[{"data":1,"prerenderedAt":18033},["ShallowReactive",2],{"wrun-open-editor-url":3,"indicators:functions/extra-indicators":4},"https://openmarket.xyz/chart/#wrun-open=v1",{"slug":5,"filePath":6,"frontmatter":7,"rawMarkdown":12,"tree":13},"functions/extra-indicators","functions/extra-indicators.md",{"title":8,"description":9,"order":10,"section":11},"Extra indicators","The TA library is the core catalog of 52 classes. The ./sdk/ta-plus module adds 30 more with the same shape: construct the class in onStart(), call update()…",47,"functions","---\ntitle: \"Extra indicators\"\ndescription: \"The TA library is the core catalog of 52 classes. The ./sdk/ta-plus module adds 30 more with the same shape: construct the class in onStart(), call update()…\"\norder: 47\nsection: \"functions\"\n---\n\n\u003C!-- source: docs/indicators/functions/extra-indicators.md; generated by packages/cli/scripts/gen-indicator-docs.ts, do not edit -->\n\n# Extra indicators\n\nThe [TA library](ta-library.md) is the core catalog of 52 classes. The\n`./sdk/ta-plus` module adds 30 more with the same shape: construct the\nclass in `onStart()`, call `update()` once per bar. Twenty-six are\ntextbook indicators the catalog never had; four are Pine's own spellings\nof classes the library has in another shape.\n\nThe 26 are the mean and percent-rank deviations, Bollinger and Keltner\nwidths, the volume lines (accumulation and distribution, the Williams\npair, the volume indices, price-volume trend, intraday intensity), the\nrunning extremes, mode, range and centre of gravity, the double and\ntriple EMAs, the zero-lag EMA, TRIX, Kaufman's efficiency ratio and\nadaptive average, the ultimate oscillator, Vortex, Aroon and choppiness.\nThe four are `Dmi` with its two lengths, `SourceStoch` and `SourceVwap`\nover any source series, and `HeikinAshi`. Every class composes the\nlibrary's own primitives and follows its three rules: `NaN` until the\nclass is warm, `NaN` while a non-finite input sits in its window (the\ntwo volume indices carry instead), and no allocation after the\nconstructor. The window arithmetic under them (`History`, `List`, the\n`stats.*` functions, rounding and a seeded random) is on\n[Stats, history and lists](stats-history-lists.md).\n\n## Every class in `./sdk/ta-plus`\n\n`update()` returns the primary stream; the extra streams are public\nfields you read after the call. \"First value\" is the bar index of the\nfirst non-`NaN` result on a clean series (bar 0 is the first bar).\nPeriods below 1 are clamped to 1.\n\n| Class | Construct | `update(...)` | Fields | Definition | First value |\n| --- | --- | --- | --- | --- | --- |\n| `Dev` | `(period)` | `(x)` | | mean absolute deviation of the last `period` values from their `Sma`: `sum(abs(x - sma)) / period` | bar `period - 1` |\n| `PercentRank` | `(period)` | `(x)` | | `100 * count(previous period values \u003C= x) / period`, the current bar excluded from the count | bar `period` |\n| `Bbw` | `(period, mult)` | `(x)` | `basis`, `upper`, `lower` | `(upper - lower) / basis` over `Bb(period, mult)`; `NaN` when the basis is 0 | bar `period - 1` |\n| `Kcw` | `(period, mult, atrPeriod)` | `(x, high, low, close)` | `basis`, `upper`, `lower` | `(upper - lower) / basis` over `Keltner(period, mult, atrPeriod)`; `NaN` when the basis is 0 | bar `max(period, atrPeriod) - 1` |\n| `AccDist` | `()` | `(high, low, close, volume)` | | running sum of `((2 * close - high - low) / (high - low)) * volume`, the term 0 when `high == low` | bar 0 |\n| `Wad` | `()` | `(high, low, close)` | | running sum of: `close - min(low, prevClose)` when the close rose, `close - max(high, prevClose)` when it fell, else 0; bar 0 returns 0 | bar 0 |\n| `Wvad` | `()` | `(open, high, low, close, volume)` | | `((close - open) / (high - low)) * volume` for this bar, never a running sum; `NaN` when `high == low` | bar 0 |\n| `Nvi` | `()` | `(close, volume)` | | starts at 1; when `volume \u003C prevVolume`: `nvi = prev + ((close - prevClose) / prevClose) * prev`, else `prev`; a close of 0 or `NaN`, on this bar or the previous one, keeps `prev` | bar 0 |\n| `Pvi` | `()` | `(close, volume)` | | the same with `volume > prevVolume` | bar 0 |\n| `Pvt` | `()` | `(close, volume)` | | running sum of `((close - prevClose) / prevClose) * volume`; bar 0 returns 0 | bar 0 |\n| `RunningMax` | `()` | `(x)` | | the largest finite `x` seen so far (a non-finite `x` is skipped) | the first finite bar |\n| `RunningMin` | `()` | `(x)` | | the smallest finite `x` seen so far (a non-finite `x` is skipped) | the first finite bar |\n| `Mode` | `(period)` | `(x)` | | the most frequent value of the window (exact equality); ties go to the smallest | bar `period - 