/*! noble-ed25519 - MIT License (c) 2019 Paul Miller (paulmillr.com) */
/**
 * 5KB JS implementation of ed25519 EdDSA signatures.
 * Targets RFC8032, FIPS 186-5, and ZIP215 behavior.
 * @module
 * @example
 * ```js
import * as ed from '@noble/ed25519';
(async () => {
  const secretKey = ed.utils.randomSecretKey();
  const message = Uint8Array.from([0xab, 0xbc, 0xcd, 0xde]);
  const pubKey = await ed.getPublicKeyAsync(secretKey); // Sync methods are also present
  const signature = await ed.signAsync(message, secretKey);
  const isValid = await ed.verifyAsync(signature, message, pubKey);
})();
```
 */
/**
 * Curve params. edwards25519 uses the RFC equation `-x² + y² = 1 + dx²y²`.
 * The stored `a` literal below is `p - 1`, i.e. the field-element encoding of RFC `a = -1`.
 * * P = `2n**255n - 19n` // field over which calculations are done
 * * N = `2n**252n + 27742317777372353535851937790883648493n` // prime-order subgroup order
 * * h = 8 // cofactor
 * * a = `Fp.create(BigInt(-1))` // equation param, stored here as `p - 1`
 * * d = -121665/121666 a.k.a. `Fp.neg(121665 * Fp.inv(121666))` // equation param
 * * Gx, Gy are coordinates of Generator / base point
 *
 * Mirror noble-curves: Point.CURVE() exposes shared params, but callers must not be able to mutate
 * that shared view and desynchronize it from the arithmetic constants captured below.
 */
const freeze = Object.freeze;
const P = 0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffedn;
const N = 0x1000000000000000000000000000000014def9dea2f79cd65812631a5cf5d3edn;
const _d = 0x52036cee2b6ffe738cc740797779e89800700a4d4141d8ab75eb4dca135978a3n;
const Gx = 0x216936d3cd6e53fec0a4e231fdd6dc5c692cc7609525a7b2c9562d608f25d51an;
const Gy = 0x6666666666666666666666666666666666666666666666666666666666666658n;
const _a = P - 1n; // field-element encoding of RFC `a = -1`
const ed25519_CURVE: EdwardsOpts = freeze({
  p: P,
  n: N,
  h: 8n,
  a: _a,
  d: _d,
  Gx,
  Gy,
});
// Shared 32-byte encoded width for Ed25519 points, scalars, signatures/2, and keys. Named LEN
// rather than RFC 8032's `L`, which names the group order (stored here as `N`).
const LEN = 32;
/** Alias to Uint8Array. */
export type Bytes = Uint8Array;
/** Edwards elliptic curve options. */
export type EdwardsOpts = Readonly<{
  /** Prime field modulus. */
  p: bigint;
  /** Group order. */
  n: bigint;
  /** Curve cofactor. */
  h: bigint;
  /** Edwards curve parameter `a`. */
  a: bigint;
  /** Edwards curve parameter `d`. */
  d: bigint;
  /** Generator x coordinate. */
  Gx: bigint;
  /** Generator y coordinate. */
  Gy: bigint;
}>;

