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-rw-r--r--Build/source/libs/mpfr/mpfr-src/src/atan2.c280
1 files changed, 0 insertions, 280 deletions
diff --git a/Build/source/libs/mpfr/mpfr-src/src/atan2.c b/Build/source/libs/mpfr/mpfr-src/src/atan2.c
deleted file mode 100644
index 866a8289eab..00000000000
--- a/Build/source/libs/mpfr/mpfr-src/src/atan2.c
+++ /dev/null
@@ -1,280 +0,0 @@
-/* mpfr_atan2 -- arc-tan 2 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"
-
-static int
-pi_div_2ui (mpfr_ptr dest, int i, int neg, mpfr_rnd_t rnd_mode)
-{
- int inexact;
- MPFR_SAVE_EXPO_DECL (expo);
-
- MPFR_SAVE_EXPO_MARK (expo);
- if (neg) /* -PI/2^i */
- {
- inexact = - mpfr_const_pi (dest, MPFR_INVERT_RND (rnd_mode));
- MPFR_CHANGE_SIGN (dest);
- }
- else /* PI/2^i */
- {
- inexact = mpfr_const_pi (dest, rnd_mode);
- }
- mpfr_div_2ui (dest, dest, i, rnd_mode); /* exact */
- MPFR_SAVE_EXPO_FREE (expo);
- return mpfr_check_range (dest, inexact, rnd_mode);
-}
-
-int
-mpfr_atan2 (mpfr_ptr dest, mpfr_srcptr y, mpfr_srcptr x, mpfr_rnd_t rnd_mode)
-{
- mpfr_t tmp, pi;
- int inexact;
- mpfr_prec_t prec;
- mpfr_exp_t e;
- MPFR_SAVE_EXPO_DECL (expo);
- MPFR_ZIV_DECL (loop);
-
- MPFR_LOG_FUNC
- (("y[%Pu]=%.*Rg x[%Pu]=%.*Rg rnd=%d",
- mpfr_get_prec (y), mpfr_log_prec, y,
- mpfr_get_prec (x), mpfr_log_prec, x, rnd_mode),
- ("atan[%Pu]=%.*Rg inexact=%d",
- mpfr_get_prec (dest), mpfr_log_prec, dest, inexact));
-
- /* Special cases */
- if (MPFR_ARE_SINGULAR (x, y))
- {
- /* atan2(0, 0) does not raise the "invalid" floating-point
- exception, nor does atan2(y, 0) raise the "divide-by-zero"
- floating-point exception.
- -- atan2(±0, -0) returns ±pi.313)
- -- atan2(±0, +0) returns ±0.
- -- atan2(±0, x) returns ±pi, for x < 0.
- -- atan2(±0, x) returns ±0, for x > 0.
- -- atan2(y, ±0) returns -pi/2 for y < 0.
- -- atan2(y, ±0) returns pi/2 for y > 0.
- -- atan2(±oo, -oo) returns ±3pi/4.
- -- atan2(±oo, +oo) returns ±pi/4.
- -- atan2(±oo, x) returns ±pi/2, for finite x.
- -- atan2(±y, -oo) returns ±pi, for finite y > 0.
- -- atan2(±y, +oo) returns ±0, for finite y > 0.
