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-rw-r--r--moon-abe/pbc-0.5.14/ecc/hilbert.c539
1 files changed, 0 insertions, 539 deletions
diff --git a/moon-abe/pbc-0.5.14/ecc/hilbert.c b/moon-abe/pbc-0.5.14/ecc/hilbert.c
deleted file mode 100644
index 753e70e0..00000000
--- a/moon-abe/pbc-0.5.14/ecc/hilbert.c
+++ /dev/null
@@ -1,539 +0,0 @@
-#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);
-}