Polynomial division, bug fixes, enhancements.
- Addition and substraction fixed, supports result and operand mixing. Former-commit-id: 0a53db4cd1fee70c6cf77a6ea2c65840de6d3ca1
This commit is contained in:
Marek Nečada
parent
b4ac597771
commit
8db97686e5
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@ -31,6 +31,7 @@ cdef extern from "polynomials.h":
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void qpq_add(qpq_t *sum, const qpq_t *addend1, const qpq_t *addend2)
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void qpq_sub(qpq_t *difference, const qpq_t *minuend, const qpq_t *substrahend)
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void qpq_mul(qpq_t *product, const qpq_t *multiplier, const qpq_t *multiplicand)
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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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void qpq_deriv(qpq_t *dPdx, const qpq_t *P)
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bint qpq_nonzero(const qpq_t *)
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@ -111,6 +112,10 @@ cdef class qpq:
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cdef qpq result = qpq()
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qpq_mul(&result.p, &self.p, &other.p)
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return result
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def __divmod__(qpq self, qpq other):
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cdef qpq q = qpq(), r = qpq()
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qpq_div(&q.p, &r.p, &self.p, &other.p)
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return (q, r)
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def derivative(self):
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cdef qpq result = qpq()
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qpq_deriv(&result.p, &self.p)
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@ -136,6 +141,6 @@ cdef class qpq:
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for exponent in range(self.p.offset, self.p.order + 1):
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i = exponent - self.p.offset
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if mpq_sgn(self.p.coeffs[i]):
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result[i] = GMPy_MPQ_From_mpq(self.p.coeffs[i])
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result[exponent] = GMPy_MPQ_From_mpq(self.p.coeffs[i])
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return result
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@ -2,11 +2,19 @@
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#include <stdlib.h>
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#include "qpms_error.h"
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#include <stdbool.h>
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#include <stdio.h>
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#define MAX(x, y) (((x) > (y)) ? (x) : (y))
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#define MIN(x, y) (((x) <= (y)) ? (x) : (y))
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static void qpq_dbgprint(const qpq_t *p) {
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for(int n = p->order; n >= p->offset; --n)
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if(mpq_sgn(p->coeffs[n - p->offset]))
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gmp_printf("%+Qdx**%d ", p->coeffs[n - p->offset], n);
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gmp_printf("[%d, %d, %d]\n", p->capacity, p->order, p->offset);
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}
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// Auxillary function to set a mpq_t to 0/1
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static inline void mpq_zero(mpq_t q) {
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// Maybe not the best way to set it to zero.
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@ -15,6 +23,10 @@ static inline void mpq_zero(mpq_t q) {
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mpq_init(q);
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}
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static inline void qpq_zero(qpq_t *q) {
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qpq_clear(q);
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}
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// qpq_t internal consistency check
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static inline void qpq_cc(const qpq_t *p) {
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if (!p->coeffs) return;
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@ -23,7 +35,7 @@ static inline void qpq_cc(const qpq_t *p) {
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_Bool qpq_nonzero(const qpq_t *p) {
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qpq_cc(p);
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if (p->capacity <= 0) return false;
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if (p->capacity == 0) return false;
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for(int i = 0; i <= p->order - p->offset; ++i)
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if (mpq_sgn(p->coeffs[i]))
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@ -42,6 +54,7 @@ void qpq_init(qpq_t *p, int capacity) {
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}
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void qpq_extend(qpq_t *p, int cap) {
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QPMS_ENSURE(p->capacity >= 0, "Got polynomial with negative capacity (%d). Is this a manually allocated one?", p->capacity);
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if (cap > 0 && cap > p->capacity) {
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QPMS_CRASHING_REALLOC(p->coeffs, sizeof(mpq_t) * cap);
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for(int i = p->capacity; i < cap; ++i)
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@ -50,6 +63,35 @@ void qpq_extend(qpq_t *p, int cap) {
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}
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}
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void qpq_shrink(qpq_t *p) {
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if (p->capacity > 0) {
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for(int n = p->capacity - 1; n > p->order - p->offset; --n)
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mpq_clear(p->coeffs[n]);
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p->capacity = p->order - p->offset + 1;
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if (p->capacity > 0)
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QPMS_CRASHING_REALLOC(p->coeffs, p->capacity * sizeof(mpq_t));
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}
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}
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void qpq_canonicalise(qpq_t *p) {
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qpq_cc(p);
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// Lower the order if necessary (here one can get -1 if the polynomial is 0)
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while (p->order >= p->offset && !mpq_sgn(p->coeffs[p->order - p->offset])) --p->order;
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if (p->order < p->offset)
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qpq_zero(p);
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else { // remove the lowest-order coefficients which are in fact zero.
