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-rw-r--r--Build/source/libs/mpfr/mpfr-src/src/erfc.c277
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diff --git a/Build/source/libs/mpfr/mpfr-src/src/erfc.c b/Build/source/libs/mpfr/mpfr-src/src/erfc.c
deleted file mode 100644
index 09111039e41..00000000000
--- a/Build/source/libs/mpfr/mpfr-src/src/erfc.c
+++ /dev/null
@@ -1,277 +0,0 @@
-/* mpfr_erfc -- The Complementary Error Function of a floating-point number
-
-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"
-
-/* erfc(x) = 1 - erf(x) */
-
-/* Put in y an approximation of erfc(x) for large x, using formulae 7.1.23 and
- 7.1.24 from Abramowitz and Stegun.
- Returns e such that the error is bounded by 2^e ulp(y),
- or returns 0 in case of underflow.
-*/
-static mpfr_exp_t
-mpfr_erfc_asympt (mpfr_ptr y, mpfr_srcptr x)
-{
- mpfr_t t, xx, err;
- unsigned long k;
- mpfr_prec_t prec = MPFR_PREC(y);
- mpfr_exp_t exp_err;
-
- mpfr_init2 (t, prec);
- mpfr_init2 (xx, prec);
- mpfr_init2 (err, 31);
- /* let u = 2^(1-p), and let us represent the error as (1+u)^err
- with a bound for err */
- mpfr_sqr (xx, x, MPFR_RNDD); /* err <= 1 */
- mpfr_ui_div (xx, 1, xx, MPFR_RNDU); /* upper bound for 1/(2x^2), err <= 2 */
- mpfr_div_2ui (xx, xx, 1, MPFR_RNDU); /* exact */
- mpfr_set_ui (t, 1, MPFR_RNDN); /* current term, exact */
- mpfr_set (y, t, MPFR_RNDN); /* current sum */
- mpfr_set_ui (err, 0, MPFR_RNDN);
- for (k = 1; ; k++)
- {
- mpfr_mul_ui (t, t, 2 * k - 1, MPFR_RNDU); /* err <= 4k-3 */
- mpfr_mul (t, t, xx, MPFR_RNDU); /* err <= 4k */
- /* for -1 < x < 1, and |nx| < 1, we have |(1+x)^n| <= 1+7/4|nx|.
- Indeed, for x>=0: log((1+x)^n) = n*log(1+x) <= n*x. Let y=n*x < 1,
- then exp(y) <= 1+7/4*y.
- For x<=0, let x=-x, we can prove by induction that (1-x)^n >= 1-n*x.*/
- mpfr_mul_2si (err, err, MPFR_GET_EXP (y) - MPFR_GET_EXP (t), MPFR_RNDU);
- mpfr_add_ui (err, err, 14 * k, MPFR_RNDU); /* 2^(1-p) * t <= 2 ulp(t) */
- mpfr_div_2si (err, err, MPFR_GET_EXP (y) - MPFR_GET_EXP (t), MPFR_RNDU);
- if (MPFR_GET_EXP (t) + (mpfr_exp_t) prec <= MPFR_GET_EXP (y))
- {
- /* the truncation error is bounded by |t| < ulp(y) */
- mpfr_add_ui (err, err, 1, MPFR_RNDU);
- break;
- }
- if (k & 1)
- mpfr_sub (y, y, t, MPFR_RNDN);
- else
- mpfr_add (y, y, t, MPFR_RNDN);
- }
- /* the error on y is bounded by err*ulp(y) */
- mpfr_sqr (t, x, MPFR_RNDU); /* rel. err <= 2^(1-p) */
- mpfr_div_2ui (err, err, 3, MPFR_RNDU); /* err/8 */
- mpfr_add (err, err, t, MPFR_RNDU); /* err/8 + xx */
- mpfr_mul_2ui (err, err, 3, MPFR_RNDU); /* err + 8*xx */
- mpfr_exp (t, t, MPFR_RNDU); /* err <= 1/2*ulp(t) + err(x*x)*t
- <= 1/2*ulp(t)+2*|x*x|*ulp(t)
- <= (2*|x*x|+1/2)*ulp(t) */
- mpfr_mul (t, t, x, MPFR_RNDN); /* err <= 1/2*ulp(t) + (4*|x*x|+1)*ulp(t)
- <= (4*|x*x|+3/2)*ulp(t) */
- mpfr_const_pi (xx, MPFR_RNDZ); /* err <= ulp(Pi) */
- mpfr_sqrt (xx, xx, MPFR_RNDN); /* err <= 1/2*ulp(xx) + ulp(Pi)/2/sqrt(Pi)
- <= 3/2*ulp(xx) */
- mpfr_mul (t, t, xx, MPFR_RNDN); /* err <= (8 |xx| + 13/2) * ulp(t) */
- mpfr_div (y, y, t, MPFR_RNDN); /* the relative error on input y is bounded
- by (1+u)^err with u = 2^(1-p), that on
- t is bounded by (1+u)^(8 |xx| + 13/2),
- thus that on output y is bounded by
- 8 |xx| + 7 + err. */
-
- if (MPFR_IS_ZERO(y))
- {
- /* If y is zero, most probably we have underflow. We check it directly
- using the fact that erfc(x) <= exp(-x^2)/sqrt(Pi)/x for x >= 0.
