/**
 * earth-now.co
 * Author:  Simon-Pierre Boucher
 * Contact: contact@spboucher.ai
 * File:    apps/web/test/consistency-shared.ts
 * Purpose: Shared fixture for the client/server consistency tests — models, instants and hand-derivable closed-form expected values
 */

import {
  SEASONAL_EPOCH_MS,
  YEAR_SECONDS,
  parseIsoUtc,
  type CounterModel,
} from "@earth-now/counter";

export const ANCHOR_ISO = "2026-01-01T00:00:00.000Z";

/** Simple linear model — closed-form value is hand-derivable. */
export const LINEAR_MODEL: CounterModel = {
  metricId: "consistency_linear",
  anchorValue: 8_231_613_070,
  anchorTime: ANCHOR_ISO,
  rateFn: { kind: "linear", perSecond: 2.3 },
  observedAt: "2025-07-01T00:00:00.000Z",
  sourceId: "un_wpp_2024",
  modelVersion: "linear-stock-v1",
  displayHints: { decimals: 0, sigFigs: 7, unit: "people" },
};

/** Seasonal model with one annual harmonic — analytic integral, exact everywhere. */
export const SEASONAL_MODEL: CounterModel = {
  metricId: "consistency_seasonal",
  anchorValue: 0,
  anchorTime: ANCHOR_ISO,
  rateFn: {
    kind: "seasonal",
    base: 4.3,
    harmonics: [{ period: "year", order: 1, amplitude: 0.5, phase: 0.25 }],
  },
  observedAt: "2025-12-01T00:00:00.000Z",
  sourceId: "un_wpp_2024",
  modelVersion: "seasonal-ytd-v1",
  displayHints: { decimals: 0, unit: "births" },
};

/** Five instants across the year, including the anchor itself. */
export const INSTANTS: readonly number[] = [
  Date.UTC(2026, 0, 1, 0, 0, 0),
  Date.UTC(2026, 1, 15, 12, 0, 0),
  Date.UTC(2026, 5, 30, 23, 59, 59),
  Date.UTC(2026, 7, 9, 7, 30, 0),
  Date.UTC(2026, 11, 31, 23, 59, 59, 999),
];

/**
 * Closed-form linear value, replicating the exact arithmetic (and operation
 * order) of counterValue for kind=linear — provably v = a + r·Δt.
 */
export function linearClosedForm(tMs: number): number {
  const anchorMs = parseIsoUtc(LINEAR_MODEL.anchorTime);
  const rateFn = LINEAR_MODEL.rateFn;
  if (rateFn.kind !== "linear") throw new Error("fixture must be linear");
  return LINEAR_MODEL.anchorValue + (rateFn.perSecond * (tMs - anchorMs)) / 1000;
}

/**
 * Closed-form seasonal value: v(t) = a + base·(τ₁−τ₀) + (A/ω)·(sin(ωτ₁+φ) − sin(ωτ₀+φ)),
 * with ω = 2π·order / YEAR_SECONDS and τ measured from the seasonal epoch —
 * the analytic integral of the declared rate, in the same operation order as the runtime.
 */
export function seasonalClosedForm(tMs: number): number {
  const rateFn = SEASONAL_MODEL.rateFn;
  if (rateFn.kind !== "seasonal") throw new Error("fixture must be seasonal");
  const anchorMs = parseIsoUtc(SEASONAL_MODEL.anchorTime);
  const tau0 = (anchorMs - SEASONAL_EPOCH_MS) / 1000;
  const tau1 = (tMs - SEASONAL_EPOCH_MS) / 1000;
  let v = SEASONAL_MODEL.anchorValue + rateFn.base * (tau1 - tau0);
  for (const h of rateFn.harmonics) {
    const omega = (2 * Math.PI * h.order) / YEAR_SECONDS;
    v += (h.amplitude / omega) * (Math.sin(omega * tau1 + h.phase) - Math.sin(omega * tau0 + h.phase));
  }
  return v;
}