用PySimpleGUI实现一个简易的分布式计算系统——简易多机协同计算原型系统(Simply Multi-Machine Collaborative Computing)
文章目录
- 0️⃣ 前言
- 1️⃣ 系统运行界面
- 2️⃣ 任务设计
-
- 2️⃣.1️⃣ 任务下发
- 2️⃣.2️⃣ 计算进程
- 3️⃣ 具体程序
-
- 3️⃣.1️⃣ 初始文件收发
- 3️⃣.2️⃣ 计算节点程序(客户端)
- 3️⃣.3️⃣ 控制节点程序(服务器端)
- 3️⃣.4️⃣ 界面`GUI`程序
- 3️⃣.5️⃣ 计算任务
- 4️⃣ 完整程序(方便大家复制运行)
-
- 4️⃣.1️⃣ `SMMCC.py`
- 4️⃣.2️⃣ `Func.py`
0️⃣ 前言
本文所有的程序在这个repo中：ExcaliburEX/SMMCC
前面，我已经将实现这个微型系统的组件程序，单独地实现了。可以在下面三篇文章中回顾。
高性能分布式计算(HPC)作业1——节点实时通信
高性能分布式计算(HPC)作业2——节点通信，发布计算任务
高性能分布式计算(HPC)作业3——节点通信，发布计算任务，并在计算任务中阻塞
1️⃣ 系统运行界面
2️⃣ 任务设计
2️⃣.1️⃣ 任务下发
服务器下即控制节点向各计算节点请求确认信息，计算节点返回确认信息。随即控制节点向各计算节点下发计算任务以及参数，然后计算节点返回确认信息。
2️⃣.2️⃣ 计算进程
- 各计算节点开始计算；
- 在某个计算节点结束后，向控制节点确认自己是第几个算完的，并返回局部结果；
- 如果自己是最后一个算完的，那么就成为规约节点，否则结束运算，当前节点结束任务；
- 若是，开始接受控制节点的所有局部结果，并进行规约计算，最后返回给控制节点最终结果。
3️⃣ 具体程序
3️⃣.1️⃣ 初始文件收发
因为程序运行在本地，节点间通过本地的socket连接，所以就把文件收发放在一开始，不用每个节点都收一次，一次即可，所有的节点都从本地调取计算函数test.py，使用方式就是通过import的方式进行。
def ReceiveFile(self):
client = socket.socket(socket.AF_INET, socket.SOCK_STREAM)
client.connect((ip, port))
while True:
with open("test.py", "ab") as f: # 接收文件
data = client.recv(1024)
if data == b'quit':
client.send("received".encode('utf-8'))
break
if data != b'success':
f.write(data)
client.send("success".encode('utf-8'))
print(time.strftime("[%Y-%m-%d %H:%M:%S] ", time.localtime()), "计算文件已经接收！存储为test.py")
f.close()
client.shutdown(socket.SHUT_RDWR)
client.close()
def SendFile(self):
conn, addr = self.server.accept()
print(conn,addr)
with open('Func.py', 'rb') as f:
for i in f:
conn.send(i)
data = conn.recv(1024)
if data == b'received':
break
print(time.strftime("[%Y-%m-%d %H:%M:%S] ", time.localtime()), "文件'Func.py'已经发送！")
conn.send('quit'.encode('utf-8'))
3️⃣.2️⃣ 计算节点程序(客户端)
刚刚也说了，一开始就接收到了计算文件，所以注释的部分就不需要了，这部分内容是假定各节点在不同的机器上，需要各自接收计算文件。除此之外，其他逻辑就是前文提到的过程。
def Node(self, cnt, window):
begin_time = time.time()
client = socket.socket(socket.AF_INET, socket.SOCK_STREAM)
client.connect((ip, port))
while True:
msg = client.recv(1024)
if msg == b'Connect': # 接收 Connect
client.send('Ready'.encode('utf-8')) # 发送 Ready
print(time.strftime("[%Y-%m-%d %H:%M:%S] ", time.localtime()), "节点%d准备完毕！" % (cnt))
window['STATUS%d'%(cnt)].update("准备就绪")
break
else:
pass
# while True:
# data = client.recv(1024)
# if data == b'exist':
# if os.path.exists("test.py"):
# client.send("Y".encode('utf-8'))
# break
# else:
# client.send("N".encode('utf-8'))
# while True:
# with open("test.py", "ab") as f: # 接收文件
# data = client.recv(1024)
# if data == b'quit':
# client.send("received".encode('utf-8'))
# break
# if data != b'success':
# f.write(data)
# client.send("success".encode('utf-8'))
# print("节点%d：计算文件已经接收！存储为test.py" % (cnt))
# f.close()
# break
time.sleep(1)
window['STATUS%d' % (cnt)].update("接收计算参数")
client.send("Para".encode('utf-8'))
rng = int(client.recv(1024)) # 接收rng
m = int(client.recv(1024)) # 接收分片个数
pos = int(client.recv(1024)) # 接收位置参数
# print(time.strftime("[%Y-%m-%d %H:%M:%S] ", time.localtime()), "%d：分别为%d,%d,%d" % (cnt, rng, m, pos))
window['STATUS%d' % (cnt)].update("计算中...")