- We compute an upper approximation of exp(-x^2)/sqrt(Pi)/x.
- */
- mpfr_sqr (t, x, MPFR_RNDD); /* t <= x^2 */
- mpfr_neg (t, t, MPFR_RNDU); /* -x^2 <= t */
- mpfr_exp (t, t, MPFR_RNDU); /* exp(-x^2) <= t */
- mpfr_const_pi (xx, MPFR_RNDD); /* xx <= sqrt(Pi), cached */
- mpfr_mul (xx, xx, x, MPFR_RNDD); /* xx <= sqrt(Pi)*x */
- mpfr_div (y, t, xx, MPFR_RNDN); /* if y is zero, this means that the upper
- approximation of exp(-x^2)/sqrt(Pi)/x
- is nearer from 0 than from 2^(-emin-1),
- thus we have underflow. */
- exp_err = 0;
- }
- else
- {
- mpfr_add_ui (err, err, 7, MPFR_RNDU);
- exp_err = MPFR_GET_EXP (err);
- }
-
- mpfr_clear (t);
- mpfr_clear (xx);
- mpfr_clear (err);
- return exp_err;
-}
-
-int
-mpfr_erfc (mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t rnd)
-{
- int inex;
- mpfr_t tmp;
- mpfr_exp_t te, err;
- mpfr_prec_t prec;
- mpfr_exp_t emin = mpfr_get_emin ();
- MPFR_SAVE_EXPO_DECL (expo);
- MPFR_ZIV_DECL (loop);
-
- MPFR_LOG_FUNC
- (("x[%Pu]=%.*Rg rnd=%d", mpfr_get_prec (x), mpfr_log_prec, x, rnd),
- ("y[%Pu]=%.*Rg inexact=%d", mpfr_get_prec (y), mpfr_log_prec, y, inex));
-
- if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
- {
- if (MPFR_IS_NAN (x))
- {
- MPFR_SET_NAN (y);
- MPFR_RET_NAN;
- }
- /* erfc(+inf) = 0+, erfc(-inf) = 2 erfc (0) = 1 */
- else if (MPFR_IS_INF (x))
- return mpfr_set_ui (y, MPFR_IS_POS (x) ? 0 : 2, rnd);
- else
- return mpfr_set_ui (y, 1, rnd);
- }
-
- if (MPFR_IS_POS (x))
- {
- /* by default, emin = 1-2^30, thus the smallest representable
- number is 1/2*2^emin = 2^(-2^30):
- for x >= 27282, erfc(x) < 2^(-2^30-1), and
- for x >= 1787897414, erfc(x) < 2^(-2^62-1).
- */
- if ((emin >= -1073741823 && mpfr_cmp_ui (x, 27282) >= 0) ||
- mpfr_cmp_ui (x, 1787897414) >= 0)
- {
- /* May be incorrect if MPFR_EMAX_MAX >= 2^62. */
- MPFR_STAT_STATIC_ASSERT ((MPFR_EMAX_MAX >> 31) >> 31 == 0);
- return mpfr_underflow (y, (rnd == MPFR_RNDN) ? MPFR_RNDZ : rnd, 1);
- }
- }
-
- /* Init stuff */
- MPFR_SAVE_EXPO_MARK (expo);
-
- if (MPFR_IS_NEG (x))
- {
- mpfr_exp_t e = MPFR_EXP(x);
- /* For x < 0 going to -infinity, erfc(x) tends to 2 by below.
- More precisely, we have 2 + 1/sqrt(Pi)/x/exp(x^2) < erfc(x) < 2.
- Thus log2 |2 - erfc(x)| <= -log2|x| - x^2 / log(2).
- If |2 - erfc(x)| < 2^(-PREC(y)) then the result is either 2 or
- nextbelow(2).
- For x <= -27282, -log2|x| - x^2 / log(2) <= -2^30.