1` |\n| `Range` | `(period)` | `(x)` | | `Highest - Lowest` of the last `period` values | bar `period - 1` |\n| `Cog` | `(period)` | `(x)` | | `-(sum of x[i] * (i + 1)) / sum(x[i])` for `i = 0` (the newest) to `period - 1`; `NaN` when the sum is 0 | bar `period - 1` |\n| `Iii` | `()` | `(high, low, close, volume)` | | `(2 * close - high - low) / ((high - low) * volume)` for this bar; `NaN` when the denominator is 0 | bar 0 |\n| `Dema` | `(period)` | `(x)` | | `2 * e1 - e2`, `e1 = Ema(period)` of `x`, `e2 = Ema(period)` of `e1` | bar `2 * period - 2` |\n| `Tema` | `(period)` | `(x)` | | `3 * e1 - 3 * e2 + e3` | bar `3 * period - 3` |\n| `Zlema` | `(period)` | `(x)` | | `Ema(period)` of `x + (x - x[lag])`, `lag = floor((period - 1) / 2)` | bar `lag + period - 1` |\n| `Trix` | `(period)` | `(x)` | | `10000 *` the one-bar change of `Ema(Ema(Ema(ln x)))`; `NaN` when `x \u003C= 0` | bar `3 * period - 2` |\n| `Ultimate` | `(p1 = 7, p2 = 14, p3 = 28)` | `(high, low, close)` | | `BP = close - min(low, prevClose)`, `TR = max(high, prevClose) - min(low, prevClose)`, `avg_n = Sum(BP, n) / Sum(TR, n)`, result `100 * (4 * avg1 + 2 * avg2 + avg3) / 7` | bar `p3` |\n| `Vortex` | `(period)` | `(high, low, close)` | `plus`, `minus` | `VM+ = abs(high - prevLow)`, `VM- = abs(low - prevHigh)`; `plus = Sum(VM+) / Sum(TR)`, `minus = Sum(VM-) / Sum(TR)` over `period`; returns `plus` | bar `period` |\n| `Aroon` | `(period)` | `(high, low)` | `up`, `down`, `osc` | `up = 100 * (Highest(period + 1).bars + period) / period`, `down` likewise with `Lowest`, `osc = up - down`; returns `osc` | bar `period` |\n| `Choppiness` | `(period)` | `(high, low, close)` | | `100 * log10(Sum(TR, period) / (Highest(high, period) - Lowest(low, period))) / log10(period)`; `NaN` when the range is 0 | bar `period - 1` |\n| `Efficiency` | `(period)` | `(x)` | | `abs(x - x[period]) / Sum(abs(x - x[1]), period)`; `NaN` when the sum is 0 | bar `period` |\n| `Kama` | `(period, fast = 2, slow = 30)` | `(x)` | | `sc = (er * (2 / (fast + 1) - 2 / (slow + 1)) + 2 / (slow + 1))^2` with `er = Efficiency(period)`; `kama = prev + sc * (x - prev)`, seeded with `x` on the first bar `er` exists | bar `period` |\n| `Dmi` | `(diLength, adxSmoothing)` | `(high, low, close)` | `adx`, `plusDi`, `minusDi` | Pine's `ta.dmi`: `+DI = 100 * Rma(+DM, diLength) / Rma(TR, diLength)`, `-DI` likewise, `DX = abs(+DI - -DI) / (+DI + -DI)` (over 1 when the sum is 0), `adx = 100 * Rma(DX, adxSmoothing)`; a zero smoothed range holds `+DI` and `-DI` (Pine's `fixnan`); a missing bar is skipped the way TradingView skips it (see below); equal lengths give the library's `Adx` on a series without a hole; returns `adx` | `plusDi`, `minusDi` at bar `diLength`; `adx` at bar `diLength + adxSmoothing - 1` |\n| `SourceStoch` | `(periodK, smoothK = 1, periodD = 1)` | `(source, high, low)` | `k`, `d` | Pine's `ta.stoch(source, high, low, length)`: raw %K is `100 * (source - Lowest(low)) / (Highest(high) - Lowest(low))` over `periodK`, `k = Sma(smoothK)` of it, `d = Sma(periodD)` of `k`; a flat window follows TradingView (the previous raw %K when the source sits on the window's value, `NaN` otherwise) where the library's `Stoch` reads 0, so fed the close it is `Stoch` on every window with a range; returns `k` | `k` at bar `periodK + smoothK - 2`, `d` at bar `periodK + smoothK + periodD - 3` |\n| `SourceVwap` | `(anchor = \"\")` | `(source, volume, tsMs = NaN)` | | Pine's `ta.vwap(source)`: the library's `Vwap` sums, `sum(source * volume) / sum(volume)` from the anchor (`\"\"`, `\"day\"`, `\"week\"`, `\"month\"`, `\"quarter\"`, `\"year\"` or a bucket width in milliseconds; `tsMs` is `bar.time() * 1000.0`, read only with an anchor), over any source; fed `(high + low + close) / 3` it is `Vwap(anchor, \"hlc3\")` | bar 0 |\n| `HeikinAshi` | `()` | `(open, high, low, close)` | `open`, `high`, `low`, `close` | Pine's `ticker.heikinashi`: `close = (open + high + low + close) / 4`, `open = (previous ha open + previous ha close) / 2` (the bar's own `(open + close) / 2` on the first bar), `high = max(high, ha open, ha close)`, `low = min(low, ha open, ha close)`; returns the smoothed close | bar 0 |\n\nA non-finite input (`NaN` or infinite) is handled by shape. A windowed\nclass (`Dev`, `PercentRank`, `Bbw`, `Mode`,\n`Range`, `Cog`, `Ultimate`, `Vortex`, `Aroon`, `Choppiness`,\n`Efficiency`, `SourceStoch`) returns `NaN` while the bad bar sits inside its window and\nheals when it leaves; the running sums (`AccDist`, `Wad`, `Pvt`) stay\n`NaN` until `reset()`; the per-bar readings (`Wvad`, `Iii`) are `NaN` on\nthat bar alone; the classes built on `Ema` (`Dema`, `Tema`, `Zlema`,\n`Trix`, and `Kcw` through `Keltner`) follow the `Ema` rule: a bad