diff options
Diffstat (limited to 'Build/source/libs/mpfr/mpfr-src/src/cot.c')
-rw-r--r-- | Build/source/libs/mpfr/mpfr-src/src/cot.c | 96 |
1 files changed, 0 insertions, 96 deletions
diff --git a/Build/source/libs/mpfr/mpfr-src/src/cot.c b/Build/source/libs/mpfr/mpfr-src/src/cot.c deleted file mode 100644 index 4adb6396c75..00000000000 --- a/Build/source/libs/mpfr/mpfr-src/src/cot.c +++ /dev/null @@ -1,96 +0,0 @@ -/* mpfr_cot - cotangent function. - -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. */ - -/* the cotangent is defined by cot(x) = 1/tan(x) = cos(x)/sin(x). - cot (NaN) = NaN. - cot (+Inf) = csc (-Inf) = NaN. - cot (+0) = +Inf. - cot (-0) = -Inf. -*/ - -#define FUNCTION mpfr_cot -#define INVERSE mpfr_tan -#define ACTION_NAN(y) do { MPFR_SET_NAN(y); MPFR_RET_NAN; } while (1) -#define ACTION_INF(y) do { MPFR_SET_NAN(y); MPFR_RET_NAN; } while (1) -#define ACTION_ZERO(y,x) do { MPFR_SET_SAME_SIGN(y,x); MPFR_SET_INF(y); \ - MPFR_SET_DIVBY0 (); MPFR_RET(0); } while (1) - -/* (This analysis is adapted from that for mpfr_coth.) - Near x=0, cot(x) = 1/x - x/3 + ..., more precisely we have - |cot(x) - 1/x| <= 0.36 for |x| <= 1. The error term has - the opposite sign as 1/x, thus |cot(x)| <= |1/x|. Then: - (i) either x is a power of two, then 1/x is exactly representable, and - as long as 1/2*ulp(1/x) > 0.36, we can conclude; - (ii) otherwise assume x has <= n bits, and y has <= n+1 bits, then - |y - 1/x| >= 2^(-2n) ufp(y), where ufp means unit in first place. - Since |cot(x) - 1/x| <= 0.36, if 2^(-2n) ufp(y) >= 0.72, then - |y - cot(x)| >= 2^(-2n-1) ufp(y), and rounding 1/x gives the correct - result. If x < 2^E, then y > 2^(-E), thus ufp(y) > 2^(-E-1). - A sufficient condition is thus EXP(x) + 1 <= -2 MAX(PREC(x),PREC(Y)). - The division can be inexact in case of underflow or overflow; but - an underflow is not possible as emin = - emax. The overflow is a - real overflow possibly except when |x| = 2^emin. */ -#define ACTION_TINY(y,x,r) \ - if (MPFR_EXP(x) + 1 <= -2 * (mpfr_exp_t) MAX(MPFR_PREC(x), MPFR_PREC(y))) \ - { \ - int two2emin; \ - int signx = MPFR_SIGN(x); \ - MPFR_STAT_STATIC_ASSERT (MPFR_EMIN_MIN + MPFR_EMAX_MAX == 0); \ - if ((two2emin = mpfr_get_exp (x) == __gmpfr_emin + 1 && \ - mpfr_powerof2_raw (x))) \ - { \ - /* Case |x| = 2^emin. 1/x is not representable; so, compute \ - 1/(2x) instead (exact), and correct the result later. */ \ - mpfr_set_si_2exp (y, signx, __gmpfr_emax, MPFR_RNDN); \ - inexact = 0; \ - } \ - else \ - inexact = mpfr_ui_div (y, 1, x, r); \ - if (inexact == 0) /* x is a power of two */ \ - { /* result always 1/x, except when rounding to zero */ \ - if (rnd_mode == MPFR_RNDA) \ - rnd_mode = (signx > 0) ? MPFR_RNDU : MPFR_RNDD; \ - if (rnd_mode == MPFR_RNDU || (rnd_mode == MPFR_RNDZ && signx < 0)) \ - { \ - if (signx < 0) \ - mpfr_nextabove (y); /* -2^k + epsilon */ \ - inexact = 1; \ - } \ - else if (rnd_mode == MPFR_RNDD || rnd_mode == MPFR_RNDZ) \ - { \ - if (signx > 0) \ - mpfr_nextbelow (y); /* 2^k - epsilon */ \ - inexact = -1; \ - } \ - else /* round to nearest */ \ - inexact = signx; \ - if (two2emin) \ - mpfr_mul_2ui (y, y, 1, r); /* overflow in MPFR_RNDN */ \ - } \ - /* Underflow is not possible with emin = - emax, but we cannot */ \ - /* add an assert as the underflow flag could have already been */ \ - /* set before the call to mpfr_cot. */ \ - MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, __gmpfr_flags); \ - goto end; \ - } - -#include "gen_inverse.h" |