sharp_legendre_table: Import Legendre table generating code from libpsht

Includes a Python wrapper. The code is tested and compared with SciPy
results through the Python tests.

libsharp/sharp_legendre_table.h

@@ -0,0 +1,87 @@
+/*
+ *  This file is part of libsharp.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * met:
+ * 
+ * 1. Redistributions of source code must retain the above copyright
+ * notice, this list of conditions and the following disclaimer.
+ * 
+ * 2. Redistributions in binary form must reproduce the above copyright
+ * notice, this list of conditions and the following disclaimer in the
+ * documentation and/or other materials provided with the distribution.
+ * 
+ * 3. Neither the name of the copyright holder nor the names of its
+ * contributors may be used to endorse or promote products derived from
+ * this software without specific prior written permission.
+ * 
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+ * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+ * HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+ * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+ * LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+ * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+ * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+ * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+/*! \file sharp_legendre_table.h
+ *  Interface for computing tables of the normalized associated Legendre transform
+ *
+ *  Copyright (C) 2017 Dag Sverre Seljebotn
+ *  \author Dag Sverre Seljebotn
+ *
+ *  Note: This code was mainly copied from libpsht; only a small high-level wrapper added
+ */
+
+#ifndef SHARP_LEGENDRE_TABLE_H
+#define SHARP_LEGENDRE_TABLE_H
+
+#include <stddef.h>
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+#ifndef NO_LEGENDRE_TABLE
+
+
+/*! Returns a table of the normalized associated Legendre polynomials. m is a single
+    fixed argument and a table for multiple l and cos(theta) is provided.
+    (Internally, sin(theta) is also used for part of the computation, making theta
+    the most convenient argument.)
+
+    \param m The m-value to compute a table for
+    \param lmax A table will be provided for l = m .. lmax
+    \param ntheta How many theta values to evaluate for
+    \param theta Contiguous 1D array of theta values
+    \param ncols Number of columns in the out-array; should have ncols >= (lmax - m)
+    \param out Contiguous 2D array that will receive the output. Each output entry
+               is assigned to out[itheta * ncols + (l - m)].
+ */
+void sharp_normalized_associated_legendre_table(
+  ptrdiff_t m,
+  ptrdiff_t lmax,
+  ptrdiff_t ntheta,
+  /* contiguous 1D array of theta values to compute for,
+     contains ntheta values */
+  double *theta,
+  /* number of columns in out; see below. Should be >= (lmax - m). */
+  ptrdiff_t ncols,
+  /* contiguous 2D array, in "theta-major ordering". Has `ntheta`
+     rows and `ncols` columns. Indexed as out[itheta * ncols + (l - m)].
+     If `ncols > lmax - m` then those entries are not accessed.
+  */
+  double *out
+);
+
+#endif
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif