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//! Point & Figure column construction (close-based, N-box reversal).
//!
//! A Point & Figure chart discards time and volume and reduces price to a grid
//! of boxes of height `box_size`. Price movement is drawn as columns: rising
//! columns of X's and falling columns of O's. A column keeps extending while
//! price advances by whole boxes, and a new (opposite) column starts only when
//! price reverses by at least `reversal` boxes from the current column's extreme
//! — the classic **N-box reversal** filter (`reversal = 3` is the traditional
//! default).
//!
//! This implements the **close-price** construction: each bar contributes its
//! close, quantised to the box grid `floor(price / box_size)`. On a reversal the
//! new column begins one box back from the prior extreme (the standard
//! `top − 1 … top − N` placement).
//!
//! Sources:
//! - Cohen, A. W. (1947), *How to Use the Three-Point Reversal Method of Point &
//! Figure Stock Market Trading* — origin of the three-box (N-box) reversal.
//! - du Plessis, J. (2012), *The Definitive Guide to Point and Figure*, 2nd ed. —
//! modern box-size / reversal construction; the close-price method.
//!
//! Two surfaces kept in parity (see the proptest):
//! - streaming: [`PointFigureBuilder::next`] pushes one close, returns a
//! completed column when a reversal starts a new one (else `None`);
//! - batch: [`point_figure_batch`] folds the builder over a close slice.
/// One completed Point & Figure column. `direction` is +1 (X, rising) or -1
/// (O, falling); `top`/`bottom` are the column's high/low box levels
/// (`top >= bottom`); `boxes` is the span between them in `box_size` units.
#[derive(Debug, Clone, Copy, PartialEq)]
pub struct PointFigureColumn {
pub top: f64,
pub bottom: f64,
pub direction: i8,
pub boxes: u32,
}
/// Stateful close-based Point & Figure builder.
#[derive(Debug, Clone)]
pub struct PointFigureBuilder {
box_size: f64,
reversal: u32,
/// Current column's high and low box indices (`floor(price / box_size)`).
hi_idx: i64,
lo_idx: i64,
/// Current column: +1 X, -1 O, 0 before the first box move establishes one.
direction: i8,
initialized: bool,
}
impl PointFigureBuilder {
/// Create a builder. `box_size` must be positive and `reversal >= 1`.
pub fn new(box_size: f64, reversal: u32) -> Self {
Self {
box_size,
reversal: reversal.max(1),
hi_idx: 0,
lo_idx: 0,
direction: 0,
initialized: false,
}
}
fn level(&self, idx: i64) -> f64 {
idx as f64 * self.box_size
}
/// Push one close; return a completed column if this close reversed the
/// current one, else `None`.
pub fn next(&mut self, close: f64) -> Option<PointFigureColumn> {
if self.box_size <= 0.0 || !close.is_finite() {
return None;
}
let i = (close / self.box_size).floor() as i64;
if !self.initialized {
self.hi_idx = i;
self.lo_idx = i;
self.initialized = true;
return None;
}
let rev = self.reversal as i64;
match self.direction {
0 => {
// First whole-box move fixes the initial column direction.
if i > self.hi_idx {
self.direction = 1;
self.hi_idx = i;
} else if i < self.lo_idx {
self.direction = -1;
self.lo_idx = i;
}
None
}
1 => {
// X column: extend up on a new high; reverse down `rev` boxes.
if i > self.hi_idx {
self.hi_idx = i;
None
} else if i <= self.hi_idx - rev {
let col = PointFigureColumn {
top: self.level(self.hi_idx),
bottom: self.level(self.lo_idx),
direction: 1,
boxes: (self.hi_idx - self.lo_idx) as u32,
};
// New O column starts one box below the prior top.
self.hi_idx -= 1;
self.lo_idx = i;
self.direction = -1;
Some(col)
} else {
None
}
}
_ => {
// O column: extend down on a new low; reverse up `rev` boxes.
