Converting between currencies with different bases returns wrong scale

[sarahdayan]

When converting between currencies with different bases (e.g., MRU and UAH), the scale is wrong. This comes from the scale calculation in convert.

Reproduction: https://codesandbox.io/s/github/dinerojs/dinero.js/tree/main/examples/starter?file=/main.js

Discussed in #446

^{Originally posted by antpv October 17, 2021}
I have currency rate like this: 0.0001234

How can i calculate "scale" and "amount" for dinero currency rate correctly?

[matheusfcorocher]

I was verifying this issue and I found that convert() function only works with amount and scale. When, both dinero objects have the same base doesn't have this problem but with different bases, this bug happen. I'm trying to make a solution about that.

Today, it works like that:

Old behavior of function:
	- multiplies amount of dinero that will be converted with amount of
	rate
	- adds scale of dinero that will be converted with scale of rate
	- returns dinero with new amount and currency, and converts 
	to highest scale

I was thinking about:

New behavior of function:
	- convert dinero base to have the same base of new currency
	- multiplies amount of dinero that will be converted with amount of
	rate
	- adds scale of dinero that will be converted with scale of rate
	- returns dinero with new amount and currency, and converts 
	to highest scale

What do you think @sarahdayan?

[matheusfcorocher]

I was verifying this issue and I found that convert() function only works with amount and scale. When, both dinero objects have the same base doesn't have this problem but with different bases, this bug happen. I'm trying to make a solution about that.

Today, it works like that:

Old behavior of function:
	- multiplies amount of dinero that will be converted with amount of
	rate
	- adds scale of dinero that will be converted with scale of rate
	- returns dinero with new amount and currency, and converts 
	to highest scale

I was thinking about:

New behavior of function:
	- convert dinero base to have the same base of new currency
	- multiplies amount of dinero that will be converted with amount of
	rate
	- adds scale of dinero that will be converted with scale of rate
	- returns dinero with new amount and currency, and converts 
	to highest scale

What do you think @sarahdayan?

I was trying to create the algorithm for converting dinero to a same currency and my idea was to use toUnit() function for getting the real value of dinero object, try to convert into another base and create new dinero object with new base.

I asked a question in MathStackExchange to verify if was possible solve the base conversion. I receive this answer in MathStackExchange by Paul Sinclair.
By his answer, in order to implement an algorithm that I was thinking, I should consider 2 types of case:

• If the real value of dinero object has a terminating expansion in the new base
  • If value is integer, keep dividing by new base until the result is no longer integer. exponent will be the number of times you divided and got an integer result. amount is the last integer result you got.
  • If value is not integer, keep multiplying by new base until you get an integer result. exponent will be the opposite of the number of times you multiplied by new base to get that integer result. amount will be the integer result.
• The real value of dinero object does not have a terminating expression in the new base

In the last case, is impossible to express with integers the number, almost all number he said.
So the algorithm would be inconsistency if the real value doesn't have a terminating expression in the new base. It implies that is not a good idea to implement it.