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b58ddff026
* merged mpfr 3.0.0 and gmp 5.0.1 in buildtools trunk git-svn-id: file:///srv/svn/repos/haiku/buildtools/trunk@37378 a95241bf-73f2-0310-859d-f6bbb57e9c96
192 lines
6.1 KiB
C
192 lines
6.1 KiB
C
/* Functions for evaluating Gamma(1/3) and Gamma(2/3). Used by mpfr_ai.
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Copyright 2010 Free Software Foundation, Inc.
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Contributed by the Arenaire and Cacao projects, INRIA.
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This file is part of the GNU MPFR Library.
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The GNU MPFR Library is free software; you can redistribute it and/or modify
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it under the terms of the GNU Lesser General Public License as published by
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the Free Software Foundation; either version 3 of the License, or (at your
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option) any later version.
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The GNU MPFR Library is distributed in the hope that it will be useful, but
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WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
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License for more details.
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You should have received a copy of the GNU Lesser General Public License
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along with the GNU MPFR Library; see the file COPYING.LESSER. If not, see
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http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
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51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */
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#define MPFR_NEED_LONGLONG_H
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#include "mpfr-impl.h"
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#define MPFR_ACC_OR_MUL(v) \
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do \
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{ \
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if (v <= ULONG_MAX / acc) \
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acc *= v; \
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else \
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{ \
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mpfr_mul_ui (y, y, acc, mode); acc = v; \
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} \
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} \
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while (0)
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#define MPFR_ACC_OR_DIV(v) \
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do \
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{ \
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if (v <= ULONG_MAX / acc) \
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acc *= v; \
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else \
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{ \
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mpfr_div_ui (y, y, acc, mode); acc = v; \
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} \
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} \
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while (0)
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static void
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mpfr_mul_ui5 (mpfr_ptr y, mpfr_srcptr x,
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unsigned long int v1, unsigned long int v2,
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unsigned long int v3, unsigned long int v4,
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unsigned long int v5, mpfr_rnd_t mode)
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{
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unsigned long int acc = v1;
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mpfr_set (y, x, mode);
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MPFR_ACC_OR_MUL (v2);
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MPFR_ACC_OR_MUL (v3);
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MPFR_ACC_OR_MUL (v4);
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MPFR_ACC_OR_MUL (v5);
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mpfr_mul_ui (y, y, acc, mode);
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}
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void
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mpfr_div_ui2 (mpfr_ptr y, mpfr_srcptr x,
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unsigned long int v1, unsigned long int v2, mpfr_rnd_t mode)
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{
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unsigned long int acc = v1;
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mpfr_set (y, x, mode);
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MPFR_ACC_OR_DIV (v2);
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mpfr_div_ui (y, y, acc, mode);
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}
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static void
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mpfr_div_ui8 (mpfr_ptr y, mpfr_srcptr x,
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unsigned long int v1, unsigned long int v2,
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unsigned long int v3, unsigned long int v4,
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unsigned long int v5, unsigned long int v6,
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unsigned long int v7, unsigned long int v8, mpfr_rnd_t mode)
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{
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unsigned long int acc = v1;
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mpfr_set (y, x, mode);
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MPFR_ACC_OR_DIV (v2);
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MPFR_ACC_OR_DIV (v3);
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MPFR_ACC_OR_DIV (v4);
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MPFR_ACC_OR_DIV (v5);
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MPFR_ACC_OR_DIV (v6);
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MPFR_ACC_OR_DIV (v7);
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MPFR_ACC_OR_DIV (v8);
