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Diffstat (limited to 'src/sin.c')
| -rw-r--r-- | src/sin.c | 183 |
1 files changed, 183 insertions, 0 deletions
diff --git a/src/sin.c b/src/sin.c new file mode 100644 index 0000000..88e73f3 --- /dev/null +++ b/src/sin.c @@ -0,0 +1,183 @@ +/* mpfr_sin -- sine of a floating-point number + +Copyright 2001, 2002, 2003, 2004, 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. */ + +#define MPFR_NEED_LONGLONG_H +#include "mpfr-impl.h" + +static int +mpfr_sin_fast (mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t rnd_mode) +{ + int inex; + + inex = mpfr_sincos_fast (y, NULL, x, rnd_mode); + inex = inex & 3; /* 0: exact, 1: rounded up, 2: rounded down */ + return (inex == 2) ? -1 : inex; +} + +int +mpfr_sin (mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t rnd_mode) +{ + mpfr_t c, xr; + mpfr_srcptr xx; + mpfr_exp_t expx, err; + mpfr_prec_t precy, m; + int inexact, sign, reduce; + MPFR_ZIV_DECL (loop); + MPFR_SAVE_EXPO_DECL (expo); + + MPFR_LOG_FUNC + (("x[%Pu]=%.*Rg rnd=%d", mpfr_get_prec (x), mpfr_log_prec, x, rnd_mode), + ("y[%Pu]=%.*Rg inexact=%d", mpfr_get_prec (y), mpfr_log_prec, y, + inexact)); + + if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x))) + { + if (MPFR_IS_NAN (x) || MPFR_IS_INF (x)) + { + MPFR_SET_NAN (y); + MPFR_RET_NAN; + + } + else /* x is zero */ + { + MPFR_ASSERTD (MPFR_IS_ZERO (x)); + MPFR_SET_ZERO (y); + MPFR_SET_SAME_SIGN (y, x); + MPFR_RET (0); + } + } + + /* sin(x) = x - x^3/6 + ... so the error is < 2^(3*EXP(x)-2) */ + MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, x, -2 * MPFR_GET_EXP (x), 2, 0, + rnd_mode, {}); + + MPFR_SAVE_EXPO_MARK (expo); + + /* Compute initial precision */ + precy = MPFR_PREC (y); + + if (precy >= MPFR_SINCOS_THRESHOLD) + return mpfr_sin_fast (y, x, rnd_mode); + + m = precy + MPFR_INT_CEIL_LOG2 (precy) + 13; + expx = MPFR_GET_EXP (x); + + mpfr_init (c); + mpfr_init (xr); + + MPFR_ZIV_INIT (loop, m); + for (;;) + { + /* first perform argument reduction modulo 2*Pi (if needed), + also helps to determine the sign of sin(x) */ + if (expx >= 2) /* If Pi < x < 4, we need to reduce too, to determine + the sign of sin(x). For 2 <= |x| < Pi, we could avoid + the reduction. */ + { + reduce = 1; + /* As expx + m - 1 will silently be converted into mpfr_prec_t + in the mpfr_set_prec call, the assert below may be useful to + avoid undefined behavior. */ + MPFR_ASSERTN (expx + m - 1 <= MPFR_PREC_MAX); + mpfr_set_prec (c, expx + m - 1); + mpfr_set_prec (xr, m); + mpfr_const_pi (c, MPFR_RNDN); + mpfr_mul_2ui (c, c, 1, MPFR_RNDN); + mpfr_remainder (xr, x, c, MPFR_RNDN); + /* The analysis is similar to that of cos.c: + |xr - x - 2kPi| <= 2^(2-m). Thus we can decide the sign + of sin(x) if xr is at distance at least 2^(2-m) of both + 0 and +/-Pi. */ + mpfr_div_2ui (c, c, 1, MPFR_RNDN); + /* Since c approximates Pi with an error <= 2^(2-expx-m) <= 2^(-m), + it suffices to check that c - |xr| >= 2^(2-m). */ + if (MPFR_SIGN (xr) > 0) + mpfr_sub (c, c, xr, MPFR_RNDZ); + else + mpfr_add (c, c, xr, MPFR_RNDZ); + if (MPFR_IS_ZERO(xr) + || MPFR_GET_EXP(xr) < (mpfr_exp_t) 3 - (mpfr_exp_t) m + || MPFR_IS_ZERO(c) + || MPFR_GET_EXP(c) < (mpfr_exp_t) 3 - (mpfr_exp_t) m) + goto ziv_next; + + /* |xr - x - 2kPi| <= 2^(2-m), thus |sin(xr) - sin(x)| <= 2^(2-m) */ + xx = xr; + } + else /* the input argument is already reduced */ + { + reduce = 0; + xx = x; + } + + sign = MPFR_SIGN(xx); + /* now that the argument is reduced, precision m is enough */ + mpfr_set_prec (c, m); + mpfr_cos (c, xx, MPFR_RNDZ); /* can't be exact */ + mpfr_nexttoinf (c); /* now c = cos(x) rounded away */ + mpfr_mul (c, c, c, MPFR_RNDU); /* away */ + mpfr_ui_sub (c, 1, c, MPFR_RNDZ); + mpfr_sqrt (c, c, MPFR_RNDZ); + if (MPFR_IS_NEG_SIGN(sign)) + MPFR_CHANGE_SIGN(c); + + /* Warning: c may be 0! */ + if (MPFR_UNLIKELY (MPFR_IS_ZERO (c))) + { + /* Huge cancellation: increase prec a lot! */ + m = MAX (m, MPFR_PREC (x)); + m = 2 * m; + } + else + { + /* the absolute error on c is at most 2^(3-m-EXP(c)), + plus 2^(2-m) if there was an argument reduction. + Since EXP(c) <= 1, 3-m-EXP(c) >= 2-m, thus the error + is at most 2^(3-m-EXP(c)) in case of argument reduction. */ + err = 2 * MPFR_GET_EXP (c) + (mpfr_exp_t) m - 3 - (reduce != 0); + if (MPFR_CAN_ROUND (c, err, precy, rnd_mode)) + break; + + /* check for huge cancellation (Near 0) */ + if (err < (mpfr_exp_t) MPFR_PREC (y)) + m += MPFR_PREC (y) - err; + /* Check if near 1 */ + if (MPFR_GET_EXP (c) == 1) + m += m; + } + + ziv_next: + /* Else generic increase */ + MPFR_ZIV_NEXT (loop, m); + } + MPFR_ZIV_FREE (loop); + + inexact = mpfr_set (y, c, rnd_