MOD operator returns wrong results for negative argument

[tingtron]

Bug report

Problem
MOD operator returns wrong results with negative argument.

Steps

1. Run PC-BASIC
2. Enter the following and press Enter
for i=-5 to 3: ? i mod 2; : next
3. Observed: -1 -2 -1 -2 -1 0 1 0 1
4. Expected: -1 0 -1 0 -1 0 1 0 1
5. Compare with GW-BASIC from MS-DOS (in DOSBox)

Note: Python works as expected:

>>> [x % 2 for x in range(-5,3)]
[1, 0, 1, 0, 1, 0, 1, 0]

The problem is in the source pcbasic\basic\values\numbers.py:

    if dividend < 0 or mod < 0:
      mod -= divisor

It should be

      mod = -mod

Program
This affects an existing program, which calculates coordinate offset.

Notes
PC-BASIC version: 2.0.7
Operating system version: Windows 11 64-bit

[robhagemans]

I can confirm this is a bug and I can reproduce.

[GBR-613]

Surprisingly, Python works wrong here:

-17 % 3
1
17 % 3
2
-17 % -3
-2

[robhagemans]

For reference, these are the results for Python and for GW-BASIC:

GW-BASIC:

? 17 mod 3                                                                      
 2                                                                              
Ok                                                                              
? 17 mod -3                                                                     
 2                                                                              
Ok                                                                              
? -17 mod 3                                                                     
-2                                                                              
Ok                                                                              
? -17 mod -3                                                                    
-2                                                                              
Ok     

Python:

>>> 17 % 3
2
>>> 17 % -3
-1
>>> -17 % 3
1
>>> -17 % -3
-2

Some background as to what Python does and why it does that, linked below. TLDR, Python's // rounds toward negative infinity, and % then does what it needs to do to ensure the relation holds that divisor*quotient + remainder = dividend.
https://stackoverflow.com/questions/3883004/how-does-the-modulo-operator-work-on-negative-numbers-in-python#3883019
http://python-history.blogspot.com/2010/08/why-pythons-integer-division-floors.html