remove pari compile time dependency from rings.fast_arith

src/sage/libs/pari/convert_sage.pxd

@@ -11,3 +11,5 @@ cpdef Gen new_gen_from_rational(Rational self)
 
 cpdef pari_is_prime(Integer p)
 cpdef pari_is_prime_power(Integer q, bint get_data)
+cpdef ulong pari_maxprime()
+cpdef list pari_prime_range(long c_start, long c_stop, bint py_ints=False)

src/sage/libs/pari/convert_sage.pyx

@@ -26,7 +26,8 @@ from cypari2.gen cimport objtogen
 from cypari2.stack cimport new_gen
 from .convert_gmp cimport INT_to_mpz, new_gen_from_mpz_t, new_gen_from_mpq_t, INTFRAC_to_mpq
 
-from sage.libs.gmp.mpz cimport mpz_fits_slong_p, mpz_sgn, mpz_get_ui, mpz_set, mpz_set_si
+from sage.ext.stdsage cimport PY_NEW
+from sage.libs.gmp.mpz cimport mpz_fits_slong_p, mpz_sgn, mpz_get_ui, mpz_set, mpz_set_si, mpz_set_ui
 from sage.libs.gmp.mpq cimport mpq_denref, mpq_numref
 from sage.rings.integer cimport smallInteger
 from sage.rings.all import RealField, ComplexField, QuadraticField
@@ -527,3 +528,49 @@ cpdef pari_is_prime_power(Integer q, bint get_data):
         return (smallInteger(p), smallInteger(n)) if get_data else True
     else:
         return (q, smallInteger(0)) if get_data else False
+
+
+cpdef ulong pari_maxprime():
+    """
+    Return to which limit PARI has computed the primes.
+
+    EXAMPLES::
+
+        sage: from sage.libs.pari.convert_sage import pari_maxprime
+        sage: a = pari_maxprime()
+        sage: res = prime_range(2, 2*a)
+        sage: b = pari_maxprime()
+        sage: b >= 2*a
+        True
+    """
+    return maxprime()
+
+
+cpdef list pari_prime_range(long c_start, long c_stop, bint py_ints=False):
+    """
+    Return a list of all primes between ``start`` and ``stop - 1``, inclusive.
+
+    .. SEEALSO::
+
+        :func:`sage.rings.fast_arith.prime_range`
+
+    TESTS::
+
+        sage: from sage.libs.pari.convert_sage import pari_prime_range
+        sage: pari_prime_range(2, 19)
+        [2, 3, 5, 7, 11, 13, 17]
+    """
+    cdef long p = 0
+    cdef byteptr pari_prime_ptr = diffptr
+    res = []
+    while p < c_start:
+        NEXT_PRIME_VIADIFF(p, pari_prime_ptr)
+    while p < c_stop:
+        if py_ints:
+            res.append(p)
+        else:
+            z = <Integer>PY_NEW(Integer)
+            mpz_set_ui(z.value, p)
+            res.append(z)
+        NEXT_PRIME_VIADIFF(p, pari_prime_ptr)
+    return res

src/sage/rings/fast_arith.pyx

@@ -36,11 +36,7 @@ Basic arithmetic with C integers
 # The int definitions
 
 from libc.math cimport sqrt
-from sage.libs.gmp.mpz cimport mpz_set_ui
 
-from sage.ext.stdsage cimport PY_NEW
-
-from sage.libs.pari.all import pari
 from sage.rings.integer cimport Integer
 
 cpdef prime_range(start, stop=None, algorithm=None, bint py_ints=False):
@@ -150,8 +146,6 @@ cpdef prime_range(start, stop=None, algorithm=None, bint py_ints=False):
     - Robert Bradshaw (speedup using Pari prime table, py_ints option)
     """
     cdef Integer z
-    cdef long c_start, c_stop, p
-    cdef byteptr pari_prime_ptr
     # input to pari.init_primes cannot be greater than 436273290 (hardcoded bound)
     DEF init_primes_max = 436273290
     DEF small_prime_max = 436273009  #  a prime < init_primes_max (preferably the largest)
@@ -185,42 +179,32 @@ cpdef prime_range(start, stop=None, algorithm=None, bint py_ints=False):
             algorithm = "pari_isprime"
 
     if algorithm == "pari_primes":
+        from sage.libs.pari.convert_sage import pari_maxprime, pari_prime_range
+        from sage.libs.pari import pari
 
         if max(start, stop or 0) > small_prime_max:
             raise ValueError('algorithm "pari_primes" is limited to primes larger than'
                 + ' {}'.format(small_prime_max - 1))
 
         if stop is None:
             # In this case, "start" is really stop
-            c_start = 1
-            c_stop = start
+            stop = start
+            start = 1
         else:
-            c_start = start
-            c_stop = stop
-            if c_start < 1:
-                c_start = 1
-        if c_stop <= c_start:
+            start = start
+            stop = stop
+            if start < 1:
+                start = 1
+        if stop <= start:
             return []
 
-        if maxprime() < c_stop:
+        if pari_maxprime() < stop:
             # Adding prime_gap_bound should be sufficient to guarantee an
             # additional prime, given that c_stop <= small_prime_max.
-            pari.init_primes(min(c_stop + prime_gap_bound, init_primes_max))
-            assert maxprime() >= c_stop
-
-        pari_prime_ptr = diffptr
-        p = 0
-        res = []
-        while p < c_start:
-            NEXT_PRIME_VIADIFF(p, pari_prime_ptr)
-        while p < c_stop:
-            if py_ints:
-                res.append(p)
-            else:
-                z = <Integer>PY_NEW(Integer)
-                mpz_set_ui(z.value, p)
-                res.append(z)
-            NEXT_PRIME_VIADIFF(p, pari_prime_ptr)
+            pari.init_primes(min(stop + prime_gap_bound, init_primes_max))
+            assert pari_maxprime() >= stop
+
+        res = pari_prime_range(start, stop, py_ints)
 
     elif (algorithm == "pari_isprime") or (algorithm == "pari_primes"):
         from sage.arith.all import primes