calculate_tau.piynb

You should first run the notebook run_this_first.ipynb.

This script converts the first billion digits of pi into tau by the incredible algorithm of multiplying by two.

In order to avoid carry-the-one problems (which would occur at more than half the positions), the program does it in chunks, for every string of digits starting with the number 4, because no decimal-based number starting with a numeral of 0, 1, 2, 3 or 4 will gain a digit via carry-the-one when doubled. (It's true, think about it. Or just multiply 49999999999999999 by 2 in your calculator and see what happens.)

import time
import os

for i in range(10):

    infilename = 'data/pi100m.dectxt.00' + str(i)
    outfilename = 'data/tau100m.dectxt.00' + str(i)
    
    if not os.path.isfile(outfilename):
    
        start=time.time()
    
        with open(infilename, 'r') as fin:
            pi = fin.read()
        
        overallcount = 100000000
        
        for subset in range(9):
            pisub = pi[subset*10000000:(subset+1)*10000000]
        
            pos = 0
            tau = ''
            pisect=''
            counter = 0
            
            print "Processing " + infilename + ", remaining (million): ",
            
            while pos < len(pisub):
                if overallcount % 1000000 == 0:
                    print (overallcount / 1000000),
                overallcount -= 1
                if pisub[pos] == '4':
                    counter += 1 # I put in this counter to work on larger chunks, but I'm not convinced it makes a difference
                    if counter % 5 == 0:
                        numsect=int(pisect)
                        pisect='4'
                        numsect *= 2
                        tau+=str(numsect)
                    else:
                        pisect+=pisub[pos]
                else:
                    pisect+=pisub[pos]
                pos += 1        
            #for the remainder
            numsect = int(pisect)
            numsect *= 2
            tau+=str(numsect)
            
            with open(outfilename, 'a+') as fout:
                fout.write(tau)
        
        print 'Finished, %0.1f minutes elapsed' % ((time.time() - start)/60)
    
    else:
        print outfilename + 'already exists.'

print '\nScript finished.'

