void _arb_poly_mullow_block(arb_ptr z, arb_srcptr x, slong xlen, arb_srcptr y, slong ylen, slong n, slong prec) { slong xmlen, xrlen, ymlen, yrlen, i; fmpz *xz, *yz, *zz; fmpz *xe, *ye; slong *xblocks, *yblocks; int squaring; fmpz_t scale, t; xlen = FLINT_MIN(xlen, n); ylen = FLINT_MIN(ylen, n); squaring = (x == y) && (xlen == ylen); /* Strip trailing zeros */ xmlen = xrlen = xlen; while (xmlen > 0 && arf_is_zero(arb_midref(x + xmlen - 1))) xmlen--; while (xrlen > 0 && mag_is_zero(arb_radref(x + xrlen - 1))) xrlen--; if (squaring) { ymlen = xmlen; yrlen = xrlen; } else { ymlen = yrlen = ylen; while (ymlen > 0 && arf_is_zero(arb_midref(y + ymlen - 1))) ymlen--; while (yrlen > 0 && mag_is_zero(arb_radref(y + yrlen - 1))) yrlen--; } /* We don't know how to deal with infinities or NaNs */ if (!_arb_vec_is_finite(x, xlen) || (!squaring && !_arb_vec_is_finite(y, ylen))) { _arb_poly_mullow_classical(z, x, xlen, y, ylen, n, prec); return; } xlen = FLINT_MAX(xmlen, xrlen); ylen = FLINT_MAX(ymlen, yrlen); /* Start with the zero polynomial */ _arb_vec_zero(z, n); /* Nothing to do */ if (xlen == 0 || ylen == 0) return; n = FLINT_MIN(n, xlen + ylen - 1); fmpz_init(scale); fmpz_init(t); xz = _fmpz_vec_init(xlen); yz = _fmpz_vec_init(ylen); zz = _fmpz_vec_init(n); xe = _fmpz_vec_init(xlen); ye = _fmpz_vec_init(ylen); xblocks = flint_malloc(sizeof(slong) * (xlen + 1)); yblocks = flint_malloc(sizeof(slong) * (ylen + 1)); _arb_poly_get_scale(scale, x, xlen, y, ylen); /* Error propagation */ /* (xm + xr)*(ym + yr) = (xm*ym) + (xr*ym + xm*yr + xr*yr) = (xm*ym) + (xm*yr + xr*(ym + yr)) */ if (xrlen != 0 || yrlen != 0) { mag_ptr tmp; double *xdbl, *ydbl; tmp = _mag_vec_init(FLINT_MAX(xlen, ylen)); xdbl = flint_malloc(sizeof(double) * xlen); ydbl = flint_malloc(sizeof(double) * ylen); /* (xm + xr)^2 = (xm*ym) + (xr^2 + 2 xm xr) = (xm*ym) + xr*(2 xm + xr) */ if (squaring) { _mag_vec_get_fmpz_2exp_blocks(xz, xdbl, xe, xblocks, scale, x, NULL, xrlen); for (i = 0; i < xlen; i++) { arf_get_mag(tmp + i, arb_midref(x + i)); mag_mul_2exp_si(tmp + i, tmp + i, 1); mag_add(tmp + i, tmp + i, arb_radref(x + i)); } _mag_vec_get_fmpz_2exp_blocks(yz, ydbl, ye, yblocks, scale, NULL, tmp, xlen); _arb_poly_addmullow_rad(z, zz, xz, xdbl, xe, xblocks, xrlen, yz, ydbl, ye, yblocks, xlen, n); } else if (yrlen == 0) { /* xr * |ym| */ _mag_vec_get_fmpz_2exp_blocks(xz, xdbl, xe, xblocks, scale, x, NULL, xrlen); for (i = 0; i < ymlen; i++) arf_get_mag(tmp + i, arb_midref(y + i)); _mag_vec_get_fmpz_2exp_blocks(yz, ydbl, ye, yblocks, scale, NULL, tmp, ymlen); _arb_poly_addmullow_rad(z, zz, xz, xdbl, xe, xblocks, xrlen, yz, ydbl, ye, yblocks, ymlen, n); } else { /* |xm| * yr */ for (i = 0; i < xmlen; i++) arf_get_mag(tmp + i, arb_midref(x + i)); _mag_vec_get_fmpz_2exp_blocks(xz, xdbl, xe, xblocks, scale, NULL, tmp, xmlen); _mag_vec_get_fmpz_2exp_blocks(yz, ydbl, ye, yblocks, scale, y, NULL, yrlen); _arb_poly_addmullow_rad(z, zz, xz, xdbl, xe, xblocks, xmlen, yz, ydbl, ye, yblocks, yrlen, n); /* xr*(|ym| + yr) */ if (xrlen != 0) { _mag_vec_get_fmpz_2exp_blocks(xz, xdbl, xe, xblocks, scale, x, NULL, xrlen); for (i = 0; i < ylen; i++) arb_get_mag(tmp + i, y + i); _mag_vec_get_fmpz_2exp_blocks(yz, ydbl, ye, yblocks, scale, NULL, tmp, ylen); _arb_poly_addmullow_rad(z, zz, xz, xdbl, xe, xblocks, xrlen, yz, ydbl, ye, yblocks, ylen, n); } } _mag_vec_clear(tmp, FLINT_MAX(xlen, ylen)); flint_free(xdbl); flint_free(ydbl); } /* multiply