executeme

#!/bin/sh
set -eu

start_dir=$(pwd)
if [ -n "${CENTL_BIN:-}" ]; then
  case "$CENTL_BIN" in
    /*) centl_bin=$CENTL_BIN ;;
    *) centl_bin="$start_dir/$CENTL_BIN" ;;
  esac
else
  centl_bin='./centl'
fi

project_root=$(CDPATH= cd -- "$(dirname -- "$0")" && pwd)
cd "$project_root"

fail() {
  echo "centl gauntlet: $*" >&2
  exit 1
}

rounds=${CENTL_STRESS_ROUNDS:-192}
case "$rounds" in
  ''|*[!0-9]*) fail "CENTL_STRESS_ROUNDS must be a positive integer" ;;
esac
[ "$rounds" -gt 0 ] || fail "CENTL_STRESS_ROUNDS must be greater than zero"
[ "$rounds" -le 5000 ] || fail "CENTL_STRESS_ROUNDS is capped at 5000"

seed_input=${CENTL_STRESS_SEED:-}
if [ -z "$seed_input" ]; then
  clock_seed=$(date +%s 2>/dev/null || printf '1')
  seed_input=$((clock_seed + $$))
fi
case "$seed_input" in
  ''|*[!0-9]*) fail "CENTL_STRESS_SEED must be a non-negative integer" ;;
esac

seed=$seed_input
rng_state=$((seed_input % 2147483647))
[ "$rng_state" -gt 0 ] || rng_state=1

rand_between() {
  rb_lo=$1
  rb_hi=$2
  rng_state=$(( (rng_state * 48271) % 2147483647 ))
  RAND_VALUE=$(( rb_lo + (rng_state % (rb_hi - rb_lo + 1)) ))
}

rand_signed() {
  rs_max=$1
  rand_between 1 "$rs_max"
  rs_mag=$RAND_VALUE
  rand_between 0 1
  if [ "$RAND_VALUE" -eq 0 ]; then
    RAND_VALUE=$rs_mag
  else
    RAND_VALUE=$((-rs_mag))
  fi
}

contracts=$(mktemp "${TMPDIR:-/tmp}/centl-gauntlet.XXXXXX") || exit 1
log=$(mktemp "${TMPDIR:-/tmp}/centl-gauntlet-log.XXXXXX") || {
  rm -f "$contracts"
  exit 1
}

cleanup() {
  rm -f "$contracts" "$log"
}
trap cleanup EXIT
trap 'exit 129' HUP
trap 'exit 130' INT
trap 'exit 143' TERM

claims=0
claim() {
  printf '%s | %s | %s\n' "$1" "$2" "$3" >> "$contracts"
  claims=$((claims + 1))
}

cat >> "$contracts" <<'EOF_HEADER'
# CENTL randomized math + physics gauntlet.
# Generated by ./executeme. Every non-comment line must verify.
EOF_HEADER

# Deterministic exact arithmetic and algebra anchors.
claim equal '0.1 + 0.2' '3/10'
claim equal '1/3 + 1/6' '1/2'
claim equal '(10^80 + 1) - 10^80' '1'
claim equal '((123456789/97) * 97)' '123456789'
claim equal '((999999937 + 1)^3)' '(999999937^3 + 3*999999937^2 + 3*999999937 + 1)'
claim equal 'sum(k, k = 1, 1000)' '500500'
claim equal 'sum(k^2, k = 1, 1000)' '333833500'
claim equal 'sum(k^3, k = 1, 100)' '25502500'
claim equal 'product((k + 1)/k, k = 1, 250)' '251'
claim equal 'factorial(30)' '265252859812191058636308480000000'
claim equal 'choose(100, 3)' '161700'
claim equal 'fibonacci(50)' '12586269025'
claim equal 'gcd(123456, 7890)' '6'
claim equal 'substitute(diff(x^5 - 3*x^3 + 7*x - 11, x), x = 2)' '51'
claim equal 'integrate(x^4 - 2*x^2 + 1, x = 0, 3)' '168/5'
claim equal 'integrate(3*x^2 + 2*x + 1, x = 0, 10)' '1110'
claim equal 'distance(0, 0, 300, 400)' '500'
claim equal 'hypot(3000, 4000)' '5000'

# Certified real-enclosure anchors. Equality is intentionally avoided here.
claim greater_than 'sqrt(2)' '1414/1000'
claim less_than 'sqrt(2)' '1415/1000'
claim greater_than 'pi' '31415/10000'
claim less_than 'pi' '31416/10000'
claim greater_than 'sin(pi / 6)' '4999/10000'
claim less_than 'sin(pi / 6)' '5001/10000'
claim greater_than 'exp(1)' '2718/1000'
claim less_than 'exp(1)' '2719/1000'
claim greater_than 'log(e)' '999/1000'
claim less_than 'log(e)' '1001/1000'

