private static final String CHECK_UPPER_BOUND_INCLUSIVE = "check upper bound is inclusive";

    private static final String CHECK_LOWER_BOUND = "check lower bound";

    private static final String CHECK_LOWER_BOUND_INCLUSIVE = "check lower bound is inclusive";

    private static final String CHECK_VERSION_RECOMMENDATION = "check version recommended";

   * guaranteed to be exactly +/-1 even when the data are perfectly (anti-)correlated, due to
   * numerical errors. However, it is guaranteed to be in the inclusive range [-1, +1].
   *
   * <h3>Non-finite values</h3>
   *
   * <p>If the dataset contains any non-finite values ({@link Double#POSITIVE_INFINITY}, {@link

        () -> UnsignedLongs.parseUnsignedLong("1234567890abcdef1", 16));
  }

  public void testParseLongThrowsExceptionForInvalidRadix() {
    // Valid radix values are Character.MIN_RADIX to Character.MAX_RADIX, inclusive.
    assertThrows(
        NumberFormatException.class,
        () -> UnsignedLongs.parseUnsignedLong("0", Character.MIN_RADIX - 1));

    assertThrows(
        NumberFormatException.class,

  /**
   * Load 8 bytes into long in a little endian manner, from the substring between position and
   * position + 8. The array must have at least 8 bytes from offset (inclusive).
   *
   * @param input the input bytes
   * @param offset the offset into the array at which to start
   * @return a long of a concatenated 8 bytes
   */
  static long load64(byte[] input, int offset) {

   * guaranteed to be exactly +/-1 even when the data are perfectly (anti-)correlated, due to
   * numerical errors. However, it is guaranteed to be in the inclusive range [-1, +1].
   *
   * <h3>Non-finite values</h3>
   *
   * <p>If the dataset contains any non-finite values ({@link Double#POSITIVE_INFINITY}, {@link

                            upperInclusive = res2.isUpperBoundInclusive();
                        }
                    }

                    // don't add if they are equal and one is not inclusive
                    if (lower == null || upper == null || lower.compareTo(upper) != 0) {
                        restrictions.add(new Restriction(lower, lowerInclusive, upper, upperInclusive));

    return indexOf(object) >= 0;
  }

  // constrain the return type to ImmutableList<E>

  /**
   * Returns an immutable list of the elements between the specified {@code fromIndex}, inclusive,
   * and {@code toIndex}, exclusive. (If {@code fromIndex} and {@code toIndex} are equal, the empty
   * immutable list is returned.)
   *

    return anyOf(sequence).negate();
  }

  /**
   * Returns a {@code char} matcher that matches any character in a given BMP range (both endpoints
   * are inclusive). For example, to match any lowercase letter of the English alphabet, use {@code
   * CharMatcher.inRange('a', 'z')}.
   *
   * @throws IllegalArgumentException if {@code endInclusive < startInclusive}
   */

  public void testIsPrimeOnUniformRandom() {
    Random rand = new Random(1);
    for (int bits = 10; bits < 63; bits++) {
      for (int i = 0; i < 2000; i++) {
        // A random long between 0 and Long.MAX_VALUE, inclusive.
        long l = rand.nextLong() & ((1L << bits) - 1);
        assertEquals(BigInteger.valueOf(l).isProbablePrime(100), LongMath.isPrime(l));
      }
    }
  }

Outro grande recurso necessário pelas APIs é a <abbr title="ler e converter para dados Python">análise</abbr> de dados vindos de requisições.

Webargs é uma ferramente feita para fornecer o que está no topo de vários frameworks, inclusive Flask.

Ele utiliza Marshmallow por baixo para validação de dados. E ele foi criado pelos mesmos desenvolvedores.

Ele é uma grande ferramenta e eu também a utilizei muito, antes de ter o **FastAPI**.

/// info