Question

I’m wondering where I find the source to show how the operator ** is implemented in Python. Can someone point me in the right direction?

Answer 1

The python grammar definition (from which the parser is generated using pgen), look for ‘power’: Gramar/Gramar

The python ast, look for ‘ast_for_power’: Python/ast.c

The python eval loop, look for ‘BINARY_POWER’: Python/ceval.c

Which calls PyNumber_Power (implemented in Objects/abstract.c):

PyObject * PyNumber_Power(PyObject *v, PyObject *w, PyObject *z) {     return ternary_op(v, w, z, NB_SLOT(nb_power), '** or pow()'); } 

Essentially, invoke the pow slot. For long objects (the only default integer type in 3.0) this is implemented in the long_pow function Objects/longobject.c, for int objects (in the 2.x branches) it is implemented in the int_pow function Object/intobject.c

If you dig into long_pow, you can see that after vetting the arguments and doing a bit of set up, the heart of the exponentiation can be see here:

if (Py_SIZE(b) <= FIVEARY_CUTOFF) {     /* Left-to-right binary exponentiation (HAC Algorithm 14.79) */     /* http://www.cacr.math.uwaterloo.ca/hac/about/chap14.pdf    */     for (i = Py_SIZE(b) - 1; i >= 0; --i) {         digit bi = b->ob_digit[i];          for (j = 1 << (PyLong_SHIFT-1); j != 0; j >>= 1) {             MULT(z, z, z)             if (bi & j)                 MULT(z, a, z)         }     } } else {     /* Left-to-right 5-ary exponentiation (HAC Algorithm 14.82) */     Py_INCREF(z);   /* still holds 1L */     table[0] = z;     for (i = 1; i < 32; ++i)         MULT(table[i-1], a, table[i])      for (i = Py_SIZE(b) - 1; i >= 0; --i) {         const digit bi = b->ob_digit[i];          for (j = PyLong_SHIFT - 5; j >= 0; j -= 5) {             const int index = (bi >> j) & 0x1f;             for (k = 0; k < 5; ++k)                 MULT(z, z, z)             if (index)                 MULT(z, table[index], z)         }     } } 

Which uses algorithms discussed in Chapter 14.6 of the Handbook of Applied Cryptography which describes efficient exponentiation algorithms for arbitrary precision arithmetic.