Number In Javascript #

The JavaScript Number type is a double-precision 64-bit binary format IEEE 754 value.

$$(-1)^{sign} \times (1 + mantissa) \times 2^{exponent - bias}$$

$bias$ is $1023$ for double-precision 64-bit and $127$ for single-precision 32-bit.

Number.parseFloat() #

This method has the same functionality as the global parseFloat() function:

// eslint-disable-next-line unicorn/prefer-number-properties
parseFloat === Number.parseFloat // true

parseFloat() use DFA to parse string to number, when it meets a abnormal character, it will stop and return the number parsed so far, parseInt() is similar.

For example:

Number.parseFloat('123.456abc') // 123.456
Number.parseFloat('12.3.41bc') // 12.3
Number.parseFloat('-0x123') // -0
Number.parseFloat('.11.1') // 0.11
Number.parseFloat('..1') // NaN
Number.parseFloat('+1.1e-2') // 0.011
Number.parseFloat('a1.1e-2') // NaN
Number.parseFloat('.1e-2.5') // 0.001

Why 0.1 + 0.2 !== 0.3 #

$0.1$ in IEEE754 is below:

$0.2$ in IEEE754 is below:

Here is the process of add-operation for double-precision 64-bit binary format IEEE 754:

1. Align the exponents, the smaller one will be shifted right until the exponents are equal.
2. Add the mantissas.
3. Normalize the result (and judge if it is overflow or underflow).
4. Round the result to the nearest representable value.

Now we can get the binary sum result of $0.1$ and $0.2$:
$0.1=1.1001... \times 2^{-4}$
$0.2=1.1001... \times 2^{-3}$
$1^{st}$. $0.1=0.1100... \times 2^{-3}$
  $0.2=1.1001... \times 2^{-3}$
$2^{nd}$. $0.1+0.2=10.1011... \times 2^{-3}$

$3^{rd}$. $0.1+0.2=1.01011... \times 2^{-2}$

$4^{th}$. sign = 0
  exponent = -2 + 1023 => 01111111101
  mantissa = 0011001100110011001100110011001100110011001100110011100
=>0011001100110011001100110011001100110011001100110100

So the sum of $0.1$ and $0.2$ in IEEE754 is below:

which is equal to $0.30000000000000004$.

Why 0.2 - 0.1 === 0.1 #

$0.1=1.1001... \times 2^{-4}$
$0.2=1.1001... \times 2^{-3}$
$1^{st}$. $0.1=0.1100... \times 2^{-3}$
  $0.2=1.1001... \times 2^{-3}$
$2^{nd}$. $0.1-0.2=0.1100... \times 2^{-3}$

$3^{rd}$. $0.1-0.2=1.100... \times 2^{-4}$

$4^{th}$. sign = 0
  exponent = -4 + 1023 => 01111111011
  mantissa = 1001100110011001100110011001100110011001100110011010 =>1001100110011001100110011001100110011001100110011010

So the subtraction of $0.2$ and $0.1$ in IEEE754 is below:

which is equal to $0.1$.