from test import test
sum_prime = test(rng, m, pos, window)
print(time.strftime("[%Y-%m-%d %H:%M:%S] ", time.localtime()), "节点%d，第%d个运算完，局部结果为：%d" % (cnt, pos, sum_prime))
window['STATUS%d' % (cnt)].update("计算完毕，发送结果，请求位置")
client.send("answer".encode('utf-8'))
client.send(str(sum_prime).encode('utf-8')) # 发送局部结果
time.sleep(1)
client.send("who".encode('utf-8')) # 发送位置请求
who = int(client.recv(1024)) # 接收位置回复
window['STATUS%d' % (cnt)].update("节点位置为:%d"%(who))
# print("我是：",who)
global compute_time
if who == self.m:
client.send("Integrate".encode('utf-8'))
data = client.recv(1024)
sumList = json.loads(data)
ans = sum(sumList)
window['STATUS%d' % (cnt)].update("规约节点，最终结果为:%d" % (ans))
client.send(str(ans).encode('utf-8'))
end_time = time.time()
run_time = end_time-begin_time
compute_time.append(run_time)
global finish
finish = True
os.remove('test.py')
else:
window['STATUS%d' % (cnt)].update("第%d节点，非规约节点，任务结束"%(who))
client.send("end".encode('utf-8'))
end_time = time.time()
run_time = end_time-begin_time
compute_time.append(run_time)
client.shutdown(socket.SHUT_RDWR)
client.close()
3️⃣.3️⃣ 控制节点程序(服务器端)
首先先等待所有的计算节点的连接，然后针对每个连接开启相应的服务器控制函数线程。
def connect(self):
NumOfConnect = 0
while True:
conn, addr = self.server.accept()
# print(conn, addr)
self.connectList.append([conn, addr])
NumOfConnect += 1
if NumOfConnect == self.m:
print(time.strftime("[%Y-%m-%d %H:%M:%S] ", time.localtime()), "计算节点与控制节点连接完毕！")
break
def Call(self):
for c in self.connectList:
threading.Thread(target=self.ServerCommand, args=(c[0], c[1])).start()
time.sleep(0.5)
def ServerCommand(self, conn, addr):
while True:
conn.send('Connect'.encode('utf-8'))
data = conn.recv(1024)
if data == b'Ready':
break
# conn.send("exist".encode('utf-8'))
# data = conn.recv(1024)
# if data == b'N':
# with open('Func.py', 'rb') as f:
# for i in f:
# conn.send(i)
# data = conn.recv(1024)
# if data == b'received':
# break
# print("文件'Func.py'已经发送！")
# conn.send('quit'.encode('utf-8'))
global pos
while True:
data = conn.recv(1024)
if data == b'Para':
time.sleep(0.5)
conn.send(str(self.rng).encode('utf-8'))
time.sleep(0.5)
conn.send(str(self.m).encode('utf-8'))
time.sleep(0.5)
conn.send(str(pos).encode('utf-8'))
pos += 1
break
while True:
data = conn.recv(1024)
if data == b'answer':
ans = int(conn.recv(1024))
global part_sum
part_sum.append(ans)
break
while True:
data = conn.recv(1024)
if data == b'who':
global who_pos
conn.send(str(who_pos).encode('utf-8'))
who_pos += 1
break
while True:
data = conn.recv(1024)
if data == b'Integrate':
sum_string = json.dumps(part_sum)
conn.send(str(sum_string).encode('utf-8'))
answer = conn.recv(1024)
print(time.strftime("[%Y-%m-%d %H:%M:%S] ",time.localtime()), "最终结果：%d" % (int(answer)))
break
else:
break
conn.close()
3️⃣.4️⃣ 界面GUI程序
这里面就是PysimpleGUI的使用，遇到并已经解决的难点：
- 实时展示程序的命令行输出；
- 展示运算进度条。
def GUI(self):
sg.theme('LightGrey1')
col = []
for i in range(100):
