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-rw-r--r--moon-abe/pbc-0.5.14/ecc/hilbert.c539
1 files changed, 539 insertions, 0 deletions
diff --git a/moon-abe/pbc-0.5.14/ecc/hilbert.c b/moon-abe/pbc-0.5.14/ecc/hilbert.c
new file mode 100644
index 00000000..753e70e0
--- /dev/null
+++ b/moon-abe/pbc-0.5.14/ecc/hilbert.c
@@ -0,0 +1,539 @@
+#include <stdarg.h>
+#include <stdio.h>
+#include <stdint.h> // for intptr_t
+#include <stdlib.h> //for pbc_malloc, pbc_free
+#include <gmp.h>
+#include <math.h>
+#include "pbc_utils.h"
+#include "pbc_field.h"
+#include "pbc_poly.h"
+#include "pbc_hilbert.h"
+#include "pbc_memory.h"
+
+#include "misc/darray.h"
+#include "mpc.h"
+
+static mpf_t pi, eulere, recipeulere, epsilon, negepsilon;
+
+static void mpf_exp(mpf_t res, mpf_t pwr) {
+ mpf_t a;
+ mpf_t f0;
+ int i;
+
+ mpf_init(a); mpf_set(a, pwr);
+
+ mpf_init(f0);
+
+ mpf_set(f0, a);
+ mpf_add_ui(res, a, 1);
+
+ for (i=2;;i++) {
+ mpf_mul(f0, f0, a);
+ mpf_div_ui(f0, f0, i);
+ if (mpf_sgn(f0) > 0) {
+ if (mpf_cmp(f0, epsilon) < 0) break;
+ } else {
+ if (mpf_cmp(f0, negepsilon) > 0) break;
+ }
+ mpf_add(res, res, f0);
+ }
+
+ mpf_clear(f0);
+ mpf_clear(a);
+}
+
+static void mpc_cis(mpc_t res, mpf_t theta) {
+ mpf_t a;
+
+ mpf_init(a); mpf_set(a, theta);
+ //res = exp(i a)
+ // = cos a + i sin a
+ //converges quickly near the origin
+ mpf_t f0;
+ mpf_ptr rx = mpc_re(res), ry = mpc_im(res);
+ int i;
+ int toggle = 1;
+
+ mpf_init(f0);
+
+ mpf_set(f0, a);
+ mpf_set_ui(rx, 1);
+ mpf_set(ry, f0);
+ i = 1;
+ for(;;) {
+ toggle = !toggle;
+ i++;
+ mpf_div_ui(f0, f0, i);
+ mpf_mul(f0, f0, a);
+ if (toggle) {
+ mpf_add(rx, rx, f0);
+ } else {
+ mpf_sub(rx, rx, f0);
+ }
+
+ i++;
+ mpf_div_ui(f0, f0, i);
+ mpf_mul(f0, f0, a);
+
+ if (toggle) {
+ mpf_add(ry, ry, f0);
+ } else {
+ mpf_sub(ry, ry, f0);
+ }
+
+ if (mpf_sgn(f0) > 0) {
+ if (mpf_cmp(f0, epsilon) < 0) break;
+ } else {
+ if (mpf_cmp(f0, negepsilon) > 0) break;
+ }
+ }
+
+ mpf_clear(f0);
+ mpf_clear(a);
+}
+
+// Computes q = exp(2 pi i tau).
+static void compute_q(mpc_t q, mpc_t tau) {
+ mpc_t z0;
+ mpf_t f0, f1;
+ mpf_ptr fp0;
+ unsigned long pwr;
+
+ mpc_init(z0);
+ mpf_init(f0);
+ mpf_init(f1);
+
+ //compute z0 = 2 pi i tau
+ mpc_set(z0, tau);
+ //first remove integral part of Re(tau)
+ //since exp(2 pi i) = 1
+ //it seems |Re(tau)| < 1 anyway?
+ fp0 = mpc_re(z0);
+ mpf_trunc(f1, fp0);
+ mpf_sub(fp0, fp0, f1);
+
+ mpc_mul_mpf(z0, z0, pi);
+ mpc_mul_ui(z0, z0, 2);
+ mpc_muli(z0, z0);
+
+ //compute q = exp(z0);
+ //first write z0 = A + a + b i
+ //where A is a (negative) integer
+ //and a, b are in [-1, 1]
+ //compute e^A separately
+ fp0 = mpc_re(z0);
+ pwr = mpf_get_ui(fp0);
+ mpf_pow_ui(f0, recipeulere, pwr);
+ mpf_add_ui(fp0, fp0, pwr);
+
+ mpf_exp(f1, mpc_re(z0));
+ mpf_mul(f0, f1, f0);
+ mpc_cis(q, mpc_im(z0));
+
+ /*
+ old_mpc_exp(q, z0);
+ */
+ mpc_mul_mpf(q, q, f0);
+
+ mpc_clear(z0);
+ mpf_clear(f0);
+ mpf_clear(f1);
+}
+
+// Computes z = Delta(q) (see Cohen).
