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Diffstat (limited to 'Build/source/libs/mpfr/mpfr-src/src/sin.c')
-rw-r--r-- | Build/source/libs/mpfr/mpfr-src/src/sin.c | 201 |
1 files changed, 0 insertions, 201 deletions
diff --git a/Build/source/libs/mpfr/mpfr-src/src/sin.c b/Build/source/libs/mpfr/mpfr-src/src/sin.c deleted file mode 100644 index 0e5d058dc83..00000000000 --- a/Build/source/libs/mpfr/mpfr-src/src/sin.c +++ /dev/null @@ -1,201 +0,0 @@ -/* mpfr_sin -- sine of a floating-point number - -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" - -static int -mpfr_sin_fast (mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t rnd_mode) -{ - int inex; - - inex = mpfr_sincos_fast (y, NULL, x, rnd_mode); - inex = inex & 3; /* 0: exact, 1: rounded up, 2: rounded down */ - return (inex == 2) ? -1 : inex; -} - -int -mpfr_sin (mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t rnd_mode) -{ - mpfr_t c, xr; - mpfr_srcptr xx; - mpfr_exp_t expx, err1, err; - mpfr_prec_t precy, m; - int inexact, sign, reduce; - MPFR_ZIV_DECL (loop); - 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_IS_INF (x)) - { - MPFR_SET_NAN (y); - MPFR_RET_NAN; - } - else /* x is zero */ - { - MPFR_ASSERTD (MPFR_IS_ZERO (x)); - MPFR_SET_ZERO (y); - MPFR_SET_SAME_SIGN (y, x); - MPFR_RET (0); - } - } - - expx = MPFR_GET_EXP (x); - err1 = -2 * expx; - - /* sin(x) = x - x^3/6 + ... so the error is < 2^(3*EXP(x)-2) */ - MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, x, err1, 2, 0, rnd_mode, {}); - - MPFR_SAVE_EXPO_MARK (expo); - - /* Compute initial precision */ - precy = MPFR_PREC (y); - - if (precy >= MPFR_SINCOS_THRESHOLD) - { - inexact = mpfr_sin_fast (y, x, rnd_mode); - goto end; - } - - /* for x large, since argument reduction is expensive, we want to avoid - any failure in Ziv's strategy, thus we take into account expx too */ - m = precy + MPFR_INT_CEIL_LOG2 (MAX(precy,expx)) + 8; - - /* since we compute sin(x) as sqrt(1-cos(x)^2), and for x small we have - cos(x)^2 ~ 1 - x^2, when subtracting cos(x)^2 from 1 we will lose - about -2*expx bits if expx < 0 */ - if (expx < 0) - { - /* The following assertion includes a check for integer overflow. - At this point, precy < MPFR_SINCOS_THRESHOLD, so that both m and - err1 should be small enough. But the assertion makes the code - safer (a smart compiler might be able to remove it). */ - MPFR_ASSERTN (err1 <= MPFR_PREC_MAX - m); - m += err1; - } - - mpfr_init (c); - mpfr_init (xr); - - MPFR_ZIV_INIT (loop, m); - for (;;) - { - /* first perform argument reduction modulo 2*Pi (if needed), - also helps to determine the sign of sin(x) */ - if (expx >= 2) /* If Pi < x < 4, we need to reduce too, to determine - the sign of sin(x). For 2 <= |x| < Pi, we could avoid - the reduction. */ - { - reduce = 1; - /* As expx + m - 1 will silently be converted into mpfr_prec_t - in the mpfr_set_prec call, the assert below may be useful to - avoid undefined behavior. */ - MPFR_ASSERTN (expx + m - 1 <= MPFR_PREC_MAX); - mpfr_set_prec (c, expx + m - 1); - mpfr_set_prec (xr, m); - mpfr_const_pi (c, MPFR_RNDN); - mpfr_mul_2ui (c, c, 1, MPFR_RNDN); - mpfr_remainder (xr, x, c, MPFR_RNDN); - /* The analysis is similar to that of cos.c: - |xr - x - 2kPi| <= 2^(2-m). Thus we can decide the sign - of sin(x) if xr is at distance at least 2^(2-m) of both - 0 and +/-Pi. */ - mpfr_div_2ui (c, c, 1, MPFR_RNDN); - /* Since c approximates Pi with an error <= 2^(2-expx-m) <= 2^(-m), - it suffices to check that c - |xr| >= 2^(2-m). */ - if (MPFR_IS_POS (xr)) - mpfr_sub (c, c, xr, MPFR_RNDZ); - else - mpfr_add (c, c, xr, MPFR_RNDZ); - if (MPFR_IS_ZERO(xr) - || MPFR_GET_EXP(xr) < (mpfr_exp_t) 3 - (mpfr_exp_t) m - || MPFR_IS_ZERO(c) - || MPFR_GET_EXP(c) < (mpfr_exp_t) 3 - (mpfr_exp_t) m) - goto ziv_next; - - /* |xr - x - 2kPi| <= 2^(2-m), thus |sin(xr) - sin(x)| <= 2^(2-m) */ - xx = xr; - } - else /* the input argument is already reduced */ - { - reduce = 0; - xx = x; - } - - sign = MPFR_SIGN(xx); - /* now that the argument is reduced, precision m is enough */ - mpfr_set_prec (c, m); - mpfr_cos (c, xx, MPFR_RNDA); /* c = cos(x) rounded away */ - mpfr_sqr (c, c, MPFR_RNDU); /* away */ - mpfr_ui_sub (c, 1, c, MPFR_RNDZ); - mpfr_sqrt (c, c, MPFR_RNDZ); - if (MPFR_IS_NEG_SIGN(sign)) - MPFR_CHANGE_SIGN(c); - - /* Warning: c may be 0! */ - if (MPFR_UNLIKELY (MPFR_IS_ZERO (c))) - { - /* Huge cancellation: increase prec a lot! */ - m = MAX (m, MPFR_PREC (x)); - m = 2 * m; - } - else - { - /* the absolute error on c is at most 2^(3-m-EXP(c)), - plus 2^(2-m) if there was an argument reduction. - Since EXP(c) <= 1, 3-m-EXP(c) >= 2-m, thus the error - is at most 2^(3-m-EXP(c)) in case of argument reduction. */ - err = 2 * MPFR_GET_EXP (c) + (mpfr_exp_t) m - 3 - (reduce != 0); - if (MPFR_CAN_ROUND (c, err, precy, rnd_mode)) - break; - - /* check for huge cancellation (Near 0) */ - if (err < (mpfr_exp_t) MPFR_PREC (y)) - m += MPFR_PREC (y) - err; - /* Check if near 1 */ - if (MPFR_GET_EXP (c) == 1) - m += m; - } - - ziv_next: - /* Else generic increase */ - MPFR_ZIV_NEXT (loop, m); - } - MPFR_ZIV_FREE (loop); - - inexact = mpfr_set (y, c, rnd_mode); - /* inexact cannot be 0, since this would mean that c was representable - within the target precision, but in that case mpfr_can_round will fail */ - - mpfr_clear (c); - mpfr_clear (xr); - - end: - MPFR_SAVE_EXPO_FREE (expo); - return mpfr_check_range (y, inexact, rnd_mode); -} |