col.append([sg.Text('节点%d' % (i+1), justification='center', font=("Noto Serif SC", 10), size=(16, 1), key='NODE%s' % (str(i+1)), text_color='saddlebrown', background_color='powderblue'),
sg.Text('未知状态%d' % (i+1), justification='center', font=("Noto Serif SC", 10),
size=(24, 1), key='STATUS%s' % (str(i+1)), text_color='mediumblue', background_color='azure'),
sg.ProgressBar(100, orientation='h', size=(
42, 20), style='winnative', bar_color=('palegreen', 'pink'), relief=sg.RELIEF_RIDGE, key='progressbar-%d' % (i+1))]
)
layout = [[sg.Text('Simply Multi-Machine Collaborative Computing', size=(
40, 1), text_color='green', border_width=1, justification='center', font=("Noto Serif SC",22), relief=sg.RELIEF_RIDGE)],
[sg.Text('计算范围：', font=("Noto Serif SC", 16)), sg.InputText('100000', font=("Noto Serif SC", 16), size=(21, 2), key='-RANGE-'),
sg.Text('节点数：', font=("Noto Serif SC", 16)), sg.InputText('10', font=("Noto Serif SC", 16), size=(21, 2), key='-NODENUM-')],
[sg.Text('节点名', size=(12, 1), text_color='white', font=(
"Noto Serif SC", 16), background_color='green', justification='center',relief=sg.RELIEF_RIDGE, pad=(0, 0)),
sg.Text('节点状态', size=(15, 1), text_color='white', font=(
"Noto Serif SC", 16), background_color='green', justification='center', relief=sg.RELIEF_RIDGE, pad=(0, 0)),
sg.Text('运算进度', size=(27, 1), text_color='white', font=("Noto Serif SC", 16), background_color='green', justification='center', relief=sg.RELIEF_RIDGE, pad=(0, 0))],
[sg.Column(col, background_color='papayawhip', size=(700, 400),scrollable=True, justification="left", element_justification="center")],
[sg.Output(size=(100, 10))],
[sg.Button('开始计算', font=(
"Noto Serif SC", 10), size=(8, 1)), sg.Button('计算加速比', font=(
"Noto Serif SC", 10), size=(8, 1)), sg.Text(
'暂无数据', font=("Noto Serif SC", 16), relief=sg.RELIEF_RIDGE,key='-JIASU-'), sg.Button('总运算时长', font=(
"Noto Serif SC", 10), size=(8, 1), button_color=('lawngreen', 'plum')), sg.Text(
'暂无数据', font=("Noto Serif SC", 16),relief=sg.RELIEF_RIDGE,key='-TIME-')],
] # button_color=(sg.YELLOWS[0], sg.BLUES[0]
window = sg.Window(
'SMMCC', layout, default_element_size=(30, 2), resizable=True)
self.server = socket.socket(socket.AF_INET, socket.SOCK_STREAM)
self.server.bind((ip, port)) # 绑定要监听的端口
self.server.listen(5) # 开始监听 表示可以使用五个链接排队
#conn, addr = server.accept()
#print("连接建立，地址在%s" % (str(addr)))
while True:
event, value = window.read()
if event == '开始计算':
self.connectList = []
global pos
pos = 1
global part_sum
part_sum = []
global who_pos
who_pos = 1
global compute_time
compute_time = []
global finish
finish = False
for i in range(100):
window['progressbar-%d' % (i+1)].update_bar(0)
self.rng = int(value['-RANGE-'])
self.m = int(value['-NODENUM-'])
threading.Thread(target=self.main,args=(window,)).start()
threading.Thread(target=self.SpeedupRatio,args=(window,)).start()
print(time.strftime("[%Y-%m-%d %H:%M:%S] ",time.localtime()), "侦听器已启动！port：%d" % (port))
window.close()
3️⃣.5️⃣ 计算任务
