When can I compare floating point numbers directly?

In the

Coursera algorithm class, there is a material (FAQ"s eighth question) that mentions that floating point numbers can be directly compared in this course project. The specific situation is as follows:
enter integers a and b in the range of [- 32 767, 32767] . Compare floating point numbers a1/b1 with a2/b2 directly to get the correct answer. The reason is that IEEE-754 specifies that floating-point budget results are represented by proximity values.

but I"m still not sure why the results can be compared directly by using proximity values. Although it is not a good habit to compare floating point numbers directly, under what circumstances can floating point numbers be compared directly?

Ieee java floating-point

Mar.31,2021

because of the result of dividing any two numbers in this range, the one with the least error is also more accurate than the floating point number.

floating-point numbers are also divided into direct comparison and indirect comparison.

for example, no matter how the ratio is equal:

        Float f1 = 0.01f;
        Float f2 = 0.09f;
        Float f3 = 0.1f;

        System.out.println(f3 == (f1 + f2)); // true
        System.out.println(f3.compareTo(f1 + f2)); // 0
        System.out.println(f3.equals(f1 + f2)); // true

The ratio of

to Double, is not equal in any way:

        Double d1 = 0.01d;
        Double d2 = 0.09d;
        Double d3 = 0.1d;

        System.out.println(d3 == (d1 + d2)); // false
        System.out.println(d3.compareTo(d1 + d2)); // -1
        System.out.println(d3.equals(d1 + d2)); // false
        System.out.println(Math.abs(d3 - (d1 + d2)) < Double.MIN_EXPONENT); // false

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