Although the [Tutorial - User Guide](../tutorial/index.md){.internal-link target=_blank} and this **Advanced User Guide** are written as a guided tutorial (like a book) and should be enough for you to **learn FastAPI**, you might want to complement it with additional courses.

Or it might be the case that you just prefer to take other courses because they adapt better to your learning style.

//
// If operating in binary mode, this assumes strict GNU binary mode; which means
// that the first byte can only be either 0x80 or 0xff. Thus, the first byte is
// equivalent to the sign bit in two's complement form.
func fitsInBase256(n int, x int64) bool {
	binBits := uint(n-1) * 8
	return n >= 9 || (x >= -1<<binBits && x < 1<<binBits)
}

// parseNumeric parses the input as being encoded in either base-256 or octal.

   * @since 19.0
   */
  Set<Range<C>> asDescendingSetOfRanges();

  /**
   * Returns a view of the complement of this {@code RangeSet}.
   *
   * <p>The returned view supports the {@link #add} operation if this {@code RangeSet} supports
   * {@link #remove}, and vice versa.
   */
  RangeSet<C> complement();

  /**
   * Returns a view of the intersection of this {@code RangeSet} with the specified range.
   *

        [language, input] << [
            ["English", """
ELF Header:
 Magic:   7f 45 4c 46 01 01 01 00 00 00 00 00 00 00 00 00
 Class:                             ELF32
 Data:                              2's complement, little endian
 Version:                           1 (current)
 OS/ABI:                            UNIX - System V
 ABI Version:                       0
 Type:                              EXEC (Executable file)

receipt. The encode algorithm looks like this:

	var u uint
	if i < 0 {
		u = (^uint(i) << 1) | 1 // complement i, bit 0 is 1
	} else {
		u = (uint(i) << 1) // do not complement i, bit 0 is 0
	}
	encodeUnsigned(u)

The low bit is therefore analogous to a sign bit, but making it the complement bit
instead guarantees that the largest negative integer is not a special case. For

   * @since 19.0
   */
  Set<Range<C>> asDescendingSetOfRanges();

  /**
   * Returns a view of the complement of this {@code RangeSet}.
   *
   * <p>The returned view supports the {@link #add} operation if this {@code RangeSet} supports
   * {@link #remove}, and vice versa.
   */
  RangeSet<C> complement();

  /**
   * Returns a view of the intersection of this {@code RangeSet} with the specified range.
   *

// This pattern checks if an i8 arith::ConstantOp tensor has all values within
// the INT4 range, i.e. [-8,7] and converts it into i4 if so. This assumes that
// the input is sign-extended two's complement.
class CheckRangeAndConvertI8ToI4 : public OpRewritePattern<arith::ConstantOp> {
 public:
  using OpRewritePattern<arith::ConstantOp>::OpRewritePattern;

  LogicalResult matchAndRewrite(arith::ConstantOp op,

//   encoding: Positive values x are written as 2*x + 0, negative values
//   are written as 2*(^x) + 1; that is, negative numbers are complemented
//   and whether to complement is encoded in bit 0.
//
// Design note:
// At most 10 bytes are needed for 64-bit values. The encoding could
// be more dense: a full 64-bit value needs an extra byte just to hold bit 63.

[[sec:preferred-version]]
`prefer`::
This is a very soft version declaration.
It applies only if there is no stronger non dynamic opinion on a version for the module.
This term does not support dynamic versions.
+
Definition can complement `strictly` or `require`.
+
When defined, this overrides any previous `prefer` declaration and clears previous `reject`.

There is also an additional term outside of the level hierarchy:

[[sec:rejected-version]]

		pos += uint64(n)
		x = x[n:]
	}
}

//go:nosplit
func (l *debugLogWriter) varint(x int64) {
	var u uint64
	if x < 0 {
		u = (^uint64(x) << 1) | 1 // complement i, bit 0 is 1
	} else {
		u = (uint64(x) << 1) // do not complement i, bit 0 is 0
	}
	l.uvarint(u)
}

//go:nosplit
func (l *debugLogWriter) uvarint(u uint64) {
	i := 0
	for u >= 0x80 {
		l.buf[i] = byte(u) | 0x80
		u >>= 7