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diff --git a/Build/source/libs/mpfr/mpfr-src/src/jyn_asympt.c b/Build/source/libs/mpfr/mpfr-src/src/jyn_asympt.c
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--- a/Build/source/libs/mpfr/mpfr-src/src/jyn_asympt.c
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@@ -1,289 +0,0 @@
-/* mpfr_jn_asympt, mpfr_yn_asympt -- shared code for mpfr_jn and mpfr_yn
-
-Copyright 2007-2020 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. */
-
-#ifdef MPFR_JN
-# define FUNCTION mpfr_jn_asympt
-#else
-# ifdef MPFR_YN
-# define FUNCTION mpfr_yn_asympt
-# else
-# error "neither MPFR_JN nor MPFR_YN is defined"
-# endif
-#endif
-
-/* Implements asymptotic expansion for jn or yn (formulae 9.2.5 and 9.2.6
- from Abramowitz & Stegun).
- Assumes |z| > p log(2)/2, where p is the target precision
- (z can be negative only for jn).
- Return 0 if the expansion does not converge enough (the value 0 as inexact
- flag should not happen for normal input).
- Note: for MPFR_RNDF, it returns 0 if the expansion failed, and a non-zero
- value otherwise (with no other meaning).
-*/
-static int
-FUNCTION (mpfr_ptr res, long n, mpfr_srcptr z, mpfr_rnd_t r)
-{
- mpfr_t s, c, P, Q, t, iz, err_t, err_s, err_u;
- mpfr_prec_t w;
- long k;
- int inex, stop, diverge = 0;
- mpfr_exp_t err2, err;
- MPFR_ZIV_DECL (loop);
-
- mpfr_init2 (c, 64);
-
- /* The terms of the asymptotic expansion grow like mu^(2k)/(8z)^(2k), where
- mu = 4n^2, thus we need mu < 8|z| so that it converges,
- i.e., n^2/2 < |z| */
- MPFR_ASSERTD (n >= 0);
- mpfr_set_ui (c, n, MPFR_RNDU);
- mpfr_mul_ui (c, c, n, MPFR_RNDU);
- mpfr_div_2ui (c, c, 1, MPFR_RNDU);
- if (mpfr_cmpabs (c, z) >= 0)
- {
- mpfr_clear (c);
- return 0; /* asymptotic expansion failed */
- }
-
- w = MPFR_PREC(res) + MPFR_INT_CEIL_LOG2(MPFR_PREC(res)) + 4;
-
- MPFR_ZIV_INIT (loop, w);
- for (;;)
- {
- mpfr_set_prec (c, w);
- mpfr_init2 (s, w);
- mpfr_init2 (P, w);
- mpfr_init2 (Q, w);
- mpfr_init2 (t, w);
- mpfr_init2 (iz, w);
- mpfr_init2 (err_t, 31);
- mpfr_init2 (err_s, 31);
- mpfr_init2 (err_u, 31);
-
- /* Approximate sin(z) and cos(z). In the following, err <= k means that
- the approximate value y and the true value x are related by
- y = x * (1 + u)^k with |u| <= 2^(-w), following Higham's method. */
- mpfr_sin_cos (s, c, z, MPFR_RNDN);
- if (MPFR_IS_NEG(z))
- mpfr_neg (s, s, MPFR_RNDN); /* compute jn/yn(|z|), fix sign later */
- /* The absolute error on s/c is bounded by 1/2 ulp(1/2) <= 2^(-w-1). */
- mpfr_add (t, s, c, MPFR_RNDN);
- mpfr_sub (c, s, c, MPFR_RNDN);
- mpfr_swap (s, t);
- /* now s approximates sin(z)+cos(z), and c approximates sin(z)-cos(z),
- with total absolute error bounded by 2^(1-w). */
-
- /* precompute 1/(8|z|) */
- mpfr_si_div (iz, MPFR_IS_POS(z) ? 1 : -1, z, MPFR_RNDN); /* err <= 1 */
- mpfr_div_2ui (iz, iz, 3, MPFR_RNDN);
-
- /* compute P and Q */
- mpfr_set_ui (P, 1, MPFR_RNDN);
- mpfr_set_ui (Q, 0, MPFR_RNDN);
- mpfr_set_ui (t, 1, MPFR_RNDN); /* current term */
- mpfr_set_ui (err_t, 0, MPFR_RNDN); /* error on t */
- mpfr_set_ui (err_s, 0, MPFR_RNDN); /* error on P and Q (sum of errors) */
- for (k = 1, stop = 0; stop < 4; k++)
- {
