Annotated ECMAScript 5.1

‟Ex igne vita”

15.8 The Math Object # Ⓣ Ⓔ ① Ⓐ

The Math object is a single object that has some named properties, some of which are functions.

The value of the [[Prototype]] internal property of the Math object is the standard built-in Object prototype object (15.2.4). The value of the [[Class]] internal property of the Math object is "Math".

The Math object does not have a [[Construct]] internal property; it is not possible to use the Math object as a constructor with the new operator.

The Math object does not have a [[Call]] internal property; it is not possible to invoke the Math object as a function.

NOTE In this specification, the phrase “the Number value for x” has a technical meaning defined in 8.5.

15.8.1 Value Properties of the Math Object # Ⓣ Ⓔ ① Ⓐ

15.8.1.1 E # Ⓣ Ⓔ ① Ⓐ

The Number value for e, the base of the natural logarithms, which is approximately 2.7182818284590452354.

This property has the attributes { [[Writable]]: false, [[Enumerable]]: false, [[Configurable]]: false }.

15.8.1.2 LN10 # Ⓣ Ⓔ ① Ⓐ

The Number value for the natural logarithm of 10, which is approximately 2.302585092994046.

This property has the attributes { [[Writable]]: false, [[Enumerable]]: false, [[Configurable]]: false }.

15.8.1.3 LN2 # Ⓣ Ⓔ ① Ⓐ

The Number value for the natural logarithm of 2, which is approximately 0.6931471805599453.

This property has the attributes { [[Writable]]: false, [[Enumerable]]: false, [[Configurable]]: false }.

15.8.1.4 LOG2E # Ⓣ Ⓔ ① Ⓐ

The Number value for the base-2 logarithm of e, the base of the natural logarithms; this value is approximately 1.4426950408889634.

This property has the attributes { [[Writable]]: false, [[Enumerable]]: false, [[Configurable]]: false }.

NOTE The value of Math.LOG2E is approximately the reciprocal of the value of Math.LN2.

15.8.1.5 LOG10E # Ⓣ Ⓔ ① Ⓐ

The Number value for the base-10 logarithm of e, the base of the natural logarithms; this value is approximately 0.4342944819032518.

This property has the attributes { [[Writable]]: false, [[Enumerable]]: false, [[Configurable]]: false }.

NOTE The value of Math.LOG10E is approximately the reciprocal of the value of Math.LN10.

15.8.1.6 PI # Ⓣ Ⓔ ① Ⓐ

The Number value for π, the ratio of the circumference of a circle to its diameter, which is approximately 3.1415926535897932.

This property has the attributes { [[Writable]]: false, [[Enumerable]]: false, [[Configurable]]: false }.

15.8.1.7 SQRT1_2 # Ⓣ Ⓔ ① Ⓐ

The Number value for the square root of ½, which is approximately 0.7071067811865476.

This property has the attributes { [[Writable]]: false, [[Enumerable]]: false, [[Configurable]]: false }.

NOTE The value of Math.SQRT1_2 is approximately the reciprocal of the value of Math.SQRT2.

15.8.1.8 SQRT2 # Ⓣ Ⓔ ① Ⓐ

The Number value for the square root of 2, which is approximately 1.4142135623730951.

This property has the attributes { [[Writable]]: false, [[Enumerable]]: false, [[Configurable]]: false }.

15.8.2 Function Properties of the Math Object # Ⓣ Ⓔ ① Ⓐ

Each of the following Math object functions applies the ToNumber abstract operator to each of its arguments (in left-to-right order if there is more than one) and then performs a computation on the resulting Number value(s).

In the function descriptions below, the symbols NaN, −0, +0, −∞ and +∞ refer to the Number values described in 8.5.

NOTE The behaviour of the functions acos, asin, atan, atan2, cos, exp, log, pow, sin, and sqrt is not precisely specified here except to require specific results for certain argument values that represent boundary cases of interest. For other argument values, these functions are intended to compute approximations to the results of familiar mathematical functions, but some latitude is allowed in the choice of approximation algorithms. The general intent is that an implementer should be able to use the same mathematical library for ECMAScript on a given hardware platform that is available to C programmers on that platform.

Although the choice of algorithms is left to the implementation, it is recommended (but not specified by this standard) that implementations use the approximation algorithms for IEEE 754 arithmetic contained in fdlibm, the freely distributable mathematical library from Sun Microsystems (http://www.netlib.org/fdlibm).

