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-rw-r--r--Build/source/libs/mpfr/mpfr-src/src/root.c331
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diff --git a/Build/source/libs/mpfr/mpfr-src/src/root.c b/Build/source/libs/mpfr/mpfr-src/src/root.c
deleted file mode 100644
index a8bd7d04eed..00000000000
--- a/Build/source/libs/mpfr/mpfr-src/src/root.c
+++ /dev/null
@@ -1,331 +0,0 @@
-/* mpfr_root -- kth root.
-
-Copyright 2005-2020 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"
-
- /* The computation of y = x^(1/k) is done as follows, except for large
- values of k, for which this would be inefficient or yield internal
- integer overflows:
-
- Let x = sign * m * 2^(k*e) where m is an integer
-
- with 2^(k*(n-1)) <= m < 2^(k*n) where n = PREC(y)
-
- and m = s^k + t where 0 <= t and m < (s+1)^k
-
- we want that s has n bits i.e. s >= 2^(n-1), or m >= 2^(k*(n-1))
- i.e. m must have at least k*(n-1)+1 bits
-
- then, not taking into account the sign, the result will be
- x^(1/k) = s * 2^e or (s+1) * 2^e according to the rounding mode.
- */
-
-static int
-mpfr_root_aux (mpfr_ptr y, mpfr_srcptr x, unsigned long k,
- mpfr_rnd_t rnd_mode);
-
-int
-mpfr_rootn_ui (mpfr_ptr y, mpfr_srcptr x, unsigned long k, mpfr_rnd_t rnd_mode)
-{
- mpz_t m;
- mpfr_exp_t e, r, sh, f;
- mpfr_prec_t n, size_m, tmp;
- int inexact, negative;
- MPFR_SAVE_EXPO_DECL (expo);
-
- MPFR_LOG_FUNC
- (("x[%Pu]=%.*Rg k=%lu rnd=%d",
- mpfr_get_prec (x), mpfr_log_prec, x, k, rnd_mode),
- ("y[%Pu]=%.*Rg inexact=%d",
- mpfr_get_prec (y), mpfr_log_prec, y, inexact));
-
- if (MPFR_UNLIKELY (k <= 1))
- {
- if (k == 0)
- {
- /* rootn(x,0) is NaN (IEEE 754-2008). */
- MPFR_SET_NAN (y);
- MPFR_RET_NAN;
- }
- else /* y = x^(1/1) = x */
- return mpfr_set (y, x, rnd_mode);
- }
-
- /* Singular values */
- if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
- {
- if (MPFR_IS_NAN (x))
- {
- MPFR_SET_NAN (y); /* NaN^(1/k) = NaN */
- MPFR_RET_NAN;
- }
-
- if (MPFR_IS_INF (x)) /* (+Inf)^(1/k) = +Inf
- (-Inf)^(1/k) = -Inf if k odd
- (-Inf)^(1/k) = NaN if k even */
- {
- if (MPFR_IS_NEG (x) && (k & 1) == 0)
- {
- MPFR_SET_NAN (y);
- MPFR_RET_NAN;
- }
- MPFR_SET_INF (y);
- MPFR_SET_SAME_SIGN (y, x);
- }
- else /* x is necessarily 0: (+0)^(1/k) = +0
- (-0)^(1/k) = -0 */
- {
- MPFR_ASSERTD (MPFR_IS_ZERO (x));
- MPFR_SET_ZERO (y);
- if (MPFR_IS_POS (x) || (k & 1) == 0)
- MPFR_SET_POS (y);
- else
- MPFR_SET_NEG (y);
- }
- MPFR_RET (0);
- }
-
- /* Returns NAN for x < 0 and k even */
- if (MPFR_UNLIKELY (MPFR_IS_NEG (x) && (k & 1) == 0))
- {
- MPFR_SET_NAN (y);
- MPFR_RET_NAN;
- }
-
- /* Special case |x| = 1. Note that if x = -1, then k is odd
- (NaN results have already been filtered), so that y = -1. */
- if (mpfr_cmpabs (x, __gmpfr_one) == 0)
- return mpfr_set (y, x, rnd_mode);
-
- /* General case */
-
- /* For large k, use exp(log(x)/k). The threshold of 100 seems to be quite
- good when the precision goes to infinity. */
- if (k > 100)
- return mpfr_root_aux (y, x, k, rnd_mode);
-
- MPFR_SAVE_EXPO_MARK (expo);
- mpz_init (m);
-
- e = mpfr_get_z_2exp (m, x); /* x = m * 2^e */
- if ((negative = MPFR_IS_NEG(x)))
- mpz_neg (m, m);
