grpc-swift/Sources/GRPCCore/Internal/Base64.swift

/*
 * Copyright 2023, gRPC Authors All rights reserved.
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *     http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */
// This base64 implementation is heavily inspired by:

// https://github.com/lemire/fastbase64/blob/a2e0967dfcb8f0129ea45b9b24cc410e4cac117f/src/chromiumbase64.c
/*
 Copyright (c) 2015-2016, Wojciech Muła, Alfred Klomp,  Daniel Lemire
 (Unless otherwise stated in the source code)
 All rights reserved.

 Redistribution and use in source and binary forms, with or without
 modification, are permitted provided that the following conditions are
 met:

 1. Redistributions of source code must retain the above copyright
 notice, this list of conditions and the following disclaimer.

 2. Redistributions in binary form must reproduce the above copyright
 notice, this list of conditions and the following disclaimer in the
 documentation and/or other materials provided with the distribution.

 THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
 IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
 TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
 PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
 HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
 SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
 TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
 PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
 LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
 NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
 SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 */

// https://github.com/client9/stringencoders/blob/e1448a9415f4ebf6f559c86718193ba067cbb99d/src/modp_b64.c
/*
 The MIT License (MIT)

 Copyright (c) 2016 Nick Galbreath

 Permission is hereby granted, free of charge, to any person obtaining a copy
 of this software and associated documentation files (the "Software"), to deal
 in the Software without restriction, including without limitation the rights
 to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
 copies of the Software, and to permit persons to whom the Software is
 furnished to do so, subject to the following conditions:

 The above copyright notice and this permission notice shall be included in all
 copies or substantial portions of the Software.

 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
 SOFTWARE.
 */

// swift-format-ignore: DontRepeatTypeInStaticProperties
enum Base64 {
  struct DecodingOptions: OptionSet {
    internal let rawValue: UInt
    internal init(rawValue: UInt) { self.rawValue = rawValue }

    internal static let base64UrlAlphabet = DecodingOptions(rawValue: UInt(1 << 0))
    internal static let omitPaddingCharacter = DecodingOptions(rawValue: UInt(1 << 1))
  }

  enum DecodingError: Error, Equatable {
    case invalidLength
    case invalidCharacter(UInt8)
    case unexpectedPaddingCharacter
    case unexpectedEnd
  }

  static func encode<Buffer: Collection>(bytes: Buffer) -> String where Buffer.Element == UInt8 {
    guard !bytes.isEmpty else {
      return ""
    }

    // In Base64, 3 bytes become 4 output characters, and we pad to the
    // nearest multiple of four.
    let base64StringLength = ((bytes.count + 2) / 3) * 4
    let alphabet = Base64.encodeBase64

    return String(customUnsafeUninitializedCapacity: base64StringLength) { backingStorage in
      var input = bytes.makeIterator()
      var offset = 0
      while let firstByte = input.next() {
        let secondByte = input.next()
        let thirdByte = input.next()

        backingStorage[offset] = Base64.encode(alphabet: alphabet, firstByte: firstByte)
        backingStorage[offset + 1] = Base64.encode(
          alphabet: alphabet,
          firstByte: firstByte,
          secondByte: secondByte
        )
        backingStorage[offset + 2] = Base64.encode(
          alphabet: alphabet,
          secondByte: secondByte,
          thirdByte: thirdByte
        )
        backingStorage[offset + 3] = Base64.encode(alphabet: alphabet, thirdByte: thirdByte)
        offset += 4
      }
      return offset
    }
  }

  static func decode(
    string encoded: String,
    options: DecodingOptions = []
  ) throws -> [UInt8] {
    let decoded = try encoded.utf8.withContiguousStorageIfAvailable {
      (characterPointer) -> [UInt8] in
      guard characterPointer.count > 0 else {
        return []
      }

      let outputLength = ((characterPointer.count + 3) / 4) * 3

      return try characterPointer.withMemoryRebound(to: UInt8.self) { (input) -> [UInt8] in
        try [UInt8](unsafeUninitializedCapacity: outputLength) { output, length in
          try Self._decodeChromium(from: input, into: output, length: &length, options: options)
        }
      }
    }