// Helpers and Precomputes sections are reused between libraries

// ## Helpers
// ----------
/** Checks if something is Uint8Array. Be careful: nodejs Buffer will return true. */
const isBytes = (a: unknown): a is Uint8Array => {
  // Plain `instanceof Uint8Array` is too strict for some Buffer / proxy / cross-realm cases.
  // The fallback still requires a real ArrayBuffer view, so plain
  // JSON-deserialized `{ constructor: ... }` spoofing is rejected, and
  // `BYTES_PER_ELEMENT === 1` keeps the fallback on byte-oriented views.
  return (
    a instanceof Uint8Array ||
    (ArrayBuffer.isView(a) &&
      a.constructor.name === 'Uint8Array' &&
      (a as Uint8Array).BYTES_PER_ELEMENT === 1)
  );
};
/** Asserts something is Bytes. */
const abytes = (value: unknown, length?: number, title: string = ''): TRet<Uint8Array> => {
  // Success path first: this runs at the start of every update() / digestInto(), and the
  // common `abytes(data)` form must not pay for length handling it does not use.
  if (isBytes(value) && (length === undefined || value.length === length))
    return value as TRet<Uint8Array>;
  // Error path: recompute freely to build the exact message.
  const bytes = isBytes(value);
  const ofLen = length !== undefined ? ` of length ${length}` : '';
  const got = bytes ? `length=${value.length}` : `type=${typeof value}`;
  const message = (title ? `"${title}" ` : '') + 'expected Uint8Array' + ofLen + ', got ' + got;
  if (!bytes) throw new TypeError(message);
  throw new RangeError(message);
};
// Validate, then take one owned copy, so later caller mutation cannot be observed — e.g. cannot
// make sign()'s nonce derivation and challenge derivation see different messages.
const snapshotBytes = (value: unknown, title: string = '', length?: number): TRet<Uint8Array> =>
  Uint8Array.from(abytes(value, length, title));
// Callers keep values non-negative and within the requested width; padStart() won't truncate over-wide inputs.
const padh = (n: number | bigint, pad: number) => n.toString(16).padStart(pad, '0');
/** Convert byte array to hex string. */
const bytesToHex = (bytes: TArg<Uint8Array>): string => {
  let hex = '';
  for (const byte of abytes(bytes)) hex += padh(byte, 2);
  return hex;
};
/** Convert hex string to byte array. */
const hexToBytes = (hex: string): TRet<Uint8Array> => {
  const e = 'hex invalid'; // Strict ASCII hex only, with one generic error for parse failures.
  if (typeof hex !== 'string') throw new TypeError(e);
  if (hex.length % 2 || !/^[\da-f]*$/i.test(hex)) throw new RangeError(e);
  const array = new Uint8Array(hex.length / 2);
  for (let ai = 0, hi = 0; ai < array.length; ai++, hi += 2) {
    const n1 = hex.charCodeAt(hi);
    const n2 = hex.charCodeAt(hi + 1);
    // Regex guarantees ASCII. For 0..9/A..F/a..f, this maps char codes to 0..15.
    array[ai] = ((n1 & 15) + (n1 >> 6) * 9) * 16 + (n2 & 15) + (n2 >> 6) * 9;
  }
  return array as TRet<Uint8Array>;
};
declare const globalThis: Record<string, any> | undefined; // Typescript symbol present in browsers
// WebCrypto is available in all modern environments
/** Copies several Uint8Arrays into one. */
const concatBytes = (...arrays: TArg<Uint8Array[]>): TRet<Uint8Array> => {
  let sum = 0;
  for (const a of arrays) sum += abytes(a).length;
  const res = new Uint8Array(sum);
  let pad = 0;
  for (const a of arrays) {
    res.set(a, pad);
    pad += a.length;
  }
  return res;
};
/**
 * WebCrypto OS-level CSPRNG (random number generator).
 * Will throw when not available; large-request ceilings are delegated to getRandomValues().
 */
const randomBytes = (len: number = LEN): TRet<Uint8Array> => {
  const c = globalThis?.crypto;
  if (typeof c?.getRandomValues !== 'function')
    throw new Error('crypto.getRandomValues must be defined, consider polyfill');
  return c.getRandomValues(new Uint8Array(len)) as TRet<Uint8Array>;
};
/** Inclusive-lower, exclusive-upper bigint range assertion. */
const arange = (n: bigint, min: bigint, max: bigint, msg = 'bad number: out of range'): bigint => {
  if (typeof n !== 'bigint') throw new TypeError(msg);
  if (min <= n && n < max) return n;
  throw new RangeError(msg);
};
/** Canonical modular reduction. Callers must provide a positive modulus. */
const mod = (a: bigint, b: bigint = P) => ((a %= b) >= 0n ? a : b + a);
// Low-255-bit mask used by the `2^255 - 19` fast reduction in `modP(...)`.
const P_MASK = (1n << 255n) - 1n;
// Fast reduction for the special prime `2^255 - 19`. This path assumes nonnegative inputs; the
// generic fallback would simply be `mod(num, P)`.
const modP = (num: bigint): bigint => {
  if (num < 0n) throw new RangeError('negative coordinate');
  let r = (num >> 255n) * 19n + (num & P_MASK);
  r = (r >> 255n) * 19n + (r & P_MASK);
  return r % P;
};
// Reduce modulo the subgroup order stored in implementation constant `N` (RFC 8032's `L`).
const modN = (a: bigint) => mod(a, N);
/** Modular inversion using extended euclidean GCD. Variable-time (non-CT). */
const invert = (number: bigint, modulo: bigint): bigint => {
  if (number === 0n) throw new Error('invert: expected non-zero number');
  // modulo = 1 is the zero ring: gcd(x, 1) = 1 makes the loop below "succeed" and return the
  // useless inverse 0. Reject it like pow() and invertCt() do.
  if (modulo <= 1n) throw new Error('invert: expected modulus > 1, got ' + modulo);
  // This is variable-time: the loop count depends on `number`.
  let a = mod(number, modulo);
  let b = modulo;
  // Only the Bézout coefficient of `number` (x/u chain) is tracked; the coefficient of `modulo`
  // never affects the output, so it is not computed.
  // prettier-ignore
  let x = 0n, u = 1n;
  while (a !== 0n) {
    const q = b / a;
    const r = b - a * q;
    const m = x - u * q;
    // prettier-ignore
    b = a, a = r, x = u, u = m;
  }
  const gcd = b;
  if (gcd !== 1n) throw new Error('invert: does not exist');
  return mod(x, modulo);
};
// Dynamic lookup keeps sync/async hash providers configurable at runtime. Both exported slots are
// caller-owned and may be unset; wrapper helpers use this lookup first and then enforce the digest
// contract instead of trusting provider output.
const _hash = (name: string) => {
  // @ts-ignore
  const fn = hashes[name];
  if (typeof fn !== 'function') throw new Error('hashes.' + name + ' not set');
  return fn;
};
// All exported provider slots are caller-configurable and may be unset or return arbitrary values,
// so wrapper helpers must enforce the exact 64-byte SHA-512 digest contract instead of trusting providers.
const callHash = (name: string, ...m: Uint8Array[]): TRet<Uint8Array> =>
  abytes(_hash(name)(concatBytes(...m)), 64, 'digest');
const callHashAsync = async (name: string, ...m: Uint8Array[]): Promise<TRet<Uint8Array>> =>
  abytes(await _hash(name)(concatBytes(...m)), 64, 'digest');
/**
 * SHA-512 helper used by the synchronous API.
 * @param msg - Message bytes to hash.
 * @returns 64-byte SHA-512 digest.
 * @example
 * Hash message bytes after wiring the synchronous SHA-512 implementation.
 *
 * ```ts
 * import * as ed from '@noble/ed25519';
 * import { sha512 } from '@noble/hashes/sha2.js';
 *
 * ed.hashes.sha512 = sha512;
 * const digest = ed.hash(new Uint8Array([1, 2, 3]));
 * ```
 */
// Public helper validates the message boundary explicitly; the configured provider is still looked
// up dynamically and its output is checked with `callHash(...)`.
const hash = (msg: TArg<Uint8Array>): TRet<Uint8Array> =>
  callHash('sha512', abytes(msg, undefined, 'message'));
// Runtime class guard: this is `instanceof Point`, so cross-realm / duplicate-bundle Point objects
// are rejected even if they are structurally identical.
const apoint = (p: unknown) => {
  if (p instanceof Point) return p;
  throw new TypeError('Point expected');
};
/** Point in 2d xy affine coordinates. */
export type AffinePoint = {
  /** Affine x coordinate. */
  x: bigint;
  /** Affine y coordinate. */
  y: bigint;
};
// ## End of Helpers
// -----------------

// Exclusive upper bound `2^256` used by 32-byte decode/serialization range checks.
const B256 = 2n ** 256n;
/**
 * Point in XYZT extended coordinates.
 * @param X - X coordinate.
 * @param Y - Y coordinate.
 * @param Z - Projective Z coordinate.
 * @param T - Cached cross-product term.
 * @example
 * Do point arithmetic with the built-in base point and encode the result as hex.
 *
 * ```ts
 * const hex = Point.BASE.double().toHex();
 * ```
 */
class Point {
  static BASE: Point;
  static ZERO: Point;
  readonly X: bigint;
  readonly Y: bigint;
  readonly Z: bigint;
  readonly T: bigint;
  // Constructor only bounds-checks and freezes XYZT coordinates; it does not prove the point is
  // on-curve or that T matches X*Y/Z.
  constructor(X: bigint, Y: bigint, Z: bigint, T: bigint) {
    const max = B256;
    this.X = arange(X, 0n, max);
    this.Y = arange(Y, 0n, max);
    this.Z = arange(Z, 1n, max);
    this.T = arange(T, 0n, max);
    freeze(this);
  }
  static CURVE(): EdwardsOpts {
    return ed25519_CURVE;
  }
  static fromAffine(p: AffinePoint): Point {
    return new Point(p.x, p.y, 1n, modP(p.x * p.y));
  }
  /** RFC8032 5.1.3: Uint8Array to Point. */
  static fromBytes(bytes: TArg<Uint8Array>, zip215 = false): Point {
    const normed = snapshotBytes(bytes, 'point', LEN); // owned copy: sign-bit mask below mutates it
    // adjust first LE byte = last BE byte
    const lastByte = normed[31];
    normed[31] = lastByte & ~0x80;
    const y = bytesToNumberLE(normed);
    // After clearing the sign bit, parsed `y` is always < 2^255. ZIP-215 still accepts the full
    // post-mask range here, while strict RFC8032 decoding further requires `y < p`.
    if (!zip215) arange(y, 0n, P);

