MATLAB: Rounding big numbers?!

rounding

How come when I try to round say 1799999999999999916113920.000000 to 3 significant digits from the left I can't get 18000000000……. Here is my instructions:

fprintf('%f %f\n',round(1799999999999999916113920.000000,3,'significant'),1799999999999999916113920.000000)

My output:

1799999999999999916113920.000000 1799999999999999916113920.000000

Best Answer

>> eps(1799999999999999916113920)
ans =
     268435456

In other words, 180000000000000000000000 is not exactly representable in 53 bit binary floating point.

Related Solutions

MATLAB: How to store only 3 digits after the decimal point

MATLAB uses IEEE 754 Binary Double Precision to represent floating point numbers. All floating point scheme that use binary mantissas cannot exactly represent 1/10, just like finite decimal representation schemes cannot exactly represent 1/3 or 1/7 .

IEEE 754 also defined a Decimal Double Precision representation scheme, which can represent 2.123 exactly. However, computing those values in software is much slower. The only systems I know of that implement IEEE 754 Decimal Double Precision in hardware are the IBM z90 series.

If you need a certain specific number of decimal places to be stored, then use rationals with a power-of-10 denominator.

MATLAB: Format Array column in fprintf

The short answer is: not easily.

Your output example has varying numbers of fractional digits

0.000000 % six decimal places

4.000000 % six decimal places
11.00000 % five decimal places

and also varying numbers of significant digits:

0.000000 % six significant figures
4.000000 % seven significant figures

11.00000 % seven significant figures

This excludes using one simple fprintf command (i.e. based on %f or %g) using only your input matrix.

The long answer: one possible approach is to create an array with the required number of significant figures (or decimal places) for each value and use this with the '*' placeholder syntax, e.g. where M is your matrix:

>> X = 7-(M==0);
>> Y = reshape(permute(cat(3,X,M),[3,2,1]),8,[]);
>> fprintf(' %9d %#9.*g %#15.*g %#15.*g\n',Y(2:end,:))
         1  0.000000        0.000000        0.000000
         2  0.000000        0.000000        4.000000
         3  0.000000        0.000000        1.000000
         4  0.000000        0.000000        2.000000
         5  0.000000        11.00000        4.000000
         6  0.000000        12.00000        4.000000
         7  0.000000        13.00000        4.000000
         8  0.000000        14.00000        4.000000
         9  0.000000        15.00000        4.000000
        10  10.00000        16.00000        4.000000
        11  10.00000        17.00000        4.000000
        12  0.000000        18.00000        4.000000
        13  0.000000        12.00000        0.000000
        14  0.000000        11.00000        0.000000
        15  0.000000        10.00000        0.000000

Best Answer

Related Solutions

MATLAB: How to store only 3 digits after the decimal point

MATLAB: Format Array column in fprintf

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