Negative zero not treated the same as positive 0 #2531
Description
I'm not sure this should be considered a bug, but I was playing around with how something should be recorded and bumped up against an odd bug creating balanced transactions. The deal is when working with costs, negating credits vs. debits works differently. I really only bumped into this because Ledger CLI handles this differently and I was exporting to there and it choked over my inputs. In tweaking the inputs to the way it expected (all costs being positive) I discovered I couldn't negate a zero in hledger. I can multiply by zero, but not negative zero.
Consider this ledger which balances in HLedger:
2000-01-01 Opening balance
Assets:Cash $10.00
Equity:Balances
2000-01-01 Vendor A ; I pay for something for somebody else
Liabilities:Reimbursable:PersonA $10.00
Assets:Cash $-10.00
2000-01-01 Person A ; They pay me back at an over generous exchange rate
Assets:Cash ₺450,00
Liabilities:Reimbursable:PersonA $-10.00 @ ₺44,00 ; market conversion rate
Liabilities:Reimbursable:PersonA 0 @@ ₺-10,00 ; "call it even between frinds"
The solution in Ledger CLI would be to keep the cost positive but make sure the posting is a debit not a credit:
2000-01-01 Opening balance
Assets:Cash $10.00
Equity:Balances
2000-01-01 Vendor A ; I pay for something for somebody else
Liabilities:Reimbursable:PersonA $10.00
Assets:Cash $-10.00
2000-01-01 Person A ; They pay me back at an over generous exchange rate
Assets:Cash ₺450,00
Liabilities:Reimbursable:PersonA $-10.00 @ ₺44,00 ; market conversion rate
Liabilities:Reimbursable:PersonA -0 @@ ₺10,00 ; "call it even between frinds"
HLedger on the other hand is not too fond of that:
9 | 2000-01-01 Person A ; They pay me back at an over generous exchange rate
| Assets:Cash ₺450,00
| Liabilities:Reimbursable:PersonA $-10.00 @ ₺44,00 ; market conversion rate
| Liabilities:Reimbursable:PersonA 0 @@ ₺10,00 ; "call it even between frinds"
This multi-commodity transaction is unbalanced.
The real postings' sum should be 0 but is: ₺20,00
Consider adjusting this entry's amounts, adding missing postings,
or recording conversion price(s) with @, @@ or equity postings.
I understand that mathematically negative zero is not particularly meaningful, but for that matter neither is 0 × <anything>. In math that would evaluate to zero no matter what. In a posting right now that's actually a way to fudge currency conversion costs using a throw-away conversion commodity rather than a throw-away conversion account.
I was taking this approach because I wanted to use my prices database to sanity check currency conversion postings. If I stuff these random amounts coming in and out of an Equity:Conversion account I kind of throw off that math. There might be a better way to handle this, but given that 0 × 𝓧 is being evaluated to 𝓧 and 0 × -𝓧 is being evaluated to -𝓧 I was surprised to find -1 × 𝓧 was evaluated to 𝓧. I expected -𝓧.