+static void compute_Delta(mpc_t z, mpc_t q) {
+ int d;
+ int n;
+ int power;
+ mpc_t z0, z1, z2;
+
+ mpc_init(z0);
+ mpc_init(z1);
+ mpc_init(z2);
+
+ mpc_set_ui(z0, 1);
+ d = -1;
+ for(n=1; n<100; n++) {
+ power = n *(3 * n - 1) / 2;
+ mpc_pow_ui(z1, q, power);
+ mpc_pow_ui(z2, q, n);
+ mpc_mul(z2, z2, z1);
+ mpc_add(z1, z1, z2);
+ if (d) {
+ mpc_sub(z0, z0, z1);
+ d = 0;
+ } else {
+ mpc_add(z0, z0, z1);
+ d = 1;
+ }
+ }
+
+ mpc_pow_ui(z0, z0, 24);
+ mpc_mul(z, z0, q);
+
+ mpc_clear(z0);
+ mpc_clear(z1);
+ mpc_clear(z2);
+}
+
+// Computes z = h(tau)
+// (called h() by Blake et al, f() by Cohen.)
+static void compute_h(mpc_t z, mpc_t tau) {
+ mpc_t z0, z1, q;
+ mpc_init(q);
+ mpc_init(z0);
+ mpc_init(z1);
+ compute_q(q, tau);
+ mpc_mul(z0, q, q);
+ compute_Delta(z0, z0);
+ compute_Delta(z1, q);
+ mpc_div(z, z0, z1);
+ mpc_clear(q);
+ mpc_clear(z0);
+ mpc_clear(z1);
+}
+
+// Computes j = j(tau).
+static void compute_j(mpc_t j, mpc_t tau) {
+ mpc_t h;
+ mpc_t z0;
+ mpc_init(h);
+ mpc_init(z0);
+ compute_h(h, tau);
+ //mpc_mul_ui(z0, h, 256);
+ mpc_mul_2exp(z0, h, 8);
+ mpc_add_ui(z0, z0, 1);
+ mpc_pow_ui(z0, z0, 3);
+ mpc_div(j, z0, h);
+ mpc_clear(z0);
+ mpc_clear(h);
+}
+
+static void compute_pi(int prec) {
+ //Chudnovsky brothers' Ramanujan formula
+ //http://www.cs.uwaterloo.ca/~alopez-o/math-faq/mathtext/node12.html
+ mpz_t k1, k2, k4, k5, d;
+ unsigned int k3 = 640320;
+ unsigned int k6 = 53360;
+ mpz_t z0, z1, z2;
+ mpq_t p, q;
+ mpf_t f1;
+ int toggle = 1;
+ int n;
+ //converges fast: each term gives over 47 bits
+ int nlimit = prec / 47 + 1;
+
+ mpz_init(k1);
+ mpz_init(k2);
+ mpz_init(k4);
+ mpz_init(k5);
+ mpz_init(d);
+ mpz_init(z0);
+ mpz_init(z1);
+ mpz_init(z2);
+ mpq_init(q);
+ mpq_init(p);
+ mpf_init(f1);
+
+ mpz_set_str(k1, "545140134", 10);
+ mpz_set_str(k2, "13591409", 10);
+ mpz_set_str(k4, "100100025", 10);
+ mpz_set_str(k5, "327843840", 10);
+
+ mpz_mul(d, k4, k5);
+ mpz_mul_2exp(d, d, 3);
+ mpq_set_ui(p, 0, 1);
+
+ for (n=0; n<nlimit; n++) {
+ mpz_fac_ui(z0, 6*n);
+ mpz_mul_ui(z1, k1, n);
+ mpz_add(z1, z1, k2);
+ mpz_mul(z0, z0, z1);
+
+ mpz_fac_ui(z1, 3*n);
+ mpz_fac_ui(z2, n);
+ mpz_pow_ui(z2, z2, 3);
+ mpz_mul(z1, z1, z2);
+ mpz_pow_ui(z2, d, n);
+ mpz_mul(z1, z1, z2);
+
+ mpz_set(mpq_numref(q), z0);
+ mpz_set(mpq_denref(q), z1);
+ mpq_canonicalize(q);
+ if (toggle) {
+ mpq_add(p, p, q);
+ } else {
+ mpq_sub(p, p, q);
+ }
+ toggle = !toggle;
+ }
+ mpq_inv(q, p);
+ mpz_mul_ui(mpq_numref(q), mpq_numref(q), k6);
