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-rw-r--r--Build/source/libs/mpfr/mpfr-src/src/log1p.c243
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diff --git a/Build/source/libs/mpfr/mpfr-src/src/log1p.c b/Build/source/libs/mpfr/mpfr-src/src/log1p.c
deleted file mode 100644
index 6f5605fdb0e..00000000000
--- a/Build/source/libs/mpfr/mpfr-src/src/log1p.c
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@@ -1,243 +0,0 @@
-/* mpfr_log1p -- Compute log(1+x)
-
-Copyright 2001-2020 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"
-
-/* Put in y an approximation of log(1+x) for x small.
- We assume |x| < 1, in which case:
- |x/2| <= |log(1+x)| = |x - x^2/2 + x^3/3 - x^4/4 + ...| <= |x|.
- Return k such that the error is bounded by 2^k*ulp(y).
-*/
-static int
-mpfr_log1p_small (mpfr_ptr y, mpfr_srcptr x)
-{
- mpfr_prec_t p = MPFR_PREC(y), err;
- mpfr_t t, u;
- unsigned long i;
- int k;
-
- MPFR_ASSERTD(MPFR_GET_EXP (x) <= 0); /* ensures |x| < 1 */
-
- /* in the following, theta represents a value with |theta| <= 2^(1-p)
- (might be a different value each time) */
-
- mpfr_init2 (t, p);
- mpfr_init2 (u, p);
- mpfr_set (t, x, MPFR_RNDF); /* t = x * (1 + theta) */
- mpfr_set (y, t, MPFR_RNDF); /* exact */
- for (i = 2; ; i++)
- {
- mpfr_mul (t, t, x, MPFR_RNDF); /* t = x^i * (1 + theta)^i */
- mpfr_div_ui (u, t, i, MPFR_RNDF); /* u = x^i/i * (1 + theta)^(i+1) */
- if (MPFR_GET_EXP (u) <= MPFR_GET_EXP (y) - p) /* |u| < ulp(y) */
- break;
- if (i & 1)
- mpfr_add (y, y, u, MPFR_RNDF); /* error <= ulp(y) */
- else
- mpfr_sub (y, y, u, MPFR_RNDF); /* error <= ulp(y) */
- }
- /* We assume |(1 + theta)^(i+1)| <= 2.
- The neglected part is at most |u| + |u|/2 + ... <= 2|u| < 2 ulp(y)
- which has to be multiplied by |(1 + theta)^(i+1)| <= 2, thus at most
- 4 ulp(y).
- The rounding error on y is bounded by:
- * for the (i-2) add/sub, each error is bounded by ulp(y),
- and since |y| <= |x|, this yields (i-2)*ulp(x)
- * from Lemma 3.1 from [Higham02] (see algorithms.tex),
- the relative error on u at step i is bounded by:
- (i+1)*epsilon/(1-(i+1)*epsilon) where epsilon = 2^(1-p).
- If (i+1)*epsilon <= 1/2, then the relative error on u at
- step i is bounded by 2*(i+1)*epsilon, and since |u| <= 1/2^(i+1)
- at step i, this gives an absolute error bound of;
- 2*epsilon*x*(3/2^3 + 4/2^4 + 5/2^5 + ...) <= 2*2^(1-p)*x =
- 4*2^(-p)*x <= 4*ulp(x).
-
- If (i+1)*epsilon <= 1/2, then the relative error on u at step i
- is bounded by (i+1)*epsilon/(1-(i+1)*epsilon) <= 1, thus it follows
- |(1 + theta)^(i+1)| <= 2.
-
- Finally the total error is bounded by 4*ulp(y) + (i-2)*ulp(x) + 4*ulp(x)
- = 4*ulp(y) + (i+2)*ulp(x).
- Since x/2 <= y, we have ulp(x) <= 2*ulp(y), thus the error is bounded by:
- (2*i+8)*ulp(y).
- */
- err = 2 * i + 8;
- k = __gmpfr_int_ceil_log2 (err);
- MPFR_ASSERTN(k < p);
- /* if k < p, since k = ceil(log2(err)), we have err <= 2^k <= 2^(p-1),
- thus i+4 = err/2 <= 2^(p-2), thus (i+4)*epsilon <= 1/2, which implies
- our assumption (i+1)*epsilon <= 1/2. */
- mpfr_clear (t);
- mpfr_clear (u);
- return k;
-}
-
-/* The computation of log1p is done by
- log1p(x) = log(1+x)
- except when x is very small, in which case log1p(x) = x + tiny error,
- or when x is small, where we use directly the Taylor expansion.