    if decoded != nil {
      return decoded!
    }

    var encoded = encoded
    encoded.makeContiguousUTF8()
    return try Self.decode(string: encoded, options: options)
  }

  private static func _decodeChromium(
    from inBuffer: UnsafeBufferPointer<UInt8>,
    into outBuffer: UnsafeMutableBufferPointer<UInt8>,
    length: inout Int,
    options: DecodingOptions = []
  ) throws {
    let remaining = inBuffer.count % 4
    switch (options.contains(.omitPaddingCharacter), remaining) {
    case (false, 1...):
      throw DecodingError.invalidLength
    case (true, 1):
      throw DecodingError.invalidLength
    default:
      // everythin alright so far
      break
    }

    let outputLength = ((inBuffer.count + 3) / 4) * 3
    let fullchunks = remaining == 0 ? inBuffer.count / 4 - 1 : inBuffer.count / 4
    guard outBuffer.count >= outputLength else {
      preconditionFailure("Expected the out buffer to be at least as long as outputLength")
    }

    try Self.withUnsafeDecodingTablesAsBufferPointers(options: options) { d0, d1, d2, d3 in
      var outIndex = 0
      if fullchunks > 0 {
        for chunk in 0 ..< fullchunks {
          let inIndex = chunk * 4
          let a0 = inBuffer[inIndex]
          let a1 = inBuffer[inIndex + 1]
          let a2 = inBuffer[inIndex + 2]
          let a3 = inBuffer[inIndex + 3]
          var x: UInt32 = d0[Int(a0)] | d1[Int(a1)] | d2[Int(a2)] | d3[Int(a3)]

          if x >= Self.badCharacter {
            // TODO: Inspect characters here better
            throw DecodingError.invalidCharacter(inBuffer[inIndex])
          }

          withUnsafePointer(to: &x) { ptr in
            ptr.withMemoryRebound(to: UInt8.self, capacity: 4) { newPtr in
              outBuffer[outIndex] = newPtr[0]
              outBuffer[outIndex + 1] = newPtr[1]
              outBuffer[outIndex + 2] = newPtr[2]
              outIndex += 3
            }
          }
        }
      }

      // inIndex is the first index in the last chunk
      let inIndex = fullchunks * 4
      let a0 = inBuffer[inIndex]
      let a1 = inBuffer[inIndex + 1]
      var a2: UInt8?
      var a3: UInt8?
      if inIndex + 2 < inBuffer.count, inBuffer[inIndex + 2] != Self.encodePaddingCharacter {
        a2 = inBuffer[inIndex + 2]
      }
      if inIndex + 3 < inBuffer.count, inBuffer[inIndex + 3] != Self.encodePaddingCharacter {
        a3 = inBuffer[inIndex + 3]
      }

      var x: UInt32 = d0[Int(a0)] | d1[Int(a1)] | d2[Int(a2 ?? 65)] | d3[Int(a3 ?? 65)]
      if x >= Self.badCharacter {
        // TODO: Inspect characters here better
        throw DecodingError.invalidCharacter(inBuffer[inIndex])
      }

      withUnsafePointer(to: &x) { ptr in
        ptr.withMemoryRebound(to: UInt8.self, capacity: 4) { newPtr in
          outBuffer[outIndex] = newPtr[0]
          outIndex += 1
          if a2 != nil {
            outBuffer[outIndex] = newPtr[1]
            outIndex += 1
          }
          if a3 != nil {
            outBuffer[outIndex] = newPtr[2]
            outIndex += 1
          }
        }
      }