Processing data/pi100m.dectxt.000, remaining (million):  100 99 98 97 96 95 94 93 92 91 Processing data/pi100m.dectxt.000, remaining (million):  90 89 88 87 86 85 84 83 82 81 Processing data/pi100m.dectxt.000, remaining (million):  80 79 78 77 76 75 74 73 72 71 Processing data/pi100m.dectxt.000, remaining (million):  70 69 68 67 66 65 64 63 62 61 Processing data/pi100m.dectxt.000, remaining (million):  60 59 58 57 56 55 54 53 52 51 Processing data/pi100m.dectxt.000, remaining (million):  50 49 48 47 46 45 44 43 42 41 Processing data/pi100m.dectxt.000, remaining (million):  40 39 38 37 36 35 34 33 32 31 Processing data/pi100m.dectxt.000, remaining (million):  30 29 28 27 26 25 24 23 22 21 Processing data/pi100m.dectxt.000, remaining (million):  20 19 18 17 16 15 14 13 12 11 Finished, 2.3 minutes elapsed
Processing data/pi100m.dectxt.001, remaining (million):  100 99 98 97 96 95 94 93 92 91 Processing data/pi100m.dectxt.001, remaining (million):  90 89 88 87 86 85 84 83 82 81 Processing data/pi100m.dectxt.001, remaining (million):  80 79 78 77 76 75 74 73 72 71 Processing data/pi100m.dectxt.001, remaining (million):  70 69 68 67 66 65 64 63 62 61 Processing data/pi100m.dectxt.001, remaining (million):  60 59 58 57 56 55 54 53 52 51 Processing data/pi100m.dectxt.001, remaining (million):  50 49 48 47 46 45 44 43 42 41 Processing data/pi100m.dectxt.001, remaining (million):  40 39 38 37 36 35 34 33 32 31 Processing data/pi100m.dectxt.001, remaining (million):  30 29 28 27 26 25 24 23 22 21 Processing data/pi100m.dectxt.001, remaining (million):  20 19 18 17 16 15 14 13 12 11 Finished, 2.4 minutes elapsed
Processing data/pi100m.dectxt.002, remaining (million):  100 99 98 97 96 95 94 93 92 91 Processing data/pi100m.dectxt.002, remaining (million):  90 89 88 87 86 85 84 83 82 81 Processing data/pi100m.dectxt.002, remaining (million):  80 79 78 77 76 75 74 73 72 71 Processing data/pi100m.dectxt.002, remaining (million):  70 69 68 67 66 65 64 63 62 61 Processing data/pi100m.dectxt.002, remaining (million):  60 59 58 57 56 55 54 53 52 51 Processing data/pi100m.dectxt.002, remaining (million):  50 49 48 47 46 45 44 43 42 41 Processing data/pi100m.dectxt.002, remaining (million):  40 39 38 37 36 35 34 33 32 31 Processing data/pi100m.dectxt.002, remaining (million):  30 29 28 27 26 25 24 23 22 21 Processing data/pi100m.dectxt.002, remaining (million):  20 19 18 17 16 15 14 13 12 11 Finished, 2.4 minutes elapsed
Processing data/pi100m.dectxt.003, remaining (million):  100 99 98 97 96 95 94 93 92 91 Processing data/pi100m.dectxt.003, remaining (million):  90 89 88 87 86 85 84 83 82 81 Processing data/pi100m.dectxt.003, remaining (million):  80 79 78 77 76 75 74 73 72 71 Processing data/pi100m.dectxt.003, remaining (million):  70 69 68 67 66 65 64 63 62 61 Processing data/pi100m.dectxt.003, remaining (million):  60 59 58 57 56 55 54 53 52 51 Processing data/pi100m.dectxt.003, remaining (million):  50 49 48 47 46 45 44 43 42 41 Processing data/pi100m.dectxt.003, remaining (million):  40 39 38 37 36 35 34 33 32 31 Processing data/pi100m.dectxt.003, remaining (million):  30 29 28 27 26 25 24 23 22 21 Processing data/pi100m.dectxt.003, remaining (million):  20 19 18 17 16 15 14 13 12 11 Finished, 2.4 minutes elapsed
Processing data/pi100m.dectxt.004, remaining (million):  100 99 98 97 96 95 94 93 92 91 Processing data/pi100m.dectxt.004, remaining (million):  90 89 88 87 86 85 84 83 82 81 Processing data/pi100m.dectxt.004, remaining (million):  80 79 78 77 76 75 74 73 72 71 Processing data/pi100m.dectxt.004, remaining (million):  70 69 68 67 66 65 64 63 62 61 Processing data/pi100m.dectxt.004, remaining (million):  60 59 58 57 56 55 54 53 52 51 Processing data/pi100m.dectxt.004, remaining (million):  50 49 48 47 46 45 44 43 42 41 Processing data/pi100m.dectxt.004, remaining (million):  40 39 38 37 36 35 34 33 32 31 Processing data/pi100m.dectxt.004, remaining (million):  30 29 28 27 26 25 24 23 22 21 Processing data/pi100m.dectxt.004, remaining (million):  20 19 18 17 16 15 14 13 12 11 Finished, 2.3 minutes elapsed
Processing data/pi100m.dectxt.005, remaining (million):  100 99 98 97 96 95 94 93 92 91 Processing data/pi100m.dectxt.005, remaining (million):  90 89 88 87 86 85 84 83 82 81 Processing data/pi100m.dectxt.005, remaining (million):  80 79 78 77 76 75 74 73 72 71 Processing data/pi100m.dectxt.005, remaining (million):  70 69 68 67 66 65 64 63 62 61 Processing data/pi100m.dectxt.005, remaining (million):  60 59 58 57 56 55 54 53 52 51 Processing data/pi100m.dectxt.005, remaining (million):  50 49 48 47 46 45 44 43 42 41 Processing data/pi100m.dectxt.005, remaining (million):  40 39 38 37 36 35 34 33 32 31 Processing data/pi100m.dectxt.005, remaining (million):  30 29 28 27 26 25 24 23 22 21 Processing data/pi100m.dectxt.005, remaining (million):  20 19 18 17 16 15 14 13 12 11 Finished, 2.3 minutes elapsed
Processing data/pi100m.dectxt.006, remaining (million):  100 99 98 97 96 95 94 93 92 91 Processing data/pi100m.dectxt.006, remaining (million):  90 89 88 87 86 85 84 83 82 81 Processing data/pi100m.dectxt.006, remaining (million):  80 79 78 77 76 75 74 73 72 71 Processing data/pi100m.dectxt.006, remaining (million):  70 69 68 67 66 65 64 63 62 61 Processing data/pi100m.dectxt.006, remaining (million):  60 59 58 57 56 55 54 53 52 51 Processing data/pi100m.dectxt.006, remaining (million):  50 49 48 47 46 45 44 43 42 41 Processing data/pi100m.dectxt.006, remaining (million):  40 39 38 37 36 35 34 33 32 31 Processing data/pi100m.dectxt.006, remaining (million):  30 29 28 27 26 25 24 23 22 21 Processing data/pi100m.dectxt.006, remaining (million):  20 19 18 17 16 15 14 13 12 11 Finished, 2.3 minutes elapsed
Processing data/pi100m.dectxt.007, remaining (million):  100 99 98 97 96 95 94 93 92 91 Processing data/pi100m.dectxt.007, remaining (million):  90 89 88 87 86 85 84 83 82 81 Processing data/pi100m.dectxt.007, remaining (million):  80 79 78 77 76 75 74 73 72 71 Processing data/pi100m.dectxt.007, remaining (million):  70 69 68 67 66 65 64 63 62 61 Processing data/pi100m.dectxt.007, remaining (million):  60 59 58 57 56 55 54 53 52 51 Processing data/pi100m.dectxt.007, remaining (million):  50 49 48 47 46 45 44 43 42 41 Processing data/pi100m.dectxt.007, remaining (million):  40 39 38 37 36 35 34 33 32 31 Processing data/pi100m.dectxt.007, remaining (million):  30 29 28 27 26 25 24 23 22 21 Processing data/pi100m.dectxt.007, remaining (million):  20 19 18 17 16 15 14 13 12 11 Finished, 2.2 minutes elapsed
Processing data/pi100m.dectxt.008, remaining (million):  100 99 98 97 96 95 94 93 92 91 Processing data/pi100m.dectxt.008, remaining (million):  90 89 88 87 86 85 84 83 82 81 Processing data/pi100m.dectxt.008, remaining (million):  80 79 78 77 76 75 74 73 72 71 Processing data/pi100m.dectxt.008, remaining (million):  70 69 68 67 66 65 64 63 62 61 Processing data/pi100m.dectxt.008, remaining (million):  60 59 58 57 56 55 54 53 52 51 Processing data/pi100m.dectxt.008, remaining (million):  50 49 48 47 46 45 44 43 42 41 Processing data/pi100m.dectxt.008, remaining (million):  40 39 38 37 36 35 34 33 32 31 Processing data/pi100m.dectxt.008, remaining (million):  30 29 28 27 26 25 24 23 22 21 Processing data/pi100m.dectxt.008, remaining (million):  20 19 18 17 16 15 14 13 12 11 Finished, 2.2 minutes elapsed
Processing data/pi100m.dectxt.009, remaining (million):  100 99 98 97 96 95 94 93 92 91 Processing data/pi100m.dectxt.009, remaining (million):  90 89 88 87 86 85 84 83 82 81 Processing data/pi100m.dectxt.009, remaining (million):  80 79 78 77 76 75 74 73 72 71 Processing data/pi100m.dectxt.009, remaining (million):  70 69 68 67 66 65 64 63 62 61 Processing data/pi100m.dectxt.009, remaining (million):  60 59 58 57 56 55 54 53 52 51 Processing data/pi100m.dectxt.009, remaining (million):  50 49 48 47 46 45 44 43 42 41 Processing data/pi100m.dectxt.009, remaining (million):  40 39 38 37 36 35 34 33 32 31 Processing data/pi100m.dectxt.009, remaining (million):  30 29 28 27 26 25 24 23 22 21 Processing data/pi100m.dectxt.009, remaining (million):  20 19 18 17 16 15 14 13 12 11 Finished, 2.2 minutes elapsed

