Is there a way to configure the %d in fprintf function to use exponential notation when writing to a text file?

As far as I can see, when the fprintf command is used with %d MATLAB is deciding to use exponential notation if the number has more digits than 19. This situation can be observed with the code given in below.

%This code writes 1234567891234567936 to the text file.
not = fopen('gemSonuc.txt','w');
a=123456789123456789;
fprintf(not,'%d',a);

%This code writes 1.234568e+19 to the text file.
not = fopen('gemSonuc.txt','w');
a=12345678912345678912;
fprintf(not,'%d',a);

My main question is: Is there a way to configure this digit rule?

For further details here is the complete code:

%Constants
combs = [8 15 16 32 64 128 213 256 367 512 971 1024 1912 2048 4096 8192 16384 32768 65536 ...
         131072 262144 724411 1048576 1451480 2097152 3070075];
u = length(combs); 
step = zeros(10, u); % preallocating
temp = 110592;

%Calculating
n=1;
while(n<10)    
    for i=1:u
        step(n+1, i) = temp*combs(i);
    end
    temp = step(n+1,u);
    n=n+1;    
end
step(1,:) = combs;

%Writing to a Text File
not = fopen('gemSonuc.txt','w');
fprintf(not, 'Baslangic (2048 spec) = 110592\n');
for k=1:n
    for l=1:u
        fprintf(not,'%21d', step(k,l));
    end
    fprintf(not, '\n');
end
fclose(not);
fprintf('end of process')

%%%%%%%%%%%% Result written to the file: %%%%%%%%%%%% 
%Baslangic (2048 spec) = 110592
%                    8                   15                   16                   32                   64                  128                  213                  256                  367                  512                  971                 1024                 1912                 2048                 4096                 8192                16384                32768                65536               131072               262144               724411              1048576              1451480              2097152              3070075
%               884736              1658880              1769472              3538944              7077888             14155776             23556096             28311552             40587264             56623104            107384832            113246208            211451904            226492416            452984832            905969664           1811939328           3623878656           7247757312          14495514624          28991029248          80114061312         115964116992         160522076160         231928233984         339525734400
%        2716205875200        5092886016000        5432411750400       10864823500800       21729647001600       43459294003200       72318981427200       86918588006400      124605944524800      173837176012800      329679488102400      347674352025600      649173204172800      695348704051200     1390697408102400     2781394816204800     5562789632409600    11125579264819200    22251158529638400    44502317059276800    89004634118553600   245956176782438400   356018536474214400   492814812966912000   712037072948428800  1042369469038080000
%  8338955752304640000         1.563554e+19         1.667791e+19         3.335582e+19         6.671165e+19         1.334233e+20         2.220247e+20         2.668466e+20         3.825496e+20         5.336932e+20         1.012141e+21         1.067386e+21         1.993010e+21         2.134773e+21         4.269545e+21         8.539091e+21         1.707818e+22         3.415636e+22         6.831273e+22         1.366255e+23         2.732509e+23         7.551039e+23         1.093004e+24         1.512978e+24         2.186007e+24         3.200152e+24
%         2.560122e+25         4.800229e+25         5.120244e+25         1.024049e+26         2.048098e+26         4.096195e+26         6.816325e+26         8.192390e+26         1.174456e+27         1.638478e+27         3.107348e+27         3.276956e+27         6.118691e+27         6.553912e+27         1.310782e+28         2.621565e+28         5.243130e+28         1.048626e+29         2.097252e+29         4.194504e+29         8.389008e+29         2.318226e+30         3.355603e+30         4.644957e+30         6.711206e+30         9.824708e+30
%         7.859766e+31         1.473706e+32         1.571953e+32         3.143907e+32         6.287813e+32         1.257563e+33         2.092663e+33         2.515125e+33         3.605668e+33         5.030251e+33         9.539791e+33         1.006050e+34         1.878484e+34         2.012100e+34         4.024200e+34         8.048401e+34         1.609680e+35         3.219360e+35         6.438721e+35         1.287744e+36         2.575488e+36         7.117127e+36         1.030195e+37         1.426037e+37         2.060391e+37         3.016259e+37
%         2.413007e+38         4.524389e+38         4.826014e+38         9.652029e+38         1.930406e+39         3.860812e+39         6.424632e+39         7.721623e+39         1.106967e+40         1.544325e+40         2.928788e+40         3.088649e+40         5.767087e+40         6.177299e+40         1.235460e+41         2.470919e+41         4.941839e+41         9.883678e+41         1.976736e+42         3.953471e+42         7.906942e+42         2.185011e+43         3.162777e+43         4.378040e+43         6.325554e+43         9.260142e+43
%         7.408113e+44         1.389021e+45         1.481623e+45         2.963245e+45         5.926491e+45         1.185298e+46         1.972410e+46         2.370596e+46         3.398472e+46         4.741192e+46         8.991597e+46         9.482385e+46         1.770539e+47         1.896477e+47         3.792954e+47         7.585908e+47         1.517182e+48         3.034363e+48         6.068726e+48         1.213745e+49         2.427491e+49         6.708148e+49         9.709962e+49         1.344091e+50         1.941992e+50         2.842933e+50
%         2.274346e+51         4.264399e+51         4.548693e+51         9.097385e+51         1.819477e+52         3.638954e+52         6.055447e+52         7.277908e+52         1.043356e+53         1.455582e+53         2.760488e+53         2.911163e+53         5.435688e+53         5.822327e+53         1.164465e+54         2.328931e+54         4.657861e+54         9.315722e+54         1.863144e+55         3.726289e+55         7.452578e+55         2.059452e+56         2.981031e+56         4.126460e+56         5.962062e+56         8.728017e+56
%         6.982414e+57         1.309203e+58         1.396483e+58         2.792966e+58         5.585931e+58         1.117186e+59         1.859068e+59         2.234372e+59         3.203182e+59         4.468745e+59         8.474905e+59         8.937490e+59         1.668797e+60         1.787498e+60         3.574996e+60         7.149992e+60         1.429998e+61         2.859997e+61         5.719993e+61         1.143999e+62         2.287997e+62         6.322672e+62         9.151989e+62         1.266854e+63         1.830398e+63         2.679567e+63