      length = outIndex
    }
  }

  private static func withUnsafeDecodingTablesAsBufferPointers<R>(
    options: Base64.DecodingOptions,
    _ body: (
      UnsafeBufferPointer<UInt32>, UnsafeBufferPointer<UInt32>, UnsafeBufferPointer<UInt32>,
      UnsafeBufferPointer<UInt32>
    ) throws -> R
  ) rethrows -> R {
    let decoding0 = options.contains(.base64UrlAlphabet) ? Self.decoding0url : Self.decoding0
    let decoding1 = options.contains(.base64UrlAlphabet) ? Self.decoding1url : Self.decoding1
    let decoding2 = options.contains(.base64UrlAlphabet) ? Self.decoding2url : Self.decoding2
    let decoding3 = options.contains(.base64UrlAlphabet) ? Self.decoding3url : Self.decoding3

    assert(decoding0.count == 256)
    assert(decoding1.count == 256)
    assert(decoding2.count == 256)
    assert(decoding3.count == 256)

    return try decoding0.withUnsafeBufferPointer { (d0) -> R in
      try decoding1.withUnsafeBufferPointer { (d1) -> R in
        try decoding2.withUnsafeBufferPointer { (d2) -> R in
          try decoding3.withUnsafeBufferPointer { (d3) -> R in
            try body(d0, d1, d2, d3)
          }
        }
      }
    }
  }

  private static let encodePaddingCharacter: UInt8 = 61

  private static let encodeBase64: [UInt8] = [
    UInt8(ascii: "A"), UInt8(ascii: "B"), UInt8(ascii: "C"), UInt8(ascii: "D"),
    UInt8(ascii: "E"), UInt8(ascii: "F"), UInt8(ascii: "G"), UInt8(ascii: "H"),
    UInt8(ascii: "I"), UInt8(ascii: "J"), UInt8(ascii: "K"), UInt8(ascii: "L"),
    UInt8(ascii: "M"), UInt8(ascii: "N"), UInt8(ascii: "O"), UInt8(ascii: "P"),
    UInt8(ascii: "Q"), UInt8(ascii: "R"), UInt8(ascii: "S"), UInt8(ascii: "T"),
    UInt8(ascii: "U"), UInt8(ascii: "V"), UInt8(ascii: "W"), UInt8(ascii: "X"),
    UInt8(ascii: "Y"), UInt8(ascii: "Z"), UInt8(ascii: "a"), UInt8(ascii: "b"),
    UInt8(ascii: "c"), UInt8(ascii: "d"), UInt8(ascii: "e"), UInt8(ascii: "f"),
    UInt8(ascii: "g"), UInt8(ascii: "h"), UInt8(ascii: "i"), UInt8(ascii: "j"),
    UInt8(ascii: "k"), UInt8(ascii: "l"), UInt8(ascii: "m"), UInt8(ascii: "n"),
    UInt8(ascii: "o"), UInt8(ascii: "p"), UInt8(ascii: "q"), UInt8(ascii: "r"),
    UInt8(ascii: "s"), UInt8(ascii: "t"), UInt8(ascii: "u"), UInt8(ascii: "v"),
    UInt8(ascii: "w"), UInt8(ascii: "x"), UInt8(ascii: "y"), UInt8(ascii: "z"),
    UInt8(ascii: "0"), UInt8(ascii: "1"), UInt8(ascii: "2"), UInt8(ascii: "3"),
    UInt8(ascii: "4"), UInt8(ascii: "5"), UInt8(ascii: "6"), UInt8(ascii: "7"),
    UInt8(ascii: "8"), UInt8(ascii: "9"), UInt8(ascii: "+"), UInt8(ascii: "/"),
  ]

  private static func encode(alphabet: [UInt8], firstByte: UInt8) -> UInt8 {
    let index = firstByte >> 2
    return alphabet[Int(index)]
  }

  private static func encode(alphabet: [UInt8], firstByte: UInt8, secondByte: UInt8?) -> UInt8 {
    var index = (firstByte & 0b00000011) << 4
    if let secondByte = secondByte {
      index += (secondByte & 0b11110000) >> 4
    }
    return alphabet[Int(index)]
  }

  private static func encode(alphabet: [UInt8], secondByte: UInt8?, thirdByte: UInt8?) -> UInt8 {
    guard let secondByte = secondByte else {
      // No second byte means we are just emitting padding.
      return Base64.encodePaddingCharacter
    }
    var index = (secondByte & 0b00001111) << 2
    if let thirdByte = thirdByte {
      index += (thirdByte & 0b11000000) >> 6
    }
    return alphabet[Int(index)]
  }