-*/
-
-int
-mpfr_log1p (mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t rnd_mode)
-{
- int comp, inexact;
- mpfr_exp_t ex;
- MPFR_SAVE_EXPO_DECL (expo);
-
- MPFR_LOG_FUNC
- (("x[%Pu]=%.*Rg rnd=%d", mpfr_get_prec (x), mpfr_log_prec, x, rnd_mode),
- ("y[%Pu]=%.*Rg inexact=%d", mpfr_get_prec (y), mpfr_log_prec, y,
- inexact));
-
- if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
- {
- if (MPFR_IS_NAN (x))
- {
- MPFR_SET_NAN (y);
- MPFR_RET_NAN;
- }
- /* check for inf or -inf (result is not defined) */
- else if (MPFR_IS_INF (x))
- {
- if (MPFR_IS_POS (x))
- {
- MPFR_SET_INF (y);
- MPFR_SET_POS (y);
- MPFR_RET (0);
- }
- else
- {
- MPFR_SET_NAN (y);
- MPFR_RET_NAN;
- }
- }
- else /* x is zero */
- {
- MPFR_ASSERTD (MPFR_IS_ZERO (x));
- MPFR_SET_ZERO (y); /* log1p(+/- 0) = +/- 0 */
- MPFR_SET_SAME_SIGN (y, x);
- MPFR_RET (0);
- }
- }
-
- ex = MPFR_GET_EXP (x);
- if (ex < 0) /* -0.5 < x < 0.5 */
- {
- /* For x > 0, abs(log(1+x)-x) < x^2/2.
- For x > -0.5, abs(log(1+x)-x) < x^2. */
- if (MPFR_IS_POS (x))
- MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, x, - ex - 1, 0, 0, rnd_mode, {});
- else
- MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, x, - ex, 0, 1, rnd_mode, {});
- }
-
- comp = mpfr_cmp_si (x, -1);
- /* log1p(x) is undefined for x < -1 */
- if (MPFR_UNLIKELY(comp <= 0))
- {
- if (comp == 0)
- /* x=0: log1p(-1)=-inf (divide-by-zero exception) */
- {
- MPFR_SET_INF (y);
- MPFR_SET_NEG (y);
- MPFR_SET_DIVBY0 ();
- MPFR_RET (0);
- }
- MPFR_SET_NAN (y);
- MPFR_RET_NAN;
- }
-
- MPFR_SAVE_EXPO_MARK (expo);
-
- /* General case */
- {
- /* Declaration of the intermediary variable */
- mpfr_t t;
- /* Declaration of the size variable */
- mpfr_prec_t Ny = MPFR_PREC(y); /* target precision */
- mpfr_prec_t Nt; /* working precision */
- mpfr_exp_t err; /* error */
- MPFR_ZIV_DECL (loop);
-
- /* compute the precision of intermediary variable */
- /* the optimal number of bits : see algorithms.tex */
- Nt = Ny + MPFR_INT_CEIL_LOG2 (Ny) + 6;
-
- /* if |x| is smaller than 2^(-e), we will loose about e bits
- in log(1+x) */
- if (MPFR_EXP(x) < 0)
- Nt += -MPFR_EXP(x);
-
- /* initialize of intermediary variable */
- mpfr_init2 (t, Nt);
-
- /* First computation of log1p */
- MPFR_ZIV_INIT (loop, Nt);
- for (;;)
- {
- int k;
- /* small case: assuming the AGM algorithm used by mpfr_log uses
- log2(p) steps for a precision of p bits, we try the special
- variant whenever EXP(x) <= -p/log2(p). */
- k = 1 + __gmpfr_int_ceil_log2 (Ny); /* the +1 avoids a division by 0
- when Ny=1 */
- if (MPFR_GET_EXP (x) <= - (mpfr_exp_t) (Ny / k))
- /* this implies EXP(x) <= 0 thus x < 1 */
- err = Nt - mpfr_log1p_small (t, x);
- else
- {
- /* compute log1p */
- inexact = mpfr_add_ui (t, x, 1, MPFR_RNDN); /* 1+x */
- /* if inexact = 0, then t = x+1, and the result is simply log(t) */
- if (inexact == 0)
- {
- inexact = mpfr_log (y, t, rnd_mode);
- goto end;
- }
- mpfr_log (t, t, MPFR_RNDN); /* log(1+x) */
-
- /* the error is bounded by (1/2+2^(1-EXP(t))*ulp(t)
- (cf algorithms.tex)
- if EXP(t)>=2, then error <= ulp(t)
- if EXP(t)<=1, then error <= 2^(2-EXP(t))*ulp(t) */
- err = Nt - MAX (0, 2 - MPFR_GET_EXP (t));
- }
-
- if (MPFR_LIKELY (MPFR_CAN_ROUND (t, err, Ny, rnd_mode)))
- break;
-
- /* increase the precision */
- MPFR_ZIV_NEXT (loop, Nt);
- mpfr_set_prec (t, Nt);
- }
- inexact = mpfr_set (y, t, rnd_mode);
-
- end:
- MPFR_ZIV_FREE (loop);
- mpfr_clear (t);
- }
-
- MPFR_SAVE_EXPO_FREE (expo);
- return mpfr_check_range (y, inexact, rnd_mode);
-}