void test_field1(flint_rand_t state) { /* tests in QQ[sqrt(5)] */ int iter; fmpq_t k; fmpq_poly_t p; arb_t emb; renf_t nf; renf_elem_t a; fmpq_poly_init(p); fmpq_poly_set_coeff_si(p, 2, 1); fmpq_poly_set_coeff_si(p, 1, -1); fmpq_poly_set_coeff_si(p, 0, -1); arb_init(emb); arb_set_d(emb, 1.61803398874989); arb_add_error_2exp_si(emb, -20); renf_init(nf, p, emb, 20 + n_randint(state, 20)); arb_clear(emb); renf_elem_init(a, nf); fmpq_init(k); /* (1+sqrt(5))/2 vs Fibonacci */ fmpq_poly_zero(p); fmpq_poly_set_coeff_si(p, 1, -1); for (iter = 1; iter < 50; iter++) { fprintf(stderr, "start iter = %d\n", iter); fflush(stderr); fmpz_fib_ui(fmpq_numref(k), iter+1); fmpz_fib_ui(fmpq_denref(k), iter); fmpq_poly_set_coeff_fmpq(p, 0, k); renf_elem_set_fmpq_poly(a, p, nf); check_ceil(a, nf, 1 - iter % 2, "sqrt(5)"); fprintf(stderr, "end\n"); fflush(stderr); } renf_elem_clear(a, nf); renf_clear(nf); fmpq_clear(k); fmpq_poly_clear(p); }
void test_field2(flint_rand_t state) { /* test in QQ[3^(1/4)] */ renf_t nf; renf_elem_t a; fmpq_t d, k; fmpq_poly_t p; fmpq_init(d); fmpq_poly_init(p); fmpq_set_si(d, 3, 1); renf_init_nth_root_fmpq(nf, d, 4, 10 + n_randint(state, 10)); fmpq_clear(d); fmpq_init(k); renf_elem_init(a, nf); /* test rationals */ /* --> 3^(1/4) */ fmpq_poly_set_coeff_si(p, 1, 1); renf_elem_set_fmpq_poly(a, p, nf); check_ceil(a, nf, 2, "3^(1/4)"); /* --> 3^(1/4) - p_34 / q_34 */ /* ceil = 1 */ fmpz_set_str(fmpq_numref(k), "3871793620206447926", 10); fmpz_set_str(fmpq_denref(k), "2941926960111028069", 10); fmpq_neg(k, k); fmpq_poly_set_coeff_fmpq(p, 0, k); renf_elem_set_fmpq_poly(a, p, nf); check_ceil(a, nf, 1, "3^(1/4)"); /* --> 3^(1/4) - p_35 / q_35 */ /* ceil = 0 */ fmpz_set_str(fmpq_numref(k), "4393442218385055959", 10); fmpz_set_str(fmpq_denref(k), "3338294180377262795", 10); fmpq_neg(k, k); fmpq_poly_set_coeff_fmpq(p, 0, k); renf_elem_set_fmpq_poly(a, p, nf); check_ceil(a, nf, 0, "3^(1/4)"); /* --> 3^(1/4) - p_200 / q_200 */ fmpz_set_str(fmpq_numref(k), "51566086581654990699052199424489069476470199719930170996263916596162993841059250500042162091", 10); fmpz_set_str(fmpq_denref(k), "39181752754141206003124111890355840072199542360218864430892618765033598468868752146602163065", 10); fmpq_neg(k, k); fmpq_poly_set_coeff_fmpq(p, 0, k); renf_elem_set_fmpq_poly(a, p, nf); check_ceil(a, nf, 1, "3^(1/4)"); /* --> 3^(1/4) - p_201 / q_201 */ fmpz_set_str(fmpq_numref(k), "80796322887694335717970676356641716096406222234122724217891106756946083353628876437327250032", 10); fmpz_set_str(fmpq_denref(k), "61391929399498685496270115285641595325756438975454257165479021482386018841773493669624721869", 10); fmpq_neg(k, k); fmpq_poly_set_coeff_fmpq(p, 0, k); renf_elem_set_fmpq_poly(a, p, nf); check_ceil(a, nf, 0, "3^(1/4)"); /* */ fmpz_set_str(fmpq_numref(k), "13231942875843754343234", 10); fmpz_set_str(fmpq_denref(k), "14321431341231112121", 10); fmpq_poly_set_coeff_fmpq(p, 3, k); fmpz_set_str(fmpq_numref(k), "148589873455543948591", 