Issue #22486: Added the math.gcd() function. The fractions.gcd() function now is

deprecated.  Based on patch by Mark Dickinson.

1 files changed, 205 insertions, 0 deletions

diff --git a/Objects/longobject.c b/Objects/longobject.c
index 27bee50..40da0b1 100644
--- a/Objects/longobject.c
+++ b/Objects/longobject.c
@@ -4327,6 +4327,211 @@ long_long(PyObject *v)
     return v;
 }
 
+PyObject *
+_PyLong_GCD(PyObject *aarg, PyObject *barg)
+{
+    PyLongObject *a, *b, *c = NULL, *d = NULL, *r;
+    stwodigits x, y, q, s, t, c_carry, d_carry;
+    stwodigits A, B, C, D, T;
+    int nbits, k;
+    Py_ssize_t size_a, size_b, alloc_a, alloc_b;
+    digit *a_digit, *b_digit, *c_digit, *d_digit, *a_end, *b_end;
+
+    a = (PyLongObject *)aarg;
+    b = (PyLongObject *)barg;
+    size_a = Py_SIZE(a);
+    size_b = Py_SIZE(b);
+    if (-2 <= size_a && size_a <= 2 && -2 <= size_b && size_b <= 2) {
+        Py_INCREF(a);
+        Py_INCREF(b);
+        goto simple;
+    }
+
+    /* Initial reduction: make sure that 0 <= b <= a. */
+    a = (PyLongObject *)long_abs(a);
+    if (a == NULL)
+        return NULL;
+    b = (PyLongObject *)long_abs(b);
+    if (b == NULL) {
+        Py_DECREF(a);
+        return NULL;
+    }
+    if (long_compare(a, b) < 0) {
+        r = a;
+        a = b;
+        b = r;
+    }
+    /* We now own references to a and b */
+
+    alloc_a = Py_SIZE(a);
+    alloc_b = Py_SIZE(b);
+    /* reduce until a fits into 2 digits */
+    while ((size_a = Py_SIZE(a)) > 2) {
+        nbits = bits_in_digit(a->ob_digit[size_a-1]);
+        /* extract top 2*PyLong_SHIFT bits of a into x, along with
+           corresponding bits of b into y */
+        size_b = Py_SIZE(b);
+        assert(size_b <= size_a);
+        if (size_b == 0) {
+            if (size_a < alloc_a) {
+                r = (PyLongObject *)_PyLong_Copy(a);
+                Py_DECREF(a);
+            }
+            else
+                r = a;
+            Py_DECREF(b);
+            Py_XDECREF(c);
+            Py_XDECREF(d);
+            return (PyObject *)r;
+        }
+        x = (((twodigits)a->ob_digit[size_a-1] << (2*PyLong_SHIFT-nbits)) |
+             ((twodigits)a->ob_digit[size_a-2] << (PyLong_SHIFT-nbits)) |
+             (a->ob_digit[size_a-3] >> nbits));
+
+        y = ((size_b >= size_a - 2 ? b->ob_digit[size_a-3] >> nbits : 0) |
+             (size_b >= size_a - 1 ? (twodigits)b->ob_digit[size_a-2] << (PyLong_SHIFT-nbits) : 0) |
+             (size_b >= size_a ? (twodigits)b->ob_digit[size_a-1] << (2*PyLong_SHIFT-nbits) : 0));
+
+        /* inner loop of Lehmer's algorithm; A, B, C, D never grow
+           larger than PyLong_MASK during the algorithm. */
+        A = 1; B = 0; C = 0; D = 1;
+        for (k=0;; k++) {
+            if (y-C == 0)
+                break;
+            q = (x+(A-1))/(y-C);
+            s = B+q*D;
+            t = x-q*y;
+            if (s > t)
+                break;
+            x = y; y = t;
+            t = A+q*C; A = D; B = C; C = s; D = t;
+        }
+
+        if (k == 0) {
+            /* no progress; do a Euclidean step */
+            if (l_divmod(a, b, NULL, &r) < 0)
+                goto error;
+            Py_DECREF(a);
+            a = b;
+            b = r;