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mpfr_div_ui (y, y, acc, mode);
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}
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/* Gives an approximation of omega = Gamma(1/3)^6 * sqrt(10) / (12pi^4) */
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/* using C. H. Brown's formula. */
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/* The computed value s satisfies |s-omega| <= 2^{1-prec}*omega */
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/* As usual, the variable s is supposed to be initialized. */
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static void
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mpfr_Browns_const (mpfr_ptr s, mp_prec_t prec)
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{
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mpfr_t uk;
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unsigned long int k;
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mp_prec_t working_prec = prec + 10 + MPFR_INT_CEIL_LOG2 (2 + prec / 10);
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mpfr_init2 (uk, working_prec);
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mpfr_set_prec (s, working_prec);
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mpfr_set_ui (uk, 1, MPFR_RNDN);
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mpfr_set (s, uk, MPFR_RNDN);
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k = 1;
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/* Invariants: uk ~ u(k-1) and s ~ sum(i=0..k-1, u(i)) */
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for (;;)
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{
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mpfr_mul_ui5 (uk, uk, 6 * k - 5, 6 * k - 4, 6 * k - 3, 6 * k - 2,
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6 * k - 1, MPFR_RNDN);
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mpfr_div_ui8 (uk, uk, k, k, 3 * k - 2, 3 * k - 1, 3 * k, 80, 160, 160,
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MPFR_RNDN);
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MPFR_CHANGE_SIGN (uk);
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mpfr_add (s, s, uk, MPFR_RNDN);
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k++;
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if (MPFR_GET_EXP (uk) + prec <= MPFR_GET_EXP (s) + 7)
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break;
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}
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mpfr_clear (uk);
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return;
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}
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/* Returns y such that |Gamma(1/3)-y| <= 2^{1-prec}*Gamma(1/3) */
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static void
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mpfr_gamma_one_third (mpfr_ptr y, mp_prec_t prec)
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{
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mpfr_t tmp, tmp2, tmp3;
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mpfr_init2 (tmp, prec + 9);
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mpfr_init2 (tmp2, prec + 9);
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mpfr_init2 (tmp3, prec + 4);
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mpfr_set_prec (y, prec + 2);
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mpfr_const_pi (tmp, MPFR_RNDN);
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mpfr_sqr (tmp, tmp, MPFR_RNDN);
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mpfr_sqr (tmp, tmp, MPFR_RNDN);
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mpfr_mul_ui (tmp, tmp, 12, MPFR_RNDN);
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mpfr_Browns_const (tmp2, prec + 9);
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mpfr_mul (tmp, tmp, tmp2, MPFR_RNDN);
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mpfr_set_ui (tmp2, 10, MPFR_RNDN);
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mpfr_sqrt (tmp2, tmp2, MPFR_RNDN);
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mpfr_div (tmp, tmp, tmp2, MPFR_RNDN);
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mpfr_sqrt (tmp3, tmp, MPFR_RNDN);
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mpfr_cbrt (y, tmp3, MPFR_RNDN);
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mpfr_clear (tmp);
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mpfr_clear (tmp2);
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mpfr_clear (tmp3);
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return;
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}
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/* Computes y1 and y2 such that: */
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/* |y1-Gamma(1/3)| <= 2^{1-prec}Gamma(1/3) */
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/* and |y2-Gamma(2/3)| <= 2^{1-prec}Gamma(2/3) */
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/* */
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/* Uses the formula Gamma(z)Gamma(1-z) = pi / sin(pi*z) */
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/* to compute Gamma(2/3) from Gamma(1/3). */
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void
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mpfr_gamma_one_and_two_third (mpfr_ptr y1, mpfr_ptr y2, mp_prec_t prec)
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{
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mpfr_t temp;
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mpfr_init2 (temp, prec + 4);
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mpfr_set_prec (y2, prec + 4);
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mpfr_gamma_one_third (y1, prec + 4);
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mpfr_set_ui (temp, 3, MPFR_RNDN);
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mpfr_sqrt (temp, temp, MPFR_RNDN);
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mpfr_mul (temp, y1, temp, MPFR_RNDN);
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mpfr_const_pi (y2, MPFR_RNDN);
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mpfr_mul_2ui (y2, y2, 1, MPFR_RNDN);
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mpfr_div (y2, y2, temp, MPFR_RNDN);
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mpfr_clear (temp);
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}
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