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-rw-r--r--Build/source/libs/mpfr/mpfr-src/src/ai.c690
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diff --git a/Build/source/libs/mpfr/mpfr-src/src/ai.c b/Build/source/libs/mpfr/mpfr-src/src/ai.c
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--- a/Build/source/libs/mpfr/mpfr-src/src/ai.c
+++ /dev/null
@@ -1,690 +0,0 @@
-/* mpfr_ai -- Airy function Ai
-
-Copyright 2010-2020 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"
-
-/* Reminder and notations:
- -----------------------
-
- Ai is the solution of:
- / y'' - x*y = 0
- { Ai(0) = 1/ ( 9^(1/3)*Gamma(2/3) )
- \ Ai'(0) = -1/ ( 3^(1/3)*Gamma(1/3) )
-
- Series development:
- Ai(x) = sum (a_i*x^i)
- = sum (t_i)
-
- Recurrences:
- a_(i+3) = a_i / ((i+2)*(i+3))
- t_(i+3) = t_i * x^3 / ((i+2)*(i+3))
-
- Values:
- a_0 = Ai(0) ~ 0.355
- a_1 = Ai'(0) ~ -0.259
-*/
-
-
-/* Airy function Ai evaluated by the most naive algorithm.
- Assume that x is a finite number. */
-static int
-mpfr_ai1 (mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t rnd)
-{
- MPFR_ZIV_DECL (loop);
- MPFR_SAVE_EXPO_DECL (expo);
- mpfr_prec_t wprec; /* working precision */
- mpfr_prec_t prec; /* target precision */
- mpfr_prec_t err; /* used to estimate the evaluation error */
- mpfr_prec_t correct_bits; /* estimates the number of correct bits*/
- unsigned long int k;
- unsigned long int cond; /* condition number of the series */
- unsigned long int assumed_exponent; /* used as a lowerbound of |EXP(Ai(x))| */
- int r;
- mpfr_t s; /* used to store the partial sum */
- mpfr_t ti, tip1; /* used to store successive values of t_i */
- mpfr_t x3; /* used to store x^3 */
- mpfr_t tmp_sp, tmp2_sp; /* small precision variables */
- unsigned long int x3u; /* used to store ceil(x^3) */
- mpfr_t temp1, temp2;
- int test1, test2;
-
- /* Logging */
- MPFR_LOG_FUNC (
- ("x[%Pu]=%.*Rg rnd=%d", mpfr_get_prec (x), mpfr_log_prec, x, rnd),
- ("y[%Pu]=%.*Rg", mpfr_get_prec (y), mpfr_log_prec, y) );
-
- /* Save current exponents range */
- MPFR_SAVE_EXPO_MARK (expo);
-
- if (MPFR_UNLIKELY (MPFR_IS_ZERO (x)))
- {
- mpfr_t y1, y2;
- prec = MPFR_ADD_PREC (MPFR_PREC (y), 3);
- mpfr_init2 (y1, prec);
- mpfr_init2 (y2, prec);
- MPFR_ZIV_INIT (loop, prec);
-
- /* ZIV loop */
- for (;;)
- {
- mpfr_gamma_one_and_two_third (y1, y2, prec); /* y2 = Gamma(2/3)(1 + delta1), |delta1| <= 2^{1-prec}. */
-
- r = mpfr_set_ui (y1, 9, MPFR_RNDN);
- MPFR_ASSERTD (r == 0);
- mpfr_cbrt (y1, y1, MPFR_RNDN); /* y1 = cbrt(9)(1 + delta2), |delta2| <= 2^{-prec}. */
- mpfr_mul (y1, y1, y2, MPFR_RNDN);
- mpfr_ui_div (y1, 1, y1, MPFR_RNDN);
- if (MPFR_LIKELY (MPFR_CAN_ROUND (y1, prec - 3, MPFR_PREC (y), rnd)))
- break;
- MPFR_ZIV_NEXT (loop, prec);
- }
- r = mpfr_set (y, y1, rnd);
- MPFR_ZIV_FREE (loop);
- MPFR_SAVE_EXPO_FREE (expo);
- mpfr_clear (y1);
- mpfr_clear (y2);
- return mpfr_check_range (y, r, rnd);
- }
-
- /* now x is not zero */
- MPFR_ASSERTD(!MPFR_IS_ZERO(x));
-
- /* FIXME: underflow for large values of |x| ? */