bar\nbefore the seed restarts the seed, a bad bar after it makes the value\n`NaN` for good. `Dmi` keeps TradingView's own rule for `ta.dmi` instead:\n`ta.rma` skips a na bar with its state untouched, `ta.tr` and the two\nchanges are na on that bar and on the next one, so each smoother is fed\nonly when its own input is a value, `fixnan` holds `plusDi` and\n`minusDi` meanwhile, `adx` keeps smoothing the DX of the held values,\nand two bars after the hole every stream continues from the state it\nhad (the library's `Adx` goes `NaN` for good there). `Kama` re-seeds with the next `x` once its efficiency\nwindow is clean again, the running extremes skip the bar, and `Nvi` and\n`Pvi` never turn `NaN`: they carry their value across a bar whose close,\nor previous close, is 0 or not a number. `SourceVwap` keeps the `Vwap`\nrule (the current bucket is `NaN` until the next one starts), and\n`HeikinAshi` reads `NaN` on the bad bar and restarts its chain on the\nnext finite one, seeding the open as the first bar does.\n\n## Deviation, rank and width\n\nSeven classes read one series. `Dev` and `PercentRank` say how far and\nhow high the newest value sits in its window; `Bbw` and `Kcw` are the\nband widths as one number, with the bands in fields; `Range`, `Mode` and\n`Cog` are the window's shape.\n\n```typescript sample=fn-extra-indicators-widths\nparam(\"period\", 20, { min: 2, max: 400, description: \"Window for every class\" });\nparam(\"mult\", 2, { min: 0.5, max: 5, description: \"Band multiplier\" });\noutput(\"dev\", line, lower, { color: \"#2563eb\", description: \"Mean absolute deviation of the close\" });\noutput(\"prank\", line, lower, { color: \"#7c3aed\", description: \"Percent rank of the close\" });\noutput(\"bbw\", line, lower, { color: \"#16a34a\", description: \"Bollinger band width\" });\noutput(\"bb_upper\", line, lower, { color: \"#15803d\", description: \"Upper Bollinger band\" });\noutput(\"kcw\", line, lower, { color: \"#ea580c\", description: \"Keltner channel width\" });\noutput(\"range\", line, lower, { color: \"#0891b2\", description: \"Highest minus lowest close\" });\noutput(\"mode\", line, lower, { color: \"#4b5563\", description: \"Most frequent close\" });\noutput(\"cog\", line, lower, { color: \"#be123c\", description: \"Centre of gravity\" });\n\nlet dev = new Dev(20);\nlet prank = new PercentRank(20);\nlet bbw = new Bbw(20, 2.0);\nlet kcw = new Kcw(20, 2.0, 10);\nlet closeRange = new Range(20);\nlet mode = new Mode(20);\nlet cog = new Cog(20);\n\nfunction onStart(): void {\n  const period = i32(p_period());\n  dev = new Dev(period);\n  prank = new PercentRank(period);\n  bbw = new Bbw(period, p_mult());\n  kcw = new Kcw(period, p_mult(), period / 2);\n  closeRange = new Range(period);\n  mode = new Mode(period);\n  cog = new Cog(period);\n}\n\nfunction onBar(): void {\n  const close = bar.close();\n  const devValue = dev.update(close);\n  const prankValue = prank.update(close);\n  const bbwValue = bbw.update(close);\n  const kcwValue = kcw.update(close, bar.high(), bar.low(), close);\n  const rangeValue = closeRange.update(close);\n  const modeValue = mode.update(close);\n  const cogValue = cog.update(close);\n  if (isNaN(devValue)) return;\n  out_dev(devValue);\n  out_prank(prankValue);\n  out_bbw(bbwValue);\n  out_bb_upper(bbw.upper);\n  out_kcw(kcwValue);\n  out_range(rangeValue);\n  out_mode(modeValue);\n  out_cog(cogValue);\n}\n```\n\n`PercentRank` counts the previous `period` values, never the current bar,\nso its first value lands one bar after `Dev`'s: `onBar()` gates on `Dev`\nand the first ready row draws a gap for the rank. `Kcw` reports its\n`basis` once the EMA is seeded and the width once the ATR is warm too.\n\n## Volume and money flow\n\n`AccDist`, `Wad` and `Pvt` are running sums: the line so far, from the\nfirst bar. `Nvi` and `Pvi` are indices that start at 1 and move only on\na bar whose volume fell (`Nvi`) or rose (`Pvi`). `Wvad` and `Iii` are\nper-bar readings with no memory; for a running line feed one to the\nlibrary's `Cum`, as the sample does for `Wvad`.