    const y2 = modP(y * y); // y²
    const u = mod(y2 - 1n); // u=y²-1
    const v = modP(_d * y2 + 1n); // v=dy²+1
    let { isValid, value: x } = uvRatio(u, v); // (uv³)(uv⁷)^(p-5)/8; square root
    if (!isValid) throw new Error('bad point: y not sqrt'); // not square root: bad point
    const isLastByteOdd = !!(lastByte & 0x80); // x_0, last bit
    // ZIP-215-compatible decoding keeps the x=0 / sign-bit=1 encoding accepted; strict RFC 8032
    // rejects it, but the vendored ZIP-215 compliance vectors include this form in A/R bytes.
    if (!zip215 && x === 0n && isLastByteOdd) throw new Error('bad point: x==0, isLastByteOdd'); // x=0, x_0=1
    if (isLastByteOdd !== !!(x & 1n)) x = mod(-x); // adjust sign of x coordinate
    return new Point(x, y, 1n, modP(x * y)); // Z=1, T=xy
  }
  static fromHex(hex: string, zip215?: boolean): Point {
    return Point.fromBytes(hexToBytes(hex), zip215);
  }
  get x(): bigint {
    return this.toAffine().x;
  }
  get y(): bigint {
    return this.toAffine().y;
  }
  /** Checks if the point is valid and on-curve. */
  assertValidity(): this {
    const a = _a;
    const d = _d;
    const p = this;
    // Intentional stricter-than-on-curve policy: reject ZERO by default because many protocols
    // require a non-zero point, and silently accepting identity points is a common caller mistake.
    if (p.is0()) throw new Error('bad point: ZERO');
    // Equation in affine coordinates: ax² + y² = 1 + dx²y²
    // Equation in projective coordinates (X/Z, Y/Z, Z):  (aX² + Y²)Z² = Z⁴ + dX²Y²
    const { X, Y, Z, T } = p;
    const X2 = modP(X * X); // X²
    const Y2 = modP(Y * Y); // Y²
    const Z2 = modP(Z * Z); // Z²
    const Z4 = modP(Z2 * Z2); // Z⁴
    const aX2 = modP(X2 * a); // aX²
    const left = modP(Z2 * (aX2 + Y2)); // (aX² + Y²)Z²
    const right = mod(Z4 + modP(d * modP(X2 * Y2))); // Z⁴ + dX²Y²
    if (left !== right) throw new Error('bad point: equation left != right (1)');
    // In Extended coordinates we also have T, which is x*y=T/Z: check X*Y == Z*T
    const XY = modP(X * Y);
    const ZT = modP(Z * T);
    if (XY !== ZT) throw new Error('bad point: equation left != right (2)');
    return this;
  }
  /** Equality check: compare points P&Q. */
  equals(other: Point): boolean {
    const { X: X1, Y: Y1, Z: Z1 } = this;
    const { X: X2, Y: Y2, Z: Z2 } = apoint(other); // checks class equality
    return modP(X1 * Z2) === modP(X2 * Z1) && modP(Y1 * Z2) === modP(Y2 * Z1);
  }
  is0(): boolean {
    return this.equals(I);
  }
  /** Flip point over y coordinate. */
  negate(): Point {
    return new Point(mod(-this.X), this.Y, this.Z, mod(-this.T));
  }
  /** Point doubling. Complete formula. Cost: `4M + 4S + 1*a + 6add + 1*2`. */
  double(): Point {
    const { X: X1, Y: Y1, Z: Z1 } = this;
    const a = _a;
    // https://hyperelliptic.org/EFD/g1p/auto-twisted-extended.html#doubling-dbl-2008-hwcd
    const A = modP(X1 * X1);
    const B = modP(Y1 * Y1);
    const C = modP(2n * Z1 * Z1);
    const D = modP(a * A);
    const x1y1 = mod(X1 + Y1);
    const E = mod(modP(x1y1 * x1y1) - A - B);
    const G = mod(D + B);
    const F = mod(G - C);
    const H = mod(D - B);
    const X3 = modP(E * F);
    const Y3 = modP(G * H);
    const T3 = modP(E * H);
    const Z3 = modP(F * G);
    return new Point(X3, Y3, Z3, T3);
  }
  /** Point addition. Complete formula. Cost: `9M + 1*a + 1*d + 7add`. */
  add(other: Point): Point {
    const { X: X1, Y: Y1, Z: Z1, T: T1 } = this;
    const { X: X2, Y: Y2, Z: Z2, T: T2 } = apoint(other); // doesn't check if other on-curve
    const a = _a;
    const d = _d;
    // https://hyperelliptic.org/EFD/g1p/auto-twisted-extended.html#addition-add-2008-hwcd
    const A = modP(X1 * X2);
    const B = modP(Y1 * Y2);
    const C = modP(modP(T1 * d) * T2);
    const D = modP(Z1 * Z2);
    const E = mod(modP(mod(X1 + Y1) * mod(X2 + Y2)) - A - B);
    const F = mod(D - C);
    const G = mod(D + C);
    const H = mod(B - modP(a * A));
    const X3 = modP(E * F);
    const Y3 = modP(G * H);
    const T3 = modP(E * H);
    const Z3 = modP(F * G);
    return new Point(X3, Y3, Z3, T3);
  }
  subtract(other: Point): Point {
    return this.add(apoint(other).negate());
  }
  /**
   * Point-by-scalar multiplication. Safe mode requires `1 <= n < CURVE.n`.
   * Unsafe mode additionally permits `n = 0` and returns the identity point for that case.
   * Uses {@link wNAF} for base point.
   * Uses fake point to mitigate side-channel leakage.
   * @param n - scalar by which point is multiplied
   * @param safe - safe mode guards against timing attacks; unsafe mode is faster
   */
  multiply(n: bigint, safe = true): Point {
    // Mirror noble-curves: unsafe mode still validates scalar range first, but intentionally keeps
    // `n = 0` as the one extra accepted case used by verification-style callers.
    if (!safe && n === 0n) return I;
    arange(n, 1n, N);
    if (!safe && this.is0()) return I;
    if (n === 1n) return this;
    if (this.equals(G)) return wNAF(n).p;
    // init result point & fake point
    let p = I;
    let f = G;
    let d: Point = this;
    // Safe mode always runs 256 iterations so ladder length can't leak the scalar's
    // leading zero bits; unsafe mode stops at the top set bit for speed.
    for (let i = 0; safe ? i < 256 : n > 0n; i++) {
      // if bit is present, add to point
      // if not present, add to fake, for timing safety
      if (n & 1n) p = p.add(d);
      else if (safe) f = f.add(d);
      d = d.double();
      n >>= 1n;
    }
    return p;
  }
  multiplyUnsafe(scalar: bigint): Point {
    return this.multiply(scalar, false);
  }
  /** Convert point to 2d xy affine point. (X, Y, Z) ∋ (x=X/Z, y=Y/Z) */
  toAffine(): AffinePoint {
    const { X, Y, Z } = this;
    // Fast-path only for the identity point; all other inputs still go through inversion.
    if (this.equals(I)) return { x: 0n, y: 1n };
    const iz = invert(Z, P);
    // (Z * Z^-1) must be 1, otherwise bad math
    if (modP(Z * iz) !== 1n) throw new Error('invalid inverse');
    // x = X*Z^-1; y = Y*Z^-1
    return { x: modP(X * iz), y: modP(Y * iz) };
  }
  toBytes(): TRet<Uint8Array> {
    const { x, y } = this.toAffine();
    const b = numTo32bLE(y);
    // store sign in first LE byte
    b[31] |= x & 1n ? 0x80 : 0;
    return b;
  }
  toHex(): string {
    return bytesToHex(this.toBytes());
  }

