py: Added optimised support for 3-argument calls to builtin.pow()

Updated modbuiltin.c to add conditional support for 3-arg calls to
pow() using MICROPY_PY_BUILTINS_POW3 config parameter. Added support in
objint_mpz.c for for optimised implementation.

py/modbuiltins.c

@@ -378,7 +378,14 @@ MP_DEFINE_CONST_FUN_OBJ_1(mp_builtin_ord_obj, mp_builtin_ord);
 STATIC mp_obj_t mp_builtin_pow(size_t n_args, const mp_obj_t *args) {
     switch (n_args) {
         case 2: return mp_binary_op(MP_BINARY_OP_POWER, args[0], args[1]);
-        default: return mp_binary_op(MP_BINARY_OP_MODULO, mp_binary_op(MP_BINARY_OP_POWER, args[0], args[1]), args[2]); // TODO optimise...
+        default:
+#if !MICROPY_PY_BUILTINS_POW3
+            mp_raise_msg(&mp_type_NotImplementedError, "3-arg pow() not supported");
+#elif MICROPY_LONGINT_IMPL != MICROPY_LONGINT_IMPL_MPZ
+            return mp_binary_op(MP_BINARY_OP_MODULO, mp_binary_op(MP_BINARY_OP_POWER, args[0], args[1]), args[2]);
+#else
+            return mp_obj_int_pow3(args[0], args[1], args[2]);
+#endif
     }
 }
 MP_DEFINE_CONST_FUN_OBJ_VAR_BETWEEN(mp_builtin_pow_obj, 2, 3, mp_builtin_pow);

py/mpconfig.h

@@ -490,6 +490,11 @@
 #define MICROPY_LONGINT_IMPL (MICROPY_LONGINT_IMPL_NONE)
 #endif
 
+// Support for calls to pow() with 3 integer arguments
+#ifndef MICROPY_PY_BUILTINS_POW3
+#define MICROPY_PY_BUILTINS_POW3 (0)
+#endif
+
 #if MICROPY_LONGINT_IMPL == MICROPY_LONGINT_IMPL_LONGLONG
 typedef long long mp_longint_impl_t;
 #endif

py/mpz.c

@@ -1395,9 +1395,6 @@ void mpz_pow_inpl(mpz_t *dest, const mpz_t *lhs, const mpz_t *rhs) {
     mpz_free(n);
 }
 
-#if 0
-these functions are unused
-
 /* computes dest = (lhs ** rhs) % mod
    can have dest, lhs, rhs the same; mod can't be the same as dest
 */
@@ -1436,6 +1433,9 @@ void mpz_pow3_inpl(mpz_t *dest, const mpz_t *lhs, const mpz_t *rhs, const mpz_t
     mpz_free(n);
 }
 
+#if 0
+these functions are unused
+
 /* computes gcd(z1, z2)
    based on Knuth's modified gcd algorithm (I think?)
    gcd(z1, z2) >= 0

py/mpz.h

@@ -123,6 +123,7 @@ void mpz_add_inpl(mpz_t *dest, const mpz_t *lhs, const mpz_t *rhs);
 void mpz_sub_inpl(mpz_t *dest, const mpz_t *lhs, const mpz_t *rhs);
 void mpz_mul_inpl(mpz_t *dest, const mpz_t *lhs, const mpz_t *rhs);
 void mpz_pow_inpl(mpz_t *dest, const mpz_t *lhs, const mpz_t *rhs);
+void mpz_pow3_inpl(mpz_t *dest, const mpz_t *lhs, const mpz_t *rhs, const mpz_t *mod);
 void mpz_and_inpl(mpz_t *dest, const mpz_t *lhs, const mpz_t *rhs);
 void mpz_or_inpl(mpz_t *dest, const mpz_t *lhs, const mpz_t *rhs);
 void mpz_xor_inpl(mpz_t *dest, const mpz_t *lhs, const mpz_t *rhs);

py/objint.h

@@ -66,5 +66,6 @@ mp_obj_t mp_obj_int_abs(mp_obj_t self_in);
 mp_obj_t mp_obj_int_unary_op(mp_uint_t op, mp_obj_t o_in);
 mp_obj_t mp_obj_int_binary_op(mp_uint_t op, mp_obj_t lhs_in, mp_obj_t rhs_in);
 mp_obj_t mp_obj_int_binary_op_extra_cases(mp_uint_t op, mp_obj_t lhs_in, mp_obj_t rhs_in);
+mp_obj_t mp_obj_int_pow3(mp_obj_t base, mp_obj_t exponent,  mp_obj_t modulus);
 