-
-
- /* Set initial precision */
- /* If we compute sum(i=0, N-1, t_i), the relative error is bounded by */
- /* 2*(4N)*2^(1-wprec)*C(|x|)/Ai(x) */
- /* where C(|x|) = 1 if 0<=x<=1 */
- /* and C(|x|) = (1/2)*x^(-1/4)*exp(2/3 x^(3/2)) if x >= 1 */
-
- /* A priori, we do not know N, so we estimate it to ~ prec */
- /* If 0<=x<=1, we estimate Ai(x) ~ 1/8 */
- /* if 1<=x, we estimate Ai(x) ~ (1/4)*x^(-1/4)*exp(-2/3 * x^(3/2)) */
- /* if x<=0, ????? */
-
- /* We begin with 11 guard bits */
- prec = MPFR_ADD_PREC (MPFR_PREC (y), 11);
- MPFR_ZIV_INIT (loop, prec);
-
- /* The working precision is heuristically chosen in order to obtain */
- /* approximately prec correct bits in the sum. To sum up: the sum */
- /* is stopped when the *exact* sum gives ~ prec correct bit. And */
- /* when it is stopped, the accuracy of the computed sum, with respect*/
- /* to the exact one should be ~prec bits. */
- mpfr_init2 (tmp_sp, MPFR_SMALL_PRECISION);
- mpfr_init2 (tmp2_sp, MPFR_SMALL_PRECISION);
- mpfr_abs (tmp_sp, x, MPFR_RNDU);
- mpfr_pow_ui (tmp_sp, tmp_sp, 3, MPFR_RNDU);
- mpfr_sqrt (tmp_sp, tmp_sp, MPFR_RNDU); /* tmp_sp ~ |x|^(3/2) */
-
- /* 0.96179669392597567 >~ 2/3 * log2(e). See algorithms.tex */
- mpfr_set_str (tmp2_sp, "0.96179669392597567", 10, MPFR_RNDU);
- mpfr_mul (tmp2_sp, tmp_sp, tmp2_sp, MPFR_RNDU);
-
- /* cond represents the number of lost bits in the evaluation of the sum */
- if (MPFR_GET_EXP (x) <= 0)
- cond = 0;
- else
- {
- MPFR_BLOCK_DECL (flags);
-
- MPFR_BLOCK (flags, cond = mpfr_get_ui (tmp2_sp, MPFR_RNDU));
- MPFR_ASSERTN (! MPFR_ERANGEFLAG (flags));
- cond -= (MPFR_GET_EXP (x) - 1) / 4 + 1;
- }
-
- /* The variable assumed_exponent is used to store the maximal assumed */
- /* exponent of Ai(x). More precisely, we assume that |Ai(x)| will be */
- /* greater than 2^{-assumed_exponent}. */
- if (MPFR_IS_POS (x))
- {
- if (MPFR_GET_EXP (x) <= 0)
- assumed_exponent = 3;
- else
- {
- unsigned long int t;
- MPFR_BLOCK_DECL (flags);
-
- MPFR_BLOCK (flags, t = mpfr_get_ui (tmp2_sp, MPFR_RNDU));
- MPFR_ASSERTN (! MPFR_ERANGEFLAG (flags));
- assumed_exponent = t + 2 + (MPFR_GET_EXP (x) / 4 + 1);
- MPFR_ASSERTN (assumed_exponent > t);
- }
- }
- /* We do not know Ai (x) yet */
- /* We cover the case when EXP (Ai (x))>=-10 */
- else
- assumed_exponent = 10;
-
- {
- unsigned long int t, u;
-
- t = assumed_exponent + cond;
- MPFR_ASSERTN (t >= cond);
- u = MPFR_INT_CEIL_LOG2 (prec) + 5;
- t += u;
- MPFR_ASSERTN (t >= u);
- wprec = MPFR_ADD_PREC (prec, t);
- }
-
- mpfr_init (ti);
- mpfr_init (tip1);
- mpfr_init (temp1);
- mpfr_init (temp2);
- mpfr_init (x3);
- mpfr_init (s);
-
- /* ZIV loop */
- for (;;)
- {
- MPFR_LOG_MSG (("Working precision: %Pu\n", wprec));
- mpfr_set_prec (ti, wprec);
- mpfr_set_prec (tip1, wprec);
- mpfr_set_prec (x3, wprec);
- mpfr_set_prec (s, wprec);
-
- mpfr_sqr (x3, x, MPFR_RNDU);
- mpfr_mul (x3, x3, x, (MPFR_IS_POS (x)?MPFR_RNDU:MPFR_RNDD)); /* x3=x^3 */
- if (MPFR_IS_NEG (x))
- MPFR_CHANGE_SIGN (x3);
