The behaviour of the overflow in multiply_pow10

[younies]

when a user call multiply_pow10 in FixedDecimal and an overflow happen, what shall we do:

1. Set the number to Zero
2. cut from the number (for example: if the number is 12345 and the user called multiply_pow10 by i16::MAX -3, the resulted number will be 34500000000......
3. Add an infinity field to FixedDecimal so that +Infinity and -Infinity can be represented, and use that value when overflowing
4. Saturate to the theoretical maximum FixedDecimal value

[sffc]

Discuss with:

• @younies
• @sffc

Optional:

• @Manishearth

[sffc]

• @younies - We need +/- infinity for units conversion and formatting
• @eggrobin - There is CLDR data for infinity
• @skius - Do we want differences between debug and release mode?
• @Manishearth - Since this behaves sort-of like an f32 or f64, we can say that it just has an infinity value. We can say that infinity is a valid value to have. But maybe for overflow... ?
• @younies - We need to find a way to set infinity. And do we need to differentiate between pow(1e6) and infinity?
• @sffc - It's not normal to overflow as it is in f32/f64. So I think we should debug assert. But it's fine when creating directly from infinity input values.
• @sffc - How about NaN?
• @younies - We could make NaN the value when overflow occurs?
• @eggrobin - That sounds like a new arithmetic standard
• @Manishearth - NaN is specifically an IEEE thing. We are not IEEE floats. There is a reason to have a NaN-like value, but we don't expose these as things for people to manipulate. This is primarily for formatting. NaNs are weird.
• @younies - What if you have infinity + infinity? So maybe infinity and overflow (and also NaN) should be different values. Then the user can know whether there was a problem.
• @sffc - For now, I think we should limit the scope of this to infinity, but we should keep the door open for NaN only because then we can support infallible conversion from f64.
• @sffc - We don't support arithmetic on FixedDecimal. We can debug assert to inform people that there was a problem. I don't think we should encode that in the data model.
• @Manishearth - I don't think we should have a sentinel value. We should debug-assert and put in a sensical value in its place.
• @younies - Is NaN formattable by CLDR?
• @sffc - Yes
• @eggrobin - I agree that this is not an arithmetic type, but to the extent that it has limited arithmetic, we should stick with an existing arithmetic standard.

Consensus: add Infinity and -Infinity to the FixedDecimal data model. Support it when reading from f32, f64, and strings (the string value is "Infinity" and "-Infinity"). Support infinity in FixedDecimalFormatter as a replacement for the # in the pattern, producing outputs such as "$∞K". When a FixedDecimal operation overflows into infinity, have a debug assertion.

LGTM: @younies @Manishearth @skius @eggrobin @sffc