10); fmpz_set_str(fmpq_denref(k), "12332111221111", 10); fmpq_neg(k, k); fmpq_poly_set_coeff_fmpq(p, 2, k); fmpz_set_str(fmpq_numref(k), "1233321469998711012392391", 10); fmpz_set_str(fmpq_denref(k), "11814121556810191", 10); fmpq_poly_set_coeff_fmpq(p, 1, k); fmpz_set_str(fmpq_numref(k), "1249152314425433983202991363672458443993964487436329478959287771807457205881969983777233465754608376177969464841", 10); fmpz_set_str(fmpq_denref(k), "10720278662399817731713810382544982753044312944075797382817281426908463944866446042500978893159281330135", 10); fmpq_neg(k, k); fmpq_poly_set_coeff_fmpq(p, 0, k); renf_elem_set_fmpq_poly(a, p, nf); check_ceil(a, nf, 231, "3^(1/4)"); renf_elem_clear(a, nf); renf_clear(nf); fmpq_clear(k); fmpq_poly_clear(p); }
int main() { slong iter; FLINT_TEST_INIT(state); { ulong k; arb_t a,b; arf_t c,d; fmpq_poly_t p; arb_init(a); arb_init(b); arf_init(c); arf_init(d); /* x+1 */ fmpq_poly_init(p); fmpq_poly_set_coeff_si(p, 0, 1); fmpq_poly_set_coeff_si(p, 1, 1); for (iter = 0; iter < 5000; iter++) { k = n_randint(state, 10000); arb_set_si(a, k); fmpq_poly_evaluate_arb(b, p, a, 30 + n_randint(state, 100)); if (!arb_equal_si(b, k + 1)) { printf("FAIL (fmpq_poly_evaluate_arb):\n"); printf("a = "); arb_print(a); printf("\n"); printf("b = "); arb_print(b); printf("\n"); printf("p = "); fmpq_poly_print(p); printf("\n"); abort(); } arf_set_si(c, k); fmpq_poly_evaluate_arf(d, p, c, 30 + n_randint(state, 100)); if (!arf_equal_si(d, k + 1)) { printf("FAIL (fmpq_poly_evaluate_arf):\n"); printf("c = "); arf_print(c); printf("\n"); printf("d = "); arf_print(d); printf("\n"); printf("p = "); fmpq_poly_print(p); printf("\n"); abort(); } } /* x^2 */ fmpq_poly_zero(p); fmpq_poly_set_coeff_si(p, 2, 1); for (iter = 0; iter < 1000; iter++) { k = n_randint(state, 10000); arb_set_si(a, k); fmpq_poly_evaluate_arb(b, p, a, 30 + n_randint(state, 100)); if (!arb_equal_si(b, k * k)) { printf("Error (test_fmpq_poly_evaluate_arb):\n"); printf("a = "); arb_print(a); printf("\n"); printf("b = "); arb_print(b); printf("\n"); printf("p = "); fmpq_poly_print(p); printf("\n"); abort(); } arf_set_si(c, k); fmpq_poly_evaluate_arf(d, p, c, 30 + n_randint(state, 100)); if (!arf_equal_si(d, k * k)) { printf("Error (test_fmpq_poly_evaluate_arf):\n"); printf("c = "); arf_print(c); printf("\n"); printf("d = "); arf_print(d); printf("\n"); printf("p = "); fmpq_poly_print(p); printf("\n"); abort(); } } fmpq_poly_clear(p); arb_clear(a); arb_clear(b); arf_clear(c); arf_clear(d); } /* check evaluate_arb agains exact evaluate_fmpq */ for (iter = 0; iter < 1000; iter++) { fmpq_poly_t p; fmpq_t x,y; arb_t a,b; fmpq_poly_init(p); fmpq_init(x); fmpq_init(y); arb_init(a); arb_init(b); fmpq_poly_randtest(p, state, 1 + n_randint(state,100), 10); fmpq_randtest(x, state, 10); arb_set_fmpq(a, x, 64); fmpq_poly_evaluate_fmpq(y, p, x); fmpq_poly_evaluate_arb(b, p, a, 60); if (!arb_contains_fmpq(b, y)) { printf("FAIL (y not in b):\n"); printf("p = "); fmpq_poly_print(p); printf("\n"); printf("x = "); fmpq_print(x); printf("\n"); printf("y = "); fmpq_print(y); printf("\n"); printf("a = "); arb_print(a); printf("\n"); printf("b = "); arb_print(b); printf("\n"); abort(); } fmpq_poly_evaluate_arb(a, p, a, 60); if (!arb_equal(a,b)) { printf("FAIL (a not equal b):\n"); printf("p = "); fmpq_poly_print(p); printf("\n"); printf("x = "); fmpq_print(x); printf("\n"); printf("y = "); fmpq_print(y); printf("\n"); printf("a = "); arb_print(a); printf("\n"); printf("b = "); arb_print(b); printf("\n"); abort(); } fmpq_poly_clear(p); fmpq_clear(x); fmpq_clear(y); arb_clear(a); arb_clear(b); } /* test aliasing */ for (iter = 0; iter < 1000; iter++) { fmpq_poly_t p; arb_t a,b; arf_t c,d; fmpq_poly_init(p); arb_init(a); arb_init(b); arf_init(c); arf_init(d); fmpq_poly_randtest(p, state, 1 + n_randint(state,100), 10); arb_randtest(a, state, 60, 10); arb_randtest(b, state, 60, 10); arf_randtest(c, state, 60, 10); arf_randtest(d, state, 60, 10); fmpq_poly_evaluate_arb(b, p, a, 60); fmpq_poly_evaluate_arb(a, p, a, 60); if (!arb_equal(a, b)) { printf("FAIL (a not equal b):\n"); printf("p = "); fmpq_poly_print(p); printf("\n"); printf("a = "); arb_print(a); printf("\n"); printf("b = "); arb_print(b); printf("\n"); abort(); } fmpq_poly_evaluate_arf(d, p, c, 60); fmpq_poly_evaluate_arf(c, p, c, 60); if (!arf_equal(c, d)) { printf("FAIL (c not equal d):\n"); printf("p = "); fmpq_poly_print(p); printf("\n"); printf("c = "); arf_print(c); printf("\n"); printf("d = "); arf_print(d); printf("\n"); } fmpq_poly_clear(p); arb_clear(a); arb_clear(b); arf_clear(c); arf_clear(d); } FLINT_TEST_CLEANUP(state); return 0; }
int main(int argc, char *argv[]) { fmpz_poly_t f, g; fmpz_poly_factor_t fac; fmpz_t t; slong compd, printd, i, j; if (argc < 2) { flint_printf("poly_roots [-refine d] [-print d] <poly>\n\n"); flint_printf("Isolates all the complex roots of a polynomial with integer coefficients.\n\n"); flint_printf("If -refine d is passed, the roots are refined to an absolute tolerance\n"); flint_printf("better than 10^(-d). By default, the roots are only computed to sufficient\n"); flint_printf("accuracy to isolate them. The refinement is not currently done efficiently.\n\n"); flint_printf("If -print d is passed, the computed roots are printed to d decimals.\n"); flint_printf("By default, the roots are not printed.\n\n"); flint_printf("The polynomial can be specified by passing the following as <poly>:\n\n"); flint_printf("a <n> Easy polynomial 1 + 2x + ... + (n+1)x^n\n"); flint_printf("t <n> Chebyshev polynomial T_n\n"); flint_printf("u <n> Chebyshev polynomial U_n\n"); flint_printf("p <n> Legendre polynomial P_n\n"); flint_printf("c <n> Cyclotomic polynomial Phi_n\n"); flint_printf("s <n> Swinnerton-Dyer polynomial S_n\n"); flint_printf("b <n> Bernoulli polynomial B_n\n"); flint_printf("w <n> Wilkinson