Add support for np.correlate and np.convolve

As title. Lack of FFT support prevents the implementation of
efficient convolution alg.

Closes #2500

docs/source/reference/numpysupported.rst

@@ -253,7 +253,9 @@ The following top-level functions are supported:
 * :func:`numpy.bincount` (only the 2 first arguments)
 * :func:`numpy.column_stack`
 * :func:`numpy.concatenate`
+* :func:`numpy.convolve` (only the 2 first arguments)
 * :func:`numpy.copy` (only the first argument)
+* :func:`numpy.correlate` (only the 2 first arguments)
 * :func:`numpy.diag`
 * :func:`numpy.digitize`
 * :func:`numpy.dstack`

numba/targets/arraymath.py

@@ -21,10 +21,20 @@
                                     impl_ret_new_ref, impl_ret_untracked)
 from numba.typing import signature
 from .arrayobj import make_array, load_item, store_item, _empty_nd_impl
+from .linalg import ensure_blas
 
 from numba.extending import intrinsic
 from numba.errors import RequireConstValue, TypingError
 
+def _check_blas():
+    # Checks if a BLAS is available so e.g. dot will work
+    try:
+        ensure_blas()
+    except ImportError:
+        return False
+    return True
+
+_HAVE_BLAS = _check_blas()
 
 @intrinsic
 def _create_tuple_result_shape(tyctx, shape_list, shape_tuple):
@@ -1450,3 +1460,158 @@ def impl(arg):
 
 generate_xinfo(np.finfo, finfo, _finfo_supported)
 generate_xinfo(np.iinfo, iinfo, _iinfo_supported)
+
+def _get_inner_prod(dta, dtb):
+    # gets an inner product implementation, if both types are float then
+    # BLAS is used else a local function
+
+    @register_jitable
+    def _innerprod(a, b):
+        acc = 0
+        for i in range(len(a)):
+            acc = acc + a[i] * b[i]
+        return acc
+
+    # no BLAS... use local function regardless
+    if not _HAVE_BLAS:
+        return _innerprod
+
+    flty = types.real_domain | types.complex_domain
+    floats = dta in flty and dtb in flty
+    if not floats:
+        return _innerprod
+    else:
+        a_dt = as_dtype(dta)
+        b_dt = as_dtype(dtb)
+        dt = np.promote_types(a_dt, b_dt)
+
+        @register_jitable
+        def _dot_wrap(a, b):
+            return np.dot(a.astype(dt), b.astype(dt))
+        return _dot_wrap
+
+def _assert_1d(a, func_name):
+    if isinstance(a, types.Array):
+        if not a.ndim <= 1:
+            raise TypingError("%s() only supported on 1D arrays " % func_name)
+
+def _np_correlate_core(ap1, ap2, mode, direction):
+    pass
+
+@overload(_np_correlate_core)
+def _np_correlate_core_impl(ap1, ap2, mode, direction):
+    a_dt = as_dtype(ap1.dtype)
+    b_dt = as_dtype(ap2.dtype)
+    dt = np.promote_types(a_dt, b_dt)
+    innerprod = _get_inner_prod(ap1.dtype, ap2.dtype)
+
+    def impl(ap1, ap2, mode, direction):
+        # Implementation loosely based on `_pyarray_correlate` from
+        # https://github.com/numpy/numpy/blob/3bce2be74f228684ca2895ad02b63953f37e2a9d/numpy/core/src/multiarray/multiarraymodule.c#L1191
+        # For "Mode":
+        # Convolve uses 'full' by default, this is denoted by the number 2
+        # Correlate uses 'valid' by default, this is denoted by the number 0
+        # For "direction", +1 to write the return values out in order 0->N
+        # -1 to write them out N->0.
+
+        if not (mode == 0 or mode == 2):
+            raise ValueError("Invalid mode")
+
+        n1 = len(ap1)
+        n2 = len(ap2)
+        length = n1
+        n = n2
+        if mode == 0: # mode == 0, correlate default
+            length = length - n + 1
+            n_left = 0
+            n_right = 0
+        elif mode == 2: # mode == 2, convolve default
+            n_right = n - 1
+            n_left = n - 1
+            length = length + n - 1
+        else:
+            raise ValueError("Invalid mode")
+
+        ret = np.zeros(length, dt)
+        n = n - n_left
+
+        if direction == 1:
+            idx = 0
+            inc = 1
+        elif direction == -1:
+            idx = length - 1
+            inc = -1
+        else:
+            raise ValueError("Invalid direction")
+
+        for i in range(n_left):
+            ret[idx] = innerprod(ap1[:idx + 1], ap2[-(idx + 1):])
+            idx = idx + inc
+
+        for i in range(n1 - n2 + 1):
+            ret[idx] = innerprod(ap1[i : i + n2], ap2)
+            idx = idx + inc
+
+        for i in range(n_right, 0, -1):
+            ret[idx] = innerprod(ap1[-i:], ap2[:i])
+            idx = idx + inc
+        return ret
+
+    return impl
+
+@overload(np.correlate)
+def _np_correlate(a, v):
+    _assert_1d(a, 'np.correlate')
+    _assert_1d(v, 'np.correlate')
+
+    @register_jitable
+    def op_conj(x):
+        return np.conj(x)
+
+    @register_jitable
+    def op_nop(x):
+        return x
+
+    if a.dtype in types.complex_domain:
+        if v.dtype in types.complex_domain:
+            a_op = op_nop
+            b_op = op_conj
+        else:
+            a_op = op_nop
+            b_op = op_nop
+    else:
+        if v.dtype in types.complex_domain:
+            a_op = op_nop
+            b_op = op_conj
+        else:
+            a_op = op_conj
+            b_op = op_nop
+
+    def impl(a, v):
+        if len(a) < len(v):
+            return _np_correlate_core(b_op(v), a_op(a), 0, -1)
+        else:
+            return _np_correlate_core(a_op(a), b_op(v), 0, 1)
+
+    return impl
+
+@overload(np.convolve)
+def np_convolve(a, v):
+    _assert_1d(a, 'np.convolve')
+    _assert_1d(v, 'np.convolve')
+
+    def impl(a, v):
+        la = len(a)
+        lv = len(v)
+
+        if la == 0:
+            raise ValueError("'a' cannot be empty")
+        if lv == 0:
+            raise ValueError("'v' cannot be empty")
+
+        if la < lv:
+            return _np_correlate_core(v, a[::-1], 2, 1)
+        else:
+            return _np_correlate_core(a, v[::-1], 2, 1)
+
+    return impl