  clearCofactor(): Point {
    return this.multiply(8n, false); // h = 8
  }
  isSmallOrder(): boolean {
    return this.clearCofactor().is0();
  }
  isTorsionFree(): boolean {
    // Multiply by big number N. We can't `mul(N)` because of checks. Instead, we `mul(N/2)*2+1`;
    // N is odd, so N/2 truncates and the final `add(this)` is always needed.
    return this.multiply(N / 2n, false)
      .double()
      .add(this)
      .is0();
  }
}
/** Generator / base point */
const G: Point = new Point(Gx, Gy, 1n, mod(Gx * Gy));
/** Identity / zero point */
const I: Point = new Point(0n, 1n, 1n, 0n);
// Static aliases
Point.BASE = G;
Point.ZERO = I;

const numTo32bLE = (num: bigint): TRet<Uint8Array> =>
  hexToBytes(padh(arange(num, 0n, B256), 64)).reverse() as TRet<Uint8Array>;
// Caller-enforced width: some sites require 32-byte RFC encodings, while others intentionally feed
// wider SHA-512 output chunks through the same little-endian parser.
const bytesToNumberLE = (b: Uint8Array): bigint =>
  BigInt('0x' + bytesToHex(Uint8Array.from(abytes(b)).reverse()));

const pow2 = (x: bigint, power: number): bigint => {
  // pow2(x, 4) == x^(2^4)
  // Negative `power` values are not rejected here and currently leave `x` unchanged.
  let r = x;
  while (power-- > 0) {
    r = modP(r * r);
  }
  return r;
};

// prettier-ignore
const pow_2_252_3 = (x: bigint) => {                    // x^(2^252-3) unrolled util for square root
  const x2 = modP(x * x);                               // x^2,       bits 1
  const b2 = modP(x2 * x);                              // x^3,       bits 11
  const b4 = modP(pow2(b2, 2) * b2);                    // x^(2^4-1), bits 1111
  const b5 = modP(pow2(b4, 1) * x);                     // x^(2^5-1), bits 11111
  const b10 = modP(pow2(b5, 5) * b5);                   // x^(2^10-1)
  const b20 = modP(pow2(b10, 10) * b10);                // x^(2^20-1)
  const b40 = modP(pow2(b20, 20) * b20);                // x^(2^40-1)
  const b80 = modP(pow2(b40, 40) * b40);                // x^(2^80-1)
  const b160 = modP(pow2(b80, 80) * b80);               // x^(2^160-1)
  const b240 = modP(pow2(b160, 80) * b80);              // x^(2^240-1)
  const b250 = modP(pow2(b240, 10) * b10);              // x^(2^250-1)
  return modP(pow2(b250, 2) * x);                       // x^((p-5)/8), used by RFC8032 point decode
};
const RM1 = 0x2b8324804fc1df0b2b4d00993dfbd7a72f431806ad2fe478c4ee1b274a0ea0b0n; // 2^((p-1)/4) = sqrt(-1)
// RFC8032 §5.1.3 square-root helper for point decompression. `value` is only meaningful when
// `isValid` is true; callers are also expected to pass canonical field elements with non-zero `v`.
// prettier-ignore
const uvRatio = (u: bigint, v: bigint): { isValid: boolean, value: bigint } => {
  const v3 = modP(v * modP(v * v));                              // v³
  const v7 = modP(modP(v3 * v3) * v);                            // v⁷
  const pow = pow_2_252_3(modP(u * v7));                         // (uv⁷)^(p-5)/8
  let x = modP(u * modP(v3 * pow));                              // (uv³)(uv⁷)^(p-5)/8
  const vx2 = modP(v * modP(x * x));                             // vx²
  const root1 = x;                                      // First root candidate
  const root2 = modP(x * RM1);                             // Second root candidate; RM1 is √-1
  const useRoot1 = vx2 === u;                           // If vx² = u (mod p), x is a square root
  const useRoot2 = vx2 === mod(-u);                       // If vx² = -u, set x <-- x * 2^((p-1)/4)
  const noRoot = vx2 === mod(-u * RM1);                   // There is no valid root, vx² = -u√-1
  if (useRoot1) x = root1;
  if (useRoot2 || noRoot) x = root2;                    // We return root2 anyway, for const-time
  if ((mod(x) & 1n) === 1n) x = mod(-x);                    // edIsNegative
  return { isValid: useRoot1 || useRoot2, value: x };
};
// Reduce a little-endian byte string modulo the subgroup order `N` (RFC 8032's `L`); the `hash`
// param name reflects the common caller shape, not an input restriction.
const modL_LE = (hash: Uint8Array): bigint => modN(bytesToNumberLE(hash));
type ExtK = {
  head: Uint8Array;
  prefix: Uint8Array;
  scalar: bigint;
  point: Point;
  pointBytes: Uint8Array;
};

// RFC8032 5.1.5. Split the 64-byte hashed seed into the clamped scalar half and nonce prefix.
const hashedToExtK = (hashed: Uint8Array): TRet<ExtK> => {
  // slice creates a copy, unlike subarray
  const copy = snapshotBytes(hashed);
  const head = copy.slice(0, 32);
  head[0] &= 248; // Clamp bits: 0b1111_1000
  head[31] &= 127; // 0b0111_1111
  head[31] |= 64; // 0b0100_0000
  const prefix = copy.slice(32); // secret key "prefix"
  // RFC words this as `[s]B`; reducing the clamped little-endian scalar modulo `N` is equivalent
  // for base-point multiplication because `G` already has subgroup order `N`.
  const scalar = modL_LE(head);
  const point = G.multiply(scalar); // public key point
  const pointBytes = point.toBytes(); // point serialized to Uint8Array
  return { head, prefix, scalar, point, pointBytes } as TRet<ExtK>;
};