  private static func encode(alphabet: [UInt8], thirdByte: UInt8?) -> UInt8 {
    guard let thirdByte = thirdByte else {
      // No third byte means just padding.
      return Base64.encodePaddingCharacter
    }
    let index = thirdByte & 0b00111111
    return alphabet[Int(index)]
  }

  private static let badCharacter: UInt32 = 0x01FF_FFFF

  private static let decoding0: [UInt32] = [
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x0000_00F8, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x0000_00FC,
    0x0000_00D0, 0x0000_00D4, 0x0000_00D8, 0x0000_00DC, 0x0000_00E0, 0x0000_00E4,
    0x0000_00E8, 0x0000_00EC, 0x0000_00F0, 0x0000_00F4, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x0000_0000,
    0x0000_0004, 0x0000_0008, 0x0000_000C, 0x0000_0010, 0x0000_0014, 0x0000_0018,
    0x0000_001C, 0x0000_0020, 0x0000_0024, 0x0000_0028, 0x0000_002C, 0x0000_0030,
    0x0000_0034, 0x0000_0038, 0x0000_003C, 0x0000_0040, 0x0000_0044, 0x0000_0048,
    0x0000_004C, 0x0000_0050, 0x0000_0054, 0x0000_0058, 0x0000_005C, 0x0000_0060,
    0x0000_0064, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x0000_0068, 0x0000_006C, 0x0000_0070, 0x0000_0074, 0x0000_0078,
    0x0000_007C, 0x0000_0080, 0x0000_0084, 0x0000_0088, 0x0000_008C, 0x0000_0090,
    0x0000_0094, 0x0000_0098, 0x0000_009C, 0x0000_00A0, 0x0000_00A4, 0x0000_00A8,
    0x0000_00AC, 0x0000_00B0, 0x0000_00B4, 0x0000_00B8, 0x0000_00BC, 0x0000_00C0,
    0x0000_00C4, 0x0000_00C8, 0x0000_00CC, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
  ]

  private static let decoding1: [UInt32] = [
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x0000_E003, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x0000_F003,
    0x0000_4003, 0x0000_5003, 0x0000_6003, 0x0000_7003, 0x0000_8003, 0x0000_9003,
    0x0000_A003, 0x0000_B003, 0x0000_C003, 0x0000_D003, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x0000_0000,
    0x0000_1000, 0x0000_2000, 0x0000_3000, 0x0000_4000, 0x0000_5000, 0x0000_6000,
    0x0000_7000, 0x0000_8000, 0x0000_9000, 0x0000_A000, 0x0000_B000, 0x0000_C000,
    0x0000_D000, 0x0000_E000, 0x0000_F000, 0x0000_0001, 0x0000_1001, 0x0000_2001,
    0x0000_3001, 0x0000_4001, 0x0000_5001, 0x0000_6001, 0x0000_7001, 0x0000_8001,
    0x0000_9001, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x0000_A001, 0x0000_B001, 0x0000_C001, 0x0000_D001, 0x0000_E001,
    0x0000_F001, 0x0000_0002, 0x0000_1002, 0x0000_2002, 0x0000_3002, 0x0000_4002,
    0x0000_5002, 0x0000_6002, 0x0000_7002, 0x0000_8002, 0x0000_9002, 0x0000_A002,
    0x0000_B002, 0x0000_C002, 0x0000_D002, 0x0000_E002, 0x0000_F002, 0x0000_0003,
    0x0000_1003, 0x0000_2003, 0x0000_3003, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
  ]