Script finished.

Verification: compare first 100000 digits to those listed on tauday.com

tauday_file = open('data/tau100K-tauday.com.txt', 'r')
tauday_string = tauday_file.read()
tauday_file.close()
this_file = open('data/tau100m.dectxt.000', 'r')
this_string = this_file.read()  
this_file.close()

print len(tauday_string)
print tauday_string[:10]
print this_string[:10]

if tauday_string[:99999] == this_string[:99999]:
    print "Verification successful. Yay."

99999
2831853071
2831853071
Verification successful. Yay.

Create 1000-character files for overlaps during tests

filelist = ['data/tau100m.dectxt.001', 'data/tau100m.dectxt.002', 'data/tau100m.dectxt.003', 
            'data/tau100m.dectxt.004', 'data/tau100m.dectxt.005', 'data/tau100m.dectxt.006', 
            'data/tau100m.dectxt.007', 'data/tau100m.dectxt.008', 'data/tau100m.dectxt.009']

for filename in filelist:
    current = open(filename, 'r')
    string1K = current.read()[:1000]
    current.close()
    newfile = open(filename+'.1K', 'w+')
    newfile.write(string1K)
    newfile.close()

    

Verify some of the regex-style search results

# verify that pi has a fibonacci sequence of 11235813 at position 48300973
this_file = open('data/pi100m.dectxt.000', 'r')
this_string = this_file.read()  
this_file.close()
print this_string[48300973:48300993]

11235813455381270624

# verify that tau has a fibonacci sequence of 1123581321 at position 809073288
this_file = open('data/tau100m.dectxt.008', 'r')
this_string = this_file.read()  
this_file.close()
print this_string[9073288:9073300]

112358132150

# verify that tau recapitulates pi at position 52,567,169
this_file = open('data/tau100m.dectxt.000', 'r')
this_string = this_file.read()  
this_file.close()
print this_string[52567169:52567189]

31415926531269297186

# verify that tau recapitulates tau at position 405747241
this_file = open('data/tau100m.dectxt.004', 'r')
this_string = this_file.read()  
this_file.close()
print this_string[5747241:5747261]

62831853035460504279