 #endif // __MICROPY_INCLUDED_PY_OBJINT_H__

py/objint_mpz.c

@@ -326,6 +326,39 @@ mp_obj_t mp_obj_int_binary_op(mp_uint_t op, mp_obj_t lhs_in, mp_obj_t rhs_in) {
     }
 }
 
+#if MICROPY_PY_BUILTINS_POW3
+STATIC mpz_t *mp_mpz_for_int(mp_obj_t arg, mpz_t *temp) {
+    if (MP_OBJ_IS_SMALL_INT(arg)) {
+        mpz_init_from_int(temp, MP_OBJ_SMALL_INT_VALUE(arg));
+        return temp;
+    } else {
+        mp_obj_int_t *arp_p = MP_OBJ_TO_PTR(arg);
+        return &(arp_p->mpz);
+    }
+}
+
+mp_obj_t mp_obj_int_pow3(mp_obj_t base, mp_obj_t exponent,  mp_obj_t modulus) {
+    if (!MP_OBJ_IS_INT(base) || !MP_OBJ_IS_INT(exponent) || !MP_OBJ_IS_INT(modulus)) {
+        mp_raise_TypeError("pow() with 3 arguments requires integers");
+    } else {
+        mp_obj_t result = mp_obj_new_int_from_ull(0); // Use the _from_ull version as this forces an mpz int
+        mp_obj_int_t *res_p = (mp_obj_int_t *) MP_OBJ_TO_PTR(result);
+
+        mpz_t l_temp, r_temp, m_temp;
+        mpz_t *lhs = mp_mpz_for_int(base,     &l_temp);
+        mpz_t *rhs = mp_mpz_for_int(exponent, &r_temp);
+        mpz_t *mod = mp_mpz_for_int(modulus,  &m_temp);
+
+        mpz_pow3_inpl(&(res_p->mpz), lhs, rhs, mod);
+
+        if (lhs == &l_temp) { mpz_deinit(lhs); }
+        if (rhs == &r_temp) { mpz_deinit(rhs); }
+        if (mod == &m_temp) { mpz_deinit(mod); }
+        return result;
+    }
+}
+#endif
+
 mp_obj_t mp_obj_new_int(mp_int_t value) {
     if (MP_SMALL_INT_FITS(value)) {
         return MP_OBJ_NEW_SMALL_INT(value);

tests/basics/builtin_pow.py

@@ -8,4 +8,32 @@ print(pow(3, 8))
 
 # 3 arg version
 print(pow(3, 4, 7))
+print(pow(555557, 1000002, 1000003))
 
+# 3 arg pow is defined to only work on integers
+try:
+    print(pow("x", 5, 6))
+except TypeError:
+    print("TypeError expected")
+
+try:
+    print(pow(4, "y", 6))
+except TypeError:
+    print("TypeError expected")
+
+try:
+    print(pow(4, 5, "z"))
+except TypeError:
+    print("TypeError expected")
+
+# Tests for 3 arg pow with large values
+
+# This value happens to be prime
+x = 0xd48a1e2a099b1395895527112937a391d02d4a208bce5d74b281cf35a57362502726f79a632f063a83c0eba66196712d963aa7279ab8a504110a668c0fc38a7983c51e6ee7a85cae87097686ccdc359ee4bbf2c583bce524e3f7836bded1c771a4efcb25c09460a862fc98e18f7303df46aaeb34da46b0c4d61d5cd78350f3edb60e6bc4befa712a849
+y = 0x3accf60bb1a5365e4250d1588eb0fe6cd81ad495e9063f90880229f2a625e98c59387238670936afb2cafc5b79448e4414d6cd5e9901aa845aa122db58ddd7b9f2b17414600a18c47494ed1f3d49d005a5
+
+print(hex(pow(2, 200, x))) # Should not overflow, just 1 << 200
+print(hex(pow(2, x-1, x))) # Should be 1, since x is prime
+print(hex(pow(y, x-1, x))) # Should be 1, since x is prime
+print(hex(pow(y, y-1, x))) # Should be a 'big value'
+print(hex(pow(y, y-1, y))) # Should be a 'big value'

unix/mpconfigport.h

@@ -80,6 +80,7 @@
 #define MICROPY_PY_BUILTINS_FROZENSET (1)
 #define MICROPY_PY_BUILTINS_COMPILE (1)
 #define MICROPY_PY_BUILTINS_NOTIMPLEMENTED (1)
+#define MICROPY_PY_BUILTINS_POW3    (1)
 #define MICROPY_PY_MICROPYTHON_MEM_INFO (1)
 #define MICROPY_PY_ALL_SPECIAL_METHODS (1)
 #define MICROPY_PY_ARRAY_SLICE_ASSIGN (1)