  private static let decoding2: [UInt32] = [
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x0080_0F00, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x00C0_0F00,
    0x0000_0D00, 0x0040_0D00, 0x0080_0D00, 0x00C0_0D00, 0x0000_0E00, 0x0040_0E00,
    0x0080_0E00, 0x00C0_0E00, 0x0000_0F00, 0x0040_0F00, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x0000_0000,
    0x0040_0000, 0x0080_0000, 0x00C0_0000, 0x0000_0100, 0x0040_0100, 0x0080_0100,
    0x00C0_0100, 0x0000_0200, 0x0040_0200, 0x0080_0200, 0x00C0_0200, 0x0000_0300,
    0x0040_0300, 0x0080_0300, 0x00C0_0300, 0x0000_0400, 0x0040_0400, 0x0080_0400,
    0x00C0_0400, 0x0000_0500, 0x0040_0500, 0x0080_0500, 0x00C0_0500, 0x0000_0600,
    0x0040_0600, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x0080_0600, 0x00C0_0600, 0x0000_0700, 0x0040_0700, 0x0080_0700,
    0x00C0_0700, 0x0000_0800, 0x0040_0800, 0x0080_0800, 0x00C0_0800, 0x0000_0900,
    0x0040_0900, 0x0080_0900, 0x00C0_0900, 0x0000_0A00, 0x0040_0A00, 0x0080_0A00,
    0x00C0_0A00, 0x0000_0B00, 0x0040_0B00, 0x0080_0B00, 0x00C0_0B00, 0x0000_0C00,
    0x0040_0C00, 0x0080_0C00, 0x00C0_0C00, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
  ]

  private static let decoding3: [UInt32] = [
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x003E_0000, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x003F_0000,
    0x0034_0000, 0x0035_0000, 0x0036_0000, 0x0037_0000, 0x0038_0000, 0x0039_0000,
    0x003A_0000, 0x003B_0000, 0x003C_0000, 0x003D_0000, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x0000_0000,
    0x0001_0000, 0x0002_0000, 0x0003_0000, 0x0004_0000, 0x0005_0000, 0x0006_0000,
    0x0007_0000, 0x0008_0000, 0x0009_0000, 0x000A_0000, 0x000B_0000, 0x000C_0000,
    0x000D_0000, 0x000E_0000, 0x000F_0000, 0x0010_0000, 0x0011_0000, 0x0012_0000,
    0x0013_0000, 0x0014_0000, 0x0015_0000, 0x0016_0000, 0x0017_0000, 0x0018_0000,
    0x0019_0000, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x001A_0000, 0x001B_0000, 0x001C_0000, 0x001D_0000, 0x001E_0000,
    0x001F_0000, 0x0020_0000, 0x0021_0000, 0x0022_0000, 0x0023_0000, 0x0024_0000,
    0x0025_0000, 0x0026_0000, 0x0027_0000, 0x0028_0000, 0x0029_0000, 0x002A_0000,
    0x002B_0000, 0x002C_0000, 0x002D_0000, 0x002E_0000, 0x002F_0000, 0x0030_0000,
    0x0031_0000, 0x0032_0000, 0x0033_0000, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
  ]

  private static let decoding0url: [UInt32] = [
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,  // 0
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,  // 6
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,  // 12
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,  // 18
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,  // 24
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,  // 30
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,  // 36
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x0000_00F8, 0x01FF_FFFF, 0x01FF_FFFF,  // 42
    0x0000_00D0, 0x0000_00D4, 0x0000_00D8, 0x0000_00DC, 0x0000_00E0, 0x0000_00E4,  // 48
    0x0000_00E8, 0x0000_00EC, 0x0000_00F0, 0x0000_00F4, 0x01FF_FFFF, 0x01FF_FFFF,  // 54
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x0000_0000,  // 60
    0x0000_0004, 0x0000_0008, 0x0000_000C, 0x0000_0010, 0x0000_0014, 0x0000_0018,  // 66
    0x0000_001C, 0x0000_0020, 0x0000_0024, 0x0000_0028, 0x0000_002C, 0x0000_0030,  // 72
    0x0000_0034, 0x0000_0038, 0x0000_003C, 0x0000_0040, 0x0000_0044, 0x0000_0048,  // 78
    0x0000_004C, 0x0000_0050, 0x0000_0054, 0x0000_0058, 0x0000_005C, 0x0000_0060,  // 84
    0x0000_0064, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x0000_00FC,  // 90
    0x01FF_FFFF, 0x0000_0068, 0x0000_006C, 0x0000_0070, 0x0000_0074, 0x0000_0078,
    0x0000_007C, 0x0000_0080, 0x0000_0084, 0x0000_0088, 0x0000_008C, 0x0000_0090,
    0x0000_0094, 0x0000_0098, 0x0000_009C, 0x0000_00A0, 0x0000_00A4, 0x0000_00A8,
    0x0000_00AC, 0x0000_00B0, 0x0000_00B4, 0x0000_00B8, 0x0000_00BC, 0x0000_00C0,
    0x0000_00C4, 0x0000_00C8, 0x0000_00CC, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
  ]

