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[TOC]
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## MPI中的集合通信与广播
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### 任务描述
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本关任务：使用MPI中的`MPI_Reduce`和`MPI_Bcast`函数实现用户自定义输入的梯形法则近似计算积分面积。
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### 相关知识
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为了完成本关任务，你需要掌握：1.MPI中的梯形法则，2.如何使用`MPI_Bcast`集合通信函数将单个进程的数据发送到通信域中所有进程，3如何使用`MPI_Reduce`集合通信函数将通信域中所有进程的数据汇总。
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#### 梯形法则
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<img width="100%" src="/api/attachments/WUpBQ3hFN3ZwY1FLcE1RWWdhU010dz09?type=image/png)" alt="" />
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梯形法则是指为了计算图（a）中从`a`到`b`阴影部分的面积，将该区域划分为`n`个子区域，每个子区域用梯形面积计算公式计算，最终将`n`个小梯形汇总求和作为所求面积大小的近似结果。
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#### MPI_Bcast
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`MPI_Bcast` - Broadcasts a message from the process with rank root to all other processes of the group.
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```c
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int MPI_Bcast(void *buffer, int count, MPI_Datatype datatype,
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int root, MPI_Comm comm)
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```
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INPUT/OUTPUT PARAMETERS
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- `buffer`: Starting address of buffer (choice).
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- `count`: Number of entries in buffer (integer).
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- `datatype`: Data type of buffer (handle).
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- `root`: Rank of broadcast root (integer).
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- `comm`: Communicator (handle).
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- `info`: Info (handle, persistent only).
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OUTPUT PARAMETERS
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- `request`: Request (handle, non-blocking and persistent only).
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- `ierror`: Fortran only: Error status (integer).
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#### MPI_Reduce
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`MPI_Reduce` - Reduces values on all processes within a group.
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```c
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int MPI_Reduce(const void *sendbuf, void *recvbuf, int count,
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MPI_Datatype datatype, MPI_Op op, int root,
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MPI_Comm comm)
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```
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INPUT PARAMETERS
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- `sendbuf`: Address of send buffer (choice).
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- `count`: Number of elements in send buffer (integer).
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- `datatype`: Data type of elements of send buffer (handle).
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- `op`: Reduce operation (handle).
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- `root`: Rank of root process (integer).
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- `comm`: Communicator (handle).
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- `info`: Info (handle, persistent only).
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OUTPUT PARAMETERS
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- `recvbuf`: Address of receive buffer (choice, significant only at root).
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- `request`: Request (handle, non-blocking and persistent only).
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- `ierror`: Fortran only: Error status (integer).
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### 编程要求
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根据提示，在右侧编辑器补充两处注释部分代码，计算并输出阴影面积的大小。
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### 测试说明
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平台会对你编写的代码进行测试：
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测试输入：`0 3 1024`；
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预期输出：
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`9.000`
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测试输入：`1 7 2048`；
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预期输出：
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`114.000`
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---
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开始你的任务吧，祝你成功！
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