a whole number (i * step or i / divisor), so 0.1 steps
    give 0.3 and not 0.30000000000000004."""
    mul, div = tick_spec(start, stop, count)
    if start == stop:
        return [float(start) + 0.0]
    reverse = stop < start
    lo = float(stop if reverse else start)
    hi = float(start if reverse else stop)
    i1, i2 = _indexes(lo, hi, mul, div)
    if i2 < i1 and count == 1:
        # No multiple of the step for one tick falls inside; d3 retries with two.
        mul, div = tick_spec(start, stop, 2)
        i1, i2 = _indexes(lo, hi, mul, div)
    ticks = []
    i = i1
    while i <= i2:
        ticks.append((i / div if div > 1 else i * mul) + 0.0)
        i += 1
    if reverse:
        ticks.reverse()
    return ticks


def _indexes(lo: float, hi: float, mul: float, div: float) -> Tuple[float, float]:
    if div > 1:
        i1 = round_float(lo * div, 0)
        i2 = round_float(hi * div, 0)
        if i1 / div < lo:
            i1 += 1
        if i2 / div > hi:
            i2 -= 1
        return i1, i2
    i1 = round_float(lo / mul, 0)
    i2 = round_float(hi / mul, 0)
    if i1 * mul < lo:
        i1 += 1
    if i2 * mul > hi:
        i2 -= 1
    return i1, i2

time_tick_interval throws on bad input 12 tests

def time_tick_interval(start: str, stop: str, count: int) -> TimeTickInterval
startdate
stopdate
countintroughly how many ticks are wanted, at least 1
returnsTimeTickInterval

For example

  • time_tick_interval(2026-01-01, 2026-01-11, 10) → interval day, step 1 ten days, ten ticks: daily
  • time_tick_interval(2026-01-01, 2026-01-31, 10) → interval day, step 2 a month, ten ticks: every other day
  • time_tick_interval(2026-01-01, 2026-04-01, 10) → interval week, step 1 a quarter, ten ticks: weekly
from fune.charts.ticks import time_tick_interval  # charts.ticks@^1
impl/python/time_tick_interval.py · 33 lines · open · raw

Imports name this capability’s declared dependencies, which fune builds next to it in your project; each one links to its page.

from .charts_ticks_tick_step import tick_step  ← tickStep, another function of this group · built into the same file, even by a slim install
from .charts_ticks_types import TimeTickInterval
from .dates_add_days import epoch_day_from_iso  ← from dates.add-days ^1.0.0 · built alongside by fune

# d3-scale's calendar ladder, from a day up, with the lengths in days it
# compares against: a month counts as 30, a quarter as 90, a year as 365.
_LADDER = [
    ("day", 1, 1),
    ("day", 2, 2),
    ("week", 1, 7),
    ("month", 1, 30),
    ("quarter", 1, 90),
    ("year", 1, 365),
]


def time_tick_interval(start: str, stop: str, count: int) -> TimeTickInterval:
    """The calendar interval for about count ticks between two dates, as d3's
    time scale picks it: the nearest rung of the ladder by ratio, or whole
    years in steps of 1, 2 or 5 x 10^k beyond a year."""
    if isinstance(count, bool) or not isinstance(count, int) or count < 1:
        raise ValueError(f"count must be a whole number of at least 1, got {count}")
    span = abs(epoch_day_from_iso(stop) - epoch_day_from_iso(start))
    target = span / count
    i = 0
    while i < len(_LADDER) and _LADDER[i][2] <= target:
        i += 1
    if i == len(_LADDER):
        return TimeTickInterval(interval="year", step=max(1, int(tick_step(0, span / 365, count))))
    if i == 0:
        return TimeTickInterval(interval="day", step=1)
    pick = _LADDER[i - 1] if target / _LADDER[i - 1][2] < _LADDER[i][2] / target else _LADDER[i]
    return TimeTickInterval(interval=pick[0], step=pick[1])

time_ticks throws on bad input 17 tests

def time_ticks(start: str, stop: str, interval: TimeInterval, step: int) -> List[str]
startdate
stopdate
intervalTimeIntervalday, week (Mondays), month, quarter or year
stepintevery step-th boundary, at least 1: day 2 is the 1st, 3rd, 5th... of each month; month 3 is January, April, July, October
returnsdate[]the boundaries between start and stop inclusive, running from start towards stop