  private static let decoding1url: [UInt32] = [
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,  // 0
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,  // 6
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,  // 12
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,  // 18
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,  // 24
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,  // 30
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,  // 36
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x0000_E003, 0x01FF_FFFF, 0x01FF_FFFF,  // 42
    0x0000_4003, 0x0000_5003, 0x0000_6003, 0x0000_7003, 0x0000_8003, 0x0000_9003,  // 48
    0x0000_A003, 0x0000_B003, 0x0000_C003, 0x0000_D003, 0x01FF_FFFF, 0x01FF_FFFF,  // 54
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x0000_0000,  // 60
    0x0000_1000, 0x0000_2000, 0x0000_3000, 0x0000_4000, 0x0000_5000, 0x0000_6000,  // 66
    0x0000_7000, 0x0000_8000, 0x0000_9000, 0x0000_A000, 0x0000_B000, 0x0000_C000,  // 72
    0x0000_D000, 0x0000_E000, 0x0000_F000, 0x0000_0001, 0x0000_1001, 0x0000_2001,  // 78
    0x0000_3001, 0x0000_4001, 0x0000_5001, 0x0000_6001, 0x0000_7001, 0x0000_8001,  // 84
    0x0000_9001, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x0000_F003,  // 90
    0x01FF_FFFF, 0x0000_A001, 0x0000_B001, 0x0000_C001, 0x0000_D001, 0x0000_E001,
    0x0000_F001, 0x0000_0002, 0x0000_1002, 0x0000_2002, 0x0000_3002, 0x0000_4002,
    0x0000_5002, 0x0000_6002, 0x0000_7002, 0x0000_8002, 0x0000_9002, 0x0000_A002,
    0x0000_B002, 0x0000_C002, 0x0000_D002, 0x0000_E002, 0x0000_F002, 0x0000_0003,
    0x0000_1003, 0x0000_2003, 0x0000_3003, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
  ]

  private static let decoding2url: [UInt32] = [
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,  // 0
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,  // 6
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,  // 12
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,  // 18
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,  // 24
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,  // 30
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,  // 36
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x0080_0F00, 0x01FF_FFFF, 0x01FF_FFFF,  // 42
    0x0000_0D00, 0x0040_0D00, 0x0080_0D00, 0x00C0_0D00, 0x0000_0E00, 0x0040_0E00,  // 48
    0x0080_0E00, 0x00C0_0E00, 0x0000_0F00, 0x0040_0F00, 0x01FF_FFFF, 0x01FF_FFFF,  // 54
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x0000_0000,  // 60
    0x0040_0000, 0x0080_0000, 0x00C0_0000, 0x0000_0100, 0x0040_0100, 0x0080_0100,  // 66
    0x00C0_0100, 0x0000_0200, 0x0040_0200, 0x0080_0200, 0x00C0_0200, 0x0000_0300,  // 72
    0x0040_0300, 0x0080_0300, 0x00C0_0300, 0x0000_0400, 0x0040_0400, 0x0080_0400,  // 78
    0x00C0_0400, 0x0000_0500, 0x0040_0500, 0x0080_0500, 0x00C0_0500, 0x0000_0600,  // 84
    0x0040_0600, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x00C0_0F00,  // 90
    0x01FF_FFFF, 0x0080_0600, 0x00C0_0600, 0x0000_0700, 0x0040_0700, 0x0080_0700,
    0x00C0_0700, 0x0000_0800, 0x0040_0800, 0x0080_0800, 0x00C0_0800, 0x0000_0900,
    0x0040_0900, 0x0080_0900, 0x00C0_0900, 0x0000_0A00, 0x0040_0A00, 0x0080_0A00,
    0x00C0_0A00, 0x0000_0B00, 0x0040_0B00, 0x0080_0B00, 0x00C0_0B00, 0x0000_0C00,
    0x0040_0C00, 0x0080_0C00, 0x00C0_0C00, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
  ]