polynomial W_n\n"); flint_printf("e <n> Taylor series of exp(x) truncated to degree n\n"); flint_printf("m <n> <m> The Mignotte-like polynomial x^n + (100x+1)^m, n > m\n"); flint_printf("coeffs <c0 c1 ... cn> c0 + c1 x + ... + cn x^n\n\n"); flint_printf("Concatenate to multiply polynomials, e.g.: p 5 t 6 coeffs 1 2 3\n"); flint_printf("for P_5(x)*T_6(x)*(1+2x+3x^2)\n\n"); return 1; } compd = 0; printd = 0; fmpz_poly_init(f); fmpz_poly_init(g); fmpz_init(t); fmpz_poly_one(f); for (i = 1; i < argc; i++) { if (!strcmp(argv[i], "-refine")) { compd = atol(argv[i+1]); i++; } else if (!strcmp(argv[i], "-print")) { printd = atol(argv[i+1]); i++; } else if (!strcmp(argv[i], "a")) { slong n = atol(argv[i+1]); fmpz_poly_zero(g); for (j = 0; j <= n; j++) fmpz_poly_set_coeff_ui(g, j, j+1); fmpz_poly_mul(f, f, g); i++; } else if (!strcmp(argv[i], "t")) { arith_chebyshev_t_polynomial(g, atol(argv[i+1])); fmpz_poly_mul(f, f, g); i++; } else if (!strcmp(argv[i], "u")) { arith_chebyshev_u_polynomial(g, atol(argv[i+1])); fmpz_poly_mul(f, f, g); i++; } else if (!strcmp(argv[i], "p")) { fmpq_poly_t h; fmpq_poly_init(h); arith_legendre_polynomial(h, atol(argv[i+1])); fmpq_poly_get_numerator(g, h); fmpz_poly_mul(f, f, g); fmpq_poly_clear(h); i++; } else if (!strcmp(argv[i], "c")) { arith_cyclotomic_polynomial(g, atol(argv[i+1])); fmpz_poly_mul(f, f, g); i++; } else if (!strcmp(argv[i], "s")) { arith_swinnerton_dyer_polynomial(g, atol(argv[i+1])); fmpz_poly_mul(f, f, g); i++; } else if (!strcmp(argv[i], "b")) { fmpq_poly_t h; fmpq_poly_init(h); arith_bernoulli_polynomial(h, atol(argv[i+1])); fmpq_poly_get_numerator(g, h); fmpz_poly_mul(f, f, g); fmpq_poly_clear(h); i++; } else if (!strcmp(argv[i], "w")) { slong n = atol(argv[i+1]); fmpz_poly_zero(g); fmpz_poly_fit_length(g, n+2); arith_stirling_number_1_vec(g->coeffs, n+1, n+2); _fmpz_poly_set_length(g, n+2); fmpz_poly_shift_right(g, g, 1); fmpz_poly_mul(f, f, g); i++; } else if (!strcmp(argv[i], "e")) { fmpq_poly_t h; fmpq_poly_init(h); fmpq_poly_set_coeff_si(h, 0, 0); fmpq_poly_set_coeff_si(h, 1, 1); fmpq_poly_exp_series(h, h, atol(argv[i+1]) + 1); fmpq_poly_get_numerator(g, h); fmpz_poly_mul(f, f, g); fmpq_poly_clear(h); i++; } else if (!strcmp(argv[i], "m")) { fmpz_poly_zero(g); fmpz_poly_set_coeff_ui(g, 0, 1); fmpz_poly_set_coeff_ui(g, 1, 100); fmpz_poly_pow(g, g, atol(argv[i+2])); fmpz_poly_set_coeff_ui(g, atol(argv[i+1]), 1); fmpz_poly_mul(f, f, g); i += 2; } else if (!strcmp(argv[i], "coeffs")) { fmpz_poly_zero(g); i++; j = 0; while (i < argc) { if (fmpz_set_str(t, argv[i], 10) != 0) { i--; break; } fmpz_poly_set_coeff_fmpz(g, j, t); i++; j++; } fmpz_poly_mul(f, f, g); } } fmpz_poly_factor_init(fac); flint_printf("computing squarefree factorization...\n"); TIMEIT_ONCE_START fmpz_poly_factor_squarefree(fac, f); TIMEIT_ONCE_STOP TIMEIT_ONCE_START for (i = 0; i < fac->num; i++) { flint_printf("roots with multiplicity %wd\n", fac->exp[i]); fmpz_poly_complex_roots_squarefree(fac->p + i, 32, compd * 3.32193 + 2, printd); } TIMEIT_ONCE_STOP fmpz_poly_factor_clear(fac); fmpz_poly_clear(f); fmpz_poly_clear(g); fmpz_clear(t); flint_cleanup(); return EXIT_SUCCESS; }