// RFC8032 5.1.5; getPublicKey async, sync. Hash secret key and extract point.
const getExtendedPublicKeyAsync = (secretKey: TArg<Uint8Array>): Promise<TRet<ExtK>> =>
  callHashAsync('sha512Async', abytes(secretKey, LEN, 'secretKey')).then(hashedToExtK);
const getExtendedPublicKey = (secretKey: TArg<Uint8Array>): TRet<ExtK> =>
  hashedToExtK(callHash('sha512', abytes(secretKey, LEN, 'secretKey')));
/**
 * Creates a 32-byte Ed25519 public key from the RFC 8032 32-byte secret-key seed. Async.
 * @param secretKey - 32-byte RFC 8032 secret-key seed, not a 64-byte expanded secret key.
 * @returns 32-byte public key.
 * @throws On wrong argument types. {@link TypeError}
 * @throws On wrong argument ranges or values. {@link RangeError}
 * @example
 * Derive the public key bytes for a newly generated signer secret.
 *
 * ```ts
 * import * as ed from '@noble/ed25519';
 *
 * const secretKey = ed.utils.randomSecretKey();
 * const publicKey = await ed.getPublicKeyAsync(secretKey);
 * ```
 */
const getPublicKeyAsync = (secretKey: TArg<Uint8Array>): Promise<TRet<Uint8Array>> =>
  getExtendedPublicKeyAsync(secretKey).then((p) => p.pointBytes as TRet<Uint8Array>);
/**
 * Creates a 32-byte Ed25519 public key from the RFC 8032 32-byte secret-key seed.
 * To use, set `hashes.sha512` first.
 * @param secretKey - 32-byte RFC 8032 secret-key seed, not a 64-byte expanded secret key.
 * @returns 32-byte public key.
 * @throws If synchronous SHA-512 has not been configured in `hashes`. {@link Error}
 * @throws On wrong argument types. {@link TypeError}
 * @throws On wrong argument ranges or values. {@link RangeError}
 * @example
 * Derive the public key entirely through the synchronous API.
 *
 * ```ts
 * import * as ed from '@noble/ed25519';
 * import { sha512 } from '@noble/hashes/sha2.js';
 *
 * ed.hashes.sha512 = sha512;
 * const secretKey = ed.utils.randomSecretKey();
 * const publicKey = ed.getPublicKey(secretKey);
 * ```
 */
const getPublicKey = (secretKey: TArg<Uint8Array>): TRet<Uint8Array> =>
  getExtendedPublicKey(secretKey).pointBytes;
type Finishable<T> = readonly [
  // Shared between sync/async sign() and verify(): hash `hashable` with SHA-512, then hand the
  // resulting 64-byte digest to `finish(...)`.
  Uint8Array,
  (hashed: Uint8Array) => T,
];
const hashFinishAsync = async <T>(res: Finishable<T>): Promise<T> =>
  res[1](await callHashAsync('sha512Async', res[0]));
const hashFinishSync = <T>(res: Finishable<T>): T => res[1](callHash('sha512', res[0]));
// Code, shared between sync & async sign
const _sign = (
  e: { pointBytes: Uint8Array; scalar: bigint },
  rBytes: Uint8Array,
  msg: Uint8Array
): Finishable<TRet<Uint8Array>> => {
  const { pointBytes: A, scalar: s } = e;
  const r = modL_LE(rBytes); // r was created outside, reduce it modulo L
  // RFC 8032 5.1.6 allows r mod L = 0, and SUPERCOP ref10 accepts the resulting identity-point
  // signature.
  // We intentionally keep the safe multiply() rejection here so a miswired all-zero SHA-512 provider
  // fails loudly instead of silently producing a degenerate signature.
  const R = G.multiply(r).toBytes(); // R = [r]B
  const hashable = concatBytes(R, A, msg); // dom2(F, C) || R || A || PH(M)
  const finish = (hashed: Uint8Array): TRet<Uint8Array> => {
    // k = SHA512(dom2(F, C) || R || A || PH(M))
    const S = modN(r + modL_LE(hashed) * s); // S = (r + k * s) mod L; 0 <= s < l
    return abytes(concatBytes(R, numTo32bLE(S)), 64); // 64-byte sig: 32-byte encoded R point || 32-byte LE(S)
  };
  return [hashable, finish];
};
/**
 * Signs message using secret key. Async.
 * Follows RFC8032 5.1.6.
 * @param message - Message bytes to sign.
 * @param secretKey - 32-byte RFC 8032 secret-key seed, not a 64-byte expanded secret key.
 * @returns 64-byte Ed25519 signature.
 * @throws On wrong argument types. {@link TypeError}
 * @throws On wrong argument ranges or values. {@link RangeError}
 * @example
 * Sign an arbitrary message with a fresh Ed25519 secret key.
 *
 * ```ts
 * import * as ed from '@noble/ed25519';
 *
 * const secretKey = ed.utils.randomSecretKey();
 * const message = new Uint8Array([1, 2, 3]);
 * const signature = await ed.signAsync(message, secretKey);
 * ```
 */
const signAsync = async (
  message: TArg<Uint8Array>,
  secretKey: TArg<Uint8Array>
): Promise<TRet<Uint8Array>> => {
  const m = snapshotBytes(message, 'message');
  const e = await getExtendedPublicKeyAsync(secretKey);
  // r = SHA512(dom2(F, C) || prefix || PH(M)); then generate R, k, S and the signature.
  return hashFinishAsync(_sign(e, await callHashAsync('sha512Async', e.prefix, m), m));
};
/**
 * Signs message using secret key. To use, set `hashes.sha512` first.
 * Follows RFC8032 5.1.6.
 * @param message - Message bytes to sign.
 * @param secretKey - 32-byte RFC 8032 secret-key seed, not a 64-byte expanded secret key.
 * @returns 64-byte Ed25519 signature.
 * @throws If synchronous SHA-512 has not been configured in `hashes`. {@link Error}
 * @throws On wrong argument types. {@link TypeError}
 * @throws On wrong argument ranges or values. {@link RangeError}
 * @example
 * Use the sync API when you've wired a SHA-512 implementation yourself.
 *
 * ```ts
 * import * as ed from '@noble/ed25519';
 * import { sha512 } from '@noble/hashes/sha2.js';
 *
 * ed.hashes.sha512 = sha512;
 * const secretKey = ed.utils.randomSecretKey();
 * const signature = ed.sign(new Uint8Array([1, 2, 3]), secretKey);
 * ```
 */
const sign = (message: TArg<Uint8Array>, secretKey: TArg<Uint8Array>): TRet<Uint8Array> => {
  const m = snapshotBytes(message, 'message');
  const e = getExtendedPublicKey(secretKey);
  // r = SHA512(dom2(F, C) || prefix || PH(M)); then generate R, k, S and the signature.
  return hashFinishSync(_sign(e, callHash('sha512', e.prefix, m), m));
};
/**
 * Verification options. zip215: true (default) follows ZIP215 spec. false would follow RFC8032.
 *
 * Any message with pubkey from `ED25519_TORSION_SUBGROUP` would be valid in sigs under ZIP215.
 */
export type EdDSAVerifyOpts = {
  /** Whether to use ZIP215 verification semantics instead of the library's stricter branch. */
  zip215?: boolean;
};
// Exported defaults favor ZIP-215 interoperability semantics; callers must opt into the stricter
// branch with `{ zip215: false }`.
// Preserves the exported ZIP-215 default for `{}` / `{ zip215: undefined }`, not just omitted opts.
const getZip215 = (options: TArg<EdDSAVerifyOpts>): boolean => {
  if (options === null || typeof options !== 'object')
    throw new TypeError('expected valid options object');
  return options.zip215 ?? true;
};
const _verify = (
  sig: Uint8Array,
  msg: Uint8Array,
  publicKey: Uint8Array,
  options: TArg<EdDSAVerifyOpts>
): Finishable<boolean> => {
  sig = abytes(sig, 64, 'signature'); // Signature hex str/Bytes, must be 64 bytes
  msg = abytes(msg, undefined, 'message'); // Message hex str/Bytes
  publicKey = abytes(publicKey, LEN, 'publicKey');
  const zip215 = getZip215(options);
  // zip215=false keeps the library's stricter branch, which still canonicalizes `R` / `A` before
  // hashing and rejects small-order public keys earlier than pure RFC8032 text would require.
  const r = sig.subarray(0, LEN);
  const s = bytesToNumberLE(sig.subarray(LEN, 64)); // Decode second half as an integer S;
  let A: Point, R: Point, SB: Point;
  let hashable: Uint8Array = Uint8Array.of();
  let finished = false;
  try {
    // zip215=true is good for consensus-critical apps. =false follows RFC8032 / NIST186-5.
    // zip215=true:  0 <= y < MASK (2^256 for ed25519)
    // zip215=false: 0 <= y < P (2^255-19 for ed25519)
    A = Point.fromBytes(publicKey, zip215);
    R = Point.fromBytes(r, zip215);
    SB = G.multiply(s, false); // 0 <= s < l is done inside
    // ZIP-215 accepts noncanonical / unreduced point encodings, so the challenge hash must use the
    // exact signature/public-key bytes rather than canonicalized re-encodings of the decoded points.
    hashable = concatBytes(r, publicKey, msg); // dom2(F, C) || R || A || PH(M)
    finished = true;
  } catch (error) {}
  const finish = (hashed: Uint8Array): boolean => {
    if (!finished) return false;
    // Policy: strict mode intentionally rejects all small-order public keys, even though the raw RFC
    // equation text is looser here. This matches libsodium and avoids weak / ambiguous verification
    // outcomes where unusual low-order public keys can make distinct key/signature combinations verify.
    if (!zip215 && A.isSmallOrder()) return false;