For example

  • time_ticks(2026-01-30, 2026-02-02, day, 1) → 2026-01-30, 2026-01-31, 2026-02-01, 2026-02-02 every day across a month end
  • time_ticks(2026-01-28, 2026-02-04, day, 2) → 2026-01-29, 2026-01-31, 2026-02-01, 2026-02-03 every other day follows the day of the month, restarting on the 1st
  • time_ticks(2024-02-28, 2024-03-01, day, 1) → 2024-02-28, 2024-02-29, 2024-03-01 a leap day
from fune.charts.ticks import time_ticks  # charts.ticks@^1
impl/python/time_ticks.py · 64 lines · open · raw

Imports name this capability’s declared dependencies, which fune builds next to it in your project; each one links to its page.

from typing import List

from .charts_ticks_types import TimeInterval
from .dates_add_days import civil_from_days, days_from_civil, epoch_day_from_iso, iso_from_epoch_day  ← from dates.add-days ^1.0.0 · built alongside by fune

# 1970-01-05, the first Monday on or after the epoch, as a day number.
_FIRST_MONDAY = 4
_MAX_TICKS = 10000


def _ceil_div(a: int, b: int) -> int:
    return -((-a) // b)


def time_ticks(start: str, stop: str, interval: TimeInterval, step: int) -> List[str]:
    """Calendar boundaries between two dates, inclusive, anchored to the
    calendar rather than to start so that panning does not move them: days by
    (day - 1) % step, weeks since 1970-01-05, months by (month - 1) % step,
    quarters by quarter of the year, years by year % step."""
    if isinstance(step, bool) or not isinstance(step, int) or step < 1:
        raise ValueError(f"step must be a whole number of at least 1, got {step}")
    a = epoch_day_from_iso(start)
    b = epoch_day_from_iso(stop)
    reverse = b < a
    lo, hi = (b, a) if reverse else (a, b)
    days: List[int] = []

    def add(day: int) -> None:
        if len(days) >= _MAX_TICKS:
            raise ValueError(f"too many ticks: more than {_MAX_TICKS}; use a longer interval or step")
        days.append(day)

    if interval == "day":
        for d in range(lo, hi + 1):
            if (civil_from_days(d).day - 1) % step == 0:
                add(d)
    elif interval == "week":
        k = _ceil_div(lo - _FIRST_MONDAY, 7)
        k = _ceil_div(k, step) * step
        d = _FIRST_MONDAY + 7 * k
        while d <= hi:
            add(d)
            d += 7 * step
    elif interval in ("month", "quarter", "year"):
        months = step if interval == "month" else 3 * step if interval == "quarter" else 12
        first = civil_from_days(lo)
        year, month = first.year, first.month
        while True:
            d = days_from_civil(year, month, 1)
            if d > hi:
                break
            on_step = (month == 1 and year % step == 0) if interval == "year" else (month - 1) % months == 0
            if d >= lo and on_step:
                add(d)
            month += 1
            if month > 12:
                month = 1
                year += 1
    else:
        raise ValueError(f'unknown time interval "{interval}"')
    ticks = [iso_from_epoch_day(d) for d in days]
    if reverse:
        ticks.reverse()
    return ticks

Install

fune build

With that line in your source, in a Python project (language python in fune.project), fune build resolves it and its 2 dependencies, pins them in fune.lock, downloads only the Python package of each, and builds the code above into your project’s .fune/build, one readable file per capability with a header linking back here. Or pin a range in fune.project and build in one step:

fune add charts.ticks

That builds the whole group. To build only what you call, and whatever it uses inside the group:

fune add charts.ticks --only tickStep
Download for Python charts.ticks-1.0.0-python.fune · 25,207 bytes sha256 2f681fcbfc0375c58129a8b49979f68b8b97a8cc14447b32148a684ed4c578d4

The manifest, vectors and README with only the Python implementation. Install it without the registry with fune add ./charts.ticks-1.0.0-python.fune, or fetch it from a terminal with fune pull charts.ticks@1.0.0:python.