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int i = 0;
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while (i <= p->order - p->offset && !mpq_sgn(p->coeffs[i])) ++i;
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if (i > 0)
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for (int j = 0; j <= p->order - p->offset - i; ++j)
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mpq_swap(p->coeffs[j], p->coeffs[j+i]);
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p->offset += i;
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// canonicalise the fractions
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for (i = 0; i <= p->order - p->offset; ++i)
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mpq_canonicalize(p->coeffs[i]);
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}
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}
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void qpq_set(qpq_t *p, const qpq_t *orig) {
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const int order = orig->order, offset = orig->offset;
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qpq_extend(p, order - offset + 1);
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@ -123,10 +165,32 @@ void qpq_clear(qpq_t *p) {
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*p = QPQ_ZERO;
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}
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// Auxillary function for lowering the offset
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void qpq_lower_offset(qpq_t *p, int dec) {
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QPMS_ENSURE(dec >= 0, "Offset decrease must be positive, is %d!", dec);
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QPMS_ENSURE(dec <= p->offset, "Offset can't be pushed below 0, (offset=%d, decr.=%d!)",
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p->offset, dec);
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if(dec > 0) {
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qpq_extend(p, p->order - p->offset + dec + 1);
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for(int i = p->order; i >= p->offset; --i)
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mpq_swap(p->coeffs[i+dec - p->offset], p->coeffs[i - p->offset]);
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p->offset -= dec;
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for(int i = dec - 1; i >= 0; --i)
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mpq_set_si(p->coeffs[i], 0, 1);
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}
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}
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void qpq_add(qpq_t *sum, const qpq_t *x, const qpq_t *y) {
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const int maxorder = MAX(x->order, y->order);
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const int minoffset = MIN(x->offset, y->offset);
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qpq_extend(sum, maxorder - minoffset + 1);
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/* if sum is actually some of the summands and that summand has higher
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* offset, we have to lower the offset.
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*/
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if ((sum == x || sum == y) && sum->offset > minoffset)
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qpq_lower_offset(sum, sum->offset - minoffset);
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for (int i = minoffset; i <= maxorder; ++i) {
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if (i - x->offset >= 0 && i <= x->order) {
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if (i - y->offset >= 0 && i <= y->order)
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@ -136,7 +200,7 @@ void qpq_add(qpq_t *sum, const qpq_t *x, const qpq_t *y) {
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mpq_set(sum->coeffs[i - minoffset], x->coeffs[i - x->offset]);
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} else {
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if (i - y->offset >= 0 && i <= y->order)
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mpq_set(sum->coeffs[i - minoffset], y->coeffs[i - x->offset]);
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mpq_set(sum->coeffs[i - minoffset], y->coeffs[i - y->offset]);
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else {
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mpq_zero(sum->coeffs[i - minoffset]);
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}
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@ -150,6 +214,12 @@ void qpq_sub(qpq_t *dif, const qpq_t *x, const qpq_t *y) {
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const int maxorder = MAX(x->order, y->order);
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const int minoffset = MIN(x->offset, y->offset);
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qpq_extend(dif, maxorder - minoffset + 1);
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/* if dif is actually some of the summands and that summand has higher
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* offset, we have to lower the offset.
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*/
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if ((dif == x || dif == y) && dif->offset > minoffset)
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qpq_lower_offset(dif, dif->offset - minoffset);
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for (int i = minoffset; i <= maxorder; ++i) {
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if (i - x->offset >= 0 && i <= x->order) {
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if (i - y->offset >= 0 && i <= y->order)
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@ -159,7 +229,7 @@ void qpq_sub(qpq_t *dif, const qpq_t *x, const qpq_t *y) {
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mpq_set(dif->coeffs[i - minoffset], x->coeffs[i - x->offset]);
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} else {
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if (i - y->offset >= 0 && i <= y->order) {
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mpq_set(dif->coeffs[i - minoffset], y->coeffs[i - x->offset]);
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mpq_set(dif->coeffs[i - minoffset], y->coeffs[i - y->offset]);
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mpq_neg(dif->coeffs[i - minoffset], dif->coeffs[i - minoffset]);
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} else {
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mpq_zero(dif->coeffs[i - minoffset]);
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@ -176,14 +246,67 @@ void qpq_mul(qpq_t *p, const qpq_t *x, const qpq_t *y) {
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// Easiest way to set p to a zero polynomial...
