javascriptecma262

BigInt and Number coercion by numeric comparison operators

Will numeric comparison, between a BigInt and a Number, coerce one argument to BigInt, or coerce one argument to Number?

For example, in the following, is 3n coerced to 3, or is 1 coerced to 1n?

console.log(3n > 1) // true

Both operands appear to be converted to a "mathematical value" in 4.k of the IsLessThan abstract operation; a process that is designated ℝ in the specification.

I have no idea what this means, however.

I note that:

console.log(19_999_999_999_999_998 > 19_999_999_999_999_999n) // true

Perhaps the "mathematical value", ℝ, of 19,999,999,999,999,998, is the descriptor for the value 20,000,000,000,000,000, which is the closest possible IEEE754 representation?

I still don't understand if coercion can be said to occur, given that a Number can have a fractional component, and a BigInt cannot.

Solution

  • Will numeric comparison between a BigInt and a Number coerce one argument to BigInt, or coerce one argument to Number?

    Neither. As you read in the spec, their mathematical values are compared.

    Consider 2n < 2.4. If both were converted to BigInt, you'd either get an exception ("cannot convert non-integer to BigInt") or you'd get the result false because 2n is not smaller than 2n. But no, we get the result true because "ℝ(2n) < ℝ(2.4)" is "2 < 2.4" which is true.

    Consider 9007199254740993n > 9007199254740992. If both were converted to Number values, you'd get the result false because 9007199254740993 is larger than the Number.MAX_SAFE_INTEGER and loses precision, becoming the number value 9007199254740992 which is not larger than 9007199254740992. But no, we get the result true because "ℝ(9007199254740993n) > ℝ(9007199254740992)" is "9007199254740993 > 9007199254740992" which is true.

    Perhaps the "mathematical value", ℝ, is the closest possible IEEE754 representation?

    No, that's the Number value for x, also denoted as 𝔽(x), which converts from a mathematical value (the real numbers) or extended mathematical value (the real numbers plus two infinities) to a concrete (IEEE 754 double-precision floating point) Number value. The mathematical values are abstract, and there are many real numbers that can neither be represented accurately as a BigInt or Number.