- r = e % (mpfr_exp_t) k;
- if (r < 0)
- r += k; /* now r = e (mod k) with 0 <= r < k */
- MPFR_ASSERTD (0 <= r && r < k);
- /* x = (m*2^r) * 2^(e-r) where e-r is a multiple of k */
-
- MPFR_MPZ_SIZEINBASE2 (size_m, m);
- /* for rounding to nearest, we want the round bit to be in the root */
- n = MPFR_PREC (y) + (rnd_mode == MPFR_RNDN);
-
- /* we now multiply m by 2^sh so that root(m,k) will give
- exactly n bits: we want k*(n-1)+1 <= size_m + sh <= k*n
- i.e. sh = k*f + r with f = max(floor((k*n-size_m-r)/k),0) */
- if ((mpfr_exp_t) size_m + r >= k * (mpfr_exp_t) n)
- f = 0; /* we already have too many bits */
- else
- f = (k * (mpfr_exp_t) n - (mpfr_exp_t) size_m - r) / k;
- sh = k * f + r;
- mpz_mul_2exp (m, m, sh);
- e = e - sh;
-
- /* invariant: x = m*2^e, with e divisible by k */
-
- /* we reuse the variable m to store the kth root, since it is not needed
- any more: we just need to know if the root is exact */
- inexact = mpz_root (m, m, k) == 0;
-
- MPFR_MPZ_SIZEINBASE2 (tmp, m);
- sh = tmp - n;
- if (sh > 0) /* we have to flush to 0 the last sh bits from m */
- {
- inexact = inexact || (mpz_scan1 (m, 0) < sh);
- mpz_fdiv_q_2exp (m, m, sh);
- e += k * sh;
- }
-
- if (inexact)
- {
- if (negative)
- rnd_mode = MPFR_INVERT_RND (rnd_mode);
- if (rnd_mode == MPFR_RNDU || rnd_mode == MPFR_RNDA
- || (rnd_mode == MPFR_RNDN && mpz_tstbit (m, 0)))
- inexact = 1, mpz_add_ui (m, m, 1);
- else
- inexact = -1;
- }
-
- /* either inexact is not zero, and the conversion is exact, i.e. inexact
- is not changed; or inexact=0, and inexact is set only when
- rnd_mode=MPFR_RNDN and bit (n+1) from m is 1 */
- inexact += mpfr_set_z (y, m, MPFR_RNDN);
- MPFR_SET_EXP (y, MPFR_GET_EXP (y) + e / (mpfr_exp_t) k);
-
- if (negative)
- {
- MPFR_CHANGE_SIGN (y);
- inexact = -inexact;
- }
-
- mpz_clear (m);
- MPFR_SAVE_EXPO_FREE (expo);
- return mpfr_check_range (y, inexact, rnd_mode);
-}
-
-/* Compute y <- x^(1/k) using exp(log(x)/k).
- Assume all special cases have been eliminated before.
- In the extended exponent range, overflows/underflows are not possible.
- Assume x > 0, or x < 0 and k odd.
- Also assume |x| <> 1 because log(1) = 0, which does not have an exponent
- and would yield a failure in the error bound computation. A priori, this
- constraint is quite artificial because if |x| is close enough to 1, then
- the exponent of log|x| does not need to be used (in the code, err would
- be 1 in such a domain). So this constraint |x| <> 1 could be avoided in
- the code. However, this is an exact case easy to detect, so that such a
- change would be useless. Values very close to 1 are not an issue, since
- an underflow is not possible before the MPFR_GET_EXP.
-*/
-static int
-mpfr_root_aux (mpfr_ptr y, mpfr_srcptr x, unsigned long k, mpfr_rnd_t rnd_mode)
-{
- int inexact, exact_root = 0;
- mpfr_prec_t w; /* working precision */
- mpfr_t absx, t;
- MPFR_GROUP_DECL(group);
- MPFR_TMP_DECL(marker);
- MPFR_ZIV_DECL(loop);
- MPFR_SAVE_EXPO_DECL (expo);
-
- MPFR_TMP_INIT_ABS (absx, x);
-
- MPFR_TMP_MARK(marker);
- w = MPFR_PREC(y) + 10;
- /* Take some guard bits to prepare for the 'expt' lost bits below.