The whole function, every language, is one file too: charts.ticks-1.0.0.fune, 42,760 bytes, sha256 c5ce85e5c19c171b83a7de93b99f92ae8d636f869f8cc071d3ef2bb16c333991. It installs into a project of any language.

Customise it in your app

The seams this capability offers. Put a marker directly above a function of your own and fune build wires it into the built code; the package on the registry is not changed, the built file’s header lists it under CUSTOMISED, and fune hooks lists every hook in the project. How hooks work.

before — your function gets the arguments and returns them, changed or not, or throws to refuse the call.

# fune: before charts.ticks.tickStep
# fune: before charts.ticks.niceTicks
# fune: before charts.ticks.timeTickInterval
# fune: before charts.ticks.timeTicks

after — your function gets the result and the arguments, and returns the final result.

# fune: after charts.ticks.tickStep
# fune: after charts.ticks.niceTicks
# fune: after charts.ticks.timeTickInterval
# fune: after charts.ticks.timeTicks

replace — inside this capability’s code only, calls to a dependency go to your function, with the same signature. Other capabilities that use it are unaffected; write in * to replace it everywhere.

# fune: replace dates.add-days in charts.ticks
# fune: replace math.round-float in charts.ticks

step — your function runs at a numbered point inside a function’s body, receives the in-scope values it names as parameters, and may return replacements. List the points with fune show charts.ticks --steps.

# fune: step charts.ticks.<fn> after <n|label>

Tests

A version published now needs at least 8 tests for every function, and one that expects the error for each function that throws; the registry refuses it otherwise. fune verify --all runs each case in TypeScript, Python and Rust, and a project runs them again with fune verify. This page lists the cases; it does not run them. The exact JSON is vectors.json.

tickStep 16 tests

CaseArgumentsExpected
ten ticks over ten 0, 10, 10 → 1
ten ticks over a hundred 0, 100, 10 → 10
a tenth, exactly the double 0.1 0, 1, 10 → 0.1
a fifth, as 1/5 rather than 0.1 * 2 0, 1, 5 → 0.2
9.7 rounds up to 10 0, 97, 10 → 10
3.7 rounds to 5 0, 37, 10 → 5
1.5 rounds to 2 0, 15, 10 → 2
negative to positive -12.5, 37.2, 5 → 10
a reversed extent still has a positive step 100, 0, 10 → 10
a small fractional step 0, 0.05, 10 → 0.005
Show the other 6 tests
CaseArgumentsExpected
0.7 for one tick rounds to 0.5 0, 0.7, 1 → 0.5
0.9 for one tick rounds up to a whole 1 0, 0.9, 1 → 1
large values 0, 1,234,567, 5 → 200,000
equal ends have no step 5, 5, 10 → 0
count of zero is an error 0, 10, 0 → error: count must be a whole number of at least 1
fractional count is an error 0, 10, 1.5 → error: count must be a whole number of at least 1

