Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
コード本文
python
1from mpi4py import MPI
2import gmpy2 as mp
3from gmpy2 import mpz
4import numpy as np
5import mmap
6import sys
7import os
89# 円周率を並列に計算する。10defcalc_PQT_root(n):11# まず自分の割り当て分を計算する。12 alloc =int(n / size)13 PQT2 = calc_PQT_local(rank * alloc,(rank +1)* alloc)1415# 各ノードの計算結果をマージする。16 level =int(mp.ceil(mp.log2(size)))17 k =118for _ inrange(level):19if(rank & k)== k:20 PQT1 = comm.recv(source=rank-k, tag=0)21 PQT2 = np.array([PQT1[0]* PQT2[0],22 PQT1[1]* PQT2[1],23 PQT1[2]* PQT2[1]+ PQT1[0]* PQT2[2]])24 k *=225else:26 comm.send(PQT2, dest=rank+k, tag=0)27break28return PQT2
2930# ノード内でP(n1, n2), Q(n1, n2), T(n1, n2)を計算する。31defcalc_PQT_local(n1, n2):32if n1 +1== n2:33 P = mpz((-1)*(2* n2 -1)*(6* n2 -5)*(6* n2 -1))34return np.array([P, C3over24 * n2 **3,(A + B * n2)* P])35else:36 m =int((n1 + n2)/2)37 PQT1 = calc_PQT_local(n1, m)38 PQT2 = calc_PQT_local(m, n2)39return np.array([PQT1[0]* PQT2[0],40 PQT1[1]* PQT2[1],41 PQT1[2]* PQT2[1]+ PQT1[0]* PQT2[2]])4243# 円周率が何桁まで一致するかを判定する。44defcheck_pi(outfile, pifile):45withopen(pifile,'rb')as f0, \
46open(outfile,'rb')as f1:47# 2つのファイルをメモリにマップして比較する。48with mmap.mmap(f0.fileno(),0, flags=mmap.MAP_PRIVATE)as mm0, \
49 mmap.mmap(f1.fileno(),0, flags=mmap.MAP_PRIVATE)as mm1:50 index = mpz(0)51 length =1024*1024# 一度にチェックする桁数52 found =False53whilenot found:54 ans = mm0.read(length)55 calc = mm1.read(length)56if ans != calc:57 maxlen =min(len(ans),len(calc))58for i inrange(maxlen):59if ans[i]!= calc[i]:60 n = index + i -261 found =True62break63else:64 n = index + maxlen -365break66else:67 index += length
68return n
6970if __name__ =='__main__':71 comm = MPI.COMM_WORLD
72 rank = comm.Get_rank()73 size = comm.Get_size()7475iflen(sys.argv)<2:76if rank == size -1:77print('python3 pi_chudnovsky.py <power> [pifile]')78 sys.exit(0)7980ifnot sys.argv[1].isdecimal():81if rank == size -1:82print('not decimal value: {}'.format(sys.argv[1]))83print('python3 pi_chudnovsky.py power [pifile]')84 sys.exit(0)85 power =int(sys.argv[1])8687iflen(sys.argv)==2:88 pifile ='/share/common/pi-10oku.txt'89else:90 pifile = sys.argv[2]91ifnot os.path.exists(pifile):92if rank == size -1:93print('{} does not exist'.format(pifile))94print('python3 pi_chudnovsky.py <power> [pifile]')95 sys.exit(0)96 outfile ='pi.txt'9798 A = mpz(13591409)99 B = mpz(545140134)100 C = mpz(640320)101 C3over24 = mpz(C**3/24)102103 n =2** power
104 digits = n *14105# gmpy2の浮動小数の精度として、求められる円周率の桁数を設定する。106 mp.get_context().precision =int(digits * mp.log2(10))107108if rank == size -1:109print('calculating...')110 start = MPI.Wtime()111 PQT = calc_PQT_root(n)112if rank == size -1:113 temp1 = C * mp.sqrt(C)* PQT[1]114 temp2 =12*(PQT[2]+ A * PQT[1])115 pi = temp1 / temp2
116 end = MPI.Wtime()117withopen(outfile,'w')as f:118 f.write(str(pi))119print('checking...')120 n = check_pi(outfile, pifile)121print('time = {:.2f} sec.'.format(end - start))122print(f'match = {n}')
プログラムのライセンス情報
MIT License
Copyright (c) 2021 Kenichi Miyata
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
https://github.com/kemusiro/openmpi-sample/からダウンロード
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