\n\n```typescript sample=fn-extra-indicators-volume\ninput(\"open\", ohlcv.open);\noutput(\"accdist\", line, lower, { color: \"#2563eb\", description: \"Accumulation/distribution line\" });\noutput(\"wad\", line, lower, { color: \"#7c3aed\", description: \"Williams accumulation/distribution\" });\noutput(\"wvad\", line, lower, { color: \"#16a34a\", description: \"Williams variable A/D of this bar\" });\noutput(\"wvad_line\", line, lower, { color: \"#65a30d\", description: \"Running total of wvad\" });\noutput(\"nvi\", line, lower, { color: \"#dc2626\", description: \"Negative volume index, from 1\" });\noutput(\"pvi\", line, lower, { color: \"#ea580c\", description: \"Positive volume index, from 1\" });\noutput(\"pvt\", line, lower, { color: \"#0891b2\", description: \"Price-volume trend\" });\noutput(\"iii\", line, lower, { color: \"#4b5563\", description: \"Intraday intensity of this bar\" });\noutput(\"running_max\", line, lower, { color: \"#15803d\", description: \"Highest close so far\" });\noutput(\"running_min\", line, lower, { color: \"#be123c\", description: \"Lowest close so far\" });\n\nlet accdist = new AccDist();\nlet wad = new Wad();\nlet wvad = new Wvad();\nlet wvadLine = new Cum();\nlet nvi = new Nvi();\nlet pvi = new Pvi();\nlet pvt = new Pvt();\nlet iii = new Iii();\nlet runningMax = new RunningMax();\nlet runningMin = new RunningMin();\n\nfunction onStart(): void {\n  accdist = new AccDist();\n  wad = new Wad();\n  wvad = new Wvad();\n  wvadLine = new Cum();\n  nvi = new Nvi();\n  pvi = new Pvi();\n  pvt = new Pvt();\n  iii = new Iii();\n  runningMax = new RunningMax();\n  runningMin = new RunningMin();\n}\n\nfunction onBar(): void {\n  const open = bar.open();\n  const high = bar.high();\n  const low = bar.low();\n  const close = bar.close();\n  const volume = bar.volume();\n  const accdistValue = accdist.update(high, low, close, volume);\n  const wadValue = wad.update(high, low, close);\n  const wvadValue = wvad.update(open, high, low, close, volume);\n  // A flat bar has no reading: add 0, Cum keeps a NaN.\n  const wvadTotal = wvadLine.update(isNaN(wvadValue) ? 0.0 : wvadValue);\n  const nviValue = nvi.update(close, volume);\n  const pviValue = pvi.update(close, volume);\n  const pvtValue = pvt.update(close, volume);\n  const iiiValue = iii.update(high, low, close, volume);\n  const maxValue = runningMax.update(close);\n  const minValue = runningMin.update(close);\n  if (isNaN(accdistValue)) return;\n  out_accdist(accdistValue);\n  out_wad(wadValue);\n  out_wvad(wvadValue);\n  out_wvad_line(wvadTotal);\n  out_nvi(nviValue);\n  out_pvi(pviValue);\n  out_pvt(pvtValue);\n  out_iii(iiiValue);\n  out_running_max(maxValue);\n  out_running_min(minValue);\n}\n```\n\nA running line depends on where the history starts: the chart feeds the\nmodule the bars it fetched, so the newest bar's value moves when that\nwindow does. Read `AccDist`, `Wad`, `Pvt` and the two indices as shapes,\nnot as levels to alert on.\n\n## Smoothers on the EMA\n\n`Dema`, `Tema` and `Zlema` stack the library's `Ema`; `Trix` stacks three\nof them over the logarithm of the price and reads the one-bar change;\n`Efficiency` and `Kama` are Kaufman's pair, the ratio of net move to\ntotal move and the average whose smoothing follows it.\n\n```typescript sample=fn-extra-indicators-smoothers\nparam(\"period\", 20, { min: 2, max: 400 });\nparam(\"fast\", 2, { min: 1, max: 100, description: \"Kama fast length\" });\nparam(\"slow\", 30, { min: 1, max: 400, description: \"Kama slow length\" });\noutput(\"dema\", line, overlay, { color: \"#2563eb\", description: \"Double EMA\" });\noutput(\"tema\", line, overlay, { color: \"#7c3aed\", description: \"Triple EMA\" });\noutput(\"zlema\", line, overlay, { color: \"#16a34a\", description: \"Zero-lag EMA\" });\noutput(\"kama\", line, overlay, { color: \"#ea580c\", width: 2, description: \"Kaufman adaptive average\" });\noutput(\"trix\", line, lower, { color: \"#dc2626\", description: \"TRIX\" });\noutput(\"efficiency\", line, lower, { color: \"#0891b2\", description: \"Efficiency ratio, 0..1\" });\n\nlet dema = new Dema(20);\nlet tema = new Tema(20);\nlet zlema = new Zlema(20);\nlet trix = new Trix(20);\nlet efficiency = new Efficiency(20);\nlet kama = new Kama(20, 2, 30);\n\nfunction onStart(): void {\n  const period = i32(p_period());\n  dema = new Dema(period);\n  tema = new Tema(period);\n  zlema = new Zlema(period);\n  trix = new Trix(period);\n  efficiency = new Efficiency(period);\n  kama = new Kama(period, i32(p_fast()), i32(p_slow()));\n}\n\nfunction onBar(): void {\n  const close = bar.close();\n  const demaValue = dema.update(close);\n  const temaValue = tema.update(close);\n  const zlemaValue = zlema.update(close);\n  const trixValue = trix.update(close);\n  const erValue = efficiency.update(close);\n  const kamaValue = kama.update(close);\n  if (isNaN(kamaValue)) return;\n  out_dema(demaValue);\n  out_tema(temaValue);\n  out_zlema(zlemaValue);\n  out_kama(kamaValue);\n  out_trix(trixValue);\n  out_efficiency(erValue);\n}\n```\n\nThe warm-ups differ: `Kama` has its first value at bar `period` while\n`Tema(20)` waits until bar 57 and `Trix(20)` until bar 58. Gate\nreadiness on the line you plot as primary, not on the slowest class.\n\n## Two oscillators\n\n`Ultimate` blends buying pressure over three windows; `Vortex` reads the\ntwo movement sums against the true range and exposes both lines.