+            alloc_a = alloc_b;
+            alloc_b = Py_SIZE(b);
+            continue;
+        }
+
+        /*
+          a, b = A*b-B*a, D*a-C*b if k is odd
+          a, b = A*a-B*b, D*b-C*a if k is even
+        */
+        if (k&1) {
+            T = -A; A = -B; B = T;
+            T = -C; C = -D; D = T;
+        }
+        if (c != NULL)
+            Py_SIZE(c) = size_a;
+        else if (Py_REFCNT(a) == 1) {
+            Py_INCREF(a);
+            c = a;
+        }
+        else {
+            alloc_a = size_a;
+            c = _PyLong_New(size_a);
+            if (c == NULL)
+                goto error;
+        }
+
+        if (d != NULL)
+            Py_SIZE(d) = size_a;
+        else if (Py_REFCNT(b) == 1 && size_a <= alloc_b) {
+            Py_INCREF(b);
+            d = b;
+            Py_SIZE(d) = size_a;
+        }
+        else {
+            alloc_b = size_a;
+            d = _PyLong_New(size_a);
+            if (d == NULL)
+                goto error;
+        }
+        a_end = a->ob_digit + size_a;
+        b_end = b->ob_digit + size_b;
+
+        /* compute new a and new b in parallel */
+        a_digit = a->ob_digit;
+        b_digit = b->ob_digit;
+        c_digit = c->ob_digit;
+        d_digit = d->ob_digit;
+        c_carry = 0;
+        d_carry = 0;
+        while (b_digit < b_end) {
+            c_carry += (A * *a_digit) - (B * *b_digit);
+            d_carry += (D * *b_digit++) - (C * *a_digit++);
+            *c_digit++ = (digit)(c_carry & PyLong_MASK);
+            *d_digit++ = (digit)(d_carry & PyLong_MASK);
+            c_carry >>= PyLong_SHIFT;
+            d_carry >>= PyLong_SHIFT;
+        }
+        while (a_digit < a_end) {
+            c_carry += A * *a_digit;
+            d_carry -= C * *a_digit++;
+            *c_digit++ = (digit)(c_carry & PyLong_MASK);
+            *d_digit++ = (digit)(d_carry & PyLong_MASK);
+            c_carry >>= PyLong_SHIFT;
+            d_carry >>= PyLong_SHIFT;
+        }
+        assert(c_carry == 0);
+        assert(d_carry == 0);
+
+        Py_INCREF(c);
+        Py_INCREF(d);
+        Py_DECREF(a);
+        Py_DECREF(b);
+        a = long_normalize(c);
+        b = long_normalize(d);
+    }
+    Py_XDECREF(c);
+    Py_XDECREF(d);
+
+simple:
+    assert(Py_REFCNT(a) > 0);
+    assert(Py_REFCNT(b) > 0);
+#if LONG_MAX >> 2*PyLong_SHIFT
+    /* a fits into a long, so b must too */
+    x = PyLong_AsLong((PyObject *)a);
+    y = PyLong_AsLong((PyObject *)b);
+#elif defined(PY_LONG_LONG) && PY_LLONG_MAX >> 2*PyLong_SHIFT
+    x = PyLong_AsLongLong((PyObject *)a);
+    y = PyLong_AsLongLong((PyObject *)b);
+#else
+# error "_PyLong_GCD"
+#endif
+    x = Py_ABS(x);
+    y = Py_ABS(y);
+    Py_DECREF(a);
+    Py_DECREF(b);
+
+    /* usual Euclidean algorithm for longs */
+    while (y != 0) {
+        t = y;
+        y = x % y;
+        x = t;
+    }
+#if LONG_MAX >> 2*PyLong_SHIFT
+    return PyLong_FromLong(x);
+#elif defined(PY_LONG_LONG) && PY_LLONG_MAX >> 2*PyLong_SHIFT
+    return PyLong_FromLongLong(x);
+#else
+# error "_PyLong_GCD"
+#endif
+
+error:
+    Py_DECREF(a);
+    Py_DECREF(b);
+    Py_XDECREF(c);
+    Py_XDECREF(d);
+    return NULL;
+}
+
 static PyObject *
 long_float(PyObject *v)
 {