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Diffstat (limited to 'Build/source/libs/mpfr/mpfr-src/src/log_ui.c')
-rw-r--r-- | Build/source/libs/mpfr/mpfr-src/src/log_ui.c | 234 |
1 files changed, 0 insertions, 234 deletions
diff --git a/Build/source/libs/mpfr/mpfr-src/src/log_ui.c b/Build/source/libs/mpfr/mpfr-src/src/log_ui.c deleted file mode 100644 index c2ca6d7e322..00000000000 --- a/Build/source/libs/mpfr/mpfr-src/src/log_ui.c +++ /dev/null @@ -1,234 +0,0 @@ -/* mpfr_log_ui -- compute natural logarithm of an unsigned long - -Copyright 2014-2020 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" - -/* FIXME: mpfr_log_ui is much slower than mpfr_log on some values of n, - e.g. about 4 times as slow for n around ULONG_MAX/3 on an - x86_64 Linux machine, for 10^6 bits of precision. The reason is that - for say n=6148914691236517205 and prec=10^6, the value of T computed - has more than 50M bits, which is much more than needed. Indeed the - binary splitting algorithm for series with a finite radius of convergence - gives rationals of size n*log(n) for a target precision n. One might - truncate the rationals inside the algorithm, but then the error analysis - should be redone. */ - -/* Cf http://www.ginac.de/CLN/binsplit.pdf: the Taylor series of log(1+x) - up to order N for x=p/2^k is T/(B*Q). - P[0] <- (-p)^(n2-n1) [with opposite sign when n1=1] - q <- k*(n2-n1) [corresponding to Q[0] = 2^q] - B[0] <- n1 * (n1+1) * ... * (n2-1) - T[0] <- B[0]*Q[0] * S(n1,n2) - where S(n1,n2) = -sum((-x)^(i-n1+1)/i, i=n1..n2-1) - Assumes p is odd or zero, and -1/3 <= x = p/2^k <= 1/3. -*/ -static void -S (mpz_t *P, unsigned long *q, mpz_t *B, mpz_t *T, unsigned long n1, - unsigned long n2, long p, unsigned long k, int need_P) -{ - MPFR_ASSERTD (n1 < n2); - MPFR_ASSERTD (p == 0 || ((unsigned long) p & 1) != 0); - if (n2 == n1 + 1) - { - mpz_set_si (P[0], (n1 == 1) ? p : -p); - *q = k; - mpz_set_ui (B[0], n1); - /* T = B*Q*S where S = P/(B*Q) thus T = P */ - mpz_set (T[0], P[0]); - /* since p is odd (or zero), there is no common factor 2 between - P and Q, or T and B */ - } - else - { - unsigned long m = (n1 / 2) + (n2 / 2) + (n1 & 1UL & n2), q1; - /* m = floor((n1+n2)/2) */ - - MPFR_ASSERTD (n1 < m && m < n2); - S (P, q, B, T, n1, m, p, k, 1); - S (P + 1, &q1, B + 1, T + 1, m, n2, p, k, need_P); - - /* T0 <- T0*B1*Q1 + P0*B0*T1 */ - mpz_mul (T[1], T[1], P[0]); - mpz_mul (T[1], T[1], B[0]); - mpz_mul (T[0], T[0], B[1]); - /* Q[1] = 2^q1 */ - mpz_mul_2exp (T[0], T[0], q1); /* mpz_mul (T[0], T[0], Q[1]) */ - mpz_add (T[0], T[0], T[1]); - if (need_P) - mpz_mul (P[0], P[0], P[1]); - *q += q1; /* mpz_mul (Q[0], Q[0], Q[1]) */ - mpz_mul (B[0], B[0], B[1]); - - /* there should be no common factors 2 between P, Q and T, - since P is odd (or zero) */ - } -} - -int -mpfr_log_ui (mpfr_ptr x, unsigned long n, mpfr_rnd_t rnd_mode) -{ - unsigned long k; - mpfr_prec_t w; /* working precision */ - mpz_t three_n, *P, *B, *T; - mpfr_t t, q; - int inexact; - unsigned long N, lgN, i, kk; - long p; - MPFR_GROUP_DECL(group); - MPFR_TMP_DECL(marker); - MPFR_ZIV_DECL(loop); - MPFR_SAVE_EXPO_DECL (expo); - - if (n <= 2) - { - if (n == 0) - { - MPFR_SET_INF (x); - MPFR_SET_NEG (x); - MPFR_SET_DIVBY0 (); - MPFR_RET (0); /* log(0) is an exact -infinity */ - } - else if (n == 1) - { - MPFR_SET_ZERO (x); - MPFR_SET_POS (x); - MPFR_RET (0); /* only "normal" case where the result is exact */ - } - /* now n=2 */ - return mpfr_const_log2 (x, rnd_mode); - } - - /* here n >= 3 */ - - /* Argument