# Deterministic mechanics anchors expressed only through shipped CENTL math.
claim equal '(3 * 14)' '42'
claim equal '((1/2) * 3 * 14^2)' '294'
claim equal '(5 * (981/100) * 12)' '2943/5'
claim equal '((1/2) * (981/100) * 10^2)' '981/2'
claim equal '((40 * 8) - (1/2) * 10 * 8^2)' '0'
claim equal '(30 * 8)' '240'
claim equal '(40^2 / (2 * 10))' '80'
claim equal '((2 * 9^2 / 3) * 3)' '(2 * 9^2)'
claim equal '(1200 * (981/100) * 15)' '(1200 * (981/100) * 20 - 1200 * (981/100) * 5)'
claim equal '(50 * (3/5))' '30'
claim equal '(12 * (5/4))' '15'
claim equal '(1 / (10*20/(10+20)))' '(1/10 + 1/20)'

iteration=1
while [ "$iteration" -le "$rounds" ]; do
  rand_signed 97; a=$RAND_VALUE
  rand_between 1 97; b=$RAND_VALUE
  rand_signed 97; c=$RAND_VALUE
  rand_between 1 97; d=$RAND_VALUE
  rand_signed 31; e=$RAND_VALUE
  rand_between 2 40; n=$RAND_VALUE
  rand_between 0 $((n - 1)); k=$RAND_VALUE
  rand_between 1 12; p=$RAND_VALUE
  rand_between 2 20; q=$RAND_VALUE

  # Exact rational arithmetic, distributivity, and polynomial evaluation.
  claim equal "(($a)/$b + ($c)/$d)" "((($a)*$d + ($c)*$b)/($b*$d))"
  claim equal "((($a)/$b) * ($b/($a)))" '1'
  claim equal "(($a)*(($c)+$e))" "(($a)*($c) + ($a)*$e)"
  claim equal "((($a)+($c))^3)" "(($a)^3 + 3*($a)^2*($c) + 3*($a)*($c)^2 + ($c)^3)"

  # Finite sums, combinatorics, and integer recurrences.
  claim equal "sum(j, j = 1, $n)" "($n*($n+1)/2)"
  claim equal "sum(j^2, j = 1, $n)" "($n*($n+1)*(2*$n+1)/6)"
  claim equal "factorial($((p + 1)))" "($((p + 1)) * factorial($p))"
  claim equal "choose($n, $k) + choose($n, $((k + 1)))" "choose($((n + 1)), $((k + 1)))"
  claim equal "fibonacci($((q + 2)))" "fibonacci($((q + 1))) + fibonacci($q)"

  # Calculus: compare production differentiation/integration with independent formulas.
  claim equal \
    "substitute(diff(($a)*x^4 + ($c)*x^3 + ($e)*x^2 + $b*x + $d, x), x = $p)" \
    "(4*($a)*$p^3 + 3*($c)*$p^2 + 2*($e)*$p + $b)"
  claim equal \
    "integrate(($a)*x^4 + ($c)*x^2 + $b*x + $d, x = 0, $p)" \
    "(($a)*$p^5/5 + ($c)*$p^3/3 + $b*$p^2/2 + $d*$p)"

  # Pythagorean geometry, useful as an exact spatial mechanics primitive.
  claim equal "distance(0, 0, $((3 * p)), $((4 * p)))" "$((5 * p))"

  # Newtonian work-energy under constant acceleration.
  rand_between 1 50; mass=$RAND_VALUE
  rand_signed 40; u=$RAND_VALUE
  rand_signed 20; acc=$RAND_VALUE
  rand_between 1 20; t=$RAND_VALUE
  claim equal \
    "((1/2)*$mass*((($u)+($acc)*$t)^2-($u)^2))" \
    "(($mass*($acc))*(($u)*$t+(1/2)*($acc)*$t^2))"

  # Impulse-momentum consistency.
  claim equal \
    "($mass*(($u)+($acc)*$t)-$mass*($u))" \
    "(($mass*($acc))*$t)"

  # Uniform-gravity mechanical energy conservation in one dimension.
  rand_between 1 30; g=$RAND_VALUE
  claim equal \
    "((1/2)*$mass*(($u)-$g*$t)^2 + $mass*$g*(($u)*$t-(1/2)*$g*$t^2))" \
    "((1/2)*$mass*($u)^2)"

