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Diffstat (limited to 'Build/source/libs/mpfr/mpfr-src/src/zeta_ui.c')
-rw-r--r--Build/source/libs/mpfr/mpfr-src/src/zeta_ui.c242
1 files changed, 0 insertions, 242 deletions
diff --git a/Build/source/libs/mpfr/mpfr-src/src/zeta_ui.c b/Build/source/libs/mpfr/mpfr-src/src/zeta_ui.c
deleted file mode 100644
index d7ad99a8d7d..00000000000
--- a/Build/source/libs/mpfr/mpfr-src/src/zeta_ui.c
+++ /dev/null
@@ -1,242 +0,0 @@
-/* mpfr_zeta_ui -- compute the Riemann Zeta function for integer argument.
-
-Copyright 2005-2020 Free Software Foundation, Inc.
-Contributed by the AriC and Caramba projects, INRIA.
-
-This file is part of the GNU MPFR Library.
-
-The GNU MPFR Library is free software; you can redistribute it and/or modify
-it under the terms of the GNU Lesser General Public License as published by
-the Free Software Foundation; either version 3 of the License, or (at your
-option) any later version.
-
-The GNU MPFR Library is distributed in the hope that it will be useful, but
-WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
-License for more details.
-
-You should have received a copy of the GNU Lesser General Public License
-along with the GNU MPFR Library; see the file COPYING.LESSER. If not, see
-https://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
-51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */
-
-#define MPFR_NEED_LONGLONG_H
-#include "mpfr-impl.h"
-
-int
-mpfr_zeta_ui (mpfr_ptr z, unsigned long m, mpfr_rnd_t r)
-{
- MPFR_ZIV_DECL (loop);
-
- MPFR_LOG_FUNC
- (("m=%lu rnd=%d prec=%Pu", m, r, mpfr_get_prec (z)),
- ("z[%Pu]=%.*Rg", mpfr_get_prec (z), mpfr_log_prec, z));
-
- if (m == 0) /* zeta(0) = -1/2 */
- return mpfr_set_si_2exp (z, -1, -1, r);
- else if (m == 1)
- {
- MPFR_SET_INF (z);
- MPFR_SET_POS (z);
- MPFR_SET_DIVBY0 ();
- return 0;
- }
- else /* m >= 2 */
- {
- mpfr_prec_t p = MPFR_PREC(z);
- unsigned long n, k, err, kbits;
- mpz_t d, t, s, q;
- mpfr_t y;
- int inex;
- MPFR_SAVE_EXPO_DECL (expo);
-
- if (r == MPFR_RNDA)
- r = MPFR_RNDU; /* since the result is always positive */
-
- MPFR_SAVE_EXPO_MARK (expo);
-
- if (m >= p) /* 2^(-m) < ulp(1) = 2^(1-p). This means that
- 2^(-m) <= 1/2*ulp(1). We have 3^(-m)+4^(-m)+... < 2^(-m)
- i.e. zeta(m) < 1+2*2^(-m) for m >= 3 */
- {
- if (m == 2) /* necessarily p=2 */
- inex = mpfr_set_ui_2exp (z, 13, -3, r);
- else if (r == MPFR_RNDZ || r == MPFR_RNDD ||
- (r == MPFR_RNDN && m > p))
- {
- mpfr_set_ui (z, 1, r);
- inex = -1;
- }
- else
- {
- mpfr_set_ui (z, 1, r);
- mpfr_nextabove (z);
- inex = 1;
- }
- goto end;
- }
-
- /* now treat also the case where zeta(m) - (1+1/2^m) < 1/2*ulp(1),
- and the result is either 1+2^(-m) or 1+2^(-m)+2^(1-p). */
- mpfr_init2 (y, 31);
-
- if (m >= p / 2) /* otherwise 4^(-m) > 2^(-p) */
- {
- /* the following is a lower bound for log(3)/log(2) */
- mpfr_set_str_binary (y, "1.100101011100000000011010001110");
- mpfr_mul_ui (y, y, m, MPFR_RNDZ); /* lower bound for log2(3^m) */
- if (mpfr_cmp_ui (y, p + 2) >= 0)
- {
- mpfr_clear (y);
- mpfr_set_ui (z, 1, MPFR_RNDZ);
- mpfr_div_2ui (z, z, m, MPFR_RNDZ);
- mpfr_add_ui (z, z, 1, MPFR_RNDZ);