- /* compute next term: t(k)/t(k-1) = (2n+2k-1)(2n-2k+1)/(8kz) */
- MPFR_LOG_MSG (("loop (k,stop) = (%ld,%d)\n", k, stop));
- mpfr_mul_si (t, t, 2 * (n + k) - 1, MPFR_RNDN); /* err <= err_k + 1 */
- mpfr_mul_si (t, t, 2 * (n - k) + 1, MPFR_RNDN); /* err <= err_k + 2 */
- mpfr_div_ui (t, t, k, MPFR_RNDN); /* err <= err_k + 3 */
- mpfr_mul (t, t, iz, MPFR_RNDN); /* err <= err_k + 5 */
- /* the relative error on t is bounded by (1+u)^(5k)-1, which is
- bounded by 6ku for 6ku <= 0.02: first |5 log(1+u)| <= |5.5u|
- for |u| <= 0.15, then |exp(5.5u)-1| <= 6u for |u| <= 0.02. */
- mpfr_mul_ui (err_t, t, 6 * k, MPFR_IS_POS(t) ? MPFR_RNDU : MPFR_RNDD);
- mpfr_abs (err_t, err_t, MPFR_RNDN); /* exact */
- /* the absolute error on t is bounded by err_t * 2^(-w) */
- mpfr_abs (err_u, t, MPFR_RNDU);
- mpfr_mul_2ui (err_u, err_u, w, MPFR_RNDU); /* t * 2^w */
- mpfr_add (err_u, err_u, err_t, MPFR_RNDU); /* max|t| * 2^w */
- if (stop >= 2)
- {
- /* take into account the neglected terms: t * 2^w */
- mpfr_div_2ui (err_s, err_s, w, MPFR_RNDU);
- if (MPFR_IS_POS(t))
- mpfr_add (err_s, err_s, t, MPFR_RNDU);
- else
- mpfr_sub (err_s, err_s, t, MPFR_RNDU);
- mpfr_mul_2ui (err_s, err_s, w, MPFR_RNDU);
- stop ++;
- }
- /* if k is odd, add to Q, otherwise to P */
- else if (k & 1)
- {
- /* if k = 1 mod 4, add, otherwise subtract */
- if ((k & 2) == 0)
- mpfr_add (Q, Q, t, MPFR_RNDN);
- else
- mpfr_sub (Q, Q, t, MPFR_RNDN);
- /* check if the next term is smaller than ulp(Q): if EXP(err_u)
- <= EXP(Q), since the current term is bounded by
- err_u * 2^(-w), it is bounded by ulp(Q) */
- if (MPFR_GET_EXP (err_u) <= MPFR_GET_EXP (Q))
- stop ++;
- else
- stop = 0;
- }
- else
- {
- /* if k = 0 mod 4, add, otherwise subtract */
- if ((k & 2) == 0)
- mpfr_add (P, P, t, MPFR_RNDN);
- else
- mpfr_sub (P, P, t, MPFR_RNDN);
- /* check if the next term is smaller than ulp(P) */
- if (MPFR_GET_EXP (err_u) <= MPFR_GET_EXP (P))
- stop ++;
- else
- stop = 0;
- }
- mpfr_add (err_s, err_s, err_t, MPFR_RNDU);
- /* the sum of the rounding errors on P and Q is bounded by
- err_s * 2^(-w) */
-
- /* stop when start to diverge */
- if (stop < 2 &&
- ((MPFR_IS_POS(z) && mpfr_cmp_ui (z, (k + 1) / 2) < 0) ||
- (MPFR_IS_NEG(z) && mpfr_cmp_si (z, - ((k + 1) / 2)) > 0)))
- {
- /* if we have to stop the series because it diverges, then
- increasing the precision will most probably fail, since
- we will stop to the same point, and thus compute a very
- similar approximation */
- diverge = 1;
- stop = 2; /* force stop */
- }
- }
- /* the sum of the total errors on P and Q is bounded by err_s * 2^(-w) */
-
- /* Now combine: the sum of the rounding errors on P and Q is bounded by
- err_s * 2^(-w), and the absolute error on s/c is bounded by 2^(1-w) */
- if ((n & 1) == 0) /* n even: P * (sin + cos) + Q (cos - sin) for jn
- Q * (sin + cos) + P (sin - cos) for yn */
- {
-#ifdef MPFR_JN
- mpfr_mul (c, c, Q, MPFR_RNDN); /* Q * (sin - cos) */
- mpfr_mul (s, s, P, MPFR_RNDN); /* P * (sin + cos) */
-#else
- mpfr_mul (c, c, P, MPFR_RNDN); /* P * (sin - cos) */
- mpfr_mul (s, s, Q, MPFR_RNDN); /* Q * (sin + cos) */
-#endif
- err = MPFR_GET_EXP (c);
- if (MPFR_GET_EXP (s) > err)
- err = MPFR_EXP (s);
-#ifdef MPFR_JN
- mpfr_sub (s, s, c, MPFR_RNDN);