- x3u = mpfr_get_ui (x3, MPFR_RNDU); /* x3u >= ceil(x^3) */
- if (MPFR_IS_NEG (x))
- MPFR_CHANGE_SIGN (x3);
-
- mpfr_gamma_one_and_two_third (temp1, temp2, wprec);
- mpfr_set_ui (ti, 9, MPFR_RNDN);
- mpfr_cbrt (ti, ti, MPFR_RNDN);
- mpfr_mul (ti, ti, temp2, MPFR_RNDN);
- mpfr_ui_div (ti, 1, ti , MPFR_RNDN); /* ti = 1/( Gamma (2/3)*9^(1/3) ) */
-
- mpfr_set_ui (tip1, 3, MPFR_RNDN);
- mpfr_cbrt (tip1, tip1, MPFR_RNDN);
- mpfr_mul (tip1, tip1, temp1, MPFR_RNDN);
- mpfr_neg (tip1, tip1, MPFR_RNDN);
- mpfr_div (tip1, x, tip1, MPFR_RNDN); /* tip1 = -x/(Gamma (1/3)*3^(1/3)) */
-
- mpfr_add (s, ti, tip1, MPFR_RNDN);
-
-
- /* Evaluation of the series */
- k = 2;
- for (;;)
- {
- mpfr_mul (ti, ti, x3, MPFR_RNDN);
- mpfr_mul (tip1, tip1, x3, MPFR_RNDN);
-
- mpfr_div_ui2 (ti, ti, k, (k+1), MPFR_RNDN);
- mpfr_div_ui2 (tip1, tip1, (k+1), (k+2), MPFR_RNDN);
-
- k += 3;
- mpfr_add (s, s, ti, MPFR_RNDN);
- mpfr_add (s, s, tip1, MPFR_RNDN);
-
- /* FIXME: if s==0 */
- test1 = MPFR_IS_ZERO (ti)
- || (MPFR_GET_EXP (ti) + (mpfr_exp_t)prec + 3 <= MPFR_GET_EXP (s));
- test2 = MPFR_IS_ZERO (tip1)
- || (MPFR_GET_EXP (tip1) + (mpfr_exp_t)prec + 3 <= MPFR_GET_EXP (s));
-
- if ( test1 && test2 && (x3u <= k*(k+1)/2) )
- break; /* FIXME: if k*(k+1) overflows */
- }
-
- MPFR_LOG_MSG (("Truncation rank: %lu\n", k));
-
- err = 4 + MPFR_INT_CEIL_LOG2 (k) + cond - MPFR_GET_EXP (s);
-
- /* err is the number of bits lost due to the evaluation error */
- /* wprec-(prec+1): number of bits lost due to the approximation error */
- MPFR_LOG_MSG (("Roundoff error: %Pu\n", err));
- MPFR_LOG_MSG (("Approxim error: %Pu\n", wprec-prec-1));
-
- if (wprec < err + 1)
- correct_bits = 0;
- else if (wprec < err + prec +1)
- correct_bits = wprec - err - 1; /* since wprec > err + 1,
- correct_bits > 0 */
- else
- correct_bits = prec;
-
- if (MPFR_LIKELY (MPFR_CAN_ROUND (s, correct_bits, MPFR_PREC (y), rnd)))
- break;
-
- if (correct_bits == 0)
- {
- assumed_exponent *= 2;
- MPFR_LOG_MSG (("Not a single bit correct (assumed_exponent=%lu)\n",
- assumed_exponent));
- wprec = prec + 5 + MPFR_INT_CEIL_LOG2 (prec) + cond +
- assumed_exponent;
- }
- else if (correct_bits < prec)
- { /* The precision was badly chosen */
- MPFR_LOG_MSG (("Bad assumption on the exponent of Ai(x)"
- " (E=%" MPFR_EXP_FSPEC "d)\n",
- (mpfr_eexp_t) MPFR_GET_EXP (s)));
- wprec = prec + err + 1;
- }
- else
- { /* We are really in a bad case of the TMD */
- MPFR_ZIV_NEXT (loop, prec);
-
- /* We update wprec */
- /* We assume that K will not be multiplied by more than 4 */
- wprec = prec + (MPFR_INT_CEIL_LOG2 (k) + 2) + 5 + cond
- - MPFR_GET_EXP (s);
- }
-
- } /* End of ZIV loop */
-
- MPFR_ZIV_FREE (loop);
-
- r = mpfr_set (y, s, rnd);
-
- mpfr_clear (ti);
- mpfr_clear (tip1);
- mpfr_clear (temp1);
- mpfr_clear (temp2);
- mpfr_clear (x3);
- mpfr_clear (s);
- mpfr_clear (tmp_sp);
- mpfr_clear (tmp2_sp);
-
- MPFR_SAVE_EXPO_FREE (expo);
- return mpfr_check_range (y, r, rnd);
-}
-
-
-/* Airy function Ai evaluated by Smith algorithm.
