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b58ddff026
* merged mpfr 3.0.0 and gmp 5.0.1 in buildtools trunk git-svn-id: file:///srv/svn/repos/haiku/buildtools/trunk@37378 a95241bf-73f2-0310-859d-f6bbb57e9c96
94 lines
5.0 KiB
C
94 lines
5.0 KiB
C
/* mpfr_coth - Hyperbolic cotangent function.
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Copyright 2005, 2006, 2007, 2008, 2009, 2010 Free Software Foundation, Inc.
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Contributed by the Arenaire and Cacao projects, INRIA.
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This file is part of the GNU MPFR Library.
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The GNU MPFR Library is free software; you can redistribute it and/or modify
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it under the terms of the GNU Lesser General Public License as published by
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the Free Software Foundation; either version 3 of the License, or (at your
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option) any later version.
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The GNU MPFR Library is distributed in the hope that it will be useful, but
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WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
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License for more details.
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You should have received a copy of the GNU Lesser General Public License
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along with the GNU MPFR Library; see the file COPYING.LESSER. If not, see
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http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
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51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */
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/* the hyperbolic cotangent is defined by coth(x) = 1/tanh(x)
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coth (NaN) = NaN.
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coth (+Inf) = 1
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coth (-Inf) = -1
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coth (+0) = +Inf.
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coth (-0) = -Inf.
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*/
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#define FUNCTION mpfr_coth
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#define INVERSE mpfr_tanh
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#define ACTION_NAN(y) do { MPFR_SET_NAN(y); MPFR_RET_NAN; } while (1)
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#define ACTION_INF(y) return mpfr_set_si (y, MPFR_IS_POS(x) ? 1 : -1, rnd_mode)
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#define ACTION_ZERO(y,x) do { MPFR_SET_SAME_SIGN(y,x); MPFR_SET_INF(y); \
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MPFR_RET(0); } while (1)
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/* We know |coth(x)| > 1, thus if the approximation z is such that
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1 <= z <= 1 + 2^(-p) where p is the target precision, then the
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result is either 1 or nextabove(1) = 1 + 2^(1-p). */
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#define ACTION_SPECIAL \
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if (MPFR_GET_EXP(z) == 1) /* 1 <= |z| < 2 */ \
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{ \
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/* the following is exact by Sterbenz theorem */ \
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mpfr_sub_si (z, z, MPFR_SIGN(z) > 0 ? 1 : -1, MPFR_RNDN); \
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if (MPFR_IS_ZERO(z) || MPFR_GET_EXP(z) <= - (mpfr_exp_t) precy) \
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{ \
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mpfr_add_si (z, z, MPFR_SIGN(z) > 0 ? 1 : -1, MPFR_RNDN); \
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break; \
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} \
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}
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/* The analysis is adapted from that for mpfr_csc:
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near x=0, coth(x) = 1/x + x/3 + ..., more precisely we have
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|coth(x) - 1/x| <= 0.32 for |x| <= 1. Like for csc, the error term has
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the same sign as 1/x, thus |coth(x)| >= |1/x|. Then:
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(i) either x is a power of two, then 1/x is exactly representable, and
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as long as 1/2*ulp(1/x) > 0.32, we can conclude;
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(ii) otherwise assume x has <= n bits, and y has <= n+1 bits, then
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|y - 1/x| >= 2^(-2n) ufp(y), where ufp means unit in first place.
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Since |coth(x) - 1/x| <= 0.32, if 2^(-2n) ufp(y) >= 0.64, then
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|y - coth(x)| >= 2^(-2n-1) ufp(y), and rounding 1/x gives the correct
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result. If x < 2^E, then y > 2^(-E), thus ufp(y) > 2^(-E-1).
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A sufficient condition is thus EXP(x) + 1 <= -2 MAX(PREC(x),PREC(Y)). */
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#define ACTION_TINY(y,x,r) \
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if (MPFR_EXP(x) + 1 <= -2 * (mpfr_exp_t) MAX(MPFR_PREC(x), MPFR_PREC(y))) \
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{ \
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int signx = MPFR_SIGN(x); \
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inexact = mpfr_ui_div (y, 1, x, r); \
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if (inexact == 0) /* x is a power of two */ \
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{ /* result always 1/x, except when rounding away from zero */ \
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if (rnd_mode == MPFR_RNDA) \
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rnd_mode = (signx > 0) ? MPFR_RNDU : MPFR_RNDD; \
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if (rnd_mode == MPFR_RNDU) \
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{ \
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if (signx > 0) \
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mpfr_nextabove (y); /* 2^k + epsilon */ \
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inexact = 1; \
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} \
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else if (rnd_mode == MPFR_RNDD) \
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{ \
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if (signx < 0) \
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mpfr_nextbelow (y); /* -2^k - epsilon */ \
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inexact = -1; \
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} \
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else /* round to zero, or nearest */ \
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inexact = -signx; \
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} \
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MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, __gmpfr_flags); \
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goto end; \
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}
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#include "gen_inverse.h"
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