int fmpq_poly_oz_sqrt_approx_pade(fmpq_poly_t f_sqrt, const fmpq_poly_t f, const long n, const int p, const mpfr_prec_t prec, const mpfr_prec_t bound, oz_flag_t flags, const fmpq_poly_t init) { fmpq_poly_t y; fmpq_poly_init(y); fmpq_poly_t y_next; fmpq_poly_init(y_next); fmpq_poly_t z; fmpq_poly_init(z); fmpq_poly_t z_next; fmpq_poly_init(z_next); mpfr_t norm; mpfr_init2(norm, prec); mpfr_t prev_norm; mpfr_init2(prev_norm, prec); mpfr_t log_f; mpfr_init2(log_f, prec); if (init) { // z = y/x fmpq_poly_set(y, init); _fmpq_poly_oz_invert_approx(z, f, n, prec); fmpq_poly_oz_mul(z, z, y, n); } else { fmpq_poly_set(y, f); fmpq_poly_set_coeff_si(z, 0, 1); } fmpq_t *xi = (fmpq_t*)calloc(p, sizeof(fmpq_t)); fmpq_t *a2 = (fmpq_t*)calloc(p, sizeof(fmpq_t)); fmpq_t *c = (fmpq_t*)calloc(p, sizeof(fmpq_t)); fmpq_poly_t *t_ = (fmpq_poly_t*)calloc(p, sizeof(fmpq_poly_t)); fmpq_poly_t *s_ = (fmpq_poly_t*)calloc(p, sizeof(fmpq_poly_t)); mpfr_t pi; mpfr_init2(pi, 4*prec); mpfr_const_pi(pi, MPFR_RNDN); #pragma omp parallel for for(int i=0; i<p; i++) { mpfr_t xi_r; mpfr_init2(xi_r, 4*prec); mpfr_t a2_r; mpfr_init2(a2_r, 4*prec); /* ζ_i = 1/2 * (1 + cos( (2·i -1)·π/(2·p) )) */ mpfr_set_si(xi_r, 2*i+1, MPFR_RNDN); mpfr_mul(xi_r, xi_r, pi, MPFR_RNDN); mpfr_div_si(xi_r, xi_r, 2*p, MPFR_RNDN); mpfr_cos(xi_r, xi_r, MPFR_RNDN); mpfr_add_si(xi_r, xi_r, 1, MPFR_RNDN); mpfr_div_si(xi_r, xi_r, 2, MPFR_RNDN); /* α_i^2 = 1/ζ_i -1 */ mpfr_set_si(a2_r, 1, MPFR_RNDN); mpfr_div(a2_r, a2_r, xi_r, MPFR_RNDN); mpfr_sub_si(a2_r, a2_r, 1, MPFR_RNDN); fmpq_init(xi[i]); fmpq_init(a2[i]); fmpq_set_mpfr(xi[i], xi_r, MPFR_RNDN); fmpq_set_mpfr(a2[i], a2_r, MPFR_RNDN); fmpq_init(c[i]); fmpq_poly_init(t_[i]); fmpq_poly_init(s_[i]); mpfr_clear(xi_r); mpfr_clear(a2_r); } mpfr_clear(pi); uint64_t t = oz_walltime(0); int r = 0; int cont = 1; for(long k=0; cont; k++) { if (k == 0 || mpfr_cmp_ui(prev_norm, 1) > 0) _fmpq_poly_oz_sqrt_approx_scale(y, z, n, prec); /* T = sum([1/xi[i] * ~(Z*Y + a2[i]) for i in range(p)]) */ #pragma omp parallel for for(int i=0; i<p; i++) { fmpq_poly_oz_mul(t_[i], z, y, n); fmpq_poly_get_coeff_fmpq(c[i], t_[i], 0); fmpq_add(c[i], c[i], a2[i]); fmpq_poly_set_coeff_fmpq(t_[i], 0, c[i]); fmpq_poly_scalar_mul_fmpq(t_[i], t_[i], xi[i]); _fmpq_poly_oz_invert_approx(s_[i], t_[i], n, prec); } for(int i=1; i<p; i++) fmpq_poly_add(s_[0], s_[0], s_[i]); #pragma omp parallel sections { #pragma omp section { fmpq_poly_oz_mul(y_next, y, s_[0], n); fmpq_poly_scalar_div_si(y_next, y_next, p); fmpq_poly_set(y, y_next); } #pragma omp section { fmpq_poly_oz_mul(z_next, z, s_[0], n); fmpq_poly_scalar_div_si(z_next, z_next, p); fmpq_poly_set(z, z_next); } } cont = !