    // k = SHA512(dom2(F, C) || R || A || PH(M))
    const k = modL_LE(hashed);
    const RkA = R.add(A.multiply(k, false));
    // Extended group equation
    // [8][S]B = [8]R + [8][k]A'
    return RkA.subtract(SB).clearCofactor().is0();
  };
  return [hashable, finish];
};

/**
 * Verifies a signature on message and public key. Async.
 * The implementation is based on RFC8032 5.1.7, but default opts use ZIP-215 semantics; pass
 * `{ zip215: false }` for the library's stricter branch.
 * @param signature - 64-byte signature.
 * @param message - Signed message bytes.
 * @param publicKey - 32-byte public key.
 * @param opts - Verification options. Defaults to ZIP-215 semantics. See {@link EdDSAVerifyOpts}.
 * @returns `true` when the signature is valid.
 * @throws On wrong argument types. {@link TypeError}
 * @throws On wrong argument ranges or values. {@link RangeError}
 * @example
 * Verify the signature against the same message and derived public key.
 *
 * ```ts
 * import * as ed from '@noble/ed25519';
 *
 * const secretKey = ed.utils.randomSecretKey();
 * const message = new Uint8Array([1, 2, 3]);
 * const publicKey = await ed.getPublicKeyAsync(secretKey);
 * const signature = await ed.signAsync(message, secretKey);
 * const isValid = await ed.verifyAsync(signature, message, publicKey);
 * ```
 */
const verifyAsync = async (
  signature: TArg<Uint8Array>,
  message: TArg<Uint8Array>,
  publicKey: TArg<Uint8Array>,
  opts: TArg<EdDSAVerifyOpts> = {}
): Promise<boolean> => hashFinishAsync(_verify(signature, message, publicKey, opts));
/**
 * Verifies a signature on message and public key using the synchronous hash path.
 * The implementation is based on RFC8032 5.1.7, but default opts use ZIP-215 semantics; pass
 * `{ zip215: false }` for the library's stricter branch.
 * @param signature - 64-byte signature.
 * @param message - Signed message bytes.
 * @param publicKey - 32-byte public key.
 * @param opts - Verification options. Defaults to ZIP-215 semantics. See {@link EdDSAVerifyOpts}.
 * @returns `true` when the signature is valid.
 * @throws If synchronous SHA-512 has not been configured in `hashes`. {@link Error}
 * @throws On wrong argument types. {@link TypeError}
 * @throws On wrong argument ranges or values. {@link RangeError}
 * @example
 * Verify a signature entirely through the synchronous API.
 *
 * ```ts
 * import * as ed from '@noble/ed25519';
 * import { sha512 } from '@noble/hashes/sha2.js';
 *
 * ed.hashes.sha512 = sha512;
 * const secretKey = ed.utils.randomSecretKey();
 * const message = new Uint8Array([1, 2, 3]);
 * const publicKey = ed.getPublicKey(secretKey);
 * const signature = ed.sign(message, secretKey);
 * const isValid = ed.verify(signature, message, publicKey);
 * ```
 */
const verify = (
  signature: TArg<Uint8Array>,
  message: TArg<Uint8Array>,
  publicKey: TArg<Uint8Array>,
  opts: TArg<EdDSAVerifyOpts> = {}
): boolean => hashFinishSync(_verify(signature, message, publicKey, opts));

