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https://github.com/vale981/arb
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rely on the fmpz_poly_cos_minpoly code from flint (available since 2.5)
This commit is contained in:
Fredrik Johansson
parent
f62ce540cf
commit
7975162629
4 changed files with 27 additions and 255 deletions
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@ -11,261 +11,7 @@
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#include "arb.h"
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#include "arb_poly.h"
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/* include minpoly code here until it appears in a flint release */
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#include "flint/fmpz_poly.h"
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#include "flint/ulong_extras.h"
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/* Use a lookup table for small n. We skip 53, 59 and 61, as the
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coefficients do not fit in 16 bits. */
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#define MINPOLY_TAB_NUM 65
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#define MINPOLY_TAB_MAX_LEN 24
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static const char
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minpoly_len_tab[MINPOLY_TAB_NUM] = {
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1, 2, 2, 2, 2, 3, 2, 4, 3, 4, 3, 6, 3, 7, 4, 5, 5, 9, 4, 10, 5, 7, 6,
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12, 5, 11, 7, 10, 7, 15, 5, 16, 9, 11, 9, 13, 7, 19, 10, 13, 9, 21, 7,
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22, 11, 13, 12, 24, 9, 22, 11, 17, 13, 27, 10, 21, 13, 19, 15, 30, 9,
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31, 16, 19, 17
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};
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static const short
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minpoly_tab[MINPOLY_TAB_NUM][MINPOLY_TAB_MAX_LEN] = {
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{1},
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{-2, 1},
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{2, 1},
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{1, 1},
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{0, 1},
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{-1, 1, 1},
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{-1, 1},
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{-1, -2, 1, 1},
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{-2, 0, 1},
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{1, -3, 0, 1},
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{-1, -1, 1},
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{1, 3, -3, -4, 1, 1},
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{-3, 0, 1},
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{-1, 3, 6, -4, -5, 1, 1},
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{1, -2, -1, 1},
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{1, 4, -4, -1, 1},
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{2, 0, -4, 0, 1},
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{1, -4, -10, 10, 15, -6, -7, 1, 1},
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{-1, -3, 0, 1},
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{1, 5, -10, -20, 15, 21, -7, -8, 1, 1},
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{5, 0, -5, 0, 1},
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{1, -8, 8, 6, -6, -1, 1},
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{-1, 3, 3, -4, -1, 1},
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{-1, -6, 15, 35, -35, -56, 28, 36, -9, -10, 1, 1},
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{1, 0, -4, 0, 1},
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{-1, 5, 25, -5, -50, 1, 35, 0, -10, 0, 1},
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{-1, -3, 6, 4, -5, -1, 1},
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{1, 9, 0, -30, 0, 27, 0, -9, 0, 1},
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{-7, 0, 14, 0, -7, 0, 1},
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{-1, 7, 28, -56, -126, 126, 210, -120, -165, 55, 66, -12, -13, 1, 1},
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{1, -4, -4, 1, 1},
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{-1, -8, 28, 84, -126, -252, 210, 330, -165, -220, 66, 78, -13, -14, 1, 1},
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{2, 0, -16, 0, 20, 0, -8, 0, 1},
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{1, -12, 12, 43, -43, -34, 34, 10, -10, -1, 1},
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{1, 4, -10, -10, 15, 6, -7, -1, 1},
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{1, 8, -40, -46, 110, 71, -113, -43, 54, 11, -12, -1, 1},
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{-3, 0, 9, 0, -6, 0, 1},
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{-1, 9, 45, -120, -330, 462, 924, -792, -1287, 715, 1001, -364, -455, 105,
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120, -16, -17, 1, 1},
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{-1, 5, 10, -20, -15, 21, 7, -8, -1, 1},
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{1, 12, -12, -79, 79, 103, -103, -53, 53, 12, -12, -1, 1},
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{1, 0, -12, 0, 19, 0, -8, 0, 1},
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{1, -10, -55, 165, 495, -792, -1716, 1716, 3003, -2002, -3003, 1365, 1820,
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-560, -680, 136, 153, -18, -19, 1, 1},
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{1, 8, 8, -6, -6, 1, 1},
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{1, 11, -55, -220, 495, 1287, -1716, -3432, 3003, 5005, -3003, -4368,
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1820, 2380, -680, -816, 153, 171, -19, -20, 1, 1},
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{-11, 0, 55, 0, -77, 0, 44, 0, -11, 0, 1},
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{1, -12, -36, 31, 105, -27, -112, 9, 54, -1, -12, 0, 1},
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{1, -6, -15, 35, 35, -56, -28, 36, 9, -10, -1, 1},
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{-1, -12, 66, 286, -715, -2002, 3003, 6435, -6435, -11440, 8008, 12376,
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-6188, -8568, 3060, 3876, -969, -1140, 190, 210, -21, -22, 1, 1},
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{1, 0, -16, 0, 20, 0, -8, 0, 1},
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{-1, 14, 49, -371, -196, 2072, 294, -5147, -210, 7007, 77, -5733, -14,
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2940, 1, -952, 0, 189, 0, -21, 0, 1},
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{-1, -5, 25, 5, -50, -1, 35, 0, -10, 0, 1},
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{1, 16, -16, -188, 188, 526, -526, -596, 596, 339, -339, -103, 103, 16,
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-16, -1, 1},
