ECMAScript Built-in Constants and Functions About Mathematics

Shen Lu

Posted on Feb 08, 2024

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8 min read (1431 words)

ECMAScript Global Object for Mathematics

A plenty of built-in objects in ECMAScript can be directly used as mathematical constants and functions.

Value Properties

Value Properties	Description	Notation	Value (Number)
`Infinity`	positive Infinity	$+\infty$	Infinity (+Infinity)
`NaN`	Not a Number	$NaN$	NaN

Function Properties

Function Properties	Description	Return Type
`isFinite(number)`	determine whether a number is a finite number or not (`Number.isFinite(Number(number))`)	boolean
`isNaN(number)`	determine whether a value is NaN or not (`Number(number) !== Number(number)`)	boolean
`parseFloat(string)`	parse an argument to a floating point number	number (float)
`parseInt(string, radix)`	parse an argument to an integer of the specified radix	number (integer)

Constructor Properties

BigInt: A built-in object whose constructor returns a bigint primitive (or BigInt)to represent whole numbers larger than $2^{53} - 1$ (Number.MAX_SAFE_INTEGER), which is the largest number JavaScript can represent with a number primitive (or Number value).
Numbers: A primitive wrapper object used to represent and manipulate numbers and its type is a double-precision 64-bit binary format IEEE 754

BigInt

Function Properties	Description	Return Type
`asIntN(bits, bigint)`	clamp a BigInt value to a signed integer value	bigint
`asUintN(bits, bigint)`	clamp a BigInt value to an unsigned integer value	bigint

Numbers

Value Properties	Description	Notation	Value (Number)
`EPSILON`	the magnitude of the difference between 1 and the smallest value greater than 1, which is approximately $2^{-52}$	$\varepsilon$	2.220446049250313e-16
~~`NaN`~~	the value identicial to the global `NaN`	$NaN$	NaN
`MAX_SAFE_INTEGER`	the maximum safe integer in JavaScript	$2^{53}-1$	9007199254740991
`MAX_VALUE`	the largest positive representable number	$2^{1024}-1$	1.7976931348623157e+308
`MIN_SAFE_INTEGER`	the minimum safe integer in JavaScript ( $-2^{53} + 1$ )	$-2^{53}+1$	-9007199254740991
`MIN_VALUE`	the smallest positive representable number—that is, the positive number closest to zero (without actually being zero)	$2^{-1074}$	5e-324
`NEGATIVE_INFINITY`	negative infinity	$-\infty$	-Infinity
~~`POSITIVE_INFINITY`~~	the value identicial to the global `Infinity`	$+\infty$	Infinity (+Infinity)

Function Properties	Description	Return Type
`isFinite(number)`	determine whether the passed value is a finite number or not	boolean
`isInteger(number)`	determine whether the passed value is an integer or not	boolean
`isNaN(number)`	determine whether the passed value is NaN or not (`typeof number === 'number' && number !== number`)	boolean
`isSafeInteger(number)`	determine whether the passed value is a safe integer (between $-2^{53} + 1$ and $2^{53} - 1$ ) or not	boolean
~~`parseFloat(string)`~~	the function identicial to the global `parseFloat`	number (float)
~~`parseInt(string, radix)`~~	the function identicial to the global `parseInt`	number (integer)

Note:

Number.isFinite(number) does not convert its argument to a Number before determining whether it is Infinity or not, which differs from the global isFinite(number) function. So Number.isNaN(number) does it as well.

Other Properties

Math: A a built-in object that has properties and methods for mathematical constants and functions. It’s not a function object. Math works with the Number type. It doesn't work with BigInt.