/**
 * Math, hex, byte helpers. Not in `utils` because utils share API with noble-curves.
 * Exposes the same low-level field-default `mod` reducer and non-CT `invert` helper used
 * internally.
 * @example
 * Convert bytes to a hex string with the low-level helper namespace.
 *
 * ```ts
 * const hex = etc.bytesToHex(new Uint8Array([1, 2, 3]));
 * ```
 */
const etc: {
  bytesToHex: (bytes: TArg<Uint8Array>) => string;
  hexToBytes: (hex: string) => TRet<Uint8Array>;
  concatBytes: (...arrs: TArg<Uint8Array[]>) => TRet<Uint8Array>;
  mod: (a: bigint, md?: bigint) => bigint;
  invert: typeof invert;
  randomBytes: (len?: number) => TRet<Uint8Array>;
} = /* @__PURE__ */ freeze({
  bytesToHex,
  hexToBytes,
  concatBytes,
  mod,
  invert,
  randomBytes,
});
/**
 * Hash implementations used by the synchronous API plus the default async WebCrypto provider.
 * Both slots are configurable API surface; wrapper helpers revalidate that providers still return
 * 64-byte SHA-512 digests.
 * @example
 * Provide a SHA-512 implementation before calling synchronous helpers.
 *
 * ```ts
 * import * as ed from '@noble/ed25519';
 * import { sha512 } from '@noble/hashes/sha2.js';
 *
 * ed.hashes.sha512 = sha512;
 * const { publicKey } = ed.keygen();
 * ```
 */
const hashes = {
  sha512Async: async (message: TArg<Uint8Array>): Promise<TRet<Uint8Array>> => {
    const s = globalThis?.crypto?.subtle;
    if (!s) throw new Error('crypto.subtle must be defined, consider polyfill');
    return new Uint8Array(await s.digest('SHA-512', concatBytes(message))) as TRet<Uint8Array>;
  },
  sha512: undefined as undefined | ((message: TArg<Uint8Array>) => TRet<Uint8Array>),
};

// Returns the final 32-byte Ed25519 secret-key seed verbatim, generating fresh random bytes only
// when omitted.
const randomSecretKey = (seed?: TArg<Uint8Array>): TRet<Uint8Array> => {
  return abytes(seed === undefined ? randomBytes() : seed, LEN, 'seed');
};

type KeysSecPub = { secretKey: Uint8Array; publicKey: Uint8Array };
/**
 * Generates a secret/public keypair.
 * @param seed - Optional 32-byte Ed25519 secret-key seed, returned verbatim as `secretKey`.
 * @returns Keypair with `secretKey` and `publicKey`.
 * @throws If synchronous SHA-512 has not been configured in `hashes`. {@link Error}
 * @throws On wrong argument types. {@link TypeError}
 * @throws On wrong argument ranges or values. {@link RangeError}
 * @example
 * Generate a new keypair through the synchronous API after wiring SHA-512.
 *
 * ```ts
 * import * as ed from '@noble/ed25519';
 * import { sha512 } from '@noble/hashes/sha2.js';
 *
 * ed.hashes.sha512 = sha512;
 * const { secretKey, publicKey } = ed.keygen();
 * ```
 */
const keygen = (seed?: TArg<Uint8Array>): TRet<KeysSecPub> => {
  const secretKey = randomSecretKey(seed);
  const publicKey = getPublicKey(secretKey);
  return { secretKey, publicKey } as TRet<KeysSecPub>;
};
/**
 * Generates a secret/public keypair asynchronously.
 * @param seed - Optional 32-byte Ed25519 secret-key seed, returned verbatim as `secretKey`.
 * @returns Keypair with `secretKey` and `publicKey`.
 * @throws On wrong argument types. {@link TypeError}
 * @throws On wrong argument ranges or values. {@link RangeError}
 * @example
 * Generate a new keypair through the asynchronous WebCrypto-backed path.
 *
 * ```ts
 * import * as ed from '@noble/ed25519';
 *
 * const { secretKey, publicKey } = await ed.keygenAsync();
 * ```
 */
const keygenAsync = async (seed?: TArg<Uint8Array>): Promise<TRet<KeysSecPub>> => {
  const secretKey = randomSecretKey(seed);
  const publicKey = await getPublicKeyAsync(secretKey);
  return { secretKey, publicKey } as TRet<KeysSecPub>;
};

/**
 * Ed25519-specific key utilities.
 * `utils.getExtendedPublicKey*` expose secret-derived internals (`head`, `prefix`, `scalar`, and
 * point objects), not just public-key bytes.
 * @example
 * Generate a new Ed25519 secret key and derive the matching public key.
 *
 * ```ts
 * import * as ed from '@noble/ed25519';
 *
 * const secretKey = ed.utils.randomSecretKey();
 * const publicKey = await ed.getPublicKeyAsync(secretKey);
 * ```
 */
const utils: {
  getExtendedPublicKeyAsync: typeof getExtendedPublicKeyAsync;
  getExtendedPublicKey: typeof getExtendedPublicKey;
  randomSecretKey: typeof randomSecretKey;
} = /* @__PURE__ */ freeze({
  getExtendedPublicKeyAsync,
  getExtendedPublicKey,
  randomSecretKey,
});

// ## Precomputes
// --------------

// Fixed W=8 window: 33 windows (ceil(256/8) + 1, NOT 32 - see wNAF loop), 128 points per window.
// Layout is grouped by window: each block stores the positive multiples `1*base .. 128*base` for
// that window, and the extra `+1` window absorbs carries from signed-digit recoding.
const precompute = () => {
  const points: Point[] = [];
  let p = G;
  let b: Point;
  for (let w = 0; w < 33; w++) {
    b = p;
    points.push(b);
    for (let i = 1; i < 128; i++) {
      b = b.add(p);
      points.push(b);
    } // i=1, bc we skip 0
    p = b.double();
  }
  return points;
};
let Gpows: Point[] | undefined = undefined; // shared process-wide cache of base-point precomputes
// Branch-based negate helper used for JS/JIT mitigation symmetry, not a strict constant-time claim.
const ctneg = (cnd: boolean, p: Point): Point => {
  const n = p.negate();
  return cnd ? n : p;
};

