Why does the FPRINTF function round my double precision floating point number in MATLAB 6.5 (R13)?

Why does the FPRINTF function round my double precision floating point number in MATLAB 6.5 (R13)?

I am experiencing a formatting problem in MATLAB 6.5 (R13), where only the first 19 significant digits are printed correctly to a text file when I use the FPRINTF function. The script below shows that the data is stored internally with the correct precision, but not when it is printed to a text file.

fid = fopen('out.txt','w+');
a = -0.00283527374267578125;
fprintf(fid, '%.25f\n', a);
fprintf('%.25f\n', a*2);
fclose(fid);

The result of printing "a" to a file:

 -0.0028352737426757813000000

 -0.0056705474853515625000000

The number should be exactly representable in floating point format, since it is only a 20 bit binary number:

 Decimal Form:
 a = -0.00283527374267578125;

 Hexidecimal Form (format hex): 
 a = bf673a0000000000;

I am inclined to think the problem is concerned with how MATLAB converts the floating point number to a decimal when using the FPRINTF function.

Answer 1

[MathWorks Support Team]

This error is due to the standard C programming I/O routines. When MATLAB initiates the FPRINTF function it calls the standard I/O functions. There is no workaround for this round off limitation because it is inherent to that library and to the bit limits on your computer.

This behavior is reproducible in C as shown below:

/* C program that writes a small decimal value to a file */
#include <stdio.h>

int main(void)
{
        FILE * fout;
        double a;

          fout = fopen("myFile.txt", "w");

          a = -0.00283527374267578125;

          fprintf(fout, "Here is what I print ... \n");
          fprintf(fout, "%.25f \n", a);
          fprintf(fout, "%.30f \n", a);

          fprintf(fout, "%.25lf \n", a);
          fprintf(fout, "%.30lf \n", a);

          fclose(fout);
  }

 /* The output results of the C program */
 -0.0028352737426757813000000
 -0.002835273742675781300000000000
 -0.0028352737426757813000000
 -0.002835273742675781300000000000

Note that MATLAB uses the IEEE-754 Double Precision floating-point standard to store data and perform arithmetical operations.

IEEE Specifications:

Exponent(max) = 1023

Exponent(max) = -1023

Exponent Bias = 1023

Precision (#bits) = 64

Sign Bits = 1

Exponent Bits = 11

*Fraction Bits = 52 -> Hitting this limitation.