Float and double range and precision

1. Scope

 

The float and double ranges are determined by the number of digits of the index. (Because the representation is in the form of 1.x * 2 ^ Y, the result of 1. x is ignored, and the index is directly used to represent the range of floating point numbers)

 

The float index has eight digits, while the double index has 11 digits. The distribution is as follows:

Float:

1bit (symbol bit) 8 bits (index bit) 23 bits (tail bit)

 

Double:

1bit (symbol bit) 11 bits (index bit) 52 bits (tail bit)

Therefore, the float index range is-127 ~ + 128, while the double index range is-1023 ~ + 1024, and the index bit is divided by complement code.

The negative index determines the smallest non-zero number of absolute values that floating point numbers can express. The positive index determines the maximum number of absolute values that floating point numbers can express, that is, the value range of floating point numbers.

Float range:-2 ^ 128 ~ + 2 ^ 128, that is,-3.40E + 38 ~ + 3.40E + 38; the double value range is-2 ^ 1024 ~ + 2 ^ 1024, that is,-1.79E + 308 ~ + 1.79E + 308.

 

2. Precision

The precision of float and double is determined by the number of digits of the ending number (the precision, that is, EPSINON in the program, is determined by the ending number ). Floating point numbers are stored in the memory in scientific notation, And the integer part is always an implicit "1". Since it remains unchanged, it cannot affect the accuracy.

Float: 2 ^ 23 = 8388608, a total of seven digits, which means that there can be a maximum of seven valid digits, but it is absolutely guaranteed to be 6 digits, that is, the float precision is 6 ~ 7 valid digits;

Double: 2 ^ 52 = 4503599627370496, a total of 16 digits. Similarly, the precision of double is 15 ~ 16 bits.

 

Therefore, we can know the reason for EPSINON when the floating point number is equal to "0.