niceTicks 12 tests

CaseArgumentsExpected
steps of two 0, 10, 5 → 0, 2, 4, 6, 8, 10
tenths are exact: the fourth tick is 0.3, not 0.30000000000000004 0, 1, 10 → 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1
ticks inside a messy extent 0.13, 0.87, 5 → 0.2, 0.4, 0.6, 0.8
negative to positive, the ends are not ticks -12.5, 37.2, 5 → -10, 0, 10, 20, 30
a reversed extent gives ticks in its direction 10, 0, 5 → 10, 8, 6, 4, 2, 0
equal ends give that one value 5, 5, 10 → 5
one tick 1.2, 3.8, 1 → 2
one tick with no whole number inside retries at two, as d3 does 2.1, 2.9, 1 → 2.5
millions 0, 1,000,000, 4 → 0, 200,000, 400,000, 600,000, 800,000, 1,000,000
thousandths 0.001, 0.006, 4 → 0.001, 0.002, 0.003, 0.004, 0.005
Show the other 2 tests
CaseArgumentsExpected
all negative -1, -0.5, 5 → -1, -0.9, -0.8, -0.7, -0.6, -0.5
count of zero is an error 0, 10, 0 → error: count must be a whole number of at least 1

timeTickInterval 12 tests

CaseArgumentsExpected
ten days, ten ticks: daily 2026-01-01, 2026-01-11, 10 → interval day, step 1
a month, ten ticks: every other day 2026-01-01, 2026-01-31, 10 → interval day, step 2
a quarter, ten ticks: weekly 2026-01-01, 2026-04-01, 10 → interval week, step 1
a year, ten ticks: monthly 2026-01-01, 2027-01-01, 10 → interval month, step 1
a reversed year is the same 2027-01-01, 2026-01-01, 10 → interval month, step 1
two years, five ticks: quarterly 2026-01-01, 2028-01-01, 5 → interval quarter, step 1
a hundred days for one tick is nearer a quarter than a year 2026-01-01, 2026-04-11, 1 → interval quarter, step 1
a decade, five ticks: every two years 2020-01-01, 2030-01-01, 5 → interval year, step 2
fifty years, five ticks: every ten years 1975-01-01, 2025-01-01, 5 → interval year, step 10
the same day: daily 2026-01-01, 2026-01-01, 5 → interval day, step 1
Show the other 2 tests
CaseArgumentsExpected
count of zero is an error 2026-01-01, 2027-01-01, 0 → error: count must be a whole number of at least 1
an impossible date is an error 2026-02-30, 2027-01-01, 5 → error: is not a real calendar date

timeTicks 17 tests

CaseArgumentsExpected
every day across a month end 2026-01-30, 2026-02-02, day, 1 → 2026-01-30, 2026-01-31, 2026-02-01, 2026-02-02
every other day follows the day of the month, restarting on the 1st 2026-01-28, 2026-02-04, day, 2 → 2026-01-29, 2026-01-31, 2026-02-01, 2026-02-03
a leap day 2024-02-28, 2024-03-01, day, 1 → 2024-02-28, 2024-02-29, 2024-03-01
Mondays in September 2026 2026-09-01, 2026-09-30, week, 1 → 2026-09-07, 2026-09-14, 2026-09-21, 2026-09-28
every other Monday, counted from 1970-01-05 2026-09-01, 2026-09-30, week, 2 → 2026-09-14, 2026-09-28
Mondays either side of 1970 1969-12-29, 1970-01-06, week, 1 → 1969-12-29, 1970-01-05
month starts, the first after a mid-month start 2026-01-15, 2026-05-01, month, 1 → 2026-02-01, 2026-03-01, 2026-04-01, 2026-05-01
every third month is January, April, July, October 2026-01-01, 2026-12-31, month, 3 → 2026-01-01, 2026-04-01, 2026-07-01, 2026-10-01
quarter starts across a year end 2025-11-15, 2026-08-01, quarter, 1 → 2026-01-01, 2026-04-01, 2026-07-01
every other quarter 2026-01-01, 2027-01-01, quarter, 2 → 2026-01-01, 2026-07-01, 2027-01-01
Show the other 7 tests
CaseArgumentsExpected
1 January each year 2023-06-01, 2026-01-01, year, 1 → 2024-01-01, 2025-01-01, 2026-01-01
every fifth year falls on multiples of five 2001-03-01, 2021-12-31, year, 5 → 2005-01-01, 2010-01-01, 2015-01-01, 2020-01-01
a reversed extent gives ticks in its direction 2026-02-02, 2026-01-30, day, 1 → 2026-02-02, 2026-02-01, 2026-01-31, 2026-01-30
no month starts inside 2026-01-02, 2026-01-30, month, 1 →
step of zero is an error 2026-01-01, 2026-02-01, day, 0 → error: step must be a whole number of at least 1
an unknown interval is an error 2026-01-01, 2026-02-01, hour, 1 → error: unknown time interval "hour"
more than 10,000 ticks is an error 2000-01-01, 2030-01-01, day, 1 → error: too many ticks: more than 10000