- */
- if (MPFR_IS_NAN (x) || MPFR_IS_NAN (y))
- {
- MPFR_SET_NAN (dest);
- MPFR_RET_NAN;
- }
- if (MPFR_IS_ZERO (y))
- {
- if (MPFR_IS_NEG (x)) /* +/- PI */
- {
- set_pi:
- if (MPFR_IS_NEG (y))
- {
- inexact = mpfr_const_pi (dest, MPFR_INVERT_RND (rnd_mode));
- MPFR_CHANGE_SIGN (dest);
- return -inexact;
- }
- else
- return mpfr_const_pi (dest, rnd_mode);
- }
- else /* +/- 0 */
- {
- set_zero:
- MPFR_SET_ZERO (dest);
- MPFR_SET_SAME_SIGN (dest, y);
- return 0;
- }
- }
- if (MPFR_IS_ZERO (x))
- {
- return pi_div_2ui (dest, 1, MPFR_IS_NEG (y), rnd_mode);
- }
- if (MPFR_IS_INF (y))
- {
- if (!MPFR_IS_INF (x)) /* +/- PI/2 */
- return pi_div_2ui (dest, 1, MPFR_IS_NEG (y), rnd_mode);
- else if (MPFR_IS_POS (x)) /* +/- PI/4 */
- return pi_div_2ui (dest, 2, MPFR_IS_NEG (y), rnd_mode);
- else /* +/- 3*PI/4: Ugly since we have to round properly */
- {
- mpfr_t tmp2;
- MPFR_ZIV_DECL (loop2);
- mpfr_prec_t prec2 = MPFR_PREC (dest) + 10;
-
- MPFR_SAVE_EXPO_MARK (expo);
- mpfr_init2 (tmp2, prec2);
- MPFR_ZIV_INIT (loop2, prec2);
- for (;;)
- {
- mpfr_const_pi (tmp2, MPFR_RNDN);
- mpfr_mul_ui (tmp2, tmp2, 3, MPFR_RNDN); /* Error <= 2 */
- mpfr_div_2ui (tmp2, tmp2, 2, MPFR_RNDN);
- if (MPFR_CAN_ROUND (tmp2, MPFR_PREC (tmp2) - 2,
- MPFR_PREC (dest), rnd_mode))
- break;
- MPFR_ZIV_NEXT (loop2, prec2);
- mpfr_set_prec (tmp2, prec2);
- }
- MPFR_ZIV_FREE (loop2);
- if (MPFR_IS_NEG (y))
- MPFR_CHANGE_SIGN (tmp2);
- inexact = mpfr_set (dest, tmp2, rnd_mode);
- mpfr_clear (tmp2);
- MPFR_SAVE_EXPO_FREE (expo);
- return mpfr_check_range (dest, inexact, rnd_mode);
- }
- }
- MPFR_ASSERTD (MPFR_IS_INF (x));
- if (MPFR_IS_NEG (x))
- goto set_pi;
- else
- goto set_zero;
- }
-
- /* When x is a power of two, we call directly atan(y/x) since y/x is
- exact. */
- if (MPFR_UNLIKELY (MPFR_IS_POS (x) && mpfr_powerof2_raw (x)))
- {
- int r;
- mpfr_t yoverx;
- mpfr_flags_t saved_flags = __gmpfr_flags;
-
- mpfr_init2 (yoverx, MPFR_PREC (y));
- if (MPFR_LIKELY (mpfr_div_2si (yoverx, y, MPFR_GET_EXP (x) - 1,
- MPFR_RNDN) == 0))
- {
- /* Here the flags have not changed due to mpfr_div_2si. */
- r = mpfr_atan (dest, yoverx, rnd_mode);
- mpfr_clear (yoverx);
- return r;
- }
- else
- {
- /* Division is inexact because of a small exponent range */
- mpfr_clear (yoverx);
- __gmpfr_flags = saved_flags;
- }
- }
-
- MPFR_SAVE_EXPO_MARK (expo);
-
- /* Set up initial prec */
- prec = MPFR_PREC (dest) + 3 + MPFR_INT_CEIL_LOG2 (MPFR_PREC (dest));
- mpfr_init2 (tmp, prec);
-
- MPFR_ZIV_INIT (loop, prec);
- if (MPFR_IS_POS (x))
- /* use atan2(y,x) = atan(y/x) */
- for (;;)
- {
- int div_inex;
- MPFR_BLOCK_DECL (flags);
-
- MPFR_BLOCK (flags, div_inex = mpfr_div (tmp, y, x, MPFR_RNDN));
- if (div_inex == 0)
- {
- /* Result is exact. */
- inexact = mpfr_atan (dest, tmp, rnd_mode);
- goto end;
- }
-
- /* Error <= ulp (tmp) except in case of underflow or overflow. */
-
- /* If the division underflowed, since |atan(z)/z| < 1, we have
- an underflow. */
- if (MPFR_UNDERFLOW (flags))
- {
- int sign;
-
- /* In the case MPFR_RNDN with 2^(emin-2) < |y/x| < 2^(emin-1):
- The smallest significand value S > 1 of |y/x| is:
- * 1 / (1 - 2^(-px)) if py <= px,
- * (1 - 2^(-px) + 2^(-py)) / (1 - 2^(-px)) if py >= px.