-#else
- mpfr_add (s, s, c, MPFR_RNDN);
-#endif
- }
- else /* n odd: P * (sin - cos) + Q (cos + sin) for jn,
- Q * (sin - cos) - P (cos + sin) for yn */
- {
-#ifdef MPFR_JN
- mpfr_mul (c, c, P, MPFR_RNDN); /* P * (sin - cos) */
- mpfr_mul (s, s, Q, MPFR_RNDN); /* Q * (sin + cos) */
-#else
- mpfr_mul (c, c, Q, MPFR_RNDN); /* Q * (sin - cos) */
- mpfr_mul (s, s, P, MPFR_RNDN); /* P * (sin + cos) */
-#endif
- err = MPFR_GET_EXP (c);
- if (MPFR_GET_EXP (s) > err)
- err = MPFR_EXP (s);
-#ifdef MPFR_JN
- mpfr_add (s, s, c, MPFR_RNDN);
-#else
- mpfr_sub (s, c, s, MPFR_RNDN);
-#endif
- }
- if ((n & 2) != 0)
- mpfr_neg (s, s, MPFR_RNDN);
- if (MPFR_GET_EXP (s) > err)
- err = MPFR_EXP (s);
- /* the absolute error on s is bounded by P*err(s/c) + Q*err(s/c)
- + err(P)*(s/c) + err(Q)*(s/c) + 3 * 2^(err - w - 1)
- <= (|P|+|Q|) * 2^(1-w) + err_s * 2^(1-w) + 2^err * 2^(1-w),
- since |c|, |old_s| <= 2. */
- err2 = (MPFR_GET_EXP (P) >= MPFR_GET_EXP (Q))
- ? MPFR_EXP (P) + 2 : MPFR_EXP (Q) + 2;
- /* (|P| + |Q|) * 2^(1 - w) <= 2^(err2 - w) */
- err = MPFR_GET_EXP (err_s) >= err ? MPFR_EXP (err_s) + 2 : err + 2;
- /* err_s * 2^(1-w) + 2^old_err * 2^(1-w) <= 2^err * 2^(-w) */
- err2 = (err >= err2) ? err + 1 : err2 + 1;
- /* now the absolute error on s is bounded by 2^(err2 - w) */
-
- /* multiply by sqrt(1/(Pi*z)) */
- mpfr_const_pi (c, MPFR_RNDN); /* Pi, err <= 1 */
- mpfr_mul (c, c, z, MPFR_RNDN); /* err <= 2 */
- mpfr_si_div (c, MPFR_IS_POS(z) ? 1 : -1, c, MPFR_RNDN); /* err <= 3 */
- mpfr_sqrt (c, c, MPFR_RNDN); /* err<=5/2, thus the absolute error is
- bounded by 3*u*|c| for |u| <= 0.25 */
- mpfr_mul (err_t, c, s, MPFR_SIGN(c)==MPFR_SIGN(s) ? MPFR_RNDU : MPFR_RNDD);
- mpfr_abs (err_t, err_t, MPFR_RNDU);
- mpfr_mul_ui (err_t, err_t, 3, MPFR_RNDU);
- /* 3*2^(-w)*|old_c|*|s| [see below] is bounded by err_t * 2^(-w) */
- err2 += MPFR_GET_EXP (c);
- /* |old_c| * 2^(err2 - w) [see below] is bounded by 2^(err2-w) */
- mpfr_mul (c, c, s, MPFR_RNDN); /* the absolute error on c is bounded by
- 1/2 ulp(c) + 3*2^(-w)*|old_c|*|s|
- + |old_c| * 2^(err2 - w) */
- /* compute err_t * 2^(-w) + 1/2 ulp(c) = (err_t + 2^EXP(c)) * 2^(-w) */
- err = (MPFR_GET_EXP (err_t) > MPFR_GET_EXP (c)) ?
- MPFR_EXP (err_t) + 1 : MPFR_EXP (c) + 1;
- /* err_t * 2^(-w) + 1/2 ulp(c) <= 2^(err - w) */
- /* now err_t * 2^(-w) bounds 1/2 ulp(c) + 3*2^(-w)*|old_c|*|s| */
- err = (err >= err2) ? err + 1 : err2 + 1;
- /* the absolute error on c is bounded by 2^(err - w) */
-
- mpfr_clear (s);
- mpfr_clear (P);
- mpfr_clear (Q);
- mpfr_clear (t);
- mpfr_clear (iz);
- mpfr_clear (err_t);
- mpfr_clear (err_s);
- mpfr_clear (err_u);
-
- err -= MPFR_GET_EXP (c);
- if (MPFR_LIKELY (MPFR_CAN_ROUND (c, w - err, MPFR_PREC(res), r)))
- break;
- if (diverge != 0)
- {
- MPFR_ZIV_FREE (loop);
- mpfr_clear (c);
- return 0; /* means that the asymptotic expansion failed */
- }
- MPFR_ZIV_NEXT (loop, w);
- }
- MPFR_ZIV_FREE (loop);
-
- inex = (MPFR_IS_POS(z) || ((n & 1) == 0)) ? mpfr_set (res, c, r)
- : mpfr_neg (res, c, r);
- mpfr_clear (c);
-
- /* for RNDF, mpfr_set or mpfr_neg may return 0, but if we return 0, it
- would mean the asymptotic expansion failed, thus we return 1 instead */
- return (r != MPFR_RNDF) ? inex : 1;
-}