- Assume that x is a finite non-zero number. */
-static int
-mpfr_ai2 (mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t rnd)
-{
- MPFR_ZIV_DECL (loop);
- MPFR_SAVE_EXPO_DECL (expo);
- mpfr_prec_t wprec; /* working precision */
- mpfr_prec_t prec; /* target precision */
- mpfr_prec_t err; /* used to estimate the evaluation error */
- mpfr_prec_t correctBits; /* estimates the number of correct bits*/
- unsigned long int i, j, L, t;
- unsigned long int cond; /* condition number of the series */
- unsigned long int assumed_exponent; /* used as a lowerbound of |EXP(Ai(x))| */
- int r; /* returned ternary value */
- mpfr_t s; /* used to store the partial sum */
- mpfr_t u0, u1;
- mpfr_t *z; /* used to store the (x^3j) */
- mpfr_t result;
- mpfr_t tmp_sp, tmp2_sp; /* small precision variables */
- unsigned long int x3u; /* used to store ceil (x^3) */
- mpfr_t temp1, temp2;
- int test0, test1;
-
- /* Logging */
- MPFR_LOG_FUNC (
- ("x[%Pu]=%.*Rg rnd=%d", mpfr_get_prec (x), mpfr_log_prec, x, rnd),
- ("y[%Pu]=%.*Rg", mpfr_get_prec (y), mpfr_log_prec, y));
-
- /* Save current exponents range */
- MPFR_SAVE_EXPO_MARK (expo);
-
- /* FIXME: underflow for large values of |x| */
-
- /* Set initial precision */
- /* See the analysis for the naive evaluation */
-
- /* We begin with 11 guard bits */
- prec = MPFR_PREC (y) + 11;
- MPFR_ZIV_INIT (loop, prec);
-
- mpfr_init2 (tmp_sp, MPFR_SMALL_PRECISION);
- mpfr_init2 (tmp2_sp, MPFR_SMALL_PRECISION);
- mpfr_abs (tmp_sp, x, MPFR_RNDU);
- mpfr_pow_ui (tmp_sp, tmp_sp, 3, MPFR_RNDU);
- mpfr_sqrt (tmp_sp, tmp_sp, MPFR_RNDU); /* tmp_sp ~ |x|^(3/2) */
-
- /* 0.96179669392597567 >~ 2/3 * log2(e). See algorithms.tex */
- mpfr_set_str (tmp2_sp, "0.96179669392597567", 10, MPFR_RNDU);
- mpfr_mul (tmp2_sp, tmp_sp, tmp2_sp, MPFR_RNDU);
-
- /* cond represents the number of lost bits in the evaluation of the sum */
- if (MPFR_GET_EXP (x) <= 0)
- cond = 0;
- else
- {
- MPFR_BLOCK_DECL (flags);
-
- MPFR_BLOCK (flags, cond = mpfr_get_ui (tmp2_sp, MPFR_RNDU));
- MPFR_ASSERTN (! MPFR_ERANGEFLAG (flags));
- cond -= (MPFR_GET_EXP (x) - 1) / 4 + 1;
- }
-
- /* This variable is used to store the maximal assumed exponent of */
- /* Ai(x). More precisely, we assume that |Ai(x)| will be greater than */
- /* 2^{-assumed_exponent}. */
- if (MPFR_IS_POS (x))
- {
- if (MPFR_GET_EXP (x) <= 0)
- assumed_exponent = 3;
- else
- {
- unsigned long int t;
- MPFR_BLOCK_DECL (flags);
-
- MPFR_BLOCK (flags, t = mpfr_get_ui (tmp2_sp, MPFR_RNDU));
