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-rw-r--r--Build/source/libs/mpfr/mpfr-src/src/bernoulli.c255
1 files changed, 0 insertions, 255 deletions
diff --git a/Build/source/libs/mpfr/mpfr-src/src/bernoulli.c b/Build/source/libs/mpfr/mpfr-src/src/bernoulli.c
deleted file mode 100644
index 3656d80fdc8..00000000000
--- a/Build/source/libs/mpfr/mpfr-src/src/bernoulli.c
+++ /dev/null
@@ -1,255 +0,0 @@
-/* bernoulli -- internal function to compute Bernoulli numbers.
-
-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. */
-
-#include "mpfr-impl.h"
-
-/* assume p >= 5 and is odd */
-static int
-is_prime (unsigned long p)
-{
- unsigned long q;
-
- MPFR_ASSERTD (p >= 5 && (p & 1) != 0);
- for (q = 3; q * q <= p; q += 2)
- if ((p % q) == 0)
- return 0;
- return 1;
-}
-
-/* Computes and stores B[2n]*(2n+1)! in b[n]
- using Von Staudt–Clausen theorem, which says that the denominator of B[n]
- divides the product of all primes p such that p-1 divides n.
- Since B[n] = zeta(n) * 2*n!/(2pi)^n, we compute an approximation of
- (2n+1)! * zeta(n) * 2*n!/(2pi)^n and round it to the nearest integer. */
-static void
-mpfr_bernoulli_internal (mpz_t *b, unsigned long n)
-{
- unsigned long p, err, zn;
- mpz_t s, t, u, den;
- mpz_ptr num;
- mpfr_t y, z;
- int ok;
- /* Prec[n/2] is minimal precision so that result is correct for B[n] */
- mpfr_prec_t prec;
- mpfr_prec_t Prec[] = {0, 5, 5, 6, 6, 9, 16, 10, 19, 23, 25, 27, 35, 31,
- 42, 51, 51, 50, 73, 60, 76, 79, 83, 87, 101, 97,
- 108, 113, 119, 125, 149, 133, 146};
-
- mpz_init (b[n]);
-
- if (n == 0)
- {
- mpz_set_ui (b[0], 1);
- return;
- }
-
- /* compute denominator */
- num = b[n];
- n = 2 * n;
- mpz_init_set_ui (den, 6);
- for (p = 5; p <= n+1; p += 2)
- {
- if ((n % (p-1)) == 0 && is_prime (p))
- mpz_mul_ui (den, den, p);
- }
- if (n <= 64)
- prec = Prec[n >> 1];
- else
- {
- /* evaluate the needed precision: zeta(n)*2*den*n!/(2*pi)^n <=
- 3.3*den*(n/e/2/pi)^n*sqrt(2*pi*n) */
- prec = __gmpfr_ceil_log2 (7.0 * (double) n); /* bound 2*pi by 7 */
- prec = (prec + 1) >> 1; /* sqrt(2*pi*n) <= 2^prec */
- mpfr_init2 (z, 53);
- mpfr_set_ui_2exp (z, 251469612, -32, MPFR_RNDU); /* 1/e/2/pi <= z */
- mpfr_mul_ui (z, z, n, MPFR_RNDU);
- mpfr_log2 (z, z, MPFR_RNDU);
- mpfr_mul_ui (z, z, n, MPFR_RNDU);
- p = mpfr_get_ui (z, MPFR_RNDU); /* (n/e/2/pi)^n <= 2^p */
- mpfr_clear (z);
- MPFR_INC_PREC (prec, p + mpz_sizeinbase (den, 2));
- /* the +2 term ensures no rounding failure up to n=10000 */
- MPFR_INC_PREC (prec, __gmpfr_ceil_log2 (prec) + 2);
- }
-
- try_again:
- mpz_init (s);
- mpz_init (t);
- mpz_init (u);
- mpz_set_ui (u, 1);
- mpz_mul_2exp (u, u, prec); /* u = 2^prec */
- mpz_ui_pow_ui (t, 3, n);
- mpz_fdiv_q (s, u, t); /* multiply all terms by 2^prec */
- /* we compute a lower bound of the series, thus the final result cannot
- be too large */
- for (p = 4; mpz_cmp_ui (t, 0) > 0; p++)
- {
- mpz_ui_pow_ui (t, p, n);
- mpz_fdiv_q (t, u, t);
- /* 2^prec/p^n-1 < t <= 2^prec/p^n */
- mpz_add (s, s, t);
- }
- /* sum(2^prec/q^n-1, q=3..p) < t <= sum(2^prec/q^n, q=3..p)
- thus the error on the truncated series is at most p-2.
- The neglected part of the series is R = sum(1/x^n, x=p+1..infinity)
- with int(1/x^n, x=p+1..infinity) <= R <= int(1/x^n, x=p..infinity)
- thus 1/(n-1)/(p+1)^(n-1) <= R <= 1/(n-1)/p^(n-1). The difference between
- the lower and upper bound is bounded by p^(-n), which is bounded by
- 2^(-prec) since t=0 in the above loop */
- mpz_ui_pow_ui (t, p, n - 1);
- mpz_mul_ui (t, t, n - 1);
- mpz_cdiv_q (t, u, t);
- mpz_add (s, s, t);
- /* now 2^prec * (zeta(n)-1-1/2^n) - p < s <= 2^prec * (zeta(n)-1-1/2^n) */
- /* add 1 which is 2^prec */
- mpz_add (s, s, u);
- /* add 1/2^n which is 2^(prec-n) */
- mpz_cdiv_q_2exp (u, u, n);
- mpz_add (s, s, u);
- /* now 2^prec * zeta(n) - p < s <= 2^prec * zeta(n) */
- /* multiply by n! */
- mpz_fac_ui (t, n);
- mpz_mul (s, s, t);
- /* multiply by 2*den */
- mpz_mul (s, s, den);
- mpz_mul_2exp (s, s, 1);
- /* now convert to mpfr */
- mpfr_init2 (z, prec);
- mpfr_set_z (z, s, MPFR_RNDZ);
- /* now (2^prec * zeta(n) - p) * 2*den*n! - ulp(z) < z <=
- 2^prec * zeta(n) * 2*den*n!.
