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
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141

/*
    Copyright (C) 2022 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 <math.h>
#include "fmpzi.h"
#include "fmpzi/impl.h"

#if FLINT_BITS == 64
#define GCD_MAX_D WORD(1125899906842623)
#define GCD_MIN_D WORD(-1125899906842623)
#else
#define GCD_MAX_D COEFF_MAX
#define GCD_MIN_D COEFF_MIN
#endif

void
_fmpzi_gcd_dddd(fmpzi_t res, double a, double b, double c, double d)
{
    double t, u, v, w, qa, qb;

    while (c != 0 || d != 0)
    {
        t = a * c + b * d;
        u = b * c - a * d;
        v = c * c + d * d;

        w = 0.5 / v;

        qa = floor((2.0 * t + v) * w);
        qb = floor((2.0 * u + v) * w);

        t = a - (qa * c - qb * d);
        u = b - (qb * c + qa * d);

        a = c;
        b = d;

        c = t;
        d = u;
    }

    if (a < 0)
    {
        a = -a;
        b = -b;
    }

    if (b > 0 && b > a)
    {
        t = b;
        b = -a;
        a = t;
    }
    else if (b < 0 && b <= -a)
    {
        t = b;
        b = a;
        a = -t;
    }

    fmpzi_set_si_si(res, a, b);
}

void
fmpzi_gcd_euclidean_improved(fmpzi_t res, const fmpzi_t X, const fmpzi_t Y)
{
    fmpzi_t x, y, q, r;
    fmpz a, b, c, d;

    if (fmpzi_is_zero(X))
    {
        fmpzi_canonicalise_unit(res, Y);
        return;
    }

    if (fmpzi_is_zero(Y))
    {
        fmpzi_canonicalise_unit(res, X);
        return;
    }

    a = *fmpzi_realref(X);
    b = *fmpzi_imagref(X);
    c = *fmpzi_realref(Y);
    d = *fmpzi_imagref(Y);

    if (GCD_MIN_D <= a && a <= GCD_MAX_D &&
        GCD_MIN_D <= b && b <= GCD_MAX_D &&
        GCD_MIN_D <= c && c <= GCD_MAX_D &&
        GCD_MIN_D <= d && d <= GCD_MAX_D)
    {
        _fmpzi_gcd_dddd(res, a, b, c, d);
        return;
    }

    fmpzi_init(x);
    fmpzi_init(y);
    fmpzi_init(q);
    fmpzi_init(r);

    fmpzi_set(x, X);
    fmpzi_set(y, Y);

    while (!fmpzi_is_zero(y))
    {
        a = *fmpzi_realref(x);
        b = *fmpzi_imagref(x);
        c = *fmpzi_realref(y);
        d = *fmpzi_imagref(y);

        if (GCD_MIN_D <= a && a <= GCD_MAX_D &&
            GCD_MIN_D <= b && b <= GCD_MAX_D &&
            GCD_MIN_D <= c && c <= GCD_MAX_D &&
            GCD_MIN_D <= d && d <= GCD_MAX_D)
        {
            _fmpzi_gcd_dddd(res, a, b, c, d);
            goto cleanup;
        }

        fmpzi_divrem_approx(q, r, x, y);
        fmpzi_swap(x, y);
        fmpzi_swap(y, r);
    }

    fmpzi_swap(res, x);
    fmpzi_canonicalise_unit(res, res);

cleanup:
    fmpzi_clear(x);
    fmpzi_clear(y);
    fmpzi_clear(q);
    fmpzi_clear(r);
}