Implemented modular GCD algorithm for univariate polynomials.

[ginac.git] / ginac / polynomial / cra_garner.cpp

diff --git a/ginac/polynomial/cra_garner.cpp b/ginac/polynomial/cra_garner.cpp
new file mode 100644 (file)
index 0000000..b400adb
--- /dev/null
+++ b/ginac/polynomial/cra_garner.cpp
@@ -0,0 +1,88 @@
+#include <cln/integer.h>
+#include <cln/modinteger.h>
+#include <vector>
+#include <cstddef>
+#include "cra_garner.hpp"
+
+namespace cln
+{
+using std::vector;
+using std::size_t;
+
+static cl_I 
+retract_symm(const cl_MI& x, const cl_modint_ring& R,
+            const cl_I& modulus)
+{
+       cl_I result = R->retract(x);
+       if (result > (modulus >> 1))
+               result = result - modulus;
+       return result;
+}
+
+static void
+compute_recips(vector<cl_MI>& dst, 
+              const vector<cl_I>& moduli)
+{
+       for (size_t k = 1; k < moduli.size(); ++k) {
+               cl_modint_ring R = find_modint_ring(moduli[k]);
+               cl_MI product = R->canonhom(moduli[0]);
+               for (size_t i = 1; i < k; ++i)
+                       product = product*moduli[i];
+               dst[k-1] = recip(product);
+       }
+}
+
+static void
+compute_mix_radix_coeffs(vector<cl_I>& dst,
+                        const vector<cl_I>& residues,
+                        const vector<cl_I>& moduli,
+                        const vector<cl_MI>& recips)
+{
+       dst[0] = residues[0];
+
+       do {
+               cl_modint_ring R = find_modint_ring(moduli[1]);
+               cl_MI tmp = R->canonhom(residues[0]);
+               cl_MI next = (R->canonhom(residues[1]) - tmp)*recips[0];
+               dst[1] = retract_symm(next, R, moduli[1]);
+       } while (0);
+
+       for (size_t k = 2; k < residues.size(); ++k) {
+               cl_modint_ring R = find_modint_ring(moduli[k]);
+               cl_MI tmp = R->canonhom(dst[k-1]);
+
+               for (size_t j = k - 1 /* NOT k - 2 */; j-- != 0; )
+                       tmp = tmp*moduli[j] + R->canonhom(dst[j]);
+
+               cl_MI next = (R->canonhom(residues[k]) - tmp)*recips[k-1];
+               dst[k] = retract_symm(next, R, moduli[k]);
+       }
+}
+
+static cl_I
+mixed_radix_2_ordinary(const vector<cl_I>& mixed_radix_coeffs,
+                      const vector<cl_I>& moduli)
+{
+       size_t k = mixed_radix_coeffs.size() - 1;
+       cl_I u = mixed_radix_coeffs[k];
+       for (; k-- != 0; )
+               u = u*moduli[k] + mixed_radix_coeffs[k];
+       return u;
+}
+
+cl_I integer_cra(const vector<cl_I>& residues,
+                const vector<cl_I>& moduli)
+{
+
+       vector<cl_MI> recips(moduli.size() - 1);
+       compute_recips(recips, moduli);
+
+       vector<cl_I> coeffs(moduli.size());
+       compute_mix_radix_coeffs(coeffs, residues, moduli, recips);
+       cl_I result = mixed_radix_2_ordinary(coeffs, moduli);
+
+       return result;
+}
+
+} // namespace cln
+