15.8.2.1 abs (x) # Ⓣ Ⓔ ① Ⓐ

Returns the absolute value of x; the result has the same magnitude as x but has positive sign.

15.8.2.2 acos (x) # Ⓣ Ⓔ ① Ⓐ

Returns an implementation-dependent approximation to the arc cosine of x. The result is expressed in radians and ranges from +0 to +π.

15.8.2.3 asin (x) # Ⓣ Ⓔ ① Ⓐ

Returns an implementation-dependent approximation to the arc sine of x. The result is expressed in radians and ranges from −π/2 to +π/2.

15.8.2.4 atan (x) # Ⓣ Ⓔ ① Ⓐ

Returns an implementation-dependent approximation to the arc tangent of x. The result is expressed in radians and ranges from −π/2 to +π/2.

15.8.2.5 atan2 (y, x) # Ⓣ Ⓔ ① Ⓐ

Returns an implementation-dependent approximation to the arc tangent of the quotient y/x of the arguments y and x, where the signs of y and x are used to determine the quadrant of the result. Note that it is intentional and traditional for the two-argument arc tangent function that the argument named y be first and the argument named x be second. The result is expressed in radians and ranges from −π to +π.

15.8.2.6 ceil (x) # Ⓣ Ⓔ ① Ⓐ

Returns the smallest (closest to −∞) Number value that is not less than x and is equal to a mathematical integer. If x is already an integer, the result is x.

The value of Math.ceil(x) is the same as the value of -Math.floor(-x).

15.8.2.7 cos (x) # Ⓣ Ⓔ ① Ⓐ

Returns an implementation-dependent approximation to the cosine of x. The argument is expressed in radians.

15.8.2.8 exp (x) # Ⓣ Ⓔ ① Ⓐ

Returns an implementation-dependent approximation to the exponential function of x (e raised to the power of x, where e is the base of the natural logarithms).

15.8.2.9 floor (x) # Ⓣ Ⓔ ① Ⓐ

Returns the greatest (closest to +∞) Number value that is not greater than x and is equal to a mathematical integer. If x is already an integer, the result is x.

NOTE The value of Math.floor(x) is the same as the value of -Math.ceil(-x).

15.8.2.10 log (x) # Ⓣ Ⓔ ① Ⓐ
15.8.2.11 max ( [ value1 [ , value2 [ , … ] ] ] ) # Ⓣ Ⓔ ① Ⓐ

Given zero or more arguments, calls ToNumber on each of the arguments and returns the largest of the resulting values.

The length property of the max method is 2.

15.8.2.12 min ( [ value1 [ , value2 [ , … ] ] ] ) # Ⓣ Ⓔ ① Ⓐ

Given zero or more arguments, calls ToNumber on each of the arguments and returns the smallest of the resulting values.

The length property of the min method is 2.

15.8.2.13 pow (x, y) # Ⓣ Ⓔ ① Ⓐ

Returns an implementation-dependent approximation to the result of raising x to the power y.

15.8.2.14 random ( ) # Ⓣ Ⓔ ① Ⓐ

Returns a Number value with positive sign, greater than or equal to 0 but less than 1, chosen randomly or pseudo randomly with approximately uniform distribution over that range, using an implementation-dependent algorithm or strategy. This function takes no arguments.

15.8.2.15 round (x) # Ⓣ Ⓔ ① Ⓐ

Returns the Number value that is closest to x and is equal to a mathematical integer. If two integer Number values are equally close to x, then the result is the Number value that is closer to +∞. If x is already an integer, the result is x.

NOTE 1 Math.round(3.5) returns 4, but Math.round(–3.5) returns –3.

NOTE 2 The value of Math.round(x) is the same as the value of Math.floor(x+0.5), except when x is −0 or is less than 0 but greater than or equal to -0.5; for these cases Math.round(x) returns −0, but Math.floor(x+0.5) returns +0.

15.8.2.16 sin (x) # Ⓣ Ⓔ ① Ⓐ

Returns an implementation-dependent approximation to the sine of x. The argument is expressed in radians.

15.8.2.17 sqrt (x) # Ⓣ Ⓔ ① Ⓐ

Returns an implementation-dependent approximation to the square root of x.

15.8.2.18 tan (x) # Ⓣ Ⓔ ① Ⓐ

Returns an implementation-dependent approximation to the tangent of x. The argument is expressed in radians.