就是简单的计算某个区间内的素数个数，分成n份分发给各个节点进行计算，其中嵌入了进度条展示。
from alive_progress import alive_bar
from math import sqrt
def Prime(n):
if n == 1:
return False
for num in range(2, int(sqrt(n))+1):
if n % num == 0:
return False
else:
return True
def test(rng, m, pos, window):
sum_prime = 0
# with alive_bar(rng // m) as bar:
for i in range(rng // m * (pos-1), rng // m * (pos)):
# bar()
window['progressbar-%d'%(pos)].update_bar(100/(rng//m) * (i-(rng // m * (pos-1))) + 1)
if Prime(i):
sum_prime += 1
return sum_prime
4️⃣ 完整程序(方便大家复制运行)
4️⃣.1️⃣ SMMCC.py
import socket
import time
import threading
import os
import sys
import json
import PySimpleGUI as sg
class SMMCC():
global ip
ip = '127.0.0.1'
global port
port = 6999
global pos
pos = 1
global part_sum
part_sum = []
global who_pos
who_pos = 1
global compute_time
compute_time = []
global finish
finish = False
house_prc
def __init__(self, rng=1000, m=5):
self.connectList = []
self.rng = rng
self.m = m
def ReceiveFile(self):
client = socket.socket(socket.AF_INET, socket.SOCK_STREAM)
client.connect((ip, port))
while True:
with open("test.py", "ab") as f: # 接收文件
data = client.recv(1024)
if data == b'quit':
client.send("received".encode('utf-8'))
break
if data != b'success':
f.write(data)
client.send("success".encode('utf-8'))
print(time.strftime("[%Y-%m-%d %H:%M:%S] ", time.localtime()), "计算文件已经接收！存储为test.py")
f.close()
client.shutdown(socket.SHUT_RDWR)
client.close()
def SendFile(self):
conn, addr = self.server.accept()
print(conn,addr)
with open('Func.py', 'rb') as f:
for i in f:
conn.send(i)
data = conn.recv(1024)
if data == b'received':
break
print(time.strftime("[%Y-%m-%d %H:%M:%S] ", time.localtime()), "文件'Func.py'已经发送！")
conn.send('quit'.encode('utf-8'))
def Node(self, cnt, window):
begin_time = time.time()
client = socket.socket(socket.AF_INET, socket.SOCK_STREAM)
client.connect((ip, port))
while True:
msg = client.recv(1024)
if msg == b'Connect': # 接收 Connect
client.send('Ready'.encode('utf-8')) # 发送 Ready
print(time.strftime("[%Y-%m-%d %H:%M:%S] ", time.localtime()), "节点%d准备完毕！" % (cnt))
window['STATUS%d'%(cnt)].update("准备就绪")
break
else:
pass
# while True:
# data = client.recv(1024)
# if data == b'exist':
# if os.path.exists("test.py"):
# client.send("Y".encode('utf-8'))
# break
# else:
# client.send("N".encode('utf-8'))
# while True:
# with open("test.py", "ab") as f: # 接收文件
# data = client.recv(1024)
# if data == b'quit':
# client.send("received".encode('utf-8'))
# break
# if data != b'success':
# f.write(data)
# client.send("success".encode('utf-8'))
# print("节点%d：计算文件已经接收！存储为test.py" % (cnt))
# f.close()
# break
time.sleep(1)
window['STATUS%d' % (cnt)].update("接收计算参数")
client.send("Para".encode('utf-8'))
rng = int(client.recv(1024)) # 接收rng
m = int(client.recv(1024)) # 接收分片个数
pos = int(client.recv(1024)) # 接收位置参数
# print(time.strftime("[%Y-%m-%d %H:%M:%S] ", time.localtime()), "%d：分别为%d,%d,%d" % (cnt, rng, m, pos))
window['STATUS%d' % (cnt)].update("计算中...")