+ mpq_canonicalize(q);
+ mpf_set_q(pi, q);
+ mpf_sqrt_ui(f1, k3);
+ mpf_mul(pi, pi, f1);
+ //mpf_out_str(stdout, 0, 14 * nlimit, pi);
+ //printf("\n");
+
+ mpz_clear(k1);
+ mpz_clear(k2);
+ mpz_clear(k4);
+ mpz_clear(k5);
+ mpz_clear(d);
+ mpz_clear(z0);
+ mpz_clear(z1);
+ mpz_clear(z2);
+ mpq_clear(q);
+ mpq_clear(p);
+ mpf_clear(f1);
+}
+
+static void precision_init(int prec) {
+ int i;
+ mpf_t f0;
+
+ mpf_set_default_prec(prec);
+ mpf_init2(epsilon, 2);
+ mpf_init2(negepsilon, 2);
+ mpf_init(recipeulere);
+ mpf_init(pi);
+ mpf_init(eulere);
+
+ mpf_set_ui(epsilon, 1);
+ mpf_div_2exp(epsilon, epsilon, prec);
+ mpf_neg(negepsilon, epsilon);
+
+ mpf_init(f0);
+ mpf_set_ui(eulere, 1);
+ mpf_set_ui(f0, 1);
+ for (i=1;; i++) {
+ mpf_div_ui(f0, f0, i);
+ if (mpf_cmp(f0, epsilon) < 0) {
+ break;
+ }
+ mpf_add(eulere, eulere, f0);
+ }
+ mpf_clear(f0);
+
+ mpf_ui_div(recipeulere, 1, eulere);
+
+ compute_pi(prec);
+}
+
+static void precision_clear(void) {
+ mpf_clear(eulere);
+ mpf_clear(recipeulere);
+ mpf_clear(pi);
+ mpf_clear(epsilon);
+ mpf_clear(negepsilon);
+}
+
+// See Cohen; my D is -D in his notation.
+size_t pbc_hilbert(mpz_t **arr, int D) {
+ int a, b;
+ int t;
+ int B = floor(sqrt((double) D / 3.0));
+ mpc_t alpha;
+ mpc_t j;
+ mpf_t sqrtD;
+ mpf_t f0;
+ darray_t Pz;
+ mpc_t z0, z1, z2;
+ double d = 1.0;
+ int h = 1;
+ int jcount = 1;
+
+ // Compute required precision.
+ b = D % 2;
+ for (;;) {
+ t = (b*b + D) / 4;
+ a = b;
+ if (a <= 1) {
+ a = 1;
+ goto step535_4;
+ }
+step535_3:
+ if (!(t % a)) {
+ jcount++;
+ if ((a == b) || (a*a == t) || !b) {
+ d += 1.0 / ((double) a);
+ h++;
+ } else {
+ d += 2.0 / ((double) a);
+ h+=2;
+ }
+ }
+step535_4:
+ a++;
+ if (a * a <= t) {
+ goto step535_3;
+ } else {
+ b += 2;
+ if (b > B) break;
+ }
+ }
+
+ //printf("modulus: %f\n", exp(3.14159265358979 * sqrt(D)) * d * 0.5);
+ d *= sqrt(D) * 3.14159265358979 / log(2);
+ precision_init(d + 34);
+ pbc_info("class number %d, %d bit precision", h, (int) d + 34);
+
+ darray_init(Pz);
+ mpc_init(alpha);
+ mpc_init(j);
+ mpc_init(z0);
+ mpc_init(z1);
+ mpc_init(z2);
+ mpf_init(sqrtD);
+ mpf_init(f0);
+
+ mpf_sqrt_ui(sqrtD, D);
+ b = D % 2;
+ h = 0;
+ for (;;) {
+ t = (b*b + D) / 4;
+ if (b > 1) {
+ a = b;
+ } else {
+ a = 1;
+ }
+step3:
+ if (t % a) {
+step4:
+ a++;
+ if (a * a <= t) goto step3;
+ } else {
+ // a, b, t/a are coeffs of an appropriate primitive reduced positive
+ // definite form.
+ // Compute j((-b + sqrt{-D})/(2a)).
