AB=CD

The simplest four-point harmonic: an A→B leg, a B→C retracement, and a C→D leg that mirrors A→B in length. Bullish (D a swing low) → +1, bearish → -1.

Quick reference

Item	Value
Family	Harmonic Patterns
Input type	Candle (uses high, low)
Output type	f64 (+1 / -1 / 0)
Output range	{-1.0, 0.0, +1.0}
Default parameters	none (swing threshold 5%, baked)
Warmup period	5
Interpretation	Reversal at the D completion

Formula

last four pivots A-B-C-D:
  BC / AB ∈ [0.382, 0.886]   (C retraces AB)
  CD / BC ∈ [1.13, 2.618]    (D extends BC)
  AB ≈ CD (within 10%)        (the two legs are equal — the defining symmetry)
direction: D a swing low → +1, a swing high → -1

The AB=CD is the structural core of the five-point harmonics; here it stands alone as a four-pivot pattern. See crates/wickra-core/src/indicators/abcd.rs.

Parameters

None. Swing threshold 0.05 is a baked-in family constant (pattern_swing.rs); the Fibonacci windows and the 10% leg-equality tolerance are documented detector constants. Abcd::new is infallible.

Inputs / Outputs

const _: fn(&mut wickra::Abcd, wickra::Candle) -> Option<f64> =
    <wickra::Abcd as wickra::Indicator>::update;

• Python. update((o,h,l,c,v,ts)) → float (never None); batch(open, high, low, close) → 1-D ndarray.
• Node. update(open, high, low, close) → number; batch(open, high, low, close) → number[].
• WASM. update(open, high, low, close) → number.

Warmup

warmup_period() == 5. Four confirmed pivots are required; the earliest bar that can confirm a fourth pivot is the fifth. Pinned by test accessors_and_metadata.

Edge cases

• Bullish AB=CD reports +1 (test bullish_abcd_is_plus_one).
• Bearish AB=CD reports -1 (test bearish_abcd_is_minus_one).
• Unequal legs report 0.0 (test unequal_legs_do_not_trigger).
• reset clears state (test reset_clears_state).
• Streaming equals batch (test batch_equals_streaming).

Examples

Rust

use wickra::{Abcd, Candle, Indicator};

fn main() -> Result<(), Box<dyn std::error::Error>> {
    // A=140 B=100 (AB=40) C=124.7 (BC=24.7, 0.618) D=84.7 (CD=40 = AB) → bullish.
    let bars = [
        (139.86, 140.0, 139.86, 139.86),
        (100.0, 138.6, 100.0, 100.0),
        (101.0, 124.7, 101.0, 101.0),
        (84.7, 123.453, 84.7, 84.7),
        (85.547, 93.17, 85.547, 85.547), // D confirms → bullish
    ];
    let mut pat = Abcd::new();
    let mut last = 0.0;
    for (ts, (o, h, l, c)) in bars.iter().enumerate() {
        last = pat.update(Candle::new(*o, *h, *l, *c, 1.0, ts as i64)?).unwrap();
    }
    println!("{last}"); // 1
    Ok(())
}

Python

import wickra as ta

bars = [
    (139.86, 140.0, 139.86, 139.86, 1.0, 0),
    (100.0, 138.6, 100.0, 100.0, 1.0, 1),
    (101.0, 124.7, 101.0, 101.0, 1.0, 2),
    (84.7, 123.453, 84.7, 84.7, 1.0, 3),
    (85.547, 93.17, 85.547, 85.547, 1.0, 4),
]
pat = ta.Abcd()
print([pat.update(b) for b in bars][-1])  # 1.0

Node

const wickra = require('wickra');
const bars = [
  [139.86, 140.0, 139.86, 139.86], [100.0, 138.6, 100.0, 100.0],
  [101.0, 124.7, 101.0, 101.0], [84.7, 123.453, 84.7, 84.7],
  [85.547, 93.17, 85.547, 85.547],
];
const pat = new wickra.Abcd();
let last = 0;
for (const [o, h, l, c] of bars) last = pat.update(o, h, l, c);
console.log(last); // 1

Streaming

pat = ta.Abcd()
for o, h, l, c, v, ts in candle_feed:
    signal = pat.update((o, h, l, c, v, ts))
    if signal != 0:
        pass  # AB=CD completed at D — reversal setup

Interpretation

1. The building block. Every five-point harmonic embeds an AB=CD into its B-C-D legs; as a standalone it is the most common, lowest-bar-count harmonic.
2. Equal legs. The defining feature is AB ≈ CD; the BC retracement and CD extension windows keep the proportions Fibonacci-consistent.

Common pitfalls

• Looser than five-point patterns. With only three legs constrained, AB=CD fires more often; treat it as a weaker standalone signal than the named five-point harmonics.
• Confirmation lag. Non-repainting but lags the visual D.

References

• Gartley, H. M. (1935); Carney, S. Harmonic Trading (2010).

See also

• Gartley, Bat, ThreeDrives.
• Indicators-Overview — full taxonomy.