- If |x| < 2^k, then log|x| < k, thus taking log2(k) bits should be fine. */
- if (MPFR_GET_EXP(x) > 0)
- w += MPFR_INT_CEIL_LOG2 (MPFR_GET_EXP(x));
- MPFR_GROUP_INIT_1(group, w, t);
- MPFR_SAVE_EXPO_MARK (expo);
- MPFR_ZIV_INIT (loop, w);
- for (;;)
- {
- mpfr_exp_t expt;
- unsigned int err;
-
- mpfr_log (t, absx, MPFR_RNDN);
- /* t = log|x| * (1 + theta) with |theta| <= 2^(-w) */
- mpfr_div_ui (t, t, k, MPFR_RNDN);
- /* No possible underflow in mpfr_log and mpfr_div_ui. */
- expt = MPFR_GET_EXP (t); /* assumes t <> 0 */
- /* t = log|x|/k * (1 + theta) + eps with |theta| <= 2^(-w)
- and |eps| <= 1/2 ulp(t), thus the total error is bounded
- by 1.5 * 2^(expt - w) */
- mpfr_exp (t, t, MPFR_RNDN);
- /* t = |x|^(1/k) * exp(tau) * (1 + theta1) with
- |tau| <= 1.5 * 2^(expt - w) and |theta1| <= 2^(-w).
- For |tau| <= 0.5 we have |exp(tau)-1| < 4/3*tau, thus
- for w >= expt + 2 we have:
- t = |x|^(1/k) * (1 + 2^(expt+2)*theta2) * (1 + theta1) with
- |theta1|, |theta2| <= 2^(-w).
- If expt+2 > 0, as long as w >= 1, we have:
- t = |x|^(1/k) * (1 + 2^(expt+3)*theta3) with |theta3| < 2^(-w).
- For expt+2 = 0, we have:
- t = |x|^(1/k) * (1 + 2^2*theta3) with |theta3| < 2^(-w).
- Finally for expt+2 < 0 we have:
- t = |x|^(1/k) * (1 + 2*theta3) with |theta3| < 2^(-w).
- */
- err = (expt + 2 > 0) ? expt + 3
- : (expt + 2 == 0) ? 2 : 1;
- /* now t = |x|^(1/k) * (1 + 2^(err-w)) thus the error is at most
- 2^(EXP(t) - w + err) */
- if (MPFR_LIKELY (MPFR_CAN_ROUND(t, w - err, MPFR_PREC(y), rnd_mode)))
- break;
-
- /* If we fail to round correctly, check for an exact result or a
- midpoint result with MPFR_RNDN (regarded as hard-to-round in
- all precisions in order to determine the ternary value). */
- {
- mpfr_t z, zk;
-
- mpfr_init2 (z, MPFR_PREC(y) + (rnd_mode == MPFR_RNDN));
- mpfr_init2 (zk, MPFR_PREC(x));
- mpfr_set (z, t, MPFR_RNDN);
- inexact = mpfr_pow_ui (zk, z, k, MPFR_RNDN);
- exact_root = !inexact && mpfr_equal_p (zk, absx);
- if (exact_root) /* z is the exact root, thus round z directly */
- inexact = mpfr_set4 (y, z, rnd_mode, MPFR_SIGN (x));
- mpfr_clear (zk);
- mpfr_clear (z);
- if (exact_root)
- break;
- }
-
- MPFR_ZIV_NEXT (loop, w);
- MPFR_GROUP_REPREC_1(group, w, t);
- }
- MPFR_ZIV_FREE (loop);
-
- if (!exact_root)
- inexact = mpfr_set4 (y, t, rnd_mode, MPFR_SIGN (x));
-
- MPFR_GROUP_CLEAR(group);
- MPFR_TMP_FREE(marker);
- MPFR_SAVE_EXPO_FREE (expo);
-
- return mpfr_check_range (y, inexact, rnd_mode);
-}
-
-int
-mpfr_root (mpfr_ptr y, mpfr_srcptr x, unsigned long k, mpfr_rnd_t rnd_mode)
-{
- MPFR_LOG_FUNC
- (("x[%Pu]=%.*Rg k=%lu rnd=%d",
- mpfr_get_prec (x), mpfr_log_prec, x, k, rnd_mode),
- ("y[%Pu]=%.*Rg",
- mpfr_get_prec (y), mpfr_log_prec, y));
-
- /* Like mpfr_rootn_ui... */
- if (MPFR_UNLIKELY (k <= 1))
- {
- if (k == 0)
- {
- /* rootn(x,0) is NaN (IEEE 754-2008). */
- MPFR_SET_NAN (y);
- MPFR_RET_NAN;
- }
- else /* y = x^(1/1) = x */
- return mpfr_set (y, x, rnd_mode);
- }
-
- if (MPFR_UNLIKELY (MPFR_IS_ZERO (x)))
- {
- /* The only case that may differ from mpfr_rootn_ui. */
- MPFR_SET_ZERO (y);
- MPFR_SET_SAME_SIGN (y, x);
- MPFR_RET (0);
- }
- else
- return mpfr_rootn_ui (y, x, k, rnd_mode);
-}