int main(void) { int i, result; flint_rand_t state; printf("shift_left/right...."); fflush(stdout); flint_randinit(state); /* Check aliasing of a and b for left shift */ for (i = 0; i < 1000; i++) { acb_poly_t a, b; long shift = n_randint(state, 100); acb_poly_init(a); acb_poly_init(b); acb_poly_randtest(a, state, n_randint(state, 100), 2 + n_randint(state, 200), 10); acb_poly_shift_left(b, a, shift); acb_poly_shift_left(a, a, shift); result = (acb_poly_equal(a, b)); if (!result) { printf("FAIL:\n"); acb_poly_printd(a, 10), printf("\n\n"); acb_poly_printd(b, 10), printf("\n\n"); abort(); } acb_poly_clear(a); acb_poly_clear(b); } /* Check aliasing of a and b for right shift */ for (i = 0; i < 1000; i++) { acb_poly_t a, b; long shift = n_randint(state, 100); acb_poly_init(a); acb_poly_init(b); acb_poly_randtest(a, state, n_randint(state, 100), 2 + n_randint(state, 200), 10); acb_poly_shift_right(b, a, shift); acb_poly_shift_right(a, a, shift); result = (acb_poly_equal(a, b)); if (!result) { printf("FAIL:\n"); acb_poly_printd(a, 10), printf("\n\n"); acb_poly_printd(b, 10), printf("\n\n"); abort(); } acb_poly_clear(a); acb_poly_clear(b); } /* Check shift left then right does nothing */ for (i = 0; i < 1000; i++) { acb_poly_t a, b, c; long shift = n_randint(state, 100); acb_poly_init(a); acb_poly_init(b); acb_poly_init(c); acb_poly_randtest(a, state, n_randint(state, 100), 2 + n_randint(state, 200), 10); acb_poly_shift_left(b, a, shift); acb_poly_shift_right(c, b, shift); result = (acb_poly_equal(c, a)); if (!result) { printf("FAIL:\n"); acb_poly_printd(a, 10), printf("\n\n"); acb_poly_printd(b, 10), printf("\n\n"); acb_poly_printd(c, 10), printf("\n\n"); abort(); } acb_poly_clear(a); acb_poly_clear(b); acb_poly_clear(c); } flint_randclear(state); flint_cleanup(); printf("PASS\n"); return 0; }
void acb_hypgeom_bessel_k_0f1_series(acb_poly_t res, const acb_poly_t nu, const acb_poly_t z, slong len, slong prec) { acb_poly_t s, u, A, B; acb_poly_struct b[2]; arb_t c; slong wlen; int singular; acb_poly_init(s); acb_poly_init(u); acb_poly_init(A); acb_poly_init(B); acb_poly_init(b + 0); acb_poly_init(b + 1); arb_init(c); singular = (nu->length == 0) || acb_is_int(nu->coeffs); wlen = len + (singular != 0); /* A = (z/2)^nu, B = 1/A */ acb_poly_scalar_mul_2exp_si(A, z, -1); acb_poly_pow_series(A, A, nu, wlen, prec); acb_poly_inv_series(B, A, wlen, prec); acb_poly_mullow(u, z, z, wlen, prec); acb_poly_scalar_mul_2exp_si(u, u, -2); acb_poly_one(b + 1); acb_poly_add_si(b + 0, nu, 1, prec); acb_hypgeom_pfq_series_direct(s, NULL, 0, b, 2, u, 1, -1, wlen, prec); acb_poly_mullow(A, A, s, wlen, prec); acb_poly_add_si(b + 0, nu, -1, prec); acb_poly_neg(b + 0, b + 0); acb_hypgeom_pfq_series_direct(s, NULL, 0, b, 2, u, 1, -1, wlen, prec); acb_poly_mullow(B, B, s, wlen, prec); acb_poly_sub(A, B, A, prec); acb_poly_scalar_mul_2exp_si(A, A, -1); /* multiply by pi csc(pi nu) */ acb_poly_sin_pi_series(B, nu, wlen, prec); if (singular) { acb_poly_shift_right(A, A, 1); acb_poly_shift_right(B, B, 1); } acb_poly_div_series(res, A, B, len, prec); arb_const_pi(c, prec); _acb_vec_scalar_mul_arb(res->coeffs, res->coeffs, res->length, c, prec); acb_poly_clear(s); acb_poly_clear(u); acb_poly_clear(A); acb_poly_clear(B); acb_poly_clear(b + 0); acb_poly_clear(b + 1); arb_clear(c); }
void acb_hypgeom_u_1f1_series(acb_poly_t res, const acb_poly_t a, const acb_poly_t b, const acb_poly_t z, long len, long prec) { acb_poly_t s, u, A, B; acb_poly_struct aa[3]; arb_t c; long wlen; int singular; acb_poly_init(s); acb_poly_init(u); acb_poly_init(A); acb_poly_init(B); acb_poly_init(aa + 0); acb_poly_init(aa + 1); acb_poly_init(aa + 2); arb_init(c); singular = (b->length == 0) || acb_is_int(b->coeffs); wlen = len + (singular != 0); /* A = rgamma(a-b+1) * 1F~1(a,b,z) */ acb_poly_sub(u, a, b, prec); acb_poly_add_si(u, u, 1, prec); acb_poly_rgamma_series(A, u, wlen, prec); /* todo: handle a = 1 efficiently */ acb_poly_set(aa, a); acb_poly_set(aa + 1, b); acb_poly_one(aa + 2); acb_hypgeom_pfq_series_direct(s, aa, 1, aa + 1, 2, z, 1, -1, wlen, prec); acb_poly_mullow(A, A, s, wlen, prec); /* B = rgamma(a) * 1F~1(a-b+1,2-b,z) * z^(1-b) */ acb_poly_set(aa, u); acb_poly_add_si(aa + 1, b, -2, prec); acb_poly_neg(aa + 1, aa + 1); acb_hypgeom_pfq_series_direct(s, aa, 1, aa + 1, 2, z, 1, -1, wlen, prec); acb_poly_rgamma_series(B, a, wlen, prec); acb_poly_mullow(B, B, s, wlen, prec); acb_poly_add_si(u, b, -1, prec); acb_poly_neg(u, u); acb_poly_pow_series(s, z, u, wlen, prec); acb_poly_mullow(B, B, s, wlen, prec); acb_poly_sub(A, A, B, prec); /* multiply by pi csc(pi b) */ acb_poly_sin_pi_series(B, b, wlen, prec); if (singular) { acb_poly_shift_right(A, A, 1); acb_poly_shift_right(B, B, 1); } acb_poly_div_series(res, A, B, len, prec); arb_const_pi(c, prec); _acb_vec_scalar_mul_arb(res->coeffs, res->coeffs, res->length, c, prec); acb_poly_clear(s); acb_poly_clear(u); acb_poly_clear(A); acb_poly_clear(B); acb_poly_clear(aa + 0); acb_poly_clear(aa + 1); acb_poly_clear(aa + 2); arb_clear(c); }