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{13, 0, -91, 0, 182, 0, -156, 0, 65, 0, -13, 0, 1},
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{0},
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{-1, 9, 0, -30, 0, 27, 0, -9, 0, 1},
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{1, 12, -108, -151, 951, 877, -2891, -2058, 4489, 2442, -4080, -1639,
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2289, 650, -801, -151, 170, 19, -20, -1, 1},
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{1, 0, -24, 0, 86, 0, -104, 0, 53, 0, -12, 0, 1},
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{1, -20, 20, 265, -265, -989, 989, 1519, -1519, -1198, 1198, 531, -531,
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-134, 134, 18, -18, -1, 1},
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{-1, -7, 28, 56, -126, -126, 210, 120, -165, -55, 66, 12, -13, -1, 1},
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{0},
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{1, 0, -8, 0, 14, 0, -7, 0, 1},
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{0},
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{1, -8, -28, 84, 126, -252, -210, 330, 165, -220, -66, 78, 13, -14, -1, 1},
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{1, 24, 72, -170, -534, 405, 1385, -459, -1782, 276, 1287, -90, -546, 15,
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135, -1, -18, 0, 1},
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{2, 0, -64, 0, 336, 0, -672, 0, 660, 0, -352, 0, 104, 0, -16, 0, 1},
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};
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/* Recurrence for coefficients in rescaled Chebyshev polynomials */
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#define CHEB_NEXT(y, x, m, k) \
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fmpz_mul2_uiui(y, x, m - 2*k + 1, m - 2*k + 2); \
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fmpz_divexact2_uiui(y, y, k, m - k); \
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fmpz_neg(y, y); \
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/* Computes the monic integer polynomial
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n odd: 2 (T(s+1,x/2) - T(s,x/2)), s = (n - 1) / 2
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n even: 2 (T(s+1,x/2) - T(s-1,x/2)), s = n / 2 */
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static void
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chebyshev_sum(fmpz * a, ulong n)
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{
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ulong s, k, m;
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if (n == 1)
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{
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fmpz_set_si(a, -2);
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fmpz_one(a + 1);
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return;
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}
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if (n == 2)
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{
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fmpz_set_si(a, -4);
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fmpz_zero(a + 1);
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fmpz_one(a + 2);
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return;
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}
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s = n / 2;
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m = s + 1;
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fmpz_one(a + m);
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for (k = 1; k <= m / 2; k++)
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{
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CHEB_NEXT(a + m - 2 * k, a + m - 2 * k + 2, m, k);
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}
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if (n % 2 == 1)
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{
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m = s;
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fmpz_set_si(a + m, -1);
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for (k = 1; k <= m / 2; k++)
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{
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CHEB_NEXT(a + m - 2 * k, a + m - 2 * k + 2, m, k);
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}
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}
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else
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{
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m = s - 1;
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/* Use the top coefficient as scratch space. */
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for (k = 1; k <= m / 2; k++)
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{
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CHEB_NEXT(a + m + 2, a + m + 2, m, k);
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fmpz_sub(a + m - 2*k, a + m - 2*k, a + m + 2);
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}
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for (k = 1 - (m % 2); k < m + 2; k += 2)
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fmpz_zero(a + k);
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fmpz_sub_ui(a + m, a + m, 1);
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/* Set the top coefficient again. */
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fmpz_one(a + m + 2);
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}
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}
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#define MUL_TMP(P, Plen, T, Tlen) \
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fmpz * swap; \
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if (Plen >= Tlen) \
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_fmpz_poly_mul(U, P, Plen, T, Tlen); \
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else \
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_fmpz_poly_mul(U, T, Tlen, P, Plen); \
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Plen = Plen + Tlen - 1; \
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swap = P; P = U; U = swap; \
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void
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_arb_fmpz_poly_cos_minpoly(fmpz * f, ulong n)
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{
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fmpz *P, *Q, *T, *U;
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int *mu;
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ulong Pdeg, Qdeg;
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ulong Plen, Qlen, Tlen;
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ulong d;
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if (n < MINPOLY_TAB_NUM && minpoly_len_tab[n] <= MINPOLY_TAB_MAX_LEN)
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{
