"""Algorithm 2 within 72 characters a line (it overflowed the page), same content; and the one
character pdflatex does not know (U+2265 in the availability statement).

    python -u apply_listing_width.py
"""
import re

PATH = "article/sim_numerics.md"
NEW = """```
state:  bracket [A,B], FA, FB; points x, xp, xp2; values fx, fp, fp2
memory: configs (configurations), moves (displacements)
flags:  last_model, in_regime,
        analogy_seen (with order m_a), shallow_seen (with order m_s)
initialise as Algorithm 1; allow <- 2^n_max * xtol/2
while |B - A| > xtol:
    far <- end of [A,B] further from x; mid <- (A+B)/2; model <- false
    f' <- derivative at x of the parabola through (x, xp, xp2)
    sigma <- |f'| * |far - x|
    if sigma is 0 or not finite:  xn <- mid
    else:
        z <- |fx| / sigma
        # the flat regime (6.1-6.3)
        c <- (xi, phi, |x-xp|, |fx-fp|), last three points, if defined
        # unkept promise, and unkept promise with a crossing
        flag      <- not in_regime and last_model and fx/fp >= 1/4
        flag_over <- not in_regime and last_model and fx/fp <= -1/4
        # order (6) of the analogous pair: the past configuration
        # nearest to c (Euclidean in (xi, phi)), if nearer than the
        # line phi = xi; inf if the pair shows L_f < 1 <= L_x; else none
        m <- order of the analogous pair
        if m >= 2:        analogy_seen <- true;  m_a <- m
        if 0 < m <= 2/3:  shallow_seen <- true;  m_s <- m
        if flag and analogy_seen:         in_regime <- true
        elif flag_over and shallow_seen:  in_regime <- true; m_a <- m_s
        append c to configs
        if in_regime:  xn <- split point (7) with m = m_a
        elif x != xp and
             sign((fx-fp)/(x-xp)) != sign((FB-FA)/(B-A)):  xn <- mid
        elif S(z) >= 1/2 and |f(far)| < |fx|:  xn <- mid
        else:
            step <- (1 - S(z)) * (far - x)               # eq. (4)
            append x - xp to moves
            # step pattern: the lag 2 .. half the history of highest
            # mean similarity of successive length ratios has mean > 1/2,
            # and step and x - xp point the same way
            if the pattern repeats:
                s <- min(|step|,|x-xp|) / max(|step|,|x-xp|)
                step <- step / (1 - s), at most |far - x| long
            if |step| < xtol/2 and last_model and |fx/fp| < 1/4:
                step <- sign(far - x) * xtol/2         # tolerance step
            xn <- x + step;  model <- true
        xn <- clamp(xn, hi - allow, lo + allow)       # projection (3)
    if xn outside (A,B) or xn in {x, xp}:
        xn <- mid;  if mid in {x, xp}: stop
    last_model <- model and xn is the model's own point
    fn <- f(xn)
    if in_regime:                                     # exit
        t <- (xn - A)/(B - A)
        if |fn - (FA(1-t) + FB t)| < |fn|:
            in_regime <- false;  analogy_seen <- false
    allow <- allow/2;  (xp2, xp, x) <- (xp, x, xn)
    keep the sign change in [A,B]
return midpoint(A,B)
```"""
src = open(PATH, encoding="utf8").read()
start = src.index("**Algorithm 2 (A′).**")
a = src.index("```", start)
b = src.index("```", a + 3) + 3
assert src.count("**Algorithm 2 (A′).**") == 1
src = src[:a] + NEW + src[b:]
assert src.count("Python ≥ 3.10") == 1
src = src.replace("Python ≥ 3.10", "Python 3.10 or later")
open(PATH, "w", encoding="utf8").write(src)
print("longest listing line:", max(len(l) for l in NEW.split("\n")))
print("non-latin1 characters left outside math:", sorted({c for c in re.sub(r"\$[^$]*\$", "", src)
                                                        if ord(c) > 0x2FFF}))