flint-sys 0.9.0

Bindings to the FLINT C library
Documentation 
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/*
    Copyright (C) 2023 Fredrik Johansson

    This file is part of FLINT.

    FLINT is free software: you can redistribute it and/or modify it under
    the terms of the GNU Lesser General Public License (LGPL) as published
    by the Free Software Foundation; either version 3 of the License, or
    (at your option) any later version.  See <https://www.gnu.org/licenses/>.
*/

#include "gr_vec.h"
#include "gr_poly.h"

int
_gr_poly_rsqrt_series_newton(gr_ptr g,
    gr_srcptr h, slong hlen, slong len, slong cutoff, gr_ctx_t ctx)
{
    slong sz = ctx->sizeof_elem;
    int status = GR_SUCCESS;
    slong a[FLINT_BITS];
    slong i, m, n;

    hlen = FLINT_MIN(hlen, len);

    if (len == 0)
        return GR_SUCCESS;

    cutoff = FLINT_MAX(cutoff, 2);
    a[i = 0] = n = len;
    while (n >= cutoff)
        a[++i] = (n = (n + 1) / 2);

    status |= _gr_poly_rsqrt_series_basecase(g, h, FLINT_MIN(hlen, n), n, ctx);

    if (status != GR_SUCCESS)
        return status;

    /* Alternative: if the basecase fails in small characteristic, fall
       back to doing Newton iteration all the way. */
#if 0
    if (status != GR_SUCCESS)
    {
        if (n == 1)
            return status;
        else
            return _gr_poly_rsqrt_series_newton(g, h, hlen, len, 2, ctx);
    }
#endif

    if (len > n)
    {
        gr_ptr t, u;
        slong tlen, ulen;

        /* Hack: until all rings have a good mulmid, implement both with and without. */
        /* Todo: tighten allocations when we have mulmid */
        int have_mulmid = (ctx->methods[GR_METHOD_POLY_MULMID] != (gr_funcptr) _gr_poly_mulmid_generic);

        GR_TMP_INIT_VEC(t, 2 * len, ctx);
        u = GR_ENTRY(t, len, sz);

        for (i--; i >= 0; i--)
        {
            m = n;
            n = a[i];

            tlen = FLINT_MIN(2 * m - 1, n);
            ulen = FLINT_MIN(n, m + tlen - 1);

            status |= _gr_poly_mullow(t, g, m, g, m, tlen, ctx);
            status |= _gr_poly_mullow(u, g, m, t, tlen, ulen, ctx);

            if (have_mulmid)
            {
                status |= _gr_poly_mulmid(GR_ENTRY(g, m, sz), u, ulen, h, FLINT_MIN(hlen, n), m, n, ctx);
                status |= _gr_vec_mul_scalar_2exp_si(GR_ENTRY(g, m, sz), GR_ENTRY(g, m, sz), n - m, -1, ctx);
            }
            else
            {
                status |= _gr_poly_mullow(t, u, ulen, h, FLINT_MIN(hlen, n), n, ctx);
                status |= _gr_vec_mul_scalar_2exp_si(GR_ENTRY(g, m, sz), GR_ENTRY(t, m, sz), n - m, -1, ctx);
            }

            status |= _gr_vec_neg(GR_ENTRY(g, m, sz), GR_ENTRY(g, m, sz), n - m, ctx);
        }

        GR_TMP_CLEAR_VEC(t, 2 * len, ctx);
    }

    return status;
}

int
gr_poly_rsqrt_series_newton(gr_poly_t res, const gr_poly_t h, slong len, slong cutoff, gr_ctx_t ctx)
{
    int status = GR_SUCCESS;
    slong hlen;

    if (len == 0)
        return gr_poly_zero(res, ctx);

    hlen = h->length;

    if (hlen == 0)
        return GR_DOMAIN;

    if (hlen == 1)
        len = 1;

    if (res == h)
    {
        gr_poly_t t;
        gr_poly_init(t, ctx);
        status = gr_poly_rsqrt_series_newton(t, h, len, cutoff, ctx);
        gr_poly_swap(res, t, ctx);
        gr_poly_clear(t, ctx);
        return status;
    }

    gr_poly_fit_length(res, len, ctx);
    status |= _gr_poly_rsqrt_series_newton(res->coeffs, h->coeffs, h->length, len, cutoff, ctx);
    _gr_poly_set_length(res, len, ctx);
    _gr_poly_normalise(res, ctx);
    return status;
}