First draft of essential polynomial arithmetic functionality.

Former-commit-id: f34d258aaffbd52c4e4d251f5b6f1ff3733e3a08

qpms/polynomials.h

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+/** \file polynomials.h
+ * \brief Basic operations with polynomials.
+ *
+ */
+#ifndef QPMS_POLYNOMIALS_H
+#include <gmp.h>
+
+/// Polynomial with rational coeffs.
+typedef struct qpq_t {
+	int order;
+	int offset;
+	int capacity;
+	mpq_t *coeffs;
+} qpq_t;
+
+/// Initiasise the coefficients array in qpq_t.
+void qpq_init(qpq_t *x, int maxorder);
+
+/// Deinitialise the coefficients array in qpq_t.
+void qpq_clear(qpq_t *x);
+
+/// Polynomial addition.
+void qpq_add(qpq_t *sum, const qpq_t *addend1, const qpq_t *addend2);
+
+/// Polynomial substraction.
+void qpq_sub(qpq_t *difference, const qpq_t *minuend, const qpq_t *substrahend);
+
+/// Polynomial multiplication.
+void qpq_mul(qpq_t product, const qpq_t *multiplier, const qpq_t *multiplicand);
+
+
+/// Polynomial with double coeffs.
+typedef struct qpz_t {
+	int order;
+	int offset;
+	int capacity;
+	double *coeffs;
+} qpz_t;
+
+/// Initiasise the coefficients array in qpz_t.
+void qpz_init(qpz_t *x, int maxorder);
+
+/// Deinitialise the coefficients array in qpz_t.
+void qpz_clear(qpz_t *x);
+
+/// Polynomial addition.
+void qpz_add(qpz_t *sum, const qpz_t *addend1, const qpz_t *addend2);
+
+/// Polynomial substraction.
+void qpz_sub(qpz_t *difference, const qpz_t *minuend, const qpz_t *substrahend);
+
+/// Polynomial multiplication.
+void qpz_mul(qpz_t product, const qpz_t *multiplier, const qpz_t *multiplicand);
+
+/// Convert rational coefficient polynomial to double coefficient polynomial
+void qpz_from_qpq(qpz_t *target, const qpq_t *src);
+
+
+
+/// Table with pre-calculated Ferrers function coeffs.
+typedef struct qpms_legendre_table_t {
+	qpms_l_t lMax;
+	// TODO
+} qpms_legendre_table_t;
+
+/// Constructor for qpms_legendre_table_t.
+qpms_legendre_table_t *qpms_legendre_table_init(qpms_l_t lMax);
+
+/// Destructor for qpms_legendre_table_t.
+void qpms_legendre_table_free(qpms_legendre_table_t *);
+
+/// Evaluates a Ferrers function.
+double qpms_legendre_table_eval(const qpms_legendre_table_t *,
+		qpms_l_t l, qpms_m_t m, double x);
+
+
+// TODO pre-calculate also the products??
+
+#endif //QPMS_POLYNOMIALS_H