I want to write the third and the fourth line of table (which are start with 2716205875200 and 8338955752304640000 values) in exponential notation without changing the first and the second line. This is why I don't use %e or %g in frpintf code.

The only solution I found is the code given in the below:

for k=1:2
    for l=1:u
        fprintf(not,'%21d', step(k,l));
    end
    fprintf(not, '\n');
end
for k=1+2:n
    for l=1:u
        fprintf(not,'%21e', step(k,l));
    end
    fprintf(not, '\n');
end

%%%%%%%%%%%% Result written to the file: %%%%%%%%%%%% 
%Baslangic (2048 spec) = 110592
%                    8                   15                   16                   32                   64                  128                  213                  256                  367                  512                  971                 1024                 1912                 2048                 4096                 8192                16384                32768                65536               131072               262144               724411              1048576              1451480              2097152              3070075
%               884736              1658880              1769472              3538944              7077888             14155776             23556096             28311552             40587264             56623104            107384832            113246208            211451904            226492416            452984832            905969664           1811939328           3623878656           7247757312          14495514624          28991029248          80114061312         115964116992         160522076160         231928233984         339525734400
%         2.716206e+12         5.092886e+12         5.432412e+12         1.086482e+13         2.172965e+13         4.345929e+13         7.231898e+13         8.691859e+13         1.246059e+14         1.738372e+14         3.296795e+14         3.476744e+14         6.491732e+14         6.953487e+14         1.390697e+15         2.781395e+15         5.562790e+15         1.112558e+16         2.225116e+16         4.450232e+16         8.900463e+16         2.459562e+17         3.560185e+17         4.928148e+17         7.120371e+17         1.042369e+18
%         8.338956e+18         1.563554e+19         1.667791e+19         3.335582e+19         6.671165e+19         1.334233e+20         2.220247e+20         2.668466e+20         3.825496e+20         5.336932e+20         1.012141e+21         1.067386e+21         1.993010e+21         2.134773e+21         4.269545e+21         8.539091e+21         1.707818e+22         3.415636e+22         6.831273e+22         1.366255e+23         2.732509e+23         7.551039e+23         1.093004e+24         1.512978e+24         2.186007e+24         3.200152e+24
%         2.560122e+25         4.800229e+25         5.120244e+25         1.024049e+26         2.048098e+26         4.096195e+26         6.816325e+26         8.192390e+26         1.174456e+27         1.638478e+27         3.107348e+27         3.276956e+27         6.118691e+27         6.553912e+27         1.310782e+28         2.621565e+28         5.243130e+28         1.048626e+29         2.097252e+29         4.194504e+29         8.389008e+29         2.318226e+30         3.355603e+30         4.644957e+30         6.711206e+30         9.824708e+30
%         7.859766e+31         1.473706e+32         1.571953e+32         3.143907e+32         6.287813e+32         1.257563e+33         2.092663e+33         2.515125e+33         3.605668e+33         5.030251e+33         9.539791e+33         1.006050e+34         1.878484e+34         2.012100e+34         4.024200e+34         8.048401e+34         1.609680e+35         3.219360e+35         6.438721e+35         1.287744e+36         2.575488e+36         7.117127e+36         1.030195e+37         1.426037e+37         2.060391e+37         3.016259e+37
%         2.413007e+38         4.524389e+38         4.826014e+38         9.652029e+38         1.930406e+39         3.860812e+39         6.424632e+39         7.721623e+39         1.106967e+40         1.544325e+40         2.928788e+40         3.088649e+40         5.767087e+40         6.177299e+40         1.235460e+41         2.470919e+41         4.941839e+41         9.883678e+41         1.976736e+42         3.953471e+42         7.906942e+42         2.185011e+43         3.162777e+43         4.378040e+43         6.325554e+43         9.260142e+43
%         7.408113e+44         1.389021e+45         1.481623e+45         2.963245e+45         5.926491e+45         1.185298e+46         1.972410e+46         2.370596e+46         3.398472e+46         4.741192e+46         8.991597e+46         9.482385e+46         1.770539e+47         1.896477e+47         3.792954e+47         7.585908e+47         1.517182e+48         3.034363e+48         6.068726e+48         1.213745e+49         2.427491e+49         6.708148e+49         9.709962e+49         1.344091e+50         1.941992e+50         2.842933e+50
%         2.274346e+51         4.264399e+51         4.548693e+51         9.097385e+51         1.819477e+52         3.638954e+52         6.055447e+52         7.277908e+52         1.043356e+53         1.455582e+53         2.760488e+53         2.911163e+53         5.435688e+53         5.822327e+53         1.164465e+54         2.328931e+54         4.657861e+54         9.315722e+54         1.863144e+55         3.726289e+55         7.452578e+55         2.059452e+56         2.981031e+56         4.126460e+56         5.962062e+56         8.728017e+56
%         6.982414e+57         1.309203e+58         1.396483e+58         2.792966e+58         5.585931e+58         1.117186e+59         1.859068e+59         2.234372e+59         3.203182e+59         4.468745e+59         8.474905e+59         8.937490e+59         1.668797e+60         1.787498e+60         3.574996e+60         7.149992e+60         1.429998e+61         2.859997e+61         5.719993e+61         1.143999e+62         2.287997e+62         6.322672e+62         9.151989e+62         1.266854e+63         1.830398e+63         2.679567e+63

I would like the learn that if there is a way to set the digit rule for exponential notation using frpintf with %d or not.

Answer 1

[Rik]

It looks like this might have something to do with flintmax, which would mean there would be no way to change this. This value is 2^53 for doubles, which works out to 9007199254740992 (so just under 17 digits). If I try writing more digits, my copy of Matlab starts rounding. I also observe the conversion to exponential notation at 20 digits. Hidden in the large doc for fprintf, you can find this:

If you specify a conversion that does not fit the data, such as a text conversion for a numeric value, 
MATLAB overrides the specified conversion, and uses %e.
Example: '%s' converts pi to 3.141593e+00.

So apparently, Matlab does not consider such large values to be integers anymore, which makes them not fit the d flag, which causes the conversion to exponential.

What you can do, is either preproces to a string, or dynamically choosing a format specificiation based on your value. You can either compare to flintmax, or use log10() to find the number of digits. (These two are not equivalent.)

%replace this:
%fprintf(not,'%21d', step(k,l));

%before the loop:
FormatSpec={'%21d','%21e'};
NumberOfDigits=@(x) 1+floor(log10(x));

%in the loop
val=step(k,l)
fprintf(not,FormatSpec{1+(val>flintmax)}, val);
%or:
%fprintf(not,FormatSpec{1+(NumberOfDigits(val)>19)}, val);

[Bilge Kaan Atay]

The information you've written explains this situation. FormatSpec option is worked well for me. In addition, basically one can use val>number (for example in my question this should be number=1e12) in fprintf code without using flintmax or NumberOfDigits.

I prefer NumberOfDigits. Thank you for your answer. It helped me a lot.

Answer 2

[Walter Roberson]

Use %21.12g .

>> sprintf('%21.12g\n', [339525734400, 2716205875200])

ans =

' 339525734400

2.7162058752e+12

'