- */
- if ((MPFR_PREC(y) <= 7 && e >= 2) || /* x <= -2 */
- (MPFR_PREC(y) <= 25 && e >= 3) || /* x <= -4 */
- (MPFR_PREC(y) <= 120 && mpfr_cmp_si (x, -9) <= 0) ||
- mpfr_cmp_si (x, -27282) <= 0)
- {
- near_two:
- mpfr_set_ui (y, 2, MPFR_RNDN);
- MPFR_SET_INEXFLAG ();
- if (rnd == MPFR_RNDZ || rnd == MPFR_RNDD)
- {
- mpfr_nextbelow (y);
- inex = -1;
- }
- else
- inex = 1;
- goto end;
- }
- else if (e >= 3) /* more accurate test */
- {
- mpfr_t t, u;
- int near_2;
- mpfr_init2 (t, 32);
- mpfr_init2 (u, 32);
- /* the following is 1/log(2) rounded to zero on 32 bits */
- mpfr_set_str_binary (t, "1.0111000101010100011101100101001");
- mpfr_sqr (u, x, MPFR_RNDZ);
- mpfr_mul (t, t, u, MPFR_RNDZ); /* t <= x^2/log(2) */
- mpfr_neg (u, x, MPFR_RNDZ); /* 0 <= u <= |x| */
- mpfr_log2 (u, u, MPFR_RNDZ); /* u <= log2(|x|) */
- mpfr_add (t, t, u, MPFR_RNDZ); /* t <= log2|x| + x^2 / log(2) */
- /* Taking into account that mpfr_exp_t >= mpfr_prec_t */
- mpfr_set_exp_t (u, MPFR_PREC (y), MPFR_RNDU);
- near_2 = mpfr_cmp (t, u) >= 0; /* 1 if PREC(y) <= u <= t <= ... */
- mpfr_clear (t);
- mpfr_clear (u);
- if (near_2)
- goto near_two;
- }
- }
-
- /* erfc(x) ~ 1, with error < 2^(EXP(x)+1) */
- MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, __gmpfr_one, - MPFR_GET_EXP (x) - 1,
- 0, MPFR_IS_NEG (x),
- rnd, inex = _inexact; goto end);
-
- prec = MPFR_PREC (y) + MPFR_INT_CEIL_LOG2 (MPFR_PREC (y)) + 3;
- if (MPFR_GET_EXP (x) > 0)
- prec += 2 * MPFR_GET_EXP(x);
-
- mpfr_init2 (tmp, prec);
-
- MPFR_ZIV_INIT (loop, prec); /* Initialize the ZivLoop controller */
- for (;;) /* Infinite loop */
- {
- /* use asymptotic formula only whenever x^2 >= p*log(2),
- otherwise it will not converge */
- if (MPFR_IS_POS (x) &&
- 2 * MPFR_GET_EXP (x) - 2 >= MPFR_INT_CEIL_LOG2 (prec))
- /* we have x^2 >= p in that case */
- {
- err = mpfr_erfc_asympt (tmp, x);
- if (err == 0) /* underflow case */
- {
- mpfr_clear (tmp);
- MPFR_SAVE_EXPO_FREE (expo);
- return mpfr_underflow (y, (rnd == MPFR_RNDN) ? MPFR_RNDZ : rnd, 1);
- }
- }
- else
- {
- mpfr_erf (tmp, x, MPFR_RNDN);
- MPFR_ASSERTD (!MPFR_IS_SINGULAR (tmp)); /* FIXME: 0 only for x=0 ? */
- te = MPFR_GET_EXP (tmp);
- mpfr_ui_sub (tmp, 1, tmp, MPFR_RNDN);
- /* See error analysis in algorithms.tex for details */
- if (MPFR_IS_ZERO (tmp))
- {
- prec *= 2;
- err = prec; /* ensures MPFR_CAN_ROUND fails */
- }
- else
- err = MAX (te - MPFR_GET_EXP (tmp), 0) + 1;
- }
- if (MPFR_LIKELY (MPFR_CAN_ROUND (tmp, prec - err, MPFR_PREC (y), rnd)))
- break;
- MPFR_ZIV_NEXT (loop, prec); /* Increase used precision */
- mpfr_set_prec (tmp, prec);
- }
- MPFR_ZIV_FREE (loop); /* Free the ZivLoop Controller */
-
- inex = mpfr_set (y, tmp, rnd); /* Set y to the computed value */
- mpfr_clear (tmp);
-
- end:
- MPFR_SAVE_EXPO_FREE (expo);
- return mpfr_check_range (y, inex, rnd);
-}