from test import test
sum_prime = test(rng, m, pos, window)
print(time.strftime("[%Y-%m-%d %H:%M:%S] ", time.localtime()), "节点%d，第%d个运算完，局部结果为：%d" % (cnt, pos, sum_prime))
window['STATUS%d' % (cnt)].update("计算完毕，发送结果，请求位置")
client.send("answer".encode('utf-8'))
client.send(str(sum_prime).encode('utf-8')) # 发送局部结果
time.sleep(1)
client.send("who".encode('utf-8')) # 发送位置请求
who = int(client.recv(1024)) # 接收位置回复
window['STATUS%d' % (cnt)].update("节点位置为:%d"%(who))
# print("我是：",who)
global compute_time
if who == self.m:
client.send("Integrate".encode('utf-8'))
data = client.recv(1024)
sumList = json.loads(data)
ans = sum(sumList)
window['STATUS%d' % (cnt)].update("规约节点，最终结果为:%d" % (ans))
client.send(str(ans).encode('utf-8'))
end_time = time.time()
run_time = end_time-begin_time
compute_time.append(run_time)
global finish
finish = True
os.remove('test.py')
else:
window['STATUS%d' % (cnt)].update("第%d节点，非规约节点，任务结束"%(who))
client.send("end".encode('utf-8'))
end_time = time.time()
run_time = end_time-begin_time
compute_time.append(run_time)
client.shutdown(socket.SHUT_RDWR)
client.close()
def connect(self):
NumOfConnect = 0
while True:
conn, addr = self.server.accept()
# print(conn, addr)
self.connectList.append([conn, addr])
NumOfConnect += 1
if NumOfConnect == self.m:
print(time.strftime("[%Y-%m-%d %H:%M:%S] ", time.localtime()), "计算节点与控制节点连接完毕！")
break
def Call(self):
for c in self.connectList:
threading.Thread(target=self.ServerCommand, args=(c[0], c[1])).start()
time.sleep(0.5)
def ServerCommand(self, conn, addr):
while True:
conn.send('Connect'.encode('utf-8'))
data = conn.recv(1024)
if data == b'Ready':
break
# conn.send("exist".encode('utf-8'))
# data = conn.recv(1024)
# if data == b'N':
# with open('Func.py', 'rb') as f:
# for i in f:
# conn.send(i)
# data = conn.recv(1024)
# if data == b'received':
# break
# print("文件'Func.py'已经发送！")
# conn.send('quit'.encode('utf-8'))
global pos
while True:
data = conn.recv(1024)
if data == b'Para':
time.sleep(0.5)
conn.send(str(self.rng).encode('utf-8'))
time.sleep(0.5)
conn.send(str(self.m).encode('utf-8'))
time.sleep(0.5)
conn.send(str(pos).encode('utf-8'))
pos += 1
break
while True:
data = conn.recv(1024)
if data == b'answer':
ans = int(conn.recv(1024))
global part_sum
part_sum.append(ans)
break
while True:
data = conn.recv(1024)
if data == b'who':
global who_pos
conn.send(str(who_pos).encode('utf-8'))
who_pos += 1
break
while True:
data = conn.recv(1024)
if data == b'Integrate':
sum_string = json.dumps(part_sum)
conn.send(str(sum_string).encode('utf-8'))
answer = conn.recv(1024)
print(time.strftime("[%Y-%m-%d %H:%M:%S] ",time.localtime()), "最终结果：%d" % (int(answer)))
break
else:
break
conn.close()
def GUI(self):
sg.theme('LightGrey1')
col = []
for i in range(100):
col.append([sg.Text('节点%d' % (i+1), justification='center', font=("Noto Serif SC", 10), size=(16, 1), key='NODE%s' % (str(i+1)), text_color='saddlebrown', background_color='powderblue'),
sg.Text('未知状态%d' % (i+1), justification='center', font=("Noto Serif SC", 10),
size=(24, 1), key='STATUS%s' % (str(i+1)), text_color='mediumblue', background_color='azure'),
sg.ProgressBar(100, orientation='h', size=(
42, 20), style='winnative', bar_color=('palegreen', 'pink'), relief=sg.RELIEF_RIDGE, key='progressbar-%d' % (i+1))]
)
layout = [[sg.Text('Simply Multi-Machine Collaborative Computing', size=(
40, 1), text_color='green', border_width=1, justification='center', font=("Noto Serif SC",22), relief=sg.RELIEF_RIDGE)],
