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diff --git a/Build/source/libs/mpfr/mpfr-src/src/agm.c b/Build/source/libs/mpfr/mpfr-src/src/agm.c
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--- a/Build/source/libs/mpfr/mpfr-src/src/agm.c
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-/* mpfr_agm -- arithmetic-geometric mean of two floating-point numbers
-
-Copyright 1999-2020 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"
-
-/* agm(x,y) is between x and y, so we don't need to save exponent range */
-int
-mpfr_agm (mpfr_ptr r, mpfr_srcptr op2, mpfr_srcptr op1, mpfr_rnd_t rnd_mode)
-{
- int compare, inexact;
- mp_size_t s;
- mpfr_prec_t p, q;
- mp_limb_t *up, *vp, *ufp, *vfp;
- mpfr_t u, v, uf, vf, sc1, sc2;
- mpfr_exp_t scaleop = 0, scaleit;
- unsigned long n; /* number of iterations */
- MPFR_ZIV_DECL (loop);
- MPFR_TMP_DECL(marker);
- MPFR_SAVE_EXPO_DECL (expo);
-
- MPFR_LOG_FUNC
- (("op2[%Pu]=%.*Rg op1[%Pu]=%.*Rg rnd=%d",
- mpfr_get_prec (op2), mpfr_log_prec, op2,
- mpfr_get_prec (op1), mpfr_log_prec, op1, rnd_mode),
- ("r[%Pu]=%.*Rg inexact=%d",
- mpfr_get_prec (r), mpfr_log_prec, r, inexact));
-
- /* Deal with special values */
- if (MPFR_ARE_SINGULAR (op1, op2))
- {
- /* If a or b is NaN, the result is NaN */
- if (MPFR_IS_NAN(op1) || MPFR_IS_NAN(op2))
- {
- MPFR_SET_NAN(r);
- MPFR_RET_NAN;
- }
- /* now one of a or b is Inf or 0 */
- /* If a and b is +Inf, the result is +Inf.
- Otherwise if a or b is -Inf or 0, the result is NaN */
- else if (MPFR_IS_INF(op1) || MPFR_IS_INF(op2))
- {
- if (MPFR_IS_STRICTPOS(op1) && MPFR_IS_STRICTPOS(op2))
- {
- MPFR_SET_INF(r);
- MPFR_SET_SAME_SIGN(r, op1);
- MPFR_RET(0); /* exact */
- }
- else
- {
- MPFR_SET_NAN(r);
- MPFR_RET_NAN;
- }
- }
- else /* a and b are neither NaN nor Inf, and one is zero */
- { /* If a or b is 0, the result is +0, in particular because the
- result is always >= 0 with our definition (Maple sometimes
- chooses a different sign for GaussAGM, but it uses another
- definition, with possible negative results). */
- MPFR_ASSERTD (MPFR_IS_ZERO (op1) || MPFR_IS_ZERO (op2));
- MPFR_SET_POS (r);
- MPFR_SET_ZERO (r);
- MPFR_RET (0); /* exact */
- }
- }
-
- /* If a or b is negative (excluding -Infinity), the result is NaN */
- if (MPFR_UNLIKELY(MPFR_IS_NEG(op1) || MPFR_IS_NEG(op2)))
- {
- MPFR_SET_NAN(r);
- MPFR_RET_NAN;
- }
-
- /* Precision of the following calculus */
- q = MPFR_PREC(r);
- p = q + MPFR_INT_CEIL_LOG2(q) + 15;
- MPFR_ASSERTD (p >= 7); /* see algorithms.tex */
- s = MPFR_PREC2LIMBS (p);
-
- /* b (op2) and a (op1) are the 2 operands but we want b >= a */
- compare = mpfr_cmp (op1, op2);
- if (MPFR_UNLIKELY( compare == 0 ))
- return mpfr_set (r, op1, rnd_mode);
- else if (compare > 0)
- {
- mpfr_srcptr t = op1;
- op1 = op2;
- op2 = t;
- }
-
- /* Now b (=op2) > a (=op1) */
-
- MPFR_SAVE_EXPO_MARK (expo);
-
- MPFR_TMP_MARK(marker);
-
- /* Main loop */
- MPFR_ZIV_INIT (loop, p);
- for (;;)
- {
- mpfr_prec_t eq;
- unsigned long err = 0; /* must be set to 0 at each Ziv iteration */
- MPFR_BLOCK_DECL (flags);
-
- /* Init temporary vars */
- MPFR_TMP_INIT (up, u, p, s);
- MPFR_TMP_INIT (vp, v, p, s);
- MPFR_TMP_INIT (ufp, uf, p, s);
- MPFR_TMP_INIT (vfp, vf, p, s);
-
- /* Calculus of un and vn */
- retry:
- MPFR_BLOCK (flags,
- mpfr_mul (u, op1, op2, MPFR_RNDN);
- /* mpfr_mul(...): faster since PREC(op) < PREC(u) */
- mpfr_add (v, op1, op2, MPFR_RNDN);
- /* mpfr_add with !=prec is still good */);
- if (MPFR_UNLIKELY (MPFR_OVERFLOW (flags) || MPFR_UNDERFLOW (flags)))
- {
- mpfr_exp_t e1 , e2;
-
- MPFR_ASSERTN (scaleop == 0);
- e1 = MPFR_GET_EXP (op1);
- e2 = MPFR_GET_EXP (op2);
-
- /* Let's determine scaleop to avoid an overflow/underflow. */
- if (MPFR_OVERFLOW (flags))
- {
- /* Let's recall that emin <= e1 <= e2 <= emax.