- Therefore S - 1 > 2^(-pz), where pz = max(px,py). We have:
- atan(|y/x|) > atan(z), where z = 2^(emin-2) * (1 + 2^(-pz)).
- > z - z^3 / 3.
- > 2^(emin-2) * (1 + 2^(-pz) - 2^(2 emin - 5))
- Assuming pz <= -2 emin + 5, we can round away from zero
- (this is what mpfr_underflow always does on MPFR_RNDN).
- In the case MPFR_RNDN with |y/x| <= 2^(emin-2), we round
- toward zero, as |atan(z)/z| < 1. */
- MPFR_ASSERTN (MPFR_PREC_MAX <=
- 2 * (mpfr_uexp_t) - MPFR_EMIN_MIN + 5);
- if (rnd_mode == MPFR_RNDN && MPFR_IS_ZERO (tmp))
- rnd_mode = MPFR_RNDZ;
- sign = MPFR_SIGN (tmp);
- mpfr_clear (tmp);
- MPFR_SAVE_EXPO_FREE (expo);
- return mpfr_underflow (dest, rnd_mode, sign);
- }
-
- mpfr_atan (tmp, tmp, MPFR_RNDN); /* Error <= 2*ulp (tmp) since
- abs(D(arctan)) <= 1 */
- /* TODO: check that the error bound is correct in case of overflow. */
- /* FIXME: Error <= ulp(tmp) ? */
- if (MPFR_LIKELY (MPFR_CAN_ROUND (tmp, prec - 2, MPFR_PREC (dest),
- rnd_mode)))
- break;
- MPFR_ZIV_NEXT (loop, prec);
- mpfr_set_prec (tmp, prec);
- }
- else /* x < 0 */
- /* Use sign(y)*(PI - atan (|y/x|)) */
- {
- mpfr_init2 (pi, prec);
- for (;;)
- {
- mpfr_div (tmp, y, x, MPFR_RNDN); /* Error <= ulp (tmp) */
- /* If tmp is 0, we have |y/x| <= 2^(-emin-2), thus
- atan|y/x| < 2^(-emin-2). */
- MPFR_SET_POS (tmp); /* no error */
- mpfr_atan (tmp, tmp, MPFR_RNDN); /* Error <= 2*ulp (tmp) since
- abs(D(arctan)) <= 1 */
- mpfr_const_pi (pi, MPFR_RNDN); /* Error <= ulp(pi) /2 */
- e = MPFR_NOTZERO(tmp) ? MPFR_GET_EXP (tmp) : __gmpfr_emin - 1;
- mpfr_sub (tmp, pi, tmp, MPFR_RNDN); /* see above */
- if (MPFR_IS_NEG (y))
- MPFR_CHANGE_SIGN (tmp);
- /* Error(tmp) <= (1/2+2^(EXP(pi)-EXP(tmp)-1)+2^(e-EXP(tmp)+1))*ulp
- <= 2^(MAX (MAX (EXP(PI)-EXP(tmp)-1, e-EXP(tmp)+1),
- -1)+2)*ulp(tmp) */
- e = MAX (MAX (MPFR_GET_EXP (pi)-MPFR_GET_EXP (tmp) - 1,
- e - MPFR_GET_EXP (tmp) + 1), -1) + 2;
- if (MPFR_LIKELY (MPFR_CAN_ROUND (tmp, prec - e, MPFR_PREC (dest),
- rnd_mode)))
- break;
- MPFR_ZIV_NEXT (loop, prec);
- mpfr_set_prec (tmp, prec);
- mpfr_set_prec (pi, prec);
- }
- mpfr_clear (pi);
- }
- inexact = mpfr_set (dest, tmp, rnd_mode);
-
- end:
- MPFR_ZIV_FREE (loop);
- mpfr_clear (tmp);
- MPFR_SAVE_EXPO_FREE (expo);
- return mpfr_check_range (dest, inexact, rnd_mode);
-}