Questions about PHP and js floating point operations

javascript

Why is 0.1 + 0.2 not equal to 0.3? (Correct result: 0.30000000000000004)

Why is 0.8 * 7 not equal to 5.6? (Correct result: 5.6000000000000005)

PHP

var_dump(intval(0.58 * 100));

The correct result is 57, not 58

The trouble caused by floating point operations

In fact, these results are not language bugs, but are related to the implementation of the language The principle is related. All numbers in js are unified as Number, including integers. In fact, all numbers are of double type.

And PHP will distinguish between int and float. No matter what language, as long as floating point operations are involved, there are similar problems, so you must pay attention when using them.

Floating point binary principle

According to the international standard IEEE 754, any binary floating point number V can be expressed in the following form:

V = (-1)s * M * E 

    1. (-1)s 表示符号位，当s=0，V为正数；当s=1，V为负数。
    2. M表示有效数字，大于等于1，小于2。
    3. 2E 表示指数位。

For example: decimal -5.0 , written in binary is -101.0, which is equivalent to -1.01×22. Then, s=1, M=1.01, E=2.
IEEE 754 stipulates that for a 32-bit floating point number, the highest 1 bit is the sign bit s, the next 8 bits are the exponent E, and the remaining 23 bits are the significant digit M.

For a 64-bit floating point number, the highest 1 bit is the sign bit S, the next 11 bits are the exponent E, and the remaining 52 bits are the significant digit M.

IEEE 754 also has some special provisions for the significant digit M and the exponent E.

As mentioned before, 1≤Me9078eed89a12476e874fb193db17ca3

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