numba/tests/test_np_functions.py

@@ -11,7 +11,7 @@
 from numba.compiler import compile_isolated, Flags, utils
 from numba import jit, typeof, types
 from numba.numpy_support import version as np_version
-from numba.errors import UntypedAttributeError
+from numba.errors import UntypedAttributeError, TypingError
 from .support import TestCase, CompilationCache
 
 no_pyobj_flags = Flags()
@@ -60,6 +60,12 @@ def finfo(*args):
 def finfo_machar(*args):
     return np.finfo(*args).machar
 
+def correlate(a, v):
+    return np.correlate(a, v)
+
+def convolve(a, v):
+    return np.convolve(a, v)
+
 
 class TestNPFunctions(TestCase):
     """
@@ -424,6 +430,61 @@ def check_values(values):
 
         check_values(values)
 
+    def _test_correlate_convolve(self, pyfunc):
+        cfunc = jit(nopython=True)(pyfunc)
+        # only 1d arrays are accepted, test varying lengths 
+        # and varying dtype
+        lengths = (1, 2, 3, 7)
+        dts = [np.int8, np.int32, np.int64, np.float32, np.float64,
+               np.complex64, np.complex128]
+
+        for dt1, dt2, n, m in itertools.product(dts, dts, lengths, lengths):
+            a = np.arange(n, dtype=dt1)
+            v = np.arange(m, dtype=dt2)
+
+            if np.issubdtype(dt1, np.complexfloating):
+                a = (a + 1j * a).astype(dt1)
+            if np.issubdtype(dt2, np.complexfloating):
+                v = (v + 1j * v).astype(dt2)
+
+            expected = pyfunc(a, v)
+            got = cfunc(a, v)
+            self.assertPreciseEqual(expected, got)
+
+        _a = np.arange(12).reshape(4, 3)
+        _b = np.arange(12)
+        for x, y in [(_a, _b), (_b, _a)]:
+            with self.assertRaises(TypingError) as raises:
+                cfunc(x, y)
+            msg = 'only supported on 1D arrays'
+            self.assertIn(msg, str(raises.exception))
+
+    def test_correlate(self):
+        self._test_correlate_convolve(correlate)
+        # correlate supports 0 dimension arrays
+        _a = np.ones(shape=(0,))
+        _b = np.arange(5)
+        cfunc = jit(nopython=True)(correlate)
+        for x, y in [(_a, _b), (_b, _a), (_a, _a)]:
+            expected = correlate(x, y)
+            got = cfunc(x, y)
+            self.assertPreciseEqual(expected, got)
+
+    def test_convolve(self):
+        self._test_correlate_convolve(convolve)
+        # convolve raises if either array has a 0 dimension
+        _a = np.ones(shape=(0,))
+        _b = np.arange(5)
+        cfunc = jit(nopython=True)(convolve)
+        for x, y in [(_a, _b), (_b, _a)]:
+            with self.assertRaises(ValueError) as raises:
+                cfunc(x, y)
+            if len(x) == 0:
+                self.assertIn("'a' cannot be empty", str(raises.exception))
+            else:
+                self.assertIn("'v' cannot be empty", str(raises.exception))
+
+
 class TestNPMachineParameters(TestCase):
     # tests np.finfo, np.iinfo, np.MachAr