diff options
Diffstat (limited to 'Build/source/libs/mpfr/mpfr-src/src/atan2.c')
-rw-r--r-- | Build/source/libs/mpfr/mpfr-src/src/atan2.c | 280 |
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); -} |