/**
 * Precomputes give 12x faster getPublicKey(), 10x sign(), 2x verify() by
 * caching multiples of G (base point). Cache is stored in 32MB of RAM.
 * Any time `G.multiply` is done, precomputes are used.
 * Not used for getSharedSecret, which instead multiplies random pubkey `P.multiply`.
 *
 * w-ary non-adjacent form (wNAF) precomputation method is 10% slower than windowed method,
 * but takes 2x less RAM. RAM reduction is possible by utilizing `.subtract`.
 * Returns the real accumulator `p` plus a fake accumulator `f`; callers only care about `p`, while
 * `f` exists to keep similar work in zero-digit branches as a JS/JIT side-channel mitigation.
 *
 * !! Precomputes can be disabled by commenting-out call of the wNAF() inside Point#multiply().
 */
const wNAF = (n: bigint): { p: Point; f: Point } => {
  const comp = Gpows || (Gpows = precompute());
  let p = I;
  let f = G; // f must be G, or could become I in the end
  for (let w = 0; w < 33; w++) {
    let wbits = Number(n & 255n); // extract W=8 bits.
    n >>= 8n; // shift number by W=8 bits.
    // We use negative indexes to reduce size of precomputed table by 2x.
    // Instead of needing precomputes 0..256, we only calculate them for 0..128.
    // If an index > 128 is found, we do (256-index) - where 256 is next window.
    // Naive: index +127 => 127, +224 => 224
    // Optimized: index +127 => 127, +224 => 256-32
    if (wbits > 128) {
      wbits -= 256;
      n += 1n;
    }
    const off = w * 128; // offset of this window's block; also the fake-add index
    const offP = off + Math.abs(wbits) - 1; // real-add index; both offsets always evaluated
    const isOddW = w % 2 !== 0; // conditions, evaluate both; alternates fake-add sign per window
    const isNeg = wbits < 0;
    if (wbits === 0) {
      // wbits == 0 means the real index would be I: can't add it. Add window offset `off` instead.
      f = f.add(ctneg(isOddW, comp[off])); // bits are 0: add garbage to fake point
    } else {
      p = p.add(ctneg(isNeg, comp[offP])); // bits are 1: add to result point
    }
  }
  if (n !== 0n) throw new Error('invalid wnaf');
  return { p, f }; // return both real and fake points for JIT/leakage-shape symmetry
};

// !! Remove the export to easily use in REPL / browser console
export {
  etc,
  getPublicKey,
  getPublicKeyAsync,
  hash,
  hashes,
  keygen,
  keygenAsync,
  Point,
  sign,
  signAsync,
  utils,
  verify,
  verifyAsync,
};

// ## TypeScript Uint8Array compat types
// -------------------------------------
/**
 * Bytes API type helpers for old + new TypeScript.
 *
 * TS 5.6 has `Uint8Array`, while TS 5.9+ made it generic `Uint8Array<ArrayBuffer>`.
 * We can't use specific return type, because TS 5.6 will error.
 * We can't use generic return type, because most TS 5.9 software will expect specific type.
 *
 * Maps typed-array input leaves to broad forms.
 * These are compatibility adapters, not ownership guarantees.
 *
 * - `TArg` keeps byte inputs broad.
 * - `TRet` marks byte outputs for TS 5.6 and TS 5.9+ compatibility.
 */
export type TypedArg<T> = T extends BigInt64Array
  ? BigInt64Array
  : T extends BigUint64Array
    ? BigUint64Array
    : T extends Float32Array
      ? Float32Array
      : T extends Float64Array
        ? Float64Array
        : T extends Int16Array
          ? Int16Array
          : T extends Int32Array
            ? Int32Array
            : T extends Int8Array
              ? Int8Array
              : T extends Uint16Array
                ? Uint16Array
                : T extends Uint32Array
                  ? Uint32Array
                  : T extends Uint8ClampedArray
                    ? Uint8ClampedArray
                    : T extends Uint8Array
                      ? Uint8Array
                      : never;
/** Maps typed-array output leaves to narrow TS-compatible forms. */
export type TypedRet<T> = T extends BigInt64Array
  ? ReturnType<typeof BigInt64Array.of>
  : T extends BigUint64Array
    ? ReturnType<typeof BigUint64Array.of>
    : T extends Float32Array
      ? ReturnType<typeof Float32Array.of>
      : T extends Float64Array
        ? ReturnType<typeof Float64Array.of>
        : T extends Int16Array
          ? ReturnType<typeof Int16Array.of>
          : T extends Int32Array
            ? ReturnType<typeof Int32Array.of>
            : T extends Int8Array
              ? ReturnType<typeof Int8Array.of>
              : T extends Uint16Array
                ? ReturnType<typeof Uint16Array.of>
                : T extends Uint32Array
                  ? ReturnType<typeof Uint32Array.of>
                  : T extends Uint8ClampedArray
                    ? ReturnType<typeof Uint8ClampedArray.of>
                    : T extends Uint8Array
                      ? ReturnType<typeof Uint8Array.of>
                      : never;
/** Recursively adapts byte-carrying API input types. See {@link TypedArg}. */
export type TArg<T> =
  | T
  | ([TypedArg<T>] extends [never]
      ? T extends (...args: infer A) => infer R
        ? ((...args: { [K in keyof A]: TRet<A[K]> }) => TArg<R>) & {
            [K in keyof T]: T[K] extends (...args: any) => any ? T[K] : TArg<T[K]>;
          }
        : T extends [infer A, ...infer R]
          ? [TArg<A>, ...{ [K in keyof R]: TArg<R[K]> }]
          : T extends readonly [infer A, ...infer R]
            ? readonly [TArg<A>, ...{ [K in keyof R]: TArg<R[K]> }]
            : T extends (infer A)[]
              ? TArg<A>[]
              : T extends readonly (infer A)[]
                ? readonly TArg<A>[]
                : T extends Promise<infer A>
                  ? Promise<TArg<A>>
                  : T extends object
                    ? { [K in keyof T]: TArg<T[K]> }
                    : T
      : TypedArg<T>);
/** Recursively adapts byte-carrying API output types. See {@link TypedArg}. */
export type TRet<T> = T extends unknown
  ? T &
      ([TypedRet<T>] extends [never]
        ? T extends (...args: infer A) => infer R
          ? ((...args: { [K in keyof A]: TArg<A[K]> }) => TRet<R>) & {
              [K in keyof T]: T[K] extends (...args: any) => any ? T[K] : TRet<T[K]>;
            }
          : T extends [infer A, ...infer R]
            ? [TRet<A>, ...{ [K in keyof R]: TRet<R[K]> }]
            : T extends readonly [infer A, ...infer R]
              ? readonly [TRet<A>, ...{ [K in keyof R]: TRet<R[K]> }]
              : T extends (infer A)[]
                ? TRet<A>[]
                : T extends readonly (infer A)[]
                  ? readonly TRet<A>[]
                  : T extends Promise<infer A>
                    ? Promise<TRet<A>>
                    : T extends object
                      ? { [K in keyof T]: TRet<T[K]> }
                      : T
        : TypedRet<T>)
  : never;