- MPFR_ASSERTN (! MPFR_ERANGEFLAG (flags));
- assumed_exponent = t + 2 + (MPFR_GET_EXP (x) / 4 + 1);
- MPFR_ASSERTN (assumed_exponent > t);
- }
- }
- /* We do not know Ai(x) yet */
- /* We cover the case when EXP(Ai(x))>=-10 */
- else
- assumed_exponent = 10;
-
- {
- unsigned long int t, u;
-
- t = assumed_exponent + cond;
- MPFR_ASSERTN (t >= cond);
- u = MPFR_INT_CEIL_LOG2 (prec) + 6;
- t += u;
- MPFR_ASSERTN (t >= u);
- wprec = MPFR_ADD_PREC (prec, t);
- }
-
- /* We assume that the truncation rank will be ~ prec */
- L = __gmpfr_isqrt (prec);
- MPFR_LOG_MSG (("size of blocks L = %lu\n", L));
-
- z = (mpfr_t *) mpfr_allocate_func ( (L + 1) * sizeof (mpfr_t) );
- MPFR_ASSERTN (z != NULL);
- for (j=0; j<=L; j++)
- mpfr_init (z[j]);
-
- mpfr_init (s);
- mpfr_init (u0); mpfr_init (u1);
- mpfr_init (result);
- mpfr_init (temp1);
- mpfr_init (temp2);
-
- /* ZIV loop */
- for (;;)
- {
- MPFR_LOG_MSG (("working precision: %Pu\n", wprec));
-
- for (j=0; j<=L; j++)
- mpfr_set_prec (z[j], wprec);
- mpfr_set_prec (s, wprec);
- mpfr_set_prec (u0, wprec); mpfr_set_prec (u1, wprec);
- mpfr_set_prec (result, wprec);
-
- mpfr_set_ui (u0, 1, MPFR_RNDN);
- mpfr_set (u1, x, MPFR_RNDN);
-
- mpfr_set_ui (z[0], 1, MPFR_RNDU);
- mpfr_sqr (z[1], u1, MPFR_RNDU);
- mpfr_mul (z[1], z[1], x, (MPFR_IS_POS (x) ? MPFR_RNDU : MPFR_RNDD) );
-
- if (MPFR_IS_NEG (x))
- MPFR_CHANGE_SIGN (z[1]);
- x3u = mpfr_get_ui (z[1], MPFR_RNDU); /* x3u >= ceil (x^3) */
- if (MPFR_IS_NEG (x))
- MPFR_CHANGE_SIGN (z[1]);
-
- for (j=2; j<=L ;j++)
- {
- if (j%2 == 0)
- mpfr_sqr (z[j], z[j/2], MPFR_RNDN);
- else
- mpfr_mul (z[j], z[j-1], z[1], MPFR_RNDN);
- }
-
- mpfr_gamma_one_and_two_third (temp1, temp2, wprec);
- mpfr_set_ui (u0, 9, MPFR_RNDN);
- mpfr_cbrt (u0, u0, MPFR_RNDN);
- mpfr_mul (u0, u0, temp2, MPFR_RNDN);
- mpfr_ui_div (u0, 1, u0 , MPFR_RNDN); /* u0 = 1/( Gamma (2/3)*9^(1/3) ) */
-
- mpfr_set_ui (u1, 3, MPFR_RNDN);
- mpfr_cbrt (u1, u1, MPFR_RNDN);
- mpfr_mul (u1, u1, temp1, MPFR_RNDN);
- mpfr_neg (u1, u1, MPFR_RNDN);
- mpfr_div (u1, x, u1, MPFR_RNDN); /* u1 = -x/(Gamma (1/3)*3^(1/3)) */
-
- mpfr_set_ui (result, 0, MPFR_RNDN);
- t = 0;
-
- /* Evaluation of the series by Smith' method */
- for (i=0; ; i++)
- {
- t += 3 * L;
-
- /* k = 0 */
- t -= 3;
- mpfr_set (s, z[L-1], MPFR_RNDN);
- for (j=L-2; ; j--)
- {
- t -= 3;
- mpfr_div_ui2 (s, s, (t+2), (t+3), MPFR_RNDN);
- mpfr_add (s, s, z[j], MPFR_RNDN);
- if (j==0)
- break;
- }
- mpfr_mul (s, s, u0, MPFR_RNDN);
- mpfr_add (result, result, s, MPFR_RNDN);
-
- mpfr_mul (u0, u0, z[L], MPFR_RNDN);