if i < self.lo_idx {
self.lo_idx = i;
None
} else if i >= self.lo_idx + rev {
let col = PointFigureColumn {
top: self.level(self.hi_idx),
bottom: self.level(self.lo_idx),
direction: -1,
boxes: (self.hi_idx - self.lo_idx) as u32,
};
// New X column starts one box above the prior bottom.
self.lo_idx += 1;
self.hi_idx = i;
self.direction = 1;
Some(col)
} else {
None
}
}
}
}
}
/// Batch Point & Figure: fold [`PointFigureBuilder`] over a close slice.
pub fn point_figure_batch(closes: &[f64], box_size: f64, reversal: u32) -> Vec<PointFigureColumn> {
let mut b = PointFigureBuilder::new(box_size, reversal);
let mut out = Vec::new();
for &c in closes {
if let Some(col) = b.next(c) {
out.push(col);
}
}
out
}
/// ATR-box Point & Figure: box size is `multiplier * atr` (a single
/// representative ATR), matching the ATR-box convention of the other bar types.
pub fn point_figure_atr_batch(
closes: &[f64],
atr: f64,
multiplier: f64,
reversal: u32,
) -> Vec<PointFigureColumn> {
point_figure_batch(closes, atr * multiplier, reversal)
}
#[cfg(test)]
mod tests {
use super::*;
use proptest::prelude::*;
#[test]
fn gold_single_x_column_on_reversal() {
// box=1, rev=3. Rise 10→13 (X column [10,13]); fall to 10 (= 13-3) starts
// an O column and completes the X column.
let cols = point_figure_batch(&[10.0, 13.0, 10.0], 1.0, 3);
assert_eq!(cols.len(), 1);
assert_eq!(cols[0].direction, 1);
assert_eq!(cols[0].bottom, 10.0);
assert_eq!(cols[0].top, 13.0);
assert_eq!(cols[0].boxes, 3);
}
#[test]
fn gold_alternating_columns() {
// X [10,13], then O completes when price turns back up 3 boxes.
let cols = point_figure_batch(&[10.0, 13.0, 10.0, 7.0, 10.0], 1.0, 3);
let dirs: Vec<i8> = cols.iter().map(|c| c.direction).collect();
assert_eq!(dirs, vec![1, -1]);
// O column ran from the reversal top (12) down to 7.
assert_eq!(cols[1].top, 12.0);
assert_eq!(cols[1].bottom, 7.0);
}
#[test]
fn no_reversal_within_threshold() {
// A 2-box pullback (< reversal 3) never starts a new column.
assert!(point_figure_batch(&[10.0, 13.0, 11.0, 13.5], 1.0, 3).is_empty());
}
#[test]
fn atr_box_reversal_param() {
let cols = point_figure_atr_batch(&[10.0, 13.0, 10.0], 1.0, 1.0, 3);
assert_eq!(cols.len(), 1);
assert_eq!(cols[0].boxes, 3);
}
proptest! {
// Streaming (one at a time) must equal batch (fold).
#[test]
fn streaming_equals_batch(
closes in prop::collection::vec(0.0f64..1000.0, 1..200),
box_size in 0.5f64..50.0,
reversal in 1u32..5,
) {
let batch = point_figure_batch(&closes, box_size, reversal);
let mut b = PointFigureBuilder::new(box_size, reversal);
let mut streamed = Vec::new();
for &c in &closes {
if let Some(col) = b.next(c) {
streamed.push(col);
}
}
prop_assert_eq!(streamed, batch);
}
// Columns strictly alternate direction, and each column's open→close sign
// matches its stated direction with a positive box span.
#[test]
fn columns_alternate_and_consistent(
closes in prop::collection::vec(0.0f64..1000.0, 1..200),
box_size in 0.5f64..50.0,
reversal in 1u32..5,
) {
let cols = point_figure_batch(&closes, box_size, reversal);
for w in cols.windows(2) {
prop_assert_eq!(w[0].direction, -w[1].direction);
}
for c in &cols {
prop_assert!(c.direction == 1 || c.direction == -1);
prop_assert!(c.top >= c.bottom);
let span = ((c.top - c.bottom) / box_size).round() as u32;
prop_assert_eq!(span, c.boxes);
}
}
}
}