- There has been an overflow. Thus e2 >= emax/2.
- If the mpfr_mul overflowed, then e1 + e2 > emax.
- If the mpfr_add overflowed, then e2 = emax.
- We want: (e1 + scale) + (e2 + scale) <= emax,
- i.e. scale <= (emax - e1 - e2) / 2. Let's take
- scale = min(floor((emax - e1 - e2) / 2), -1).
- This is OK, as:
- 1. emin <= scale <= -1.
- 2. e1 + scale >= emin. Indeed:
- * If e1 + e2 > emax, then
- e1 + scale >= e1 + (emax - e1 - e2) / 2 - 1
- >= (emax + e1 - emax) / 2 - 1
- >= e1 / 2 - 1 >= emin.
- * Otherwise, mpfr_mul didn't overflow, therefore
- mpfr_add overflowed and e2 = emax, so that
- e1 > emin (see restriction below).
- e1 + scale > emin - 1, thus e1 + scale >= emin.
- 3. e2 + scale <= emax, since scale < 0. */
- if (e1 + e2 > MPFR_EMAX_MAX)
- {
- scaleop = - (((e1 + e2) - MPFR_EMAX_MAX + 1) / 2);
- MPFR_ASSERTN (scaleop < 0);
- }
- else
- {
- /* The addition necessarily overflowed. */
- MPFR_ASSERTN (e2 == MPFR_EMAX_MAX);
- /* The case where e1 = emin and e2 = emax is not supported
- here. This would mean that the precision of e2 would be
- huge (and possibly not supported in practice anyway). */
- MPFR_ASSERTN (e1 > MPFR_EMIN_MIN);
- /* Note: this case is probably impossible to have in practice
- since we need e2 = emax, and no overflow in the product.
- Since the product is >= 2^(e1+e2-2), it implies
- e1 + e2 - 2 <= emax, thus e1 <= 2. Now to get an overflow
- we need op1 >= 1/2 ulp(op2), which implies that the
- precision of op2 should be at least emax-2. On a 64-bit
- computer this is impossible to have, and would require
- a huge amount of memory on a 32-bit computer. */
- scaleop = -1;
- }
-
- }
- else /* underflow only (in the multiplication) */
- {
- /* We have e1 + e2 <= emin (so, e1 <= e2 <= 0).
- We want: (e1 + scale) + (e2 + scale) >= emin + 1,
- i.e. scale >= (emin + 1 - e1 - e2) / 2. let's take
- scale = ceil((emin + 1 - e1 - e2) / 2). This is OK, as:
- 1. 1 <= scale <= emax.
- 2. e1 + scale >= emin + 1 >= emin.
