How java stores float v double

Question

How java stores float v double

I understand that a decimal can be so precise that it is stored as a float in the binary, but I don’t understand what happens in 7 decimal places in my 10/7 release.

In my first test release, I noticed that 5 (7th place) at the end of the float is v 4 (7th place), followed by 2 in double. I would think that the 7th place in the float will be 4, since the 8th place in the double is 2.

Float 1.4285715 Dual 1.4285714285714286

Then I performed the following test output using the float format up to 17 places. The 8th place in each is different - the float is 6, so the 7th place is rounded to 5, I suppose.

Float 1.428571462631225600 Dual 1.428571428571428600

In the third test, I tried live streaming with a string format to see what would happen. I got the same results as the second test.

If I have a simplified question about a complex floating point storage method - I apologize.

    float f = 10/7f;
    double d = 10/7d;

    System.out.format
        ("Float  %1s\nDouble %2s\n", f,d);
    /*
     *  Float  1.4285715
        Double 1.4285714285714286
     */

    System.out.format
        ("Float  %1$.17f\nDouble %2$.17f\n", f,d);
    /*
     *  Float  1.428571462631225600
        Double 1.428571428571428600
     */

    System.out.format
        ("Float  %1s\nDouble %2s\n", (double)f,d);
    /*
     *  Float  1.4285714626312256
        Double 1.4285714285714286
     */

+5

java floating-point-precision

user1178761 Jan 30 '12 at 19:49

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4 answers

David Schwartz · Answer 1 · 2012-01-30T20:12:00+0000

In my first test release, I noticed that 5 (7th place) at the end of the float is v 4 (7th place), followed by 2 in double. I would think that the 7th place in the float will be 4, since the 8th place in the double is 2.

This expectation makes sense only if you think the float is stored inside a decimal number and rounded to a certain number of decimal digits. But this is not so, floats are stored internally in binary and rounded to a certain number of binary digits.

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