[sg.Text('计算范围：', font=("Noto Serif SC", 16)), sg.InputText('100000', font=("Noto Serif SC", 16), size=(21, 2), key='-RANGE-'),
sg.Text('节点数：', font=("Noto Serif SC", 16)), sg.InputText('10', font=("Noto Serif SC", 16), size=(21, 2), key='-NODENUM-')],
[sg.Text('节点名', size=(12, 1), text_color='white', font=(
"Noto Serif SC", 16), background_color='green', justification='center',relief=sg.RELIEF_RIDGE, pad=(0, 0)),
sg.Text('节点状态', size=(15, 1), text_color='white', font=(
"Noto Serif SC", 16), background_color='green', justification='center', relief=sg.RELIEF_RIDGE, pad=(0, 0)),
sg.Text('运算进度', size=(27, 1), text_color='white', font=("Noto Serif SC", 16), background_color='green', justification='center', relief=sg.RELIEF_RIDGE, pad=(0, 0))],
[sg.Column(col, background_color='papayawhip', size=(700, 400),scrollable=True, justification="left", element_justification="center")],
[sg.Output(size=(100, 10))],
[sg.Button('开始计算', font=(
"Noto Serif SC", 10), size=(8, 1)), sg.Button('计算加速比', font=(
"Noto Serif SC", 10), size=(8, 1)), sg.Text(
'暂无数据', font=("Noto Serif SC", 16), relief=sg.RELIEF_RIDGE,key='-JIASU-'), sg.Button('总运算时长', font=(
"Noto Serif SC", 10), size=(8, 1), button_color=('lawngreen', 'plum')), sg.Text(
'暂无数据', font=("Noto Serif SC", 16),relief=sg.RELIEF_RIDGE,key='-TIME-')],
] # button_color=(sg.YELLOWS[0], sg.BLUES[0]
window = sg.Window(
'SMMCC', layout, default_element_size=(30, 2), resizable=True)
self.server = socket.socket(socket.AF_INET, socket.SOCK_STREAM)
self.server.bind((ip, port)) # 绑定要监听的端口
self.server.listen(5) # 开始监听 表示可以使用五个链接排队
#conn, addr = server.accept()
#print("连接建立，地址在%s" % (str(addr)))
while True:
event, value = window.read()
if event == '开始计算':
self.connectList = []
global pos
pos = 1
global part_sum
part_sum = []
global who_pos
who_pos = 1
global compute_time
compute_time = []
global finish
finish = False
for i in range(100):
window['progressbar-%d' % (i+1)].update_bar(0)
self.rng = int(value['-RANGE-'])
self.m = int(value['-NODENUM-'])
threading.Thread(target=self.main,args=(window,)).start()
threading.Thread(target=self.SpeedupRatio,args=(window,)).start()
print(time.strftime("[%Y-%m-%d %H:%M:%S] ",time.localtime()), "侦听器已启动！port：%d" % (port))
window.close()
def SpeedupRatio(self, window):
global finish
global compute_time
while True:
time.sleep(2)
if finish == True:
window['-JIASU-'].update(sum(compute_time) / (max(compute_time) * self.m))
print(time.strftime("[%Y-%m-%d %H:%M:%S] ", time.localtime()),
"加速比为：%lf" % (sum(compute_time) / (max(compute_time) * self.m)))
window['-TIME-'].update(str(max(compute_time))+'s')
print(time.strftime("[%Y-%m-%d %H:%M:%S] ", time.localtime()), "总运算时长为：%lfs" % (max(compute_time)))
finish = False
break
def main(self, window):
threading.Thread(target=self.SendFile).start()
threading.Thread(target=self.ReceiveFile).start()
time.sleep(1)
for i in range(1, self.m + 1):
threading.Thread(target=self.Node,args=(i,window)).start()
self.connect()
self.Call()
if __name__ == "__main__":
s = SMMCC(100000, 10)
s.GUI()
4️⃣.2️⃣ Func.py
from alive_progress import alive_bar
from math import sqrt
def Prime(n):
if n == 1:
return False
for num in range(2, int(sqrt(n))+1):
if n % num == 0:
return False
else:
return True
def test(rng, m, pos, window):
sum_prime = 0
# with alive_bar(rng // m) as bar:
for i in range(rng // m * (pos-1), rng // m * (pos)):
# bar()
window['progressbar-%d'%(pos)].update_bar(100/(rng//m) * (i-(rng // m * (pos-1))) + 1)
if Prime(i):
sum_prime += 1
return sum_prime