- 3. e2 + scale <= scale <= emax. */
- MPFR_ASSERTN (e1 <= e2 && e2 <= 0);
- scaleop = (MPFR_EMIN_MIN + 2 - e1 - e2) / 2;
- MPFR_ASSERTN (scaleop > 0);
- }
-
- MPFR_ALIAS (sc1, op1, MPFR_SIGN (op1), e1 + scaleop);
- MPFR_ALIAS (sc2, op2, MPFR_SIGN (op2), e2 + scaleop);
- op1 = sc1;
- op2 = sc2;
- MPFR_LOG_MSG (("Exception in pre-iteration, scale = %"
- MPFR_EXP_FSPEC "d\n", scaleop));
- goto retry;
- }
-
- MPFR_CLEAR_FLAGS ();
- mpfr_sqrt (u, u, MPFR_RNDN);
- mpfr_div_2ui (v, v, 1, MPFR_RNDN);
-
- scaleit = 0;
- n = 1;
- while (mpfr_cmp2 (u, v, &eq) != 0 && eq <= p - 2)
- {
- MPFR_BLOCK_DECL (flags2);
-
- MPFR_LOG_MSG (("Iteration n = %lu\n", n));
-
- retry2:
- mpfr_add (vf, u, v, MPFR_RNDN); /* No overflow? */
- mpfr_div_2ui (vf, vf, 1, MPFR_RNDN);
- /* See proof in algorithms.tex */
- if (eq > p / 4)
- {
- mpfr_t w;
- MPFR_BLOCK_DECL (flags3);
-
- MPFR_LOG_MSG (("4*eq > p\n", 0));
-
- /* vf = V(k) */
- mpfr_init2 (w, (p + 1) / 2);
- MPFR_BLOCK
- (flags3,
- mpfr_sub (w, v, u, MPFR_RNDN); /* e = V(k-1)-U(k-1) */
- mpfr_sqr (w, w, MPFR_RNDN); /* e = e^2 */
- mpfr_div_2ui (w, w, 4, MPFR_RNDN); /* e*= (1/2)^2*1/4 */
- mpfr_div (w, w, vf, MPFR_RNDN); /* 1/4*e^2/V(k) */
- );
- if (MPFR_LIKELY (! MPFR_UNDERFLOW (flags3)))
- {
- mpfr_sub (v, vf, w, MPFR_RNDN);
- err = MPFR_GET_EXP (vf) - MPFR_GET_EXP (v); /* 0 or 1 */
- mpfr_clear (w);
- break;
- }
- /* There has been an underflow because of the cancellation
- between V(k-1) and U(k-1). Let's use the conventional
- method. */
- MPFR_LOG_MSG (("4*eq > p -> underflow\n", 0));
- mpfr_clear (w);
- MPFR_CLEAR_UNDERFLOW ();
- }
- /* U(k) increases, so that U.V can overflow (but not underflow). */
- MPFR_BLOCK (flags2, mpfr_mul (uf, u, v, MPFR_RNDN););
- if (MPFR_UNLIKELY (MPFR_OVERFLOW (flags2)))
- {
- mpfr_exp_t scale2;
-
- scale2 = - (((MPFR_GET_EXP (u) + MPFR_GET_EXP (v))
- - MPFR_EMAX_MAX + 1) / 2);
- MPFR_EXP (u) += scale2;
- MPFR_EXP (v) += scale2;
- scaleit += scale2;
- MPFR_LOG_MSG (("Overflow in iteration n = %lu, scaleit = %"
- MPFR_EXP_FSPEC "d (%" MPFR_EXP_FSPEC "d)\n",
- n, scaleit, scale2));
- MPFR_CLEAR_OVERFLOW ();
- goto retry2;
- }
- mpfr_sqrt (u, uf, MPFR_RNDN);
- mpfr_swap (v, vf);
- n ++;
- }
-
- MPFR_LOG_MSG (("End of iterations (n = %lu)\n", n));
-
- /* the error on v is bounded by (18n+51) ulps, or twice if there
- was an exponent loss in the final subtraction */
- err += MPFR_INT_CEIL_LOG2(18 * n + 51); /* 18n+51 should not overflow
- since n is about log(p) */
- /* we should have n+2 <= 2^(p/4) [see algorithms.tex] */
- if (MPFR_LIKELY (MPFR_INT_CEIL_LOG2(n + 2) <= p / 4 &&
- MPFR_CAN_ROUND (v, p - err, q, rnd_mode)))
- break; /* Stop the loop */
-
- /* Next iteration */
- MPFR_ZIV_NEXT (loop, p);
- s = MPFR_PREC2LIMBS (p);
- }
- MPFR_ZIV_FREE (loop);
-
- if (MPFR_UNLIKELY ((__gmpfr_flags & (MPFR_FLAGS_ALL ^ MPFR_FLAGS_INEXACT))
- != 0))
- {
- MPFR_ASSERTN (! mpfr_overflow_p ()); /* since mpfr_clear_flags */
- MPFR_ASSERTN (! mpfr_underflow_p ()); /* since mpfr_clear_flags */
- MPFR_ASSERTN (! mpfr_divby0_p ()); /* since mpfr_clear_flags */
- MPFR_ASSERTN (! mpfr_nanflag_p ()); /* since mpfr_clear_flags */
- }
-
- /* Setting of the result */
- inexact = mpfr_set (r, v, rnd_mode);
- MPFR_EXP (r) -= scaleop + scaleit;
-
- /* Let's clean */
- MPFR_TMP_FREE(marker);
-
- MPFR_SAVE_EXPO_FREE (expo);
- /* From the definition of the AGM, underflow and overflow
- are not possible. */
- return mpfr_check_range (r, inexact, rnd_mode);
- /* agm(u,v) can be exact for u, v rational only for u=v.
- Proof (due to Nicolas Brisebarre): it suffices to consider
- u=1 and v<1. Then 1/AGM(1,v) = 2F1(1/2,1/2,1;1-v^2),
- and a theorem due to G.V. Chudnovsky states that for x a
- non-zero algebraic number with |x|<1, then
- 2F1(1/2,1/2,1;x) and 2F1(-1/2,1/2,1;x) are algebraically
- independent over Q. */
-}