More from the author

`tickStep` is d3-array's rule: divide the extent by `count`, take the power of ten at or below it, and round the leftover factor to 1, 2, 5 or 10 on a log scale (the cut-offs are √2, √10 and √50). `niceTicks` returns every multiple of that step between the two ends inclusive, in the direction from `start` to `stop`; the ends themselves are ticks only if they are multiples. Equal ends give `[start]` (and a step of 0). If one tick is asked for and no multiple falls inside, it tries again for two, as d3 does.

The arithmetic is chosen so that the three languages print the same ticks:

- The power of ten is found by multiplying whole numbers, never with `log10`, whose last bit is platform-dependent. - A fractional step is kept as a whole-number divisor: a step of 0.2 is "divide by 5", so the tick is `i / 5`, one correctly rounded division. Adding 0.1 three times gives 0.30000000000000004; here the third tenth is exactly the double 0.3. `tickStep` returns `factor / 10^k` the same way. - Tick indexes are rounded with `math.round-float` and then corrected by comparison, so a product that lands a hair either side of a whole number cannot add or lose a tick.

## Calendar ticks

`timeTicks` returns the calendar boundaries inside a date range, inclusive:

| interval | a tick on | `step` counts | |-----------|----------------------------------------|----------------------------------------| | `day` | days with (day of month - 1) % step = 0 | restarts each month, as d3's timeDay.every | | `week` | Mondays (ISO weeks) | whole weeks since Monday 1970-01-05 | | `month` | the 1st, (month - 1) % step = 0 | month 3 is January, April, July, October | | `quarter` | 1 January, April, July, October | quarter of the year % step = 0 | | `year` | 1 January, year % step = 0 | every fifth year is 2005, 2010, ... |

Steps are anchored to the calendar, not to the first date, so an axis that pans by a day keeps the same ticks instead of shifting them all. Dates are counted as whole days (via `dates.add-days`), never through a `Date` object, so time zones and clock changes cannot move a tick. More than 10,000 ticks is an error, since it is always a wrong interval.

`timeTickInterval` picks the interval for about `count` ticks the way d3's time scale does: the ideal spacing is the span in days over `count`, and it takes whichever neighbouring rung of the ladder day, 2 days, week, month (30 days), quarter (90 days), year (365 days) is nearer by ratio. Beyond a year it uses whole years in a `tickStep` of 1, 2 or 5 x 10^k.

Sources: Mike Bostock, d3-array `ticks.js` (tickIncrement, ticks) and d3-scale `time.js` (tickIntervals), github.com/d3; ISO 8601 for weeks starting on Monday.

Files

PathBytes
README.md3,230
impl/python/nice_ticks.py1,480
impl/python/tick_step.py1,653
impl/python/time_tick_interval.py1,411
impl/python/time_ticks.py2,374
impl/rust/nice_ticks.rs2,016
impl/rust/tick_step.rs2,109
impl/rust/time_tick_interval.rs1,921
impl/rust/time_ticks.rs3,230
impl/typescript/nice_ticks.ts1,568
impl/typescript/tick_step.ts1,943
impl/typescript/time_tick_interval.ts1,480
impl/typescript/time_ticks.ts2,418
vectors.json7,976