Fixes Pairingmodule: Improve PyLongObject handling, optimize, and address Windows/MinGW issues

[Komorebi-Z]

This Pull Request introduces several improvements and fixes to the pairing module.

Problem Background:

Upon further testing, I discovered that my previous attempt in #328 did not fully resolve the underlying issues. I've created a simple test script, test.py, that exposes several lingering problems:

from charm.toolbox.pairinggroup import PairingGroup, G1, G2, GT, ZR, pair, pc_element as Element

group = PairingGroup("MNT159")
print("********************** PairingGroup ZR Test **********************")
m = group.order()
print("m(Z):\t", m)

r1 = group.random(ZR)
print("r1(ZR):\t", r1)
print("0*ZR:\t", 0 * r1)
print("1*ZR:\t", 1 * r1)

r2 = group.random(ZR)
print("r2(ZR):\t", r2)
print("ZR^2:\t", r1 * r2)
print("Z*ZR:\t", int(r1) * r2)
print("ZR*Z:\t", r1 * int(r2))
print("Z^2mod:\t", int(r1) * int(r2) % m)

a = group.init(ZR, 1)
print("a(ZR):\t", a)
b = group.init(ZR, -1)
print("b(ZR):\t", b)
c = group.init(ZR, m + 123456789)
print("c(ZR):\t", c)
d = group.init(ZR, -m - 123456789)
print("d(ZR):\t", d)
r3 = group.init(ZR, int(r1 * m + r2))
print("r3(ZR):\t", r3)
print("r2 = r3:", r2 == r3)

print("*****************************************************************")

Key Contributions in this PR:

1. Refined PyLongObject Size Handling & Macro Naming:

   • Problem: The PyLongObj_Size and Py_SET_SIZE macros, crucial for correctly getting/setting the signed length of the PyLongObject's ob_digit array, had incorrect logic, affecting Python 3.12+ environments. This can be demonstrated by b = group.init(ZR, -1) and m = group.order() respectively.
   • Solution: The logic for PyLongObj_Size and Py_SET_SIZE has been refined to better interpret the lv_tag field and extract the signed length. All related macros have been consistently renamed (e.g., PyLongObj_Sizel to PyLong_SIZE) for better readability.
   • NOTE: Everything seems normal now but MORE TESTS ARE NEEDED. Furthermore, the lv_tag field, which these macros interact with, appears to be an internal CPython design. Making reliance on its specific bit-level interpretation might be unstable (Python 3.14+ may introduce new C APIs per PEP 757).

2. Fixed incorrect PyLong_SHIFT when compiled with MinGW for Windows 64-bit System:

   • Problem: On Windows 64-bit systems, when compiled with MinGW and run with Python 3.10 and below, the PyLong_SHIFT value was erroneously set to 15 bits, leading to incorrect longObjToMPZ behavior with very large integers. This can be demonstrated by c = group.init(ZR, m + 123456789) or d = group.init(ZR, -m - 123456789).
   • Solution: We defined the MS_WIN64 macro in the relevant header files, which sets SIZEOF_VOID_P to 8 in <your_python>/include/pyconfig.h, which further ensures PYLONG_BITS_IN_DIGIT is set to 30 in <your_python>/include/pyport.h, leading to the correct PyLong_SHIFT value.

3. Enhanced Element_mul for Larger Integer Support:

   • Problem: In the Element_mul function, the variable z was limited to a signed long int type. This restricted its ability to process larger integer inputs, potentially causing overflows for certain operations. This can be demonstrated by print("Z*ZR:\t", int(r1) * r2) or print("ZR*Z:\t", r1 * int(r2)).
   • Solution: The type of z has been changed from signed long int to mpz_t. This allows the function to handle arbitrary-precision integers, expanding its capability to process much larger inputs without limitation.

4. Optimized longObjToMPZ Performance:

   • The implementation of longObjToMPZ has been fine-tuned to eliminate redundant mpz related operations.

[jakinyele]

Great!