124 lines
3.7 KiB
C
124 lines
3.7 KiB
C
/** \file polynomials.h
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* \brief Basic operations with polynomials.
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*
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*/
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#ifndef QPMS_POLYNOMIALS_H
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#include <gmp.h>
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/// Polynomial with rational coeffs.
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// TODO more docs about initialisation etc.
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typedef struct qpq_t {
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int order;
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int offset;
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int capacity;
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mpq_t *coeffs;
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} qpq_t;
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const static qpq_t QPQ_ZERO = {-1, 0, 0, NULL};
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/// Initiasise the coefficients array in qpq_t.
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/** Do not use on qpq_t that has already been initialised
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* (and not recently cleared),
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* otherwise you can get a memory leak.
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*/
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void qpq_init(qpq_t *p, int capacity);
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/// Extend capacity of a qpq_t instance.
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/** If the requested new_capacity is larger than the qpq_t's
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* capacity, the latter is extended to match new_capacity.
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* Otherwise, nothing happend (this function does _not_ trim
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* the capacity).
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*/
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void qpq_extend(qpq_t *p, int new_capacity);
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/// Shrinks the capacity to the minimum that can store the current polynomial.
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void qpq_shrink(qpq_t *p);
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/// Canonicalises the coefficients and (re)sets the correct degree.
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void qpq_canonicalise(qpq_t *p);
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void qpq_set(qpq_t *copy, const qpq_t *orig);
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void qpq_set_elem(qpq_t *p, int exponent, const mpq_t coeff);
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void qpq_set_elem_si(qpq_t *p, int exponent, long numerator, unsigned long denominator);
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void qpq_get_elem(mpq_t coeff, const qpq_t *p, int exponent);
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/** \returns zero if the result fits into long / unsigned long; non-zero otherwise. */
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int qpq_get_elem_si(long *numerator, unsigned long *denominator, const qpq_t *p, int exponent);
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/// Deinitialise the coefficients array in qpq_t.
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void qpq_clear(qpq_t *p);
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/// Polynomial addition.
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/** Supports operand and result pointer mixing. */
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void qpq_add(qpq_t *sum, const qpq_t *addend1, const qpq_t *addend2);
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/// Polynomial substraction.
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/** Supports operand and result pointer mixing. */
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void qpq_sub(qpq_t *difference, const qpq_t *minuend, const qpq_t *substrahend);
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/// Polynomial multiplication.
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/** Does not support operand and result pointer mixing. */
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void qpq_mul(qpq_t *product, const qpq_t *multiplier, const qpq_t *multiplicand);
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/// Polynomial division with remainder.
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/** Does not support operand and result pointer mixing. */
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void qpq_div(qpq_t *quotient, qpq_t *remainder, const qpq_t *dividend, const qpq_t *divisor);
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/// Polynomial derivative.
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/** Supports operand and result pointer mixing. */
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void qpq_deriv(qpq_t *dPdx, const qpq_t *P);
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/// Tests whether a polynomial is non-zero.
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_Bool qpq_nonzero(const qpq_t *);
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/// Polynomial with double coeffs.
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typedef struct qpz_t {
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int order;
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int offset;
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int capacity;
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double *coeffs;
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} qpz_t;
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/// Initiasise the coefficients array in qpz_t.
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void qpz_init(qpz_t *p, int maxorder);
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/// Deinitialise the coefficients array in qpz_t.
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void qpz_clear(qpz_t *p);
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/// Polynomial addition.
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void qpz_add(qpz_t *sum, const qpz_t *addend1, const qpz_t *addend2);
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/// Polynomial substraction.
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void qpz_sub(qpz_t *difference, const qpz_t *minuend, const qpz_t *substrahend);
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/// Polynomial multiplication.
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void qpz_mul(qpz_t product, const qpz_t *multiplier, const qpz_t *multiplicand);
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/// Convert rational coefficient polynomial to double coefficient polynomial
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void qpz_from_qpq(qpz_t *target, const qpq_t *src);
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#if 0 // This will go elsewhere
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/// Table with pre-calculated Ferrers function coeffs.
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typedef struct qpms_legendre_table_t {
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qpms_l_t lMax;
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// TODO
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} qpms_legendre_table_t;
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/// Constructor for qpms_legendre_table_t.
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qpms_legendre_table_t *qpms_legendre_table_init(qpms_l_t lMax);
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/// Destructor for qpms_legendre_table_t.
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void qpms_legendre_table_free(qpms_legendre_table_t *);
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/// Evaluates a Ferrers function.
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double qpms_legendre_table_eval(const qpms_legendre_table_t *,
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qpms_l_t l, qpms_m_t m, double x);
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// TODO pre-calculate also the products??
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#endif
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#endif //QPMS_POLYNOMIALS_H
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