_fmpq_poly_oz_sqrt_approx_break(norm, y, f, n, bound, prec); if(flags & OZ_VERBOSE) { mpfr_log2(log_f, norm, MPFR_RNDN); mpfr_fprintf(stderr, "Computing sqrt(Σ):: k: %4d, Δ=|sqrt(Σ)^2-Σ|: %7.2Rf", k, log_f); fprintf(stderr, " <? %4ld, ", -bound); fprintf(stderr, "t: %8.2fs\n", oz_seconds(oz_walltime(t))); fflush(0); } if (cont) { if (k>0 && mpfr_cmp_ui_2exp(norm, 1, bound) >= 0) { /* something went really wrong */ r = -1; break; } if (k>0 && mpfr_cmp(norm, prev_norm) >= 0) { /* we don't converge any more */ r = 1; break; } mpfr_set(prev_norm, norm, MPFR_RNDN); } } for(int i=0; i<p; i++) { fmpq_clear(xi[i]); fmpq_clear(a2[i]); fmpq_clear(c[i]); fmpq_poly_clear(t_[i]); fmpq_poly_clear(s_[i]); } free(xi); free(a2); free(c); free(t_); free(s_); mpfr_clear(log_f); fmpq_poly_set(f_sqrt, y); mpfr_clear(norm); mpfr_clear(prev_norm); fmpq_poly_clear(y_next); fmpq_poly_clear(y); fmpq_poly_clear(z_next); fmpq_poly_clear(z); return r; }
int fmpq_poly_oz_sqrt_approx_db(fmpq_poly_t f_sqrt, const fmpq_poly_t f, const long n, const mpfr_prec_t prec, const mpfr_prec_t bound, oz_flag_t flags, const fmpq_poly_t init) { fmpq_poly_t y; fmpq_poly_init(y); fmpq_poly_t y_next; fmpq_poly_init(y_next); fmpq_poly_t z; fmpq_poly_init(z); fmpq_poly_t z_next; fmpq_poly_init(z_next); mpfr_t norm; mpfr_init2(norm, prec); mpfr_t prev_norm; mpfr_init2(prev_norm, prec); mpfr_t log_f; mpfr_init2(log_f, prec); uint64_t t = oz_walltime(0); if (init) { // z = y/x fmpq_poly_set(y, init); _fmpq_poly_oz_invert_approx(z, f, n, prec); fmpq_poly_oz_mul(z, z, y, n); } else { fmpq_poly_set(y, f); fmpq_poly_set_coeff_si(z, 0, 1); } int r = 0; for(long k=0; ; k++) { if (k == 0 || mpfr_cmp_ui(prev_norm, 1) > 0) _fmpq_poly_oz_sqrt_approx_scale(y, z, n, prec); #pragma omp parallel sections { #pragma omp section { _fmpq_poly_oz_invert_approx(y_next, z, n, prec); fmpq_poly_add(y_next, y_next, y); fmpq_poly_scalar_div_si(y_next, y_next, 2); flint_cleanup(); } #pragma omp section { _fmpq_poly_oz_invert_approx(z_next, y, n, prec); fmpq_poly_add(z_next, z_next, z); fmpq_poly_scalar_div_si(z_next, z_next, 2); flint_cleanup(); } } fmpq_poly_set(y, y_next); fmpq_poly_set(z, z_next); r = _fmpq_poly_oz_sqrt_approx_break(norm, y, f, n, bound, prec); if(flags & OZ_VERBOSE) { mpfr_log2(log_f, norm, MPFR_RNDN); mpfr_fprintf(stderr, "Computing sqrt(Σ):: k: %4d, Δ=|sqrt(Σ)^2-Σ|: %7.2Rf", k, log_f); fprintf(stderr, " <? %4ld, ", -bound); fprintf(stderr, "t: %8.2fs\n", oz_seconds(oz_walltime(t))); fflush(0); } if(r) { r = 0; break; } if (k>0 && mpfr_cmp_ui_2exp(norm, 1, bound) >= 0) { /* something went really wrong */ r = -1; break; } mpfr_div_ui(prev_norm, prev_norm, 2, MPFR_RNDN); if (k>0 && mpfr_cmp(norm, prev_norm) >= 0) { /* we don't converge any more */ r = 1; break; } mpfr_set(prev_norm, norm, MPFR_RNDN); } mpfr_clear(log_f); fmpq_poly_set(f_sqrt, y); mpfr_clear(norm); mpfr_clear(prev_norm); fmpq_poly_clear(y_next); fmpq_poly_clear(y); fmpq_poly_clear(z_next); fmpq_poly_clear(z); return r; }