  private static let decoding3url: [UInt32] = [
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,  // 0
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,  // 6
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,  // 12
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,  // 18
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,  // 24
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,  // 30
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,  // 36
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x003E_0000, 0x01FF_FFFF, 0x01FF_FFFF,  // 42
    0x0034_0000, 0x0035_0000, 0x0036_0000, 0x0037_0000, 0x0038_0000, 0x0039_0000,  // 48
    0x003A_0000, 0x003B_0000, 0x003C_0000, 0x003D_0000, 0x01FF_FFFF, 0x01FF_FFFF,  // 54
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x0000_0000,  // 60
    0x0001_0000, 0x0002_0000, 0x0003_0000, 0x0004_0000, 0x0005_0000, 0x0006_0000,  // 66
    0x0007_0000, 0x0008_0000, 0x0009_0000, 0x000A_0000, 0x000B_0000, 0x000C_0000,  // 72
    0x000D_0000, 0x000E_0000, 0x000F_0000, 0x0010_0000, 0x0011_0000, 0x0012_0000,  // 78
    0x0013_0000, 0x0014_0000, 0x0015_0000, 0x0016_0000, 0x0017_0000, 0x0018_0000,  // 84
    0x0019_0000, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x003F_0000,  // 90
    0x01FF_FFFF, 0x001A_0000, 0x001B_0000, 0x001C_0000, 0x001D_0000, 0x001E_0000,
    0x001F_0000, 0x0020_0000, 0x0021_0000, 0x0022_0000, 0x0023_0000, 0x0024_0000,
    0x0025_0000, 0x0026_0000, 0x0027_0000, 0x0028_0000, 0x0029_0000, 0x002A_0000,
    0x002B_0000, 0x002C_0000, 0x002D_0000, 0x002E_0000, 0x002F_0000, 0x0030_0000,
    0x0031_0000, 0x0032_0000, 0x0033_0000, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
    0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF, 0x01FF_FFFF,
  ]
}

extension String {
  /// This is a backport of a proposed String initializer that will allow writing directly into an uninitialized String's backing memory.
  ///
  /// As this API does not exist prior to 5.3 on Linux, or on older Apple platforms, we fake it out with a pointer and accept the extra copy.
  init(
    backportUnsafeUninitializedCapacity capacity: Int,
    initializingUTF8With initializer: (_ buffer: UnsafeMutableBufferPointer<UInt8>) throws -> Int
  ) rethrows {

    // The buffer will store zero terminated C string
    let buffer = UnsafeMutableBufferPointer<UInt8>.allocate(capacity: capacity + 1)
    defer {
      buffer.deallocate()
    }

    let initializedCount = try initializer(buffer)
    precondition(initializedCount <= capacity, "Overran buffer in initializer!")

    // add zero termination
    buffer[initializedCount] = 0

    self = String(cString: buffer.baseAddress!)
  }

  init(
    customUnsafeUninitializedCapacity capacity: Int,
    initializingUTF8With initializer: (_ buffer: UnsafeMutableBufferPointer<UInt8>) throws -> Int
  ) rethrows {
    if #available(macOS 11.0, iOS 14.0, tvOS 14.0, watchOS 7.0, *) {
      try self.init(unsafeUninitializedCapacity: capacity, initializingUTF8With: initializer)
    } else {
      try self.init(
        backportUnsafeUninitializedCapacity: capacity,
        initializingUTF8With: initializer
      )
    }
  }
}