\n\n```typescript sample=fn-extra-indicators-oscillators\nparam(\"period\", 14, { min: 2, max: 400, description: \"Vortex window\" });\ninput(\"high\", ohlcv.high);\noutput(\"ultimate\", line, lower, { color: \"#2563eb\", description: \"Ultimate oscillator (7, 14, 28)\" });\noutput(\"vortex_plus\", line, lower, { color: \"#16a34a\", description: \"VI+\" });\noutput(\"vortex_minus\", line, lower, { color: \"#dc2626\", description: \"VI-\" });\n\nlet ultimate = new Ultimate(7, 14, 28);\nlet vortex = new Vortex(14);\n\nfunction onStart(): void {\n  ultimate = new Ultimate(7, 14, 28);\n  vortex = new Vortex(i32(p_period()));\n}\n\nfunction onBar(): void {\n  const high = bar.high();\n  const low = bar.low();\n  const close = bar.close();\n  const ultimateValue = ultimate.update(high, low, close);\n  const plus = vortex.update(high, low, close);\n  const minus = vortex.minus;\n  if (isNaN(plus)) return;\n  out_ultimate(ultimateValue);\n  out_vortex_plus(plus);\n  out_vortex_minus(minus);\n}\n```\n\n## A regime from Aroon and choppiness\n\n`Aroon` says which way the recent extreme sits, `Choppiness` says whether\nthe window went anywhere at all. Together they make a three-way regime:\ntrending up, trending down, or ranging. The regime is a data-only output\nthat tints a shape through `color_by`\n([Colors](colors-kit.md)).\n\n```typescript sample=fn-extra-indicators-regime\nparam(\"period\", 25, { min: 2, max: 400, description: \"Aroon and choppiness window\" });\nparam(\"chop_ceiling\", 61.8, { min: 0, max: 100, description: \"Choppiness above this reads as ranging\" });\ninput(\"high\", ohlcv.high);\noutput(\"aroon_up\", line, lower, { color: \"#16a34a\", description: \"Aroon up\" });\noutput(\"aroon_down\", line, lower, { color: \"#dc2626\", description: \"Aroon down\" });\noutput(\"chop\", line, lower, { color: \"#4b5563\", description: \"Choppiness index, 0..100\" });\noutput(\"regime\", none, overlay, { description: \"0 ranging, 1 trending up, 2 trending down\" });\noutput(\"regime_mark\", shape, overlay, {\n  color: \"#94a3b8\",\n  color_by: \"regime\",\n  colors: [\"#94a3b8\", \"#16a34a\", \"#dc2626\"],\n  description: \"The close, tinted by regime\",\n});\n\nlet aroon = new Aroon(25);\nlet chop = new Choppiness(25);\nlet chopCeiling: f64 = 61.8;\n\nfunction onStart(): void {\n  const period = i32(p_period());\n  aroon = new Aroon(period);\n  chop = new Choppiness(period);\n  chopCeiling = p_chop_ceiling();\n}\n\nfunction onBar(): void {\n  const high = bar.high();\n  const low = bar.low();\n  const close = bar.close();\n  const osc = aroon.update(high, low);\n  const chopValue = chop.update(high, low, close);\n  if (isNaN(osc) || isNaN(chopValue)) return;\n  let regime: f64 = 0.0;\n  if (chopValue > chopCeiling) regime = 0.0;\n  else regime = osc > 0.0 ? 1.0 : 2.0;\n  out_aroon_up(aroon.up);\n  out_aroon_down(aroon.down);\n  out_chop(chopValue);\n  out_regime(regime);\n  out_regime_mark(close);\n}\n```\n\n`Aroon` runs a `Highest` and a `Lowest` over `period + 1` bars and reads\ntheir `bars` offsets, so `up` is 100 on the bar of a fresh high and falls\nby `100 / period` on every bar the high ages; `Choppiness` is the log\nratio of the true-range sum to the window's range, near 100 when the\nbars overlap and near 0 when they march in one direction. `onBar()`\nreturns before writing until both are warm: `Aroon` needs `period + 1`\nbars, `Choppiness` needs `period`.\n\n## Pine's spellings of four library classes\n\nThe library's `Adx`, `Stoch` and `Vwap` are the engine's forms: one\nlength, the close as the source, a named bar price. Four classes\nhere carry the Pine spellings a ported script writes. `Dmi(diLength,\nadxSmoothing)` is `ta.dmi` with its two lengths (`+DI` and `-DI`\nsmoothed over `diLength`, ADX over `adxSmoothing`, both with the\nlibrary's `Rma`); with equal lengths it is `Adx` to the last bit of the\narithmetic, and across a missing bar it keeps TradingView's state rules\n(nothing restarts, nothing is poisoned). `SourceStoch` is\n`ta.stoch(source, high, low, length)` over any source, smoothed like\n`Stoch`; fed the close it is `Stoch` on every window with a range (a\nflat window follows TradingView: the previous raw %K when the source\nsits on the window's value, `NaN` otherwise, where `Stoch` reads 0).\n`SourceVwap` is `ta.vwap(source)` over any source with `Vwap`'s anchors;\nfed `(high + low + close) / 3` it is `Vwap(anchor, \"hlc3\")`.\n`HeikinAshi` is `ticker.heikinashi` as a class over the bars you feed it\n(this chart's, or another market's candles); the recursion forgets its\nstart by half every bar, so after about 50 bars the values no longer\ndepend on where the loaded history begins.