- for (j=0; j<=L-1; j++)
- {
- mpfr_div_ui2 (u0, u0, (t + 2), (t + 3), MPFR_RNDN);
- t += 3;
- }
-
- t++;
-
- /* k = 1 */
- t -= 3;
- mpfr_set (s, z[L-1], MPFR_RNDN);
- for (j=L-2; ; j--)
- {
- t -= 3;
- mpfr_div_ui2 (s, s, (t + 2), (t + 3), MPFR_RNDN);
- mpfr_add (s, s, z[j], MPFR_RNDN);
- if (j==0)
- break;
- }
- mpfr_mul (s, s, u1, MPFR_RNDN);
- mpfr_add (result, result, s, MPFR_RNDN);
-
- mpfr_mul (u1, u1, z[L], MPFR_RNDN);
- for (j=0; j<=L-1; j++)
- {
- mpfr_div_ui2 (u1, u1, (t + 2), (t + 3), MPFR_RNDN);
- t += 3;
- }
-
- t++;
-
- /* k = 2 */
- t++;
-
- /* End of the loop over k */
- t -= 3;
-
- test0 = MPFR_IS_ZERO (u0) ||
- MPFR_GET_EXP (u0) + (mpfr_exp_t)prec + 4 <= MPFR_GET_EXP (result);
- test1 = MPFR_IS_ZERO (u1) ||
- MPFR_GET_EXP (u1) + (mpfr_exp_t)prec + 4 <= MPFR_GET_EXP (result);
-
- if ( test0 && test1 && (x3u <= (t + 2) * (t + 3) / 2) )
- break;
- }
-
- MPFR_LOG_MSG (("Truncation rank: %lu\n", t));
-
- err = (5 + MPFR_INT_CEIL_LOG2 (L+1) + MPFR_INT_CEIL_LOG2 (i+1)
- + cond - MPFR_GET_EXP (result));
-
- /* err is the number of bits lost due to the evaluation error */
- /* wprec-(prec+1): number of bits lost due to the approximation error */
- MPFR_LOG_MSG (("Roundoff error: %Pu\n", err));
- MPFR_LOG_MSG (("Approxim error: %Pu\n", wprec - prec - 1));
-
- if (wprec < err+1)
- correctBits = 0;
- else
- {
- if (wprec < err+prec+1)
- correctBits = wprec - err - 1;
- else
- correctBits = prec;
- }
-
- if (MPFR_LIKELY (MPFR_CAN_ROUND (result, correctBits,
- MPFR_PREC (y), rnd)))
- break;
-
- for (j=0; j<=L; j++)
- mpfr_clear (z[j]);
- mpfr_free_func (z, (L + 1) * sizeof (mpfr_t));
- L = __gmpfr_isqrt (t);
- MPFR_LOG_MSG (("size of blocks L = %lu\n", L));
- z = (mpfr_t *) mpfr_allocate_func ( (L + 1) * sizeof (mpfr_t));
- MPFR_ASSERTN (z != NULL);
- for (j=0; j<=L; j++)
- mpfr_init (z[j]);
-
- if (correctBits == 0)
- {
- assumed_exponent *= 2;
- MPFR_LOG_MSG (("Not a single bit correct (assumed_exponent=%lu)\n",
- assumed_exponent));
- wprec = prec + 6 + MPFR_INT_CEIL_LOG2 (t) + cond + assumed_exponent;
- }
- else
- {
- if (correctBits < prec)
- { /* The precision was badly chosen */
- MPFR_LOG_MSG (("Bad assumption on the exponent of Ai(x)"
- " (E=%" MPFR_EXP_FSPEC "d)\n",
- (mpfr_eexp_t) MPFR_GET_EXP (result)));
- wprec = prec + err + 1;
- }
- else
- { /* We are really in a bad case of the TMD */
- MPFR_ZIV_NEXT (loop, prec);
-
- /* We update wprec */
- /* We assume that t will not be multiplied by more than 4 */