  # Hooke/spring work checked through exact integration.
  rand_between 1 60; spring_k=$RAND_VALUE
  rand_between 1 15; x1=$RAND_VALUE
  rand_between 1 15; x2=$RAND_VALUE
  claim equal \
    "integrate($spring_k*x, x = $x1, $x2)" \
    "((1/2)*$spring_k*($x2^2-$x1^2))"

  # Inverse-square force scaling (G and masses cancel exactly).
  rand_between 1 100; m1=$RAND_VALUE
  rand_between 1 100; m2=$RAND_VALUE
  rand_between 1 30; r=$RAND_VALUE
  claim equal \
    "((($m1*$m2)/($r^2))/(($m1*$m2)/((2*$r)^2)))" \
    '4'

  # Centripetal-force invariant F*r = m*v^2.
  rand_between 1 80; speed=$RAND_VALUE
  claim equal \
    "((($mass*$speed^2)/$r)*$r)" \
    "($mass*$speed^2)"

  # Wave relation v = f*lambda with exact rational wavelength.
  rand_between 1 1000; wave_v=$RAND_VALUE
  rand_between 1 200; freq=$RAND_VALUE
  claim equal "($freq*($wave_v/$freq))" "$wave_v"

  # Thin-lens reciprocal identity with an exact constructed focal length.
  rand_between 2 100; obj=$RAND_VALUE
  rand_between 2 100; img=$RAND_VALUE
  claim equal \
    "(1/(($obj*$img)/($obj+$img)))" \
    "(1/$obj + 1/$img)"

  # Hydrostatic pressure difference.
  rand_between 1 2000; rho=$RAND_VALUE
  rand_between 1 100; h1=$RAND_VALUE
  rand_between "$h1" $((h1 + 100)); h2=$RAND_VALUE
  claim equal \
    "($rho*$g*($h2-$h1))" \
    "($rho*$g*$h2-$rho*$g*$h1)"

  # Ohmic power equivalence P = VI = I^2 R.
  rand_between 1 100; current=$RAND_VALUE
  rand_between 1 100; resistance=$RAND_VALUE
  claim equal \
    "(($current*$resistance)*$current)" \
    "($current^2*$resistance)"

  # Rotational work-energy for constant angular acceleration.
  rand_between 1 40; inertia=$RAND_VALUE
  rand_signed 20; omega=$RAND_VALUE
  rand_between 1 20; alpha=$RAND_VALUE
  rand_between 1 20; theta=$RAND_VALUE
  claim equal \
    "(($inertia*$alpha)*$theta)" \
    "((1/2)*$inertia*((($omega)^2+2*($alpha)*$theta)-($omega)^2))"

  # General 1D elastic collision: independently check momentum and kinetic energy.
  rand_between 1 30; cm1=$RAND_VALUE
  rand_between 1 30; cm2=$RAND_VALUE
  rand_signed 30; cu1=$RAND_VALUE
  rand_signed 30; cu2=$RAND_VALUE
  v1="((($cm1-$cm2)*($cu1)+2*$cm2*($cu2))/($cm1+$cm2))"
  v2="((2*$cm1*($cu1)+($cm2-$cm1)*($cu2))/($cm1+$cm2))"
  claim equal \
    "($cm1*($cu1)+$cm2*($cu2))" \
    "($cm1*$v1+$cm2*$v2)"
  claim equal \
    "($cm1*($cu1)^2+$cm2*($cu2)^2)" \
    "($cm1*($v1)^2+$cm2*($v2)^2)"

  # Periodically force very large arbitrary-precision polynomial cancellation.
  if [ $((iteration % 16)) -eq 0 ]; then
    rand_between 100000 999999; big1=$RAND_VALUE
    rand_between 100000 999999; big2=$RAND_VALUE
    big="${big1}${big2}${big1}${big2}"
    claim equal \
      "(($big+1)^3)" \
      "($big^3+3*$big^2+3*$big+1)"
  fi

  iteration=$((iteration + 1))
done

if [ "${CENTL_STRESS_VERBOSE:-0}" = 1 ]; then
  echo "centl gauntlet seed=$seed rounds=$rounds claims=$claims" >&2
fi

if "$centl_bin" check "$contracts" >"$log" 2>&1; then
  printf '1\n'
else
  status=$?
  echo "centl gauntlet: FAIL (seed=$seed rounds=$rounds claims=$claims exit=$status)" >&2
  echo "replay: CENTL_STRESS_SEED=$seed CENTL_STRESS_ROUNDS=$rounds ./executeme" >&2
  cat "$log" >&2
  exit "$status"
fi