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qpq_clear(p);
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qpq_init(p, maxorder - minoffset + 1);
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mpq_t tmp; mpq_init(tmp);
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for (int xi = x->offset; xi <= x->order; ++xi)
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for (int yi = y->offset; yi <= y->order; ++yi)
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mpq_mul(p->coeffs[xi + yi - minoffset],
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x->coeffs[xi - x->offset], y->coeffs[yi - y->offset]);
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for (int yi = y->offset; yi <= y->order; ++yi) {
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mpq_mul(tmp, x->coeffs[xi - x->offset], y->coeffs[yi - y->offset]);
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mpq_add(p->coeffs[xi + yi - minoffset], p->coeffs[xi + yi - minoffset], tmp);
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}
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p->order = maxorder;
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p->offset = minoffset;
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mpq_clear(tmp);
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}
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void qpq_div(qpq_t *q, qpq_t *r, const qpq_t *dend, const qpq_t *dor) {
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// Split the divisor into "head" and "tail"
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qpq_t dor_tail[1]; qpq_init(dor_tail, dor->order - dor->offset); // divisor tail
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qpq_set(dor_tail, dor);
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qpq_canonicalise(dor_tail);
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QPMS_ENSURE(qpq_nonzero(dor_tail), "The divisor must be non-zero");
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const int dor_order = dor_tail->order;
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mpq_t dor_head; mpq_init(dor_head);
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mpq_set(dor_head, dor_tail->coeffs[dor_order - dor_tail->offset]);
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dor_tail->order--;
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qpq_zero(q);
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qpq_extend(q, dend->order - dor_order + 1);
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q->order = dend->order - dor_order;
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q->offset = 0;
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// Assign the dividend to r but with extended capacity (with zero offset)
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qpq_extend(r, dend->order + 1);
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r->offset = 0;
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r->order = dend->order;
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for (int n = 0; n < dend->offset; ++n)
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mpq_set_si(r->coeffs[n], 0, 1);
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for (int n = dend->offset; n <= dend->order; ++n)
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mpq_set(r->coeffs[n], dend->coeffs[n - dend->offset]);
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qpq_t f[1]; qpq_init(f, 1);
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qpq_t ftail[1]; qpq_init(ftail, dor_tail->order - dor_tail->offset + 1);
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for(; r->order >= dor_order; --r->order) {
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// Compute the current order (r->order - dor_order) of q
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mpq_t * const hicoeff = &(q->coeffs[r->order - dor_order]);
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mpq_div(*hicoeff, r->coeffs[r->order], dor_head);
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mpq_canonicalize(*hicoeff);
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// Update the remainder
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f->offset = f->order = r->order - dor_order;
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mpq_set(f->coeffs[0], *hicoeff);
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qpq_mul(ftail, f, dor_tail);
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qpq_sub(r, r, ftail);
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}
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qpq_clear(ftail);
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qpq_clear(f);
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mpq_clear(dor_head);
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qpq_clear(dor_tail);
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qpq_canonicalise(r);
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qpq_canonicalise(q);
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}
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void qpq_deriv(qpq_t *dp, const qpq_t *p) {
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if (p->order <= 0) { // p is constant, dp is zero.
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qpq_clear(dp);
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@ -21,7 +21,7 @@ const static qpq_t QPQ_ZERO = {-1, 0, 0, NULL};
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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 *x, int capacity);
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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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@ -29,31 +29,46 @@ void qpq_init(qpq_t *x, int 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 *x, int new_capacity);
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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 *x, int exponent, const mpq_t coeff);
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void qpq_set_elem_si(qpq_t *x, int exponent, long numerator, unsigned long denominator);
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void qpq_get_elem(mpq_t coeff, const qpq_t *x, int exponent);
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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 *x, int exponent);
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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 *x);
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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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@ -66,10 +81,10 @@ typedef struct qpz_t {
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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 *x, int maxorder);
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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 *x);
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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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