flint-sys 0.9.0

Bindings to the FLINT C library
Documentation 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124

/*
    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"

/* todo: generalize */
#include "arb.h"
#include "acb.h"

static int
want_division(gr_srcptr f, gr_ctx_t ctx)
{
    if (ctx->which_ring == GR_CTX_RR_ARB)
        return arb_bits(f) <= 0.25 * _gr_ctx_get_real_prec(ctx);

    if (ctx->which_ring == GR_CTX_CC_ACB)
        return acb_bits(f) <= 0.25 * _gr_ctx_get_real_prec(ctx);

    return 0;
}

int
_gr_poly_taylor_shift_convolution(gr_ptr res, gr_srcptr poly, slong len, gr_srcptr c, gr_ctx_t ctx)
{
    int status = GR_SUCCESS;
    slong sz = ctx->sizeof_elem;
    slong i, n = len - 1;
    gr_ptr f, d, t, u;

    if (res != poly)
        status |= _gr_vec_set(res, poly, len, ctx);

    if (gr_is_zero(c, ctx) == T_TRUE  || len <= 1)
        return status;

    GR_TMP_INIT_VEC(t, 2 * len + 2, ctx);
    u = GR_ENTRY(t, len, sz);
    f = GR_ENTRY(u, len, sz);
    d = GR_ENTRY(f, 1, sz);

    status |= gr_one(f, ctx);

    /* todo: vector function for Borel transform */
    for (i = 2; i <= n; i++)
    {
        status |= gr_mul_ui(f, f, i, ctx);
        status |= gr_mul(GR_ENTRY(res, i, sz), GR_ENTRY(res, i, sz), f, ctx);
    }

    status |= _gr_poly_reverse(res, res, len, len, ctx);

    status |= gr_one(GR_ENTRY(t, n, sz), ctx);
    for (i = n; i > 0; i--)
        status |= gr_mul_ui(GR_ENTRY(t, i - 1, sz), GR_ENTRY(t, i, sz), i, ctx);

    if (gr_is_neg_one(c, ctx) == T_TRUE)
    {
        for (i = 1; i <= n; i += 2)
            status |= gr_neg(GR_ENTRY(t, i, sz), GR_ENTRY(t, i, sz), ctx);
    }
    else if (gr_is_one(c, ctx) != T_TRUE)
    {
        status |= gr_set(d, c, ctx);

        for (i = 1; i <= n; i++)
        {
            status |= gr_mul(GR_ENTRY(t, i, sz), GR_ENTRY(t, i, sz), d, ctx);
            status |= gr_mul(d, d, c, ctx);
        }
    }

    status |= _gr_poly_mullow(u, res, len, t, len, len, ctx);
    status |= gr_mul(f, f, f, ctx);

    if (want_division(f, ctx))
    {
        for (i = 0; i <= n; i++)
            status |= gr_div(GR_ENTRY(u, i, sz), GR_ENTRY(u, i, sz), f, ctx);

        status |= gr_one(f, ctx);
    }
    else
    {
        status |= gr_inv(f, f, ctx);
    }

    for (i = n; i >= 0; i--)
    {
        status |= gr_mul(GR_ENTRY(res, i, sz), GR_ENTRY(u, n - i, sz), f, ctx);
        status |= gr_mul_ui(f, f, (i == 0) ? 1 : i, ctx);
    }

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

    return status;
}

int
gr_poly_taylor_shift_convolution(gr_poly_t res, const gr_poly_t f, gr_srcptr c, gr_ctx_t ctx)
{
    int status = GR_SUCCESS;

    if (res != f)
        status |= gr_poly_set(res, f, ctx);

    status |= _gr_poly_taylor_shift_convolution(res->coeffs, res->coeffs, res->length, c, ctx);

    /* Normally the leading coefficient does not change, but it may have
       exactified from maybe-zero to definitely-zero when working with
       inexact represenations of the zero ring; it may also have been
       mutated to a temporary value by an algorithm which fails with GR_UNABLE. */
    _gr_poly_normalise(res, ctx);

    return status;
}