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Diffstat (limited to 'Build/source/libs/mpfr/mpfr-src/src/coth.c')
-rw-r--r-- | Build/source/libs/mpfr/mpfr-src/src/coth.c | 93 |
1 files changed, 0 insertions, 93 deletions
diff --git a/Build/source/libs/mpfr/mpfr-src/src/coth.c b/Build/source/libs/mpfr/mpfr-src/src/coth.c deleted file mode 100644 index 217904aaaa2..00000000000 --- a/Build/source/libs/mpfr/mpfr-src/src/coth.c +++ /dev/null @@ -1,93 +0,0 @@ -/* mpfr_coth - Hyperbolic 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 hyperbolic cotangent is defined by coth(x) = 1/tanh(x) - coth (NaN) = NaN. - coth (+Inf) = 1 - coth (-Inf) = -1 - coth (+0) = +Inf. - coth (-0) = -Inf. -*/ - -#define FUNCTION mpfr_coth -#define INVERSE mpfr_tanh -#define ACTION_NAN(y) do { MPFR_SET_NAN(y); MPFR_RET_NAN; } while (1) -#define ACTION_INF(y) return mpfr_set_si (y, MPFR_IS_POS(x) ? 1 : -1, rnd_mode) -#define ACTION_ZERO(y,x) do { MPFR_SET_SAME_SIGN(y,x); MPFR_SET_INF(y); \ - MPFR_SET_DIVBY0 (); MPFR_RET(0); } while (1) - -/* We know |coth(x)| > 1, thus if the approximation z is such that - 1 <= z <= 1 + 2^(-p) where p is the target precision, then the - result is either 1 or nextabove(1) = 1 + 2^(1-p). */ -#define ACTION_SPECIAL \ - if (MPFR_GET_EXP(z) == 1) /* 1 <= |z| < 2 */ \ - { \ - /* the following is exact by Sterbenz theorem */ \ - mpfr_sub_si (z, z, MPFR_SIGN (z), MPFR_RNDN); \ - if (MPFR_IS_ZERO(z) || MPFR_GET_EXP(z) <= - (mpfr_exp_t) precy) \ - { \ - mpfr_add_si (z, z, MPFR_SIGN (z), MPFR_RNDN); \ - break; \ - } \ - } - -/* The analysis is adapted from that for mpfr_csc: - near x=0, coth(x) = 1/x + x/3 + ..., more precisely we have - |coth(x) - 1/x| <= 0.32 for |x| <= 1. Like for csc, the error term has - the same sign as 1/x, thus |coth(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) > 0.32, 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 |coth(x) - 1/x| <= 0.32, if 2^(-2n) ufp(y) >= 0.64, then - |y - coth(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)). */ -#define ACTION_TINY(y,x,r) \ - if (MPFR_EXP(x) + 1 <= -2 * (mpfr_exp_t) MAX(MPFR_PREC(x), MPFR_PREC(y))) \ - { \ - int signx = MPFR_SIGN(x); \ - inexact = mpfr_ui_div (y, 1, x, r); \ - if (inexact == 0) /* x is a power of two */ \ - { /* result always 1/x, except when rounding away from zero */ \ - if (rnd_mode == MPFR_RNDA) \ - rnd_mode = (signx > 0) ? MPFR_RNDU : MPFR_RNDD; \ - if (rnd_mode == MPFR_RNDU) \ - { \ - if (signx > 0) \ - mpfr_nextabove (y); /* 2^k + epsilon */ \ - inexact = 1; \ - } \ - else if (rnd_mode == MPFR_RNDD) \ - { \ - if (signx < 0) \ - mpfr_nextbelow (y); /* -2^k - epsilon */ \ - inexact = -1; \ - } \ - else /* round to zero, or nearest */ \ - inexact = -signx; \ - } \ - MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, __gmpfr_flags); \ - goto end; \ - } - -#include "gen_inverse.h" |