+ h++;
+ pbc_info("[%d/%d] a b c = %d %d %d", h, jcount, a, b, t/a);
+ mpf_set_ui(f0, 1);
+ mpf_div_ui(f0, f0, 2 * a);
+ mpf_mul(mpc_im(alpha), sqrtD, f0);
+ mpf_mul_ui(f0, f0, b);
+ mpf_neg(mpc_re(alpha), f0);
+
+ compute_j(j, alpha);
+if (0) {
+ int i;
+ for (i=Pz->count - 1; i>=0; i--) {
+ printf("P %d = ", i);
+ mpc_out_str(stdout, 10, 4, Pz->item[i]);
+ printf("\n");
+ }
+}
+ if (a == b || a * a == t || !b) {
+ // P *= X - j
+ int i, n;
+ mpc_ptr p0;
+ p0 = (mpc_ptr) pbc_malloc(sizeof(mpc_t));
+ mpc_init(p0);
+ mpc_neg(p0, j);
+ n = Pz->count;
+ if (n) {
+ mpc_set(z1, Pz->item[0]);
+ mpc_add(Pz->item[0], z1, p0);
+ for (i=1; i<n; i++) {
+ mpc_mul(z0, z1, p0);
+ mpc_set(z1, Pz->item[i]);
+ mpc_add(Pz->item[i], z1, z0);
+ }
+ mpc_mul(p0, p0, z1);
+ }
+ darray_append(Pz, p0);
+ } else {
+ // P *= X^2 - 2 Re(j) X + |j|^2
+ int i, n;
+ mpc_ptr p0, p1;
+ p0 = (mpc_ptr) pbc_malloc(sizeof(mpc_t));
+ p1 = (mpc_ptr) pbc_malloc(sizeof(mpc_t));
+ mpc_init(p0);
+ mpc_init(p1);
+ // p1 = - 2 Re(j)
+ mpf_mul_ui(f0, mpc_re(j), 2);
+ mpf_neg(f0, f0);
+ mpf_set(mpc_re(p1), f0);
+ // p0 = |j|^2
+ mpf_mul(f0, mpc_re(j), mpc_re(j));
+ mpf_mul(mpc_re(p0), mpc_im(j), mpc_im(j));
+ mpf_add(mpc_re(p0), mpc_re(p0), f0);
+ n = Pz->count;
+ if (!n) {
+ } else if (n == 1) {
+ mpc_set(z1, Pz->item[0]);
+ mpc_add(Pz->item[0], z1, p1);
+ mpc_mul(p1, z1, p1);
+ mpc_add(p1, p1, p0);
+ mpc_mul(p0, p0, z1);
+ } else {
+ mpc_set(z2, Pz->item[0]);
+ mpc_set(z1, Pz->item[1]);
+ mpc_add(Pz->item[0], z2, p1);
+ mpc_mul(z0, z2, p1);
+ mpc_add(Pz->item[1], z1, z0);
+ mpc_add(Pz->item[1], Pz->item[1], p0);
+ for (i=2; i<n; i++) {
+ mpc_mul(z0, z1, p1);
+ mpc_mul(alpha, z2, p0);
+ mpc_set(z2, z1);
+ mpc_set(z1, Pz->item[i]);
+ mpc_add(alpha, alpha, z0);
+ mpc_add(Pz->item[i], z1, alpha);
+ }
+ mpc_mul(z0, z2, p0);
+ mpc_mul(p1, p1, z1);
+ mpc_add(p1, p1, z0);
+ mpc_mul(p0, p0, z1);
+ }
+ darray_append(Pz, p1);
+ darray_append(Pz, p0);
+ }
+ goto step4;
+ }
+ b+=2;
+ if (b > B) break;
+ }
+
+ // Round polynomial and assign.
+ int k = 0;
+ {
+ *arr = pbc_malloc(sizeof(mpz_t) * (Pz->count + 1));
+ int i;
+ for (i=Pz->count - 1; i>=0; i--) {
+ if (mpf_sgn(mpc_re(Pz->item[i])) < 0) {
+ mpf_set_d(f0, -0.5);
+ } else {
+ mpf_set_d(f0, 0.5);
+ }
+ mpf_add(f0, f0, mpc_re(Pz->item[i]));
+ mpz_init((*arr)[k]);
+ mpz_set_f((*arr)[k], f0);
+ k++;
+ mpc_clear(Pz->item[i]);
+ pbc_free(Pz->item[i]);
+ }
+ mpz_init((*arr)[k]);
+ mpz_set_ui((*arr)[k], 1);
+ k++;
+ }
+ darray_clear(Pz);
+ mpc_clear(z0);
+ mpc_clear(z1);
+ mpc_clear(z2);
+ mpf_clear(f0);
+ mpf_clear(sqrtD);
+ mpc_clear(alpha);
+ mpc_clear(j);
+
+ precision_clear();
+ return k;
+}
+
+void pbc_hilbert_free(mpz_t *arr, size_t n) {
+ size_t i;
+
+ for (i = 0; i < n; i++) mpz_clear(arr[i]);
+ pbc_free(arr);
+}