midpoints */ if (xmlen != 0 && ymlen != 0) { _arb_vec_get_fmpz_2exp_blocks(xz, xe, xblocks, scale, x, xmlen, prec); if (squaring) { _arb_poly_addmullow_block(z, zz, xz, xe, xblocks, xmlen, xz, xe, xblocks, xmlen, n, prec, 1); } else { _arb_vec_get_fmpz_2exp_blocks(yz, ye, yblocks, scale, y, ymlen, prec); _arb_poly_addmullow_block(z, zz, xz, xe, xblocks, xmlen, yz, ye, yblocks, ymlen, n, prec, 0); } } /* Unscale. */ if (!fmpz_is_zero(scale)) { fmpz_zero(t); for (i = 0; i < n; i++) { arb_mul_2exp_fmpz(z + i, z + i, t); fmpz_add(t, t, scale); } } _fmpz_vec_clear(xz, xlen); _fmpz_vec_clear(yz, ylen); _fmpz_vec_clear(zz, n); _fmpz_vec_clear(xe, xlen); _fmpz_vec_clear(ye, ylen); flint_free(xblocks); flint_free(yblocks); fmpz_clear(scale); fmpz_clear(t); }
void acb_hypgeom_pfq_series_direct(acb_poly_t res, const acb_poly_struct * a, long p, const acb_poly_struct * b, long q, const acb_poly_t z, int regularized, long n, long len, long prec) { acb_poly_t s, t, err; arb_poly_t C, T; long i; int is_real; int terminating; /* default algorithm to choose number of terms */ if (n < 0) { n = acb_hypgeom_pfq_series_choose_n(a, p, b, q, z, len, prec); } terminating = 0; /* check if it terminates due to a root of the numerator */ for (i = 0; i < p; i++) { if (acb_poly_length(a + i) == 0 && n > 0) { terminating = 1; } else if (acb_poly_length(a + i) == 1) { acb_srcptr c = acb_poly_get_coeff_ptr(a + i, 0); if (acb_is_int(c) && arb_is_negative(acb_realref(c)) && arf_cmpabs_ui(arb_midref(acb_realref(c)), n) < 0) { terminating = 1; } } } /* check if it terminates (to order n) due to z */ /* the following tests could be made stronger... */ if (z->length == 0 && n >= 1) { terminating = 1; } else if (!terminating && z->length > 0 && acb_is_zero(z->coeffs) && n >= len) { if (regularized) { terminating = 1; } else { terminating = 1; for (i = 0; i < q; i++) { acb_srcptr c = acb_poly_get_coeff_ptr(b + i, 0); if (!arb_is_positive(acb_realref(c)) && acb_contains_int(c)) terminating = 0; } } } acb_poly_init(s); acb_poly_init(t); acb_poly_init(err); arb_poly_init(C); arb_poly_init(T); acb_hypgeom_pfq_series_sum_forward(s, t, a, p, b, q, z, regularized, n, len, prec); if (!terminating) { is_real = acb_poly_is_real(z); for (i = 0; i < p; i++) is_real = is_real && acb_poly_is_real(a + i); for (i = 0; i < q; i++) is_real = is_real && acb_poly_is_real(b + i); acb_poly_majorant(T, t, MAG_BITS); acb_hypgeom_pfq_series_bound_factor(C, a, p, b, q, z, n, len, MAG_BITS); if (!_arb_vec_is_finite(T->coeffs, T->length) || !_arb_vec_is_finite(C->coeffs, C->length)) { arb_poly_fit_length(T, len); _arb_vec_indeterminate(T->coeffs, len); _arb_poly_set_length(T, len); } else { arb_poly_mullow(T, T, C, len, MAG_BITS); } /* create polynomial of errors */ acb_poly_fit_length(err, len); for (i = 0; i < FLINT_MIN(len, T->length); i++) { arb_add_error(acb_realref(err->coeffs + i), T->coeffs + i); if (!is_real) arb_add_error(acb_imagref(err->coeffs + i), T->coeffs + i); } _acb_poly_set_length(err, len); _acb_poly_normalise(err); acb_poly_add(s, s, err, prec); } acb_poly_set(res, s); acb_poly_clear(s); acb_poly_clear(t); acb_poly_clear(err); arb_poly_clear(C); arb_poly_clear(T); }