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

/*
    Copyright (C) 2014 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 "test_helpers.h"
#include "acb.h"
#include "acb_modular.h"

TEST_FUNCTION_START(acb_modular_lambda, state)
{
    slong iter;

    for (iter = 0; iter < 10000 * 0.1 * flint_test_multiplier(); iter++)
    {
        acb_t tau1, tau2, z1, z2, z3, t;
        slong e0, prec0, prec1, prec2, step;

        acb_init(tau1);
        acb_init(tau2);
        acb_init(z1);
        acb_init(z2);
        acb_init(z3);
        acb_init(t);

        e0 = 1 + n_randint(state, 100);
        prec0 = 2 + n_randint(state, 1000);
        prec1 = 2 + n_randint(state, 1000);
        prec2 = 2 + n_randint(state, 1000);

        acb_randtest(tau1, state, prec0, e0);
        acb_randtest(tau2, state, prec0, e0);
        acb_randtest(z1, state, prec0, e0);
        acb_randtest(z2, state, prec0, e0);

        acb_set(tau2, tau1);

        step = n_randint(state, 10);

        /* Test invariance */
        while (step --> 0)
        {
            if (n_randint(state, 2))
            {
                acb_add_ui(tau2, tau2, 2, prec0);
            }
            else
            {
                acb_mul_si(z1, tau2, -2, prec0);
                acb_add_ui(z1, z1, 1, prec0);
                acb_div(tau2, tau2, z1, prec0);
            }
        }

        acb_modular_lambda(z1, tau1, prec1);
        acb_modular_lambda(z2, tau2, prec2);

        /* Compare with eta */
        acb_mul_2exp_si(tau1, tau1, -1);
        acb_modular_eta(z3, tau1, prec2);
        acb_mul_2exp_si(tau1, tau1, 2);
        acb_modular_eta(t, tau1, prec2);
        acb_mul(t, t, t, prec2);
        acb_mul(z3, z3, t, prec2);
        acb_mul_2exp_si(tau1, tau1, -1);
        acb_modular_eta(t, tau1, prec2);
        acb_pow_ui(t, t, 3, prec2);
        acb_div(z3, z3, t, prec2);
        acb_pow_ui(z3, z3, 8, prec2);
        acb_mul_2exp_si(z3, z3, 4);

        if (!acb_overlaps(z1, z2) || !acb_overlaps(z1, z3))
        {
            flint_printf("FAIL (overlap)\n");
            flint_printf("tau1 = "); acb_printd(tau1, 15); flint_printf("\n\n");
            flint_printf("tau2 = "); acb_printd(tau2, 15); flint_printf("\n\n");
            flint_printf("z1 = "); acb_printd(z1, 15); flint_printf("\n\n");
            flint_printf("z2 = "); acb_printd(z2, 15); flint_printf("\n\n");
            flint_printf("z3 = "); acb_printd(z3, 15); flint_printf("\n\n");
            flint_abort();
        }

        acb_modular_lambda(tau1, tau1, prec2);

        if (!acb_overlaps(z1, tau1))
        {
            flint_printf("FAIL (aliasing)\n");
            flint_printf("tau1 = "); acb_printd(tau1, 15); flint_printf("\n\n");
            flint_printf("tau2 = "); acb_printd(tau2, 15); flint_printf("\n\n");
            flint_printf("z1 = "); acb_printd(z1, 15); flint_printf("\n\n");
            flint_printf("z2 = "); acb_printd(z2, 15); flint_printf("\n\n");
            flint_abort();
        }

        acb_clear(tau1);
        acb_clear(tau2);
        acb_clear(z1);
        acb_clear(z2);
        acb_clear(z3);
        acb_clear(t);
    }

    TEST_FUNCTION_END(state);
}