- Since z <= 2^prec * zeta(n) * 2*den*n!,
- ulp(z) <= 2*zeta(n) * 2*den*n!, thus
- (2^prec * zeta(n)-(p+1)) * 2*den*n! < z <= 2^prec * zeta(n) * 2*den*n! */
- mpfr_div_2ui (z, z, prec, MPFR_RNDZ);
- /* now (zeta(n) - (p+1)/2^prec) * 2*den*n! < z <= zeta(n) * 2*den*n! */
- /* divide by (2pi)^n */
- mpfr_init2 (y, prec);
- mpfr_const_pi (y, MPFR_RNDU);
- /* pi <= y <= pi * (1 + 2^(1-prec)) */
- mpfr_mul_2ui (y, y, 1, MPFR_RNDU);
- /* 2pi <= y <= 2pi * (1 + 2^(1-prec)) */
- mpfr_pow_ui (y, y, n, MPFR_RNDU);
- /* (2pi)^n <= y <= (2pi)^n * (1 + 2^(1-prec))^(n+1) */
- mpfr_div (z, z, y, MPFR_RNDZ);
- /* now (zeta(n) - (p+1)/2^prec) * 2*den*n! / (2pi)^n / (1+2^(1-prec))^(n+1)
- <= z <= zeta(n) * 2*den*n! / (2pi)^n, and since zeta(n) >= 1:
- den * B[n] * (1 - (p+1)/2^prec) / (1+2^(1-prec))^(n+1)
- <= z <= den * B[n]
- Since 1 / (1+2^(1-prec))^(n+1) >= (1 - 2^(1-prec))^(n+1) >=
- 1 - (n+1) * 2^(1-prec):
- den * B[n] / (2pi)^n * (1 - (p+1)/2^prec) * (1-(n+1)*2^(1-prec))
- <= z <= den * B[n] thus
- den * B[n] * (1 - (2n+p+3)/2^prec) <= z <= den * B[n] */
-
- /* the error is bounded by 2^(EXP(z)-prec) * (2n+p+3) */
- for (err = 0, p = 2 * n + p + 3; p > 1; err++, p = (p + 1) >> 1);
- zn = MPFR_LIMB_SIZE(z) * GMP_NUMB_BITS; /* total number of bits of z */
- if (err >= prec)
- ok = 0;
- else
- {
- err = prec - err;
- /* now the absolute error is bounded by 2^(EXP(z) - err):
- den * B[n] - 2^(EXP(z) - err) <= z <= den * B[n]
- thus if subtracting 2^(EXP(z) - err) does not change the rounding
- (up) we are ok */
- err = mpn_scan1 (MPFR_MANT(z), zn - err);
- /* weight of this 1 bit is 2^(EXP(z) - zn + err) */
- ok = MPFR_EXP(z) < zn - err;
- }
- mpfr_get_z (num, z, MPFR_RNDU);
- if ((n & 2) == 0)
- mpz_neg (num, num);
-
- /* multiply by (n+1)! */
- mpz_mul_ui (t, t, n + 1);
- mpz_divexact (t, t, den); /* t was still n! */
- mpz_mul (num, num, t);
-
- mpfr_clear (y);
- mpfr_clear (z);
- mpz_clear (s);
- mpz_clear (t);
- mpz_clear (u);
-
- if (!ok)
- {
- MPFR_INC_PREC (prec, prec / 10);
- goto try_again;
- }
-
- mpz_clear (den);
-}
-
-static MPFR_THREAD_ATTR mpz_t *bernoulli_table = NULL;
-static MPFR_THREAD_ATTR unsigned long bernoulli_size = 0;
-static MPFR_THREAD_ATTR unsigned long bernoulli_alloc = 0;
-
-mpz_srcptr
-mpfr_bernoulli_cache (unsigned long n)
-{
- unsigned long i;
-
- if (n >= bernoulli_size)
- {
- if (bernoulli_alloc == 0)
- {
- bernoulli_alloc = MAX(16, n + n/4);
- bernoulli_table = (mpz_t *)
- mpfr_allocate_func (bernoulli_alloc * sizeof (mpz_t));
- bernoulli_size = 0;
- }
- else if (n >= bernoulli_alloc)
- {
- bernoulli_table = (mpz_t *) mpfr_reallocate_func
- (bernoulli_table, bernoulli_alloc * sizeof (mpz_t),
- (n + n/4) * sizeof (mpz_t));
- bernoulli_alloc = n + n/4;
- }
- MPFR_ASSERTD (bernoulli_alloc > n);
- MPFR_ASSERTD (bernoulli_size >= 0);
- for (i = bernoulli_size; i <= n; i++)
- mpfr_bernoulli_internal (bernoulli_table, i);
- bernoulli_size = n+1;
- }
- MPFR_ASSERTD (bernoulli_size > n);
- return bernoulli_table[n];
-}
-
-void
-mpfr_bernoulli_freecache (void)
-{
- unsigned long i;
-
- if (bernoulli_table != NULL)
- {
- for (i = 0; i < bernoulli_size; i++)
- {
- mpz_clear (bernoulli_table[i]);
- }
- mpfr_free_func (bernoulli_table, bernoulli_alloc * sizeof (mpz_t));
- bernoulli_table = NULL;
- bernoulli_alloc = 0;
- bernoulli_size = 0;
- }
-}