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78 lines
3.9 KiB
C
78 lines
3.9 KiB
C
/* mpfr_csch - Hyperbolic cosecant function.
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Copyright 2005, 2006, 2007 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 MPFR Library.
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The 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 2.1 of the License, or (at your
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option) any later version.
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The 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 MPFR Library; see the file COPYING.LIB. If not, write to
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the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston,
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MA 02110-1301, USA. */
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/* the hyperbolic cosecant is defined by csch(x) = 1/sinh(x).
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csch (NaN) = NaN.
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csch (+Inf) = +0.
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csch (-Inf) = -0.
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csch (+0) = +Inf.
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csch (-0) = -Inf.
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*/
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#define FUNCTION mpfr_csch
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#define INVERSE mpfr_sinh
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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) do { MPFR_SET_SAME_SIGN(y,x); MPFR_SET_ZERO (y); \
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MPFR_RET(0); } while (1)
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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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/* (This analysis is adapted from that for mpfr_csc.)
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Near x=0, we have csch(x) = 1/x - x/6 + ..., more precisely we have
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|csch(x) - 1/x| <= 0.2 for |x| <= 1. The error term has the opposite
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sign as 1/x, thus |csch(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) > 0.2, 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 |csch(x) - 1/x| <= 0.2, if 2^(-2n) ufp(y) >= 0.4, then
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|y - csch(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) <= -2 MAX(PREC(x),PREC(Y)). */
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#define ACTION_TINY(y,x,r) \
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if (MPFR_EXP(x) <= -2 * (mp_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 to zero */ \
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if (rnd_mode == GMP_RNDU || (rnd_mode == GMP_RNDZ && signx < 0)) \
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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 == GMP_RNDD || rnd_mode == GMP_RNDZ) \
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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 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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