- if (r != MPFR_RNDU)
- inex = -1;
- else
- {
- mpfr_nextabove (z);
- inex = 1;
- }
- goto end;
- }
- }
-
- mpz_init (s);
- mpz_init (d);
- mpz_init (t);
- mpz_init (q);
-
- p += MPFR_INT_CEIL_LOG2(p); /* account of the n term in the error */
-
- p += MPFR_INT_CEIL_LOG2(p) + 15; /* initial value */
-
- MPFR_ZIV_INIT (loop, p);
- for(;;)
- {
- /* 0.39321985067869744 = log(2)/log(3+sqrt(8)) */
- n = 1 + (unsigned long) (0.39321985067869744 * (double) p);
- err = n + 4;
-
- mpfr_set_prec (y, p);
-
- /* computation of the d[k] */
- mpz_set_ui (s, 0);
- mpz_set_ui (t, 1);
- mpz_mul_2exp (t, t, 2 * n - 1); /* t[n] */
- mpz_set (d, t);
- for (k = n; k > 0; k--)
- {
- count_leading_zeros (kbits, k);
- kbits = GMP_NUMB_BITS - kbits;
- /* if k^m is too large, use mpz_tdiv_q */
- if (m * kbits > 2 * GMP_NUMB_BITS)
- {
- /* if we know in advance that k^m > d, then floor(d/k^m) will
- be zero below, so there is no need to compute k^m */
- kbits = (kbits - 1) * m + 1;
- /* k^m has at least kbits bits */
- if (kbits > mpz_sizeinbase (d, 2))
- mpz_set_ui (q, 0);
- else
- {
- mpz_ui_pow_ui (q, k, m);
- mpz_tdiv_q (q, d, q);
- }
- }
- else /* use several mpz_tdiv_q_ui calls */
- {
- unsigned long km = k, mm = m - 1;
- while (mm > 0 && km < ULONG_MAX / k)
- {
- km *= k;
- mm --;
- }
- mpz_tdiv_q_ui (q, d, km);
- while (mm > 0)
- {
- km = k;
- mm --;
- while (mm > 0 && km < ULONG_MAX / k)
- {
- km *= k;
- mm --;
- }
- mpz_tdiv_q_ui (q, q, km);
- }
- }
- if (k % 2)
- mpz_add (s, s, q);
- else
- mpz_sub (s, s, q);
-
- /* we have d[k] = sum(t[i], i=k+1..n)
- with t[i] = n*(n+i-1)!*4^i/(n-i)!/(2i)!
- t[k-1]/t[k] = k*(2k-1)/(n-k+1)/(n+k-1)/2 */
-#if (GMP_NUMB_BITS == 32)
-#define KMAX 46341 /* max k such that k*(2k-1) < 2^32 */
-#elif (GMP_NUMB_BITS == 64)
-#define KMAX 3037000500
-#endif
-#ifdef KMAX
- if (k <= KMAX)
- mpz_mul_ui (t, t, k * (2 * k - 1));
- else
-#endif
- {
- mpz_mul_ui (t, t, k);
- mpz_mul_ui (t, t, 2 * k - 1);
- }
- mpz_fdiv_q_2exp (t, t, 1);
- /* Warning: the test below assumes that an unsigned long
- has no padding bits. */
- if (n < 1UL << ((sizeof(unsigned long) * CHAR_BIT) / 2))
- /* (n - k + 1) * (n + k - 1) < n^2 */
- mpz_divexact_ui (t, t, (n - k + 1) * (n + k - 1));
- else
- {
- mpz_divexact_ui (t, t, n - k + 1);
- mpz_divexact_ui (t, t, n + k - 1);
- }
- mpz_add (d, d, t);
- }
-
- /* multiply by 1/(1-2^(1-m)) = 1 + 2^(1-m) + 2^(2-m) + ... */
- mpz_fdiv_q_2exp (t, s, m - 1);
- do
- {
- err ++;
- mpz_add (s, s, t);
- mpz_fdiv_q_2exp (t, t, m - 1);
- }
- while (mpz_cmp_ui (t, 0) > 0);
-
- /* divide by d[n] */
- mpz_mul_2exp (s, s, p);
- mpz_tdiv_q (s, s, d);
- mpfr_set_z (y, s, MPFR_RNDN);
- mpfr_div_2ui (y, y, p, MPFR_RNDN);
-
- err = MPFR_INT_CEIL_LOG2 (err);
-
- if (MPFR_LIKELY(MPFR_CAN_ROUND (y, p - err, MPFR_PREC(z), r)))
- break;
-
- MPFR_ZIV_NEXT (loop, p);
- }
- MPFR_ZIV_FREE (loop);
-
- mpz_clear (d);
- mpz_clear (t);
- mpz_clear (q);
- mpz_clear (s);
- inex = mpfr_set (z, y, r);
- mpfr_clear (y);
-
- end:
- MPFR_LOG_VAR (z);
- MPFR_LOG_MSG (("inex = %d before mpfr_check_range\n", inex));
- MPFR_SAVE_EXPO_FREE (expo);
- return mpfr_check_range (z, inex, r);
- }
-}