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+/* mpfr_csc - cosecant function.
+
+Copyright 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013 Free Software Foundation, Inc.
+Contributed by the AriC and Caramel 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
+http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
+51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */
+
+/* the cosecant is defined by csc(x) = 1/sin(x).
+ csc (NaN) = NaN.
+ csc (+Inf) = csc (-Inf) = NaN.
+ csc (+0) = +Inf.
+ csc (-0) = -Inf.
+*/
+
+#define FUNCTION mpfr_csc
+#define INVERSE mpfr_sin
+#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)
+/* near x=0, we have csc(x) = 1/x + x/6 + ..., more precisely we have
+ |csc(x) - 1/x| <= 0.2 for |x| <= 1. The analysis is similar to that for
+ gamma(x) near x=0 (see gamma.c), except here the error term has the same
+ sign as 1/x, thus |csc(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) > 0.2, 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 |csc(x) - 1/x| <= 0.2, if 2^(-2n) ufp(y) >= 0.4, then
+ |y - csc(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) <= -2 MAX(PREC(x),PREC(Y)). */
+#define ACTION_TINY(y,x,r) \
+ if (MPFR_EXP(x) <= -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"