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for (d = 0; d < minpoly_len_tab[n]; d++)
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fmpz_set_si(f + d, minpoly_tab[n][d]);
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return;
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}
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/* Compute values of the Moebius function. We do this as a precomputation
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as it allows us to bound in advance the degrees of the numerator and
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denominator. */
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mu = flint_calloc(n + 1, sizeof(int));
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Pdeg = Qdeg = 0;
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for (d = 1; d <= n; d++)
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{
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if (n % d == 0)
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{
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mu[d] = n_moebius_mu(n / d);
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if (mu[d] == 1)
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Pdeg += (d / 2 + 1);
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else if (mu[d] == -1)
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Qdeg += (d / 2 + 1);
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}
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}
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/* We use two extra arrays as scratch space (note that Qdeg < Pdeg). */
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P = _fmpz_vec_init(Pdeg + 1);
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Q = _fmpz_vec_init(Pdeg + 1);
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T = _fmpz_vec_init(Pdeg + 1);
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U = _fmpz_vec_init(Pdeg + 1);
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Plen = Qlen = 1;
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fmpz_one(P);
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fmpz_one(Q);
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for (d = 1; d <= n; d++)
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{
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if (n % d == 0 && mu[d] != 0)
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{
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chebyshev_sum(T, d);
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Tlen = d / 2 + 2;
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if (mu[d] > 0)
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{
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MUL_TMP(P, Plen, T, Tlen);
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}
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else
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{
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MUL_TMP(Q, Qlen, T, Tlen);
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}
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}
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}
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_fmpz_poly_div(f, P, Plen, Q, Qlen);
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_fmpz_vec_clear(P, Pdeg + 1);
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_fmpz_vec_clear(Q, Pdeg + 1);
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_fmpz_vec_clear(T, Pdeg + 1);
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_fmpz_vec_clear(U, Pdeg + 1);
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flint_free(mu);
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}
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void
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arb_fmpz_poly_cos_minpoly(fmpz_poly_t f, ulong n)
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{
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slong len = (n < MINPOLY_TAB_NUM) ?
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minpoly_len_tab[n] : n_euler_phi(n) / 2 + 1;
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fmpz_poly_fit_length(f, len);
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_arb_fmpz_poly_cos_minpoly(f->coeffs, n);
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_fmpz_poly_set_length(f, len);
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}
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#include "arb_fmpz_poly.h" /* for minpoly */
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void
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_arb_cos_pi_fmpq_algebraic(arb_t c, ulong p, ulong q, slong prec)
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@ -47,6 +47,12 @@ ulong arb_fmpz_poly_deflation(const fmpz_poly_t input);
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void arb_fmpz_poly_complex_roots(acb_ptr roots, const fmpz_poly_t poly, int flags, slong target_prec);
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ARB_FMPZ_POLY_INLINE
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void arb_fmpz_poly_cos_minpoly(fmpz_poly_t res, ulong n)
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{
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fmpz_poly_cos_minpoly(res, n);
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}
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void arb_fmpz_poly_gauss_period_minpoly(fmpz_poly_t res, ulong q, ulong n);
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#endif
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14
arb_fmpz_poly/inlines.c
Normal file
14
arb_fmpz_poly/inlines.c
Normal file
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@ -0,0 +1,14 @@
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/*
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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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#define ARB_FMPZ_POLY_INLINES_C
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#include "arb_fmpz_poly.h"
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@ -109,6 +109,12 @@ Special polynomials
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Note: see also the methods available in FLINT (e.g. for cyclotomic polynomials).
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.. function:: void arb_fmpz_poly_cos_minpoly(fmpz_poly_t res, ulong n)
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Sets *res* to the monic minimal polynomial of `2 \cos(2 \pi / n)`.
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This is a wrapper of FLINT's *fmpz_poly_cos_minpoly*, provided here
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for backward compatibility.
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.. function:: void arb_fmpz_poly_gauss_period_minpoly(fmpz_poly_t res, ulong q, ulong n)
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Sets *res* to the minimal polynomial of the Gaussian periods
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