Limit exponent of intl mathematical value

[sffc]

In order to support implementations that limit the number of exponent digits or significant digits, we should put some limit on the intl mathematical values. Consider the ICU4X limits as a model.

[sffc]

My proposal is to limit the strings as follows:

1. Maximum number of significant digits: 100
2. Minimum exponent: -1000
3. Maximum exponent: 1000

Semantics for overflow:

• If there are too many significant digits, truncate to 100 significant digits
• If the number is greater than or equal to 100e1000, make it Infinity
• If the number is less than or equal to -100e1000, make it -Infinity
• If the number is smaller in magnitude than 1e-1000, make it 0 or -0 depending on the sign

This is intended to be consistent with Number semantics, but with larger limits.

[ljharb]

Why would mathematical values have any limits? They're math values.

[Constellation]

@sffc Could you offer the background of this issue? My understanding is that ICU4C can have very large amount of exponent as a decimal by using string. What is the reason of not doing it in ICU4X too?

[sffc]

CC @FrankYFTang

The V8 implementation requires an intermediate type to represent the intl mathematical value because it is used for certain operations such as < ~and ==~ for the purposes of range formatting. There has been pushback to making it a string with unbounded length for both the mantissa and the exponent. There is a desire to use a more compact representation for one or both pieces.

The ICU4X intermediate representation, FixedDecimal, allows for values with up to u16::MAX significant digits and exponents ranging from i16::MIN to i16::MAX.

[sffc]

2022-05-19 discussion: https://github.com/tc39/ecma402/blob/master/meetings/notes-2022-05-19.md#limit-exponent-of-intl-mathematical-value-98

Conclusion: Proceed with adding a limit upon parsing the string. Internally we will still use a mathematical value; this is only on the string parsing step. The limit should be set in a way that is implementable to check.

[sffc]

@romulocintra Please see the meeting minutes. It looks like we agreed on +/- 10K.

[sffc]

@romulocintra Do you plan to write the spec for this? It would be nice to present it at this week's TC39 meeting so that we can have a clean Stage 4 in January.