## Number validations: greater than and less than or equal { #number-validations-greater-than-and-less-than-or-equal }

The same applies for:

* `gt`: `g`reater `t`han
* `le`: `l`ess than or `e`qual

{* ../../docs_src/path_params_numeric_validations/tutorial005_an_py310.py hl[10] *}

## Number validations: floats, greater than and less than { #number-validations-floats-greater-than-and-less-than }

        float | None,
        Doc(
            """
            Greater than. If set, value must be greater than this. Only applicable to
            numbers.
            """
        ),
    ] = None,
    ge: Annotated[
        float | None,
        Doc(
            """
            Greater than or equal. If set, value must be greater than or equal to
            this. Only applicable to numbers.
            """

## 數值驗證：大於或等於 { #number-validations-greater-than-or-equal }

使用 `Query` 和 `Path`（以及你之後會看到的其他類別）可以宣告數值限制。

這裡用 `ge=1`，代表 `item_id` 必須是「大於（`g`reater）或等於（`e`qual）」`1` 的整數。

{* ../../docs_src/path_params_numeric_validations/tutorial004_an_py310.py hl[10] *}

## 數值驗證：大於與小於或等於 { #number-validations-greater-than-and-less-than-or-equal }

同樣也適用於：

* `gt`：大於（`g`reater `t`han）
* `le`：小於或等於（`l`ess than or `e`qual）

{* ../../docs_src/path_params_numeric_validations/tutorial005_an_py310.py hl[10] *}

## 숫자 검증: 부동소수, 크거나 및 작거나 { #number-validations-floats-greater-than-and-less-than }

숫자 검증은 `float` 값에도 동작합니다.

여기에서 <abbr title="greater than - 보다 큼"><code>gt</code></abbr>를, <abbr title="greater than or equal - 크거나 같음"><code>ge</code></abbr>뿐만 아니라 선언할 수 있다는 점이 중요해집니다. 예를 들어 값이 `1`보다 작더라도, 반드시 `0`보다 커야 한다고 요구할 수 있습니다.

## 数值校验：大于等于 { #number-validations-greater-than-or-equal }

使用 `Query` 和 `Path`（以及你稍后会看到的其他类）你可以声明数值约束。

在这里，使用 `ge=1` 后，`item_id` 必须是一个整数，值要「`g`reater than or `e`qual」1。

{* ../../docs_src/path_params_numeric_validations/tutorial004_an_py310.py hl[10] *}

## 数值校验：大于和小于等于 { #number-validations-greater-than-and-less-than-or-equal }

同样适用于：

* `gt`：大于（`g`reater `t`han）
* `le`：小于等于（`l`ess than or `e`qual）

      assertTrue(t.equals(t));

      for (int j = i + 1; j < valuesInExpectedOrder.size(); j++) {
        T greater = valuesInExpectedOrder.get(j);
        assertTrue(greater + ".compareTo(" + t + ')', greater.compareTo(t) > 0);
        assertFalse(greater.equals(t));
      }
    }
  }

  /**
   * Returns a collection that simulates concurrent modification by having its size method return

      assertTrue(t.equals(t));

      for (int j = i + 1; j < valuesInExpectedOrder.size(); j++) {
        T greater = valuesInExpectedOrder.get(j);
        assertTrue(greater + ".compareTo(" + t + ')', greater.compareTo(t) > 0);
        assertFalse(greater.equals(t));
      }
    }
  }

  /**
   * Returns a collection that simulates concurrent modification by having its size method return

## 数値の検証: 浮動小数点、 大なり小なり { #number-validations-floats-greater-than-and-less-than }

数値のバリデーションは`float`の値に対しても有効です。

ここで重要になってくるのは<abbr title="greater than – より大きい"><code>gt</code></abbr>だけでなく<abbr title="greater than or equal – 以上"><code>ge</code></abbr>も宣言できることです。これと同様に、例えば、値が`1`より小さくても`0`より大きくなければならないことを要求することができます。

したがって、`0.5`は有効な値ですが、`0.0`や`0`はそうではありません。

  }

  /**
   * Returns the {@code byte} value that, when treated as unsigned, is equal to {@code value}, if
   * possible.
   *
   * @param value a value between 0 and 255 inclusive
   * @return the {@code byte} value that, when treated as unsigned, equals {@code value}
   * @throws IllegalArgumentException if {@code value} is negative or greater than 255
   */
  @CanIgnoreReturnValue

   * greater than or equal to that.
   */
  private static int partition(double[] array, int from, int to) {
    // Select a pivot, and move it to the start of the slice i.e. to index from.
    movePivotToStartOfSlice(array, from, to);
    double pivot = array[from];

    // Move all elements with indexes in (from, to] which are greater than the pivot to the end of