Stage: 0

Author: qntm

A mathematical constant is a real number with a fixed and unambiguously defined value which is used, and useful, across multiple mathematical problems. Examples of mathematical constants are:

• e, the base of the natural logarithm, equal to 2.7182818284590452353602874713527...
• ln(10), the natural logarithm of 10, equal to 2.3025850929940456840179914546844...
• ln(2), the natural logarithm of 2, equal to 0.69314718055994530941723212145818...
• log(e), the base 10 logarithm of e, equal to 0.43429448190325182765112891891661...
• log₂(e), the base 2 logarithm of e, equal to 1.4426950408889634073599246810019...
• π, the ratio of a circle's circumference to its diameter, equal to 3.1415926535897932384626433832795...
• √½, the square root of one-half, equal to 0.70710678118654752440084436210485...
• √2, the square root of 2, equal to 1.4142135623730950488016887242097...

In order to carry out mathematics using ECMAScript it is advantageous to be able to make use of mathematical constants. As a result, ECMAScript's Math object has, since the very earliest versions of the programming language, exposed the following respective value properties, which have the following exact values:

• Math.E = 2.718281828459045090795598298427648842334747314453125
• Math.LN10 = 2.30258509299404590109361379290930926799774169921875
• Math.LN2 = 0.69314718055994528622676398299518041312694549560546875
• Math.LOG10E = 0.43429448190325181666793241674895398318767547607421875
• Math.LOG2E = 1.442695040888963387004650940070860087871551513671875
• Math.PI = 3.141592653589793115997963468544185161590576171875
• Math.SQRT1_2 = 0.70710678118654757273731092936941422522068023681640625
• Math.SQRT2 = 1.4142135623730951454746218587388284504413604736328125

Note that these values are, of necessity, approximated. They are not exactly equal to the actual mathematical constants, because the constants are all irrational and therefore impossible to represent as IEEE 754 64-bit floating point numbers. Despite this, these approximate values are still useful for doing mathematics in ECMAScript.

However, as of ECMAScript 2020, ECMAScript has a second numeric type, alongside the IEEE 754 64-bit floating point number: the BigInt.

Therefore, for symmetry, this proposal introduces a corresponding collection of mathematical constants for use with BigInt calculations. Again, these values are, of necessity, approximated. They are as follows:

• BigInt.E = 3
• BigInt.LN10 = 2
• BigInt.LN2 = 1
• BigInt.LOG10E = 0
• BigInt.LOG2E = 1
• BigInt.PI = 3
• BigInt.SQRT1_2 = 1
• BigInt.SQRT2 = 1

When do we get BigInt.abs() and BigInt.sign()? Please? Yes, I can write these two-and-a-half lines of code myself every time but it's frankly humiliating.

Edit: Getting closer!