PRDV402: Introduction to JavaScript II

Number

Number values represent floating-point numbers like 37 or -9.25.

The Number constructor contains constants and methods for working with numbers. Values of other types can be converted to numbers using the Number() function.

Description

Numbers are most commonly expressed in literal forms like 255 or 3.14159. The lexical grammar contains a more detailed reference.

255; // two-hundred and fifty-five
255.0; // same number
255 === 255.0; // true
255 === 0xff; // true (hexadecimal notation)
255 === 0b11111111; // true (binary notation)
255 === 0.255e3; // true (decimal exponential notation)

A number literal like 37 in JavaScript code is a floating-point value, not an integer. There is no separate integer type in common everyday use. (JavaScript also has a BigInt type, but it's not designed to replace Number for everyday uses. 37 is still a number, not a BigInt.)

When used as a function, Number(value) converts a string or other value to the Number type. If the value can't be converted, it returns NaN.

Number("123"); // returns the number 123
Number("123") === 123; // true

Number("unicorn"); // NaN
Number(undefined); // NaN

Number encoding

The JavaScript Number type is a double-precision 64-bit binary format IEEE 754 value, like double in Java or C#. This means it can represent fractional values, but there are some limits to the stored number's magnitude and precision. Very briefly, an IEEE 754 double-precision number uses 64 bits to represent 3 parts:

• 1 bit for the sign (positive or negative)
• 11 bits for the exponent (-1022 to 1023)
• 52 bits for the mantissa (representing a number between 0 and 1)

The mantissa (also called significand) is the part of the number representing the actual value (significant digits). The exponent is the power of 2 that the mantissa should be multiplied by. Thinking about it as scientific notation:

$Number = ( − 1 )^{\text{sign}} ⋅ ( 1 + mantissa ) ⋅ 2 ^{\text{exponent}}$

The mantissa is stored with 52 bits, interpreted as digits after 1.… in a binary fractional number. Therefore, the mantissa's precision is 2^-52 (obtainable via Number.EPSILON), or about 15 to 17 decimal places; arithmetic above that level of precision is subject to rounding.

The largest value a number can hold is 2¹⁰²⁴ - 1 (with the exponent being 1023 and the mantissa being 0.1111… in base 2), which is obtainable via Number.MAX_VALUE. Values higher than that are replaced with the special number constant Infinity.

Integers can only be represented without loss of precision in the range -2⁵³ + 1 to 2⁵³ - 1, inclusive (obtainable via Number.MIN_SAFE_INTEGER and Number.MAX_SAFE_INTEGER), because the mantissa can only hold 53 bits (including the leading 1).

More details on this are described in the ECMAScript standard.

Number coercion

Many built-in operations that expect numbers first coerce their arguments to numbers (which is largely why Number objects behave similarly to number primitives). The operation can be summarized as follows:

• Numbers are returned as-is.
• undefined turns into NaN.
• null turns into 0.
• true turns into 1; false turns into 0.
• Strings are converted by parsing them as if they contain a number literal. Parsing failure results in NaN. There are some minor differences compared to an actual number literal:
  • Leading and trailing whitespace/line terminators are ignored.
  • A leading 0 digit does not cause the number to become an octal literal (or get rejected in strict mode).
  • + and - are allowed at the start of the string to indicate its sign. (In actual code, they "look like" part of the literal, but are actually separate unary operators.) However, the sign can only appear once, and must not be followed by whitespace.
  • Infinity and -Infinity are recognized as literals. In actual code, they are global variables.
  • Empty or whitespace-only strings are converted to 0.
  • Numeric separators are not allowed.
• BigInts throw a TypeError to prevent unintended implicit coercion causing loss of precision.
• Symbols throw a TypeError.
• Objects are first converted to a primitive by calling their [@@toPrimitive]() (with "number" as hint), valueOf(), and toString() methods, in that order. The resulting primitive is then converted to a number.

There are two ways to achieve nearly the same effect in JavaScript.

• Unary plus: +x does exactly the number coercion steps explained above to convert x.
• The Number() function: Number(x) uses the same algorithm to convert x, except that BigInts don't throw a TypeError, but return their number value, with possible loss of precision.

Number.parseFloat() and Number.parseInt() are similar to Number() but only convert strings, and have slightly different parsing rules. For example, parseInt() doesn't recognize the decimal point, and parseFloat() doesn't recognize the 0x prefix.

Integer conversion

Some operations expect integers, most notably those that work with array/string indices, date/time components, and number radixes. After performing the number coercion steps above, the result is truncated to an integer (by discarding the fractional part). If the number is ±Infinity, it's returned as-is. If the number is NaN or -0, it's returned as 0. The result is therefore always an integer (which is not -0) or ±Infinity.

Notably, when converted to integers, both undefined and null become 0, because undefined is converted to NaN, which also becomes 0.

Fixed-width number conversion

JavaScript has some lower-level functions that deal with the binary encoding of integer numbers, most notably bitwise operators and TypedArray objects. Bitwise operators always convert the operands to 32-bit integers. In these cases, after converting the value to a number, the number is then normalized to the given width by first truncating the fractional part and then taking the lowest bits in the integer's two's complement encoding.

new Int32Array([1.1, 1.9, -1.1, -1.9]); // Int32Array(4) [ 1, 1, -1, -1 ]

new Int8Array([257, -257]); // Int8Array(2) [ 1, -1 ]
// 257 = 0001 0000 0001
//     =      0000 0001 (mod 2^8)
//     = 1
// -257 = 1110 1111 1111
//      =      1111 1111 (mod 2^8)
//      = -1 (as signed integer)

new Uint8Array([257, -257]); // Uint8Array(2) [ 1, 255 ]
// -257 = 1110 1111 1111
//      =      1111 1111 (mod 2^8)
//      = 255 (as unsigned integer)

Source: Mozilla, https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Number
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