- wprec = (prec + (MPFR_INT_CEIL_LOG2 (t) + 2) + 6 + cond
- - MPFR_GET_EXP (result));
- }
- }
- } /* End of ZIV loop */
-
- MPFR_ZIV_FREE (loop);
-
- r = mpfr_set (y, result, rnd);
-
- mpfr_clear (tmp_sp);
- mpfr_clear (tmp2_sp);
- for (j=0; j<=L; j++)
- mpfr_clear (z[j]);
- mpfr_free_func (z, (L + 1) * sizeof (mpfr_t));
-
- mpfr_clear (s);
- mpfr_clear (u0); mpfr_clear (u1);
- mpfr_clear (result);
- mpfr_clear (temp1);
- mpfr_clear (temp2);
-
- MPFR_SAVE_EXPO_FREE (expo);
- return mpfr_check_range (y, r, rnd);
-}
-
-/* We consider that the boundary between the area where the naive method
- should preferably be used and the area where Smith' method should preferably
- be used has the following form:
- it is a triangle defined by two lines (one for the negative values of x, and
- one for the positive values of x) crossing at x=0.
-
- More precisely,
-
- * If x<0 and MPFR_AI_THRESHOLD1*x + MPFR_AI_THRESHOLD2*prec > MPFR_AI_SCALE,
- use Smith' algorithm;
- * If x>0 and MPFR_AI_THRESHOLD3*x + MPFR_AI_THRESHOLD2*prec > MPFR_AI_SCALE,
- use Smith' algorithm;
- * otherwise, use the naive method.
-*/
-
-#define MPFR_AI_SCALE 1048576
-
-int
-mpfr_ai (mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t rnd)
-{
- mpfr_t temp1, temp2;
- int use_ai2;
- MPFR_SAVE_EXPO_DECL (expo);
-
- /* Special cases */
- if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
- {
- if (MPFR_IS_NAN (x))
- {
- MPFR_SET_NAN (y);
- MPFR_RET_NAN;
- }
- else if (MPFR_IS_INF (x))
- return mpfr_set_ui (y, 0, rnd);
- /* the cases x = +0 or -0 will be treated below */
- }
-
- /* The exponent range must be large enough for the computation of temp1. */
- MPFR_SAVE_EXPO_MARK (expo);
-
- mpfr_init2 (temp1, MPFR_SMALL_PRECISION);
- mpfr_init2 (temp2, MPFR_SMALL_PRECISION);
-
- mpfr_set (temp1, x, MPFR_RNDN);
- mpfr_set_si (temp2, MPFR_AI_THRESHOLD2, MPFR_RNDN);
- mpfr_mul_ui (temp2, temp2, MPFR_PREC (y) > ULONG_MAX ?
- ULONG_MAX : (unsigned long) MPFR_PREC (y), MPFR_RNDN);
-
- if (MPFR_IS_NEG (x))
- mpfr_mul_si (temp1, temp1, MPFR_AI_THRESHOLD1, MPFR_RNDN);
- else
- mpfr_mul_si (temp1, temp1, MPFR_AI_THRESHOLD3, MPFR_RNDN);
-
- mpfr_add (temp1, temp1, temp2, MPFR_RNDN);
- mpfr_clear (temp2);
-
- use_ai2 = mpfr_cmp_si (temp1, MPFR_AI_SCALE) > 0;
- mpfr_clear (temp1);
-
- MPFR_SAVE_EXPO_FREE (expo); /* Ignore all previous exceptions. */
-
- /* we use ai2 if |x|*AI_THRESHOLD1/3 + PREC(y)*AI_THRESHOLD2 > AI_SCALE,
- which means x cannot be zero in mpfr_ai2 */
- return use_ai2 ? mpfr_ai2 (y, x, rnd) : mpfr_ai1 (y, x, rnd);
-}