diff options
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.c | 242 |
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); - } -} |