\n\n```typescript\nparam(\"di_length\", 14, { min: 1, max: 200 });\nparam(\"adx_smoothing\", 7, { min: 1, max: 200 });\nparam(\"stoch_length\", 14, { min: 1, max: 200 });\noutput(\"adx\", line, lower, { color: \"#111827\", description: \"ADX over its own smoothing\" });\noutput(\"plus_di\", line, lower, { color: \"#16a34a\", description: \"+DI\" });\noutput(\"minus_di\", line, lower, { color: \"#dc2626\", description: \"-DI\" });\noutput(\"stoch_hl2\", line, lower, { color: \"#2563eb\", description: \"Stochastic of the bar midpoint\" });\noutput(\"vwap_ohlc4\", line, overlay, { color: \"#f59e0b\", description: \"Session VWAP over ohlc4\" });\noutput(\"ha_close\", line, overlay, { color: \"#7c3aed\", description: \"Heikin Ashi close\" });\n\nlet dmi = new Dmi(14, 7);\nlet stoch = new SourceStoch(14);\nconst vwap = new SourceVwap(\"day\");\nconst ha = new HeikinAshi();\n\nfunction onStart(): void {\n  dmi = new Dmi(i32(p_di_length()), i32(p_adx_smoothing()));\n  stoch = new SourceStoch(i32(p_stoch_length()));\n}\n\nfunction onBar(): void {\n  const o = bar.open();\n  const h = bar.high();\n  const l = bar.low();\n  const c = bar.close();\n  const adx = dmi.update(h, l, c);\n  const k = stoch.update((h + l) / 2.0, h, l);\n  const vwapValue = vwap.update((o + h + l + c) / 4.0, bar.volume(), bar.time() * 1000.0);\n  const haClose = ha.update(o, h, l, c);\n  if (isNaN(adx)) return;\n  out_adx(adx);\n  out_plus_di(dmi.plusDi);\n  out_minus_di(dmi.minusDi);\n  out_stoch_hl2(k);\n  out_vwap_ohlc4(vwapValue);\n  out_ha_close(haClose);\n}\n```\n\n`Dmi` warms up last (`diLength + adxSmoothing - 1` bars), so the sample\ngates on it. `SourceStoch(length)` is the raw %K; pass `smoothK` and\n`periodD` for the `ta.sma` smoothing a Pine script applies afterwards.\n`SourceVwap` takes the bar's open time in milliseconds like `Vwap`\n([Volume and VWAP](volume-indicators.md#vwap)); `HeikinAshi` exposes the\nfour smoothed values as fields, read after `update()`.\n\n## History and lists\n\n`History` (Pine's `close[1]` as `history.ago(1)`), `List`, the `stats.*`\nwindow functions, `HandleRing`, `roundTo`, `roundToTick` and `Random` have\ntheir own page: [Stats, history and lists](stats-history-lists.md).\n\n## From Pine\n\nOne to one: the class returns Pine's value on the same bars. The second\ntable holds the three that share Pine's formula with one difference. The\n`array.*`, `x[n]`, `math.round` and `math.random` rows are on\n[Stats, history and lists](stats-history-lists.md#from-pine).\n\n| Pine | Extra indicators |\n| --- | --- |\n| `ta.dev(source, length)` | `new Dev(length)`, `.update(x)` |\n| `ta.percentrank(source, length)` | `new PercentRank(length)`, `.update(x)` |\n| `ta.bbw(source, length, mult)` | `new Bbw(length, mult)`, `.update(x)` |\n| `ta.accdist` | `new AccDist()`, `.update(high, low, close, volume)` |\n| `ta.wad` | `new Wad()`, `.update(high, low, close)` |\n| `ta.wvad` | `new Wvad()`, `.update(open, high, low, close, volume)` |\n| `ta.nvi` | `new Nvi()`, `.update(close, volume)` |\n| `ta.pvi` | `new Pvi()`, `.update(close, volume)` |\n| `ta.max(source)` | `new RunningMax()`, `.update(x)` |\n| `ta.min(source)` | `new RunningMin()`, `.update(x)` |\n| `ta.mode(source, length)` | `new Mode(length)`, `.update(x)` |\n| `ta.range(source, length)` | `new Range(length)`, `.update(x)` |\n| `ta.cog(source, length)` | `new Cog(length)`, `.update(x)` |\n| `ta.iii` | `new Iii()`, `.update(high, low, close, volume)` |\n\n| Pine | Extra indicators | The difference |\n| --- | --- | --- |\n| `ta.stoch(source, high, low, length)` with a `na` source, high or low | `new SourceStoch(length)`, `.update(source, high, low)` | TradingView carries the previous %K over a bar whose input is `na`; here the class reads `NaN` while that bar sits in its windows (the library's windowed rule) and heals when it leaves |\n| `ta.pvt` | `new Pvt()`, `.update(close, volume)` | the same line from the second bar on; the first bar, with no previous close, reads 0 here |\n| `ta.kcw(source, length, mult, true)` | `new Kcw(length, mult, length)`, `.update(x, high, low, close)` | the range average is the library's Wilder `Atr`; Pine's is an EMA of the true range, so the widths track each other without being equal |\n",{"type":14,"children":15,"data":18026,"position":18028},"root",[16,26,29,30,133,134,352,353,381,382,425,427,6370,6371,7244,7245,7259,7260,7388,7389,8884,8885,9013,9014,9028,9029,9219,9220,10925,10926,10989,10990,11005,11006,11130,11131,12401,12402,12488,12489,12504,12505,12548,12549,13253,13254,13269,13270,13353,13354,14436,14437,14669,14670,14684,14685,15121,15122,16283,16284,16489,16490,16505,16506,16689,16690,16705,16706,16810,16812,17666,17668],{"type":17,"value":18,"position":19},"comment"," source: docs/indicators/functions/extra-indicators.md; generated by packages/cli/scripts/gen-indicator-docs.ts, do not edit ",{"start":20,"end":23},{"line":21,"column":21,"offset":22},1,0,{"line":21,"column":24,"offset":25},133,132,{"type":27,"value":28},"text","\n",{"type":27,"value":28},{"type":31,"tagName":32,"properties":33,"children":34,"position":130},"element","p",{},[35,43,62,68,81,89,102,109,122],{"type":27,"value":36,"position":37},"The ",{"start":38,"end":41},{"line":39,"column":21,"offset":40},5,154,{"line":39,"column":39,"offset":42},158,{"type":31,"tagName":44,"properties":45,"children":47,"position":57},"a",{"href":46},"ta-library.md",[48],{"type":27,"value":49,"position":50},"TA library",{"start":51,"end":54},{"line":39,"column":52,"offset":53},6,159,{"line":39,"column":55,"offset":56},16,169,{"start":58,"end":59},{"line":39,"column":39,"offset":42},{"line":39,"column":60,"offset":61},32,185,{"type":27,"value":63,"position":64}," is the core catalog of 52 classes. The\n",{"start":65,"end":66},{"line":39,"column":60,"offset":61},{"line":52,"column":21,"offset":67},225,{"type":31,"tagName":69,"properties":70,"children":71,"position":78},"code",{},[72],{"type":27,"value":73,"position":74},"./sdk/ta-plus",{"start":75,"end":76},{"line":52,"column":21,"offset":67},{"line":52,"column":55,"offset":77},240,{"start":79,"end":80},{"line":52,"column":21,"offset":67},{"line":52,"column":55,"offset":77},{"type":27,"value":82,"position":83}," module adds 30 more with the same shape: construct the\nclass in ",{"start":84,"end":85},{"line":52,"column":55,"offset":77},{"line":86,"column":87,"offset":88},7,10,305,{"type":31,"tagName":69,"properties":90,"children":91,"position":99},{},[92],{"type":27,"value":93,"position":94},"onStart()",{"start":95,"end":96},{"line":86,"column":87,"offset":88},{"line":86,"column":97,"offset":98},21,316,{"start":100,"end":101},{"line":86,"column":87,"offset":88},{"line":86,"column":97,"offset":98},{"type":27,"value":103,"position":104},", call ",{"start":105,"end":106},{"line":86,"column":97,"offset":98},{"line":86,"column":107,"offset":108},28,323,{"type":31,"tagName":69,"properties":110,"children":111,"position":119},{},[112],{"type":27,"value":113,"position":114},"update()",{"start":115,"end":116},{"line":86,"column":107,"offset":108},{"line":86,"column":117,"offset":118},38,333,{"start":120,"end":121},{"line":86,"column":107,"offset":108},{"line":86,"column":117,"offset":118},{"type":27,"value":123,"position":124}," once per bar. Twenty-six are\ntextbook indicators the catalog never had; four are Pine's own spellings\nof classes the library has in another shape.",{"start":125,"end":126},{"line":86,"column":117,"offset":118},{"line":127,"column":128,"offset":129},9,45,480,{"start":131,"end":132},{"line":39,"column":21,"offset":40},{"line":127,"column":128,"offset":129},{"type":27,"value":28},{"type":31,"tagName":32,"properties":135,"children":136,"position":349},{},[137,147,160,167,180,187,200,208,221,227,239,246,257,265,278,285,298,305,317,324,342],{"type":27,"value":138,"position":139},"The 26 are the mean and percent-rank deviations, Bollinger and Keltner\nwidths, the volume lines (accumulation and distribution, the Williams\npair, the volume indices, price-volume trend, intraday intensity), the\nrunning extremes, mode, range and centre of gravity, the double and\ntriple EMAs, the zero-lag EMA, TRIX, Kaufman's efficiency ratio and\nadaptive average, the ultimate oscillator, Vortex, Aroon and choppiness.\nThe four are ",{"start":140,"end":143},{"line":141,"column":21,"offset":142},11,482,{"line":144,"column":145,"offset":146},17,14,916,{"type":31,"tagName":69,"properties":148,"children":149,"position":157},{},[150],{"type":27,"value":151,"position":152},"Dmi",{"start":153,"end":154},{"line":144,"column":145,"offset":146},{"line":144,"column":155,"offset":156},19,921,{"start":158,"end":159},{"line":144,"column":145,"offset":146},{"line":144,"column":155,"offset":156},{"type":27,"value":161,"position":162}," with its two lengths, ",{"start":163,"end":164},{"line":144,"column":155,"offset":156},{"line":144,"column":165,"offset":166},42,944,{"type":31,"tagName":69,"properties":168,"children":169,"position":177},{},[170],{"type":27,"value":171,"position":172},"SourceStoch",{"start":173,"end":174},{"line":144,"column":165,"offset":166},{"line":144,"column":175,"offset":176},55,957,{"start":178,"end":179},{"line":144,"column":165,"offset":166},{"line":144,"column":175,"offset":176},{"type":27,"value":181,"position":182}," and ",{"start":183,"end":184},{"line":144,"column":175,"offset":176},{"line":144,"column":185,"offset":186},60,962,{"type":31,"tagName":69,"properties":188,"children":189,"position":197},{},[190],{"type":27,"value":191,"position":192},"SourceVwap",{"start":193,"end":194},{"line":144,"column":185,"offset":186},{"line":144,"column":195,"offset":196},72,974,{"start":198,"end":199},{"line":144,"column":185,"offset":186},{"line":144,"column":195,"offset":196},{"type":27,"value":201,"position":202},"\nover any source series, and ",{"start":203,"end":204},{"line":144,"column":195,"offset":196},{"line":205,"column":206,"offset":207},18,29,1003,{"type":31,"tagName":69,"properties":209,"children":210,"position":218},{},[211],{"type":27,"value":212,"position":213},"HeikinAshi",{"start":214,"end":215},{"line":205,"column":206,"offset":207},{"line":205,"column":216,"offset":217},41,1015,{"start":219,"end":220},{"line":205,"column":206,"offset":207},{"line":205,"column":216,"offset":217},{"type":27,"value":222,"position":223},". Every class composes the\nlibrary's own primitives and follows its three rules: ",{"start":224,"end":225},{"line":205,"column":216,"offset":217},{"line":155,"column":175,"offset":226},1096,{"type":31,"tagName":69,"properties":228,"children":229,"position":236},{},[230],{"type":27,"value":231,"position":232},"NaN",{"start":233,"end":234},{"line":155,"column":175,"offset":226},{"line":155,"column":185,"offset":235},1101,{"start":237,"end":238},{"line":155,"column":175,"offset":226},{"line":155,"column":185,"offset":235},{"type":27,"value":240,"position":241}," until the\nclass is warm, ",{"start":242,"end":243},{"line":155,"column":185,"offset":235},{"line":244,"column":55,"offset":245},20,1127,{"type":31,"tagName":69,"properties":247,"children":248,"position":254},{},[249],{"type":27,"value":231,"position":250},{"start":251,"end":252},{"line":244,"column":55,"offset":245},{"line":244,"column":97,"offset":253},1132,{"start":255,"end":256},{"line":244,"column":55,"offset":245},{"line":244,"column":97,"offset":253},{"type":27,"value":258,"position":259}," while a non-finite input sits in its window (the\ntwo volume indices carry instead), and no allocation after the\nconstructor. The window arithmetic under them (",{"start":260,"end":261},{"line":244,"column":97,"offset":253},{"line":262,"column":263,"offset":264},22,48,1292,{"type":31,"tagName":69,"properties":266,"children":267,"position":275},{},[268],{"type":27,"value":269,"position":270},"History",{"start":271,"end":272},{"line":262,"column":263,"offset":264},{"line":262,"column":273,"offset":274},57,1301,{"start":276,"end":277},{"line":262,"column":263,"offset":264},{"line":262,"column":273,"offset":274},{"type":27,"value":279,"position":280},", ",{"start":281,"end":282},{"line":262,"column":273,"offset":274},{"line":262,"column":283,"offset":284},59,1303,{"type":31,"tagName":69,"properties":286,"children":287,"position":295},{},[288],{"type":27,"value":289,"position":290},"List",{"start":291,"end":292},{"line":262,"column":283,"offset":284},{"line":262,"column":293,"offset":294},65,1309,{"start":296,"end":297},{"line":262,"column":283,"offset":284},{"line":262,"column":293,"offset":294},{"type":27,"value":299,"position":300},", the\n",{"start":301,"end":302},{"line":262,"column":293,"offset":294},{"line":303,"column":21,"offset":304},23,1315,{"type":31,"tagName":69,"properties":306,"children":307,"position":314},{},[308],{"type":27,"value":309,"position":310},"stats.*",{"start":311,"end":312},{"line":303,"column":21,"offset":304},{"line":303,"column":87,"offset":313},1324,{"start":315,"end":316},{"line":303,"column":21,"offset":304},{"line":303,"column":87,"offset":313},{"type":27,"value":318,"position":319}," functions, rounding and a seeded random) is on\n",{"start":320,"end":321},{"line":303,"column":87,"offset":313},{"line":322,"column":21,"offset":323},24,1372,{"type":31,"tagName":44,"properties":325,"children":327,"position":337},{"href":326},"stats-history-lists.md",[328],{"type":27,"value":329,"position":330},"Stats, history and lists",{"start":331,"end":334},{"line":322,"column":332,"offset":333},2,1373,{"line":322,"column":335,"offset":336},26,1397,{"start":338,"end":339},{"line":322,"column":21,"offset":323},{"line":322,"column":340,"offset":341},51,1422,{"type":27,"value":343,"position":344},".",{"start":345,"end":346},{"line":322,"column":340,"offset":341},{"line":322,"column":347,"offset":348},52,1423,{"start":350,"end":351},{"line":141,"column":21,"offset":142},{"line":322,"column":347,"offset":348},{"type":27,"value":28},{"type":31,"tagName":354,"properties":355,"children":356,"position":377},"h2",{},[357,365],{"type":27,"value":358,"position":359},"Every class in 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