reduction: compute k such that 2/3 <= n/2^k < 4/3, - i.e., 2^(k+1) <= 3n < 2^(k+2). - - FIXME: we could do better by considering n/(2^k*3^i*5^j), - which reduces the maximal distance to 1 from 1/3 to 1/8, - thus needing about 1.89 less terms in the Taylor expansion of - the reduced argument. Then log(2^k*3^i*5^j) can be computed - using a combination of log(16/15), log(25/24) and log(81/80), - see Section 6.5 of "A Fortran Multiple-Precision Arithmetic Package", - Richard P. Brent, ACM Transactions on Mathematical Software, 1978. */ - - mpz_init_set_ui (three_n, n); - mpz_mul_ui (three_n, three_n, 3); - k = mpz_sizeinbase (three_n, 2) - 2; - MPFR_ASSERTD (k >= 2); - mpz_clear (three_n); - - /* The reduced argument is n/2^k - 1 = (n-2^k)/2^k. - Compute p = n-2^k. One has: |p| = |n-2^k| < 2^k/3 < n/2 <= LONG_MAX, - so that p and -p both fit in a long. */ - if (k < sizeof (unsigned long) * CHAR_BIT) - n -= 1UL << k; - /* n is now the value of p mod ULONG_MAX+1 */ - p = n > LONG_MAX ? - (long) - n : (long) n; - - MPFR_TMP_MARK(marker); - w = MPFR_PREC(x) + MPFR_INT_CEIL_LOG2 (MPFR_PREC(x)) + 10; - MPFR_GROUP_INIT_2(group, w, t, q); - MPFR_SAVE_EXPO_MARK (expo); - - kk = k; - if (p != 0) - while ((p % 2) == 0) /* replace p/2^kk by (p/2)/2^(kk-1) */ - { - p /= 2; - kk --; - } - - MPFR_ZIV_INIT (loop, w); - for (;;) - { - mpfr_t tmp; - unsigned int err; - unsigned long q0; - - /* we need at most w/log2(2^kk/|p|) terms for an accuracy of w bits */ - mpfr_init2 (tmp, 32); - mpfr_set_ui (tmp, (p > 0) ? p : -p, MPFR_RNDU); - mpfr_log2 (tmp, tmp, MPFR_RNDU); - mpfr_ui_sub (tmp, kk, tmp, MPFR_RNDD); - MPFR_ASSERTN (w <= ULONG_MAX); - mpfr_ui_div (tmp, w, tmp, MPFR_RNDU); - N = mpfr_get_ui (tmp, MPFR_RNDU); - if (N < 2) - N = 2; - lgN = MPFR_INT_CEIL_LOG2 (N) + 1; - mpfr_clear (tmp); - P = (mpz_t *) MPFR_TMP_ALLOC (3 * lgN * sizeof (mpz_t)); - B = P + lgN; - T = B + lgN; - for (i = 0; i < lgN; i++) - { - mpz_init (P[i]); - mpz_init (B[i]); - mpz_init (T[i]); - } - - S (P, &q0, B, T, 1, N, p, kk, 0); - /* mpz_mul (Q[0], B[0], Q[0]); */ - /* mpz_mul_2exp (B[0], B[0], q0); */ - - mpfr_set_z (t, T[0], MPFR_RNDN); /* t = P[0] * (1 + theta_1) */ - mpfr_set_z (q, B[0], MPFR_RNDN); /* q = B[0] * (1 + theta_2) */ - mpfr_mul_2ui (q, q, q0, MPFR_RNDN); /* B[0]*Q[0] */ - mpfr_div (t, t, q, MPFR_RNDN); /* t = T[0]/(B[0]*Q[0])*(1 + theta_3)^3 - = log(n/2^k) * (1 + theta_4)^4 - for |theta_i| < 2^(-w) */ - - /* argument reconstruction: add k*log(2) */ - mpfr_const_log2 (q, MPFR_RNDN); - mpfr_mul_ui (q, q, k, MPFR_RNDN); - mpfr_add (t, t, q, MPFR_RNDN); - for (i = 0; i < lgN; i++) - { - mpz_clear (P[i]); - mpz_clear (B[i]); - mpz_clear (T[i]); - } - /* The maximal error is 5 ulps for P/Q, since |(1+/-u)^4 - 1| < 5*u - for u < 2^(-12), k ulps for k*log(2), and 1 ulp for the addition, - thus at most k+6 ulps. - Note that there might be some cancellation in the addition: the worst - case is when log(1 + p/2^kk) = log(2/3) ~ -0.405, and with n=3 which - gives k=2, thus we add 2*log(2) = 1.386. Thus in the worst case we - have an exponent decrease of 1, which accounts for +1 in the error. */ - err = MPFR_INT_CEIL_LOG2 (k + 6) + 1; - if (MPFR_LIKELY (MPFR_CAN_ROUND (t, w - err, MPFR_PREC(x), rnd_mode))) - break; - - MPFR_ZIV_NEXT (loop, w); - MPFR_GROUP_REPREC_2(group, w, t, q); - } - MPFR_ZIV_FREE (loop); - - inexact = mpfr_set (x, t, rnd_mode); - - MPFR_GROUP_CLEAR(group); - MPFR_TMP_FREE(marker); - - MPFR_SAVE_EXPO_FREE (expo); - return mpfr_check_range (x, inexact, rnd_mode); -} |