Math

Value Properties	Description	Notation	Value (Number)
`E`	the base of the natural logarithms	$e$	2.7182818284590452354
`LN10`	the natural logarithm of 10	$\ln(10)$	2.302585092994046
`LN2`	the natural logarithm of 2	$\ln(2)$	0.6931471805599453
`LOG10E`	the base-10 logarithm of $e$	$\log_{10}(e)$	0.4342944819032518
`LOG2E`	the base-2 logarithm of $e$	$\log_{2}(e)$	1.4426950408889634
`PI`	the ratio of the circumference of a circle to its diameter	$\pi$	3.1415926535897932
`SQRT1_2`	the square root of ½	$\frac{1}{\sqrt{2}}$	0.7071067811865476
`SQRT2`	the square root of 2	$\sqrt{2}$	1.4142135623730951

Function Properties	Description	Notation	Return Type
`abs(x)`	return the absolute value of x	$\lvert x \rvert$	number
`acos(x)`	return the inverse cosine of x	$\arccos(x)$	number
`acosh(x)`	return the inverse hyperbolic cosine of x	$\operatorname{arcosh}(x)$	number
`asin(x)`	return the inverse sine of x	$\arcsin(x)$	number
`asinh(x)`	return the inverse hyperbolic sine of x	$\operatorname{arsinh}(x)$	number
`atan(x)`	return the inverse tangent of x	$\arctan(x)$	number
`atanh(x)`	return the inverse hyperbolic tangent of x	$\operatorname{arctanh}(x)$	number
`atan2(y, x)`	return the inverse tangent of the quotient y / x of the arguments y and x	$arctan(\frac{y}{x})$	number
`cbrt(x)`	return the cube root of x	$\sqrt[3]{x}$	number
`ceil(x)`	return the smallest integer greater than or equal to x	$\lceil x \rceil$	number
`clz32(x)`	return the number of leading zero bits of the 32-bit integer x		number
`cos(x)`	return the cosine of x	$\cos(x)$	number
`cosh(x)`	return the hyperbolic cosine of x	$\frac{e^x + e^{-x}}{2}$	number
`exp(x)`	return the exponential function of x	$e^x$	number
`expm1(x)`	return the result of subtracting 1 from the exponential function of x	$e^x - 1$	number
`floor(x)`	return the largest integer less than or equal to x	$\lfloor x \rfloor$	number
`fround(x)`	return the nearest single precision float representation of x		number
`hypot(...args)`	return the square root of the sum of squares of its arguments.	$\sqrt{\sum\_{i=1}^{n}{x_n^2}}$	number
`imul(x, y)`	return the result of the 32-bit integer multiplication of x and y.		number
`log(x)`	return the natural logarithm of x	$\ln(x)$	number
`log1p(x)`	return the natural logarithm of 1 + x	$\ln(1+x)$	number
`log10(x)`	return the base 10 logarithm of x	$\log_{10} x$	number
`log2(x)`	return the base 2 logarithm of x	$\log_{2} x$	number
`max(...args)`	return the largest of the resulting values	$\max \left \{ f\left ( x_1 \right ) ,...,f\left ( x_n \right ) \right \}$	number
`min(...args)`	return the smallest of the resulting values	$\min \left \{ f\left ( x_1 \right ) ,...,f\left ( x_n \right ) \right \}$	number
~~`pow(base, exponent)`~~	return base x to the exponent power y (that is, x^y)	$x^y$	number
`random()`	return a pseudo-random number between 0 and 1	$x \in \left (0, 1 \right ]$	number
`round(x)`	return the value of the number x rounded to the nearest integer	$\lfloor x + \frac{1}{2} \rfloor$	number
`sign(x)`	return the sign of the x, indicating whether x is positive, negative, or zero	$\pm$	number
`sin(x)`	return the sine of x	$\sin x$	number
`sinh(x)`	return the hyperbolic sine of x	$\frac{e^x - e^{-x}}{2}$	number
`sqrt(x)`	return the positive square root of x	$\sqrt{x}$	number
`tan(x)`	return the tangent of x	$\tan(x)$	number
`tanh(x)`	return the hyperbolic tangent of x	$\frac{e^{2x} - 1}{e^{2x}+1}$	number
~~`trunc(x)`~~	return the integer portion of x, removing any fractional digits		number

Note:

x ** y is recommended to implement x ^ y instead of Math.pow(x, y).

~~x is recommended to get the integer part of the given number instead of Math.trunc(x).