e := new(Number)
	*e = x
	return e
}

func sub1(x *Number) *Number {
	return *x
}

func add(x, y *Number) *Number {
	if is_zero(y) {
		return x
	}

	return add(add1(x), sub1(y))
}

func mul(x, y *Number) *Number {
	if is_zero(x) || is_zero(y) {
		return zero()
	}

	return add(mul(x, sub1(y)), x)
}

func fact(n *Number) *Number {
	if is_zero(n) {

		{uint128{0, 0}, sub1, uint128{^uint64(0), ^uint64(0)}},
		{uint128{0, 1}, sub1, uint128{0, 0}},
		{uint128{0, 2}, sub1, uint128{0, 1}},
		{uint128{1, 0}, sub1, uint128{0, ^uint64(0)}},
		{uint128{1, 1}, sub1, uint128{1, 0}},
	}
	for _, tt := range tests {
		var got uint128
		switch tt.op {
		case add1:
			got = tt.in.addOne()
		case sub1:
			got = tt.in.subOne()
		default:

    RangeMap<Integer, Integer> sub1 = rangeMap.subRangeMap(Range.closed(5, 11));
    assertEquals(
        ImmutableMap.of(Range.closedOpen(5, 7), 1, Range.closed(9, 10), 2), sub1.asMapOfRanges());
    RangeMap<Integer, Integer> sub2 = sub1.subRangeMap(Range.open(6, 15));
    assertEquals(
        ImmutableMap.of(Range.open(6, 7), 1, Range.closed(9, 10), 2), sub2.asMapOfRanges());
  }

	SETCC	AX
	SETCC	foo+4(SB)

// LTYPE2 rimnon	{ outcode(int($1), &$2); }
	DIVB	AX
	DIVB	foo+4(SB)
	PUSHL	$foo+4(SB)
	POPL		AX

// LTYPE3 rimrem	{ outcode(int($1), &$2); }
	SUBB	$1, AX
	SUBB	$1, foo+4(SB)
	SUBB	BX, AX
	SUBB	BX, foo+4(SB)

// LTYPE4 remrim	{ outcode(int($1), &$2); }
	CMPB	AX, $1
	CMPB	foo+4(SB), $4
	CMPB	BX, AX
	CMPB	foo+4(SB), BX

// LTYPER nonrel	{ outcode(int($1), &$2); }
label:

# Sub-dependencies

You can create dependencies that have **sub-dependencies**.

They can be as **deep** as you need them to be.

**FastAPI** will take care of solving them.

## First dependency "dependable"

You could create a first dependency ("dependable") like:

=== "Python 3.10+"

    ```Python hl_lines="8-9"
    {!> ../../../docs_src/dependencies/tutorial005_an_py310.py!}
    ```

=== "Python 3.9+"

下图显示的是主应用 API 文档，只包括其自有的*路径操作*。

<img src="/img/tutorial/sub-applications/image01.png">

然后查看子应用文档 <a href="http://127.0.0.1:8000/subapi/docs" class="external-link" target="_blank">http://127.0.0.1:8000/subapi/docs。</a>

下图显示的是子应用的 API 文档，也是只包括其自有的*路径操作*，所有这些路径操作都在 `/subapi` 子路径前缀下。

<img src="/img/tutorial/sub-applications/image02.png">

两个用户界面都可以正常运行，因为浏览器能够与每个指定的应用或子应用会话。

### 技术细节：`root_path`

LeeeeT <******@****.***> 1680341164 +0300

<img src="/img/tutorial/sub-applications/image01.png">

و سپس اسناد زیر برنامه را در آدرس <a href="http://127.0.0.1:8000/subapi/docs" class="external-link" target="_blank">http://127.0.0.1:8000/subapi/docs</a>. باز کنید.

اسناد API خودکار برای زیر برنامه را خواهید دید، که فقط شامل path operations خود می شود، همه در زیر مسیر `/subapi` قرار دارند:

<img src="/img/tutorial/sub-applications/image02.png">

### Technical Details: `root_path`

When you mount a sub-application as described above, FastAPI will take care of communicating the mount path for the sub-application using a mechanism from the ASGI specification called a `root_path`.

That way, the sub-application will know to use that path prefix for the docs UI.

        given:
        projectDir.createFile('settings.gradle') << """
            include ':sub1'
            include ':sub2'
        """
        projectDir.createFile('build.gradle')

        [projectDir.createDir('sub1'), projectDir.createDir('sub2')].eachWithIndex { TestFile it, def index ->
            it.file('build.gradle') << """
            apply plugin: 'java'