Fix NumPy Alignment: int //, int %, and signed right-shift semantics; bool ** dtype

[ajpotts]

Fix NumPy Alignment: int //, int %, and signed right-shift semantics; bool ** dtype

Summary

The NumPy alignment suite currently fails for several binary operations where Arkouda semantics diverge from NumPy:

1. Signed integer floor division (//) differs for negative values.
2. Signed integer modulo (%) / remainder differs for negative values (tied to floor-division semantics).
3. Signed integer right shift (>>) differs for negative values (arithmetic vs logical / truncation behavior).
4. Boolean power (**) dtype promotion differs (NumPy returns signed int; Arkouda returns unsigned).

These should be fixed in Arkouda to match NumPy semantics.

Evidence (from alignment tests)

• floordiv mismatches with max absolute difference 1 on many elements → consistent with floor vs trunc behavior.
• mod mismatches with large differences → consistent with NumPy remainder sign rules.
• rshift mismatches on negatives (NumPy often yields -1 where Arkouda yields 0) → consistent with arithmetic vs logical shift.
• pow on bool: expected dtype kind 'i' but got 'u'.

Expected NumPy Semantics

1) Floor division (a // b)

For signed integers, NumPy uses mathematical floor:

• -3 // 2 == -2
• 3 // -2 == -2
• -3 // -2 == 1

2) Remainder / modulo (a % b)

NumPy defines remainder consistent with floor division:

• a == (a // b) * b + (a % b)
• a % b has the same sign as b (the divisor)
  Examples:
• -3 % 2 == 1
• 3 % -2 == -1

3) Right shift (a >> k) for signed ints

NumPy behaves like an arithmetic right shift on signed integers (sign-propagating) for typical two's-complement behavior:

• -1 >> 1 == -1
• -3 >> 1 == -2

4) Boolean power dtype

NumPy’s bool ** bool results are promoted to a signed integer dtype (alignment suite expects kind 'i').

Current Arkouda Likely Semantics (inferred)

• // and % appear to use truncation toward zero and a remainder consistent with truncation (C-like), not floor.
• >> appears to behave like a logical shift (zero-fill) for signed ints, not arithmetic shift.
• bool ** bool appears to promote to uint rather than signed int.

Proposed Fixes

A) Signed integer floor division and remainder

Implement NumPy-compatible floor-division and remainder for signed integer types.

For a and b integers (b != 0), let:

• q0 = trunc_div(a, b) (current behavior)
• r0 = a - q0*b
  Then adjust to floor-division:
• If r0 != 0 and ((r0 > 0) != (b > 0)) (i.e., remainder and divisor have opposite signs),
  • q = q0 - 1
  • r = r0 + b
    Else:
  • q = q0
  • r = r0

This ensures:

• q == floor(a/b)
• r == a % b per NumPy

B) Signed right shift

Ensure signed right shift is arithmetic:

• Preserve sign bit when shifting right for signed integer dtypes.
• For unsigned dtypes, keep logical shift.

C) bool ** bool dtype promotion

Align dtype promotion with NumPy for power on bool operands:

• Ensure result is signed int (likely int64) rather than uint64.

Tests to Add / Update

1. Targeted unit tests with small explicit vectors:
   • a = [-3, -2, -1, 0, 1, 2, 3], b = [2, -2, 3, -3, 5, -5, 7] (broadcast as needed)
   • Assert Arkouda matches NumPy for // and %
2. Right shift explicit tests:
   • a = [-1, -2, -3, -4, 1, 2, 3], shift counts [1, 2, 3]
3. bool power dtype/value:
   • a = [False, True], b = [False, True]
   • Assert values match NumPy and dtype kind is 'i'