mirror of
https://github.com/vale981/arb
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108 lines
2.3 KiB
C
108 lines
2.3 KiB
C
/*
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Copyright (C) 2014 Fredrik Johansson
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This file is part of Arb.
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Arb is free software: you can redistribute it and/or modify it under
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the terms of the GNU Lesser General Public License (LGPL) as published
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by the Free Software Foundation; either version 2.1 of the License, or
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(at your option) any later version. See <http://www.gnu.org/licenses/>.
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*/
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#include "acb_modular.h"
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/* convert theta_{m,n} to theta_i */
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static int
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swappy1(int m, int n)
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{
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m = m & 1;
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n = n & 1;
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if (m == 0 && n == 0) return 2;
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if (m == 0 && n == 1) return 3;
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if (m == 1 && n == 0) return 1;
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return 0;
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}
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/* extra phase shift picked up: a factor (-1)^n when m is congruent
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to 2,3 (mod 4), and possibly a factor i = sqrt(-1) when converting
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from theta_1 to theta_{1,1} */
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static int
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swappy2(int m, int n)
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{
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m = m & 3;
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n = n & 1;
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if (m == 1 && n == 1) return 2; /* i */
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if (m == 2 && n == 1) return 4; /* (-1)^n */
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if (m == 3 && n == 1) return 6; /* (-1)^n * i */
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return 0;
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}
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void
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acb_modular_theta_transform(int * R, int * S, int * C, const psl2z_t g)
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{
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R[0] = 0;
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R[1] = 0;
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R[2] = 0;
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R[3] = 0;
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S[0] = 0;
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S[1] = 1;
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S[2] = 2;
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S[3] = 3;
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if (fmpz_is_zero(&g->c))
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{
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C[0] = 0;
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if (fmpz_is_odd(&g->b))
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{
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S[2] = 3;
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S[3] = 2;
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}
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/* -b mod 8 */
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R[0] = (- (int) fmpz_fdiv_ui(&g->b, 8)) & 7;
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R[1] = R[0];
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}
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else
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{
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int a, b, c, d, e1, e2;
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psl2z_t h;
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psl2z_init(h);
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psl2z_inv(h, g);
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e1 = acb_modular_epsilon_arg(h);
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e2 = acb_modular_epsilon_arg(g);
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psl2z_clear(h);
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C[0] = 1;
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a = fmpz_fdiv_ui(&g->a, 8);
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b = fmpz_fdiv_ui(&g->b, 8);
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c = fmpz_fdiv_ui(&g->c, 8);
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d = fmpz_fdiv_ui(&g->d, 8);
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R[0] = e1 + 1;
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R[1] = -e2 + 5 + (2 - c) * a;
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R[2] = -e2 + 4 + (c - d - 2) * (b - a);
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R[3] = -e2 + 3 - (2 + d) * b;
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S[1] = swappy1(1 - c, 1 + a);
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R[1] += swappy2(1 - c, 1 + a);
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S[2] = swappy1(1 + d - c, 1 - b + a);
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R[2] += swappy2(1 + d - c, 1 - b + a);
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S[3] = swappy1(1 + d, 1 - b);
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R[3] += swappy2(1 + d, 1 - b);
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/* floor mod by 8 */
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R[0] &= 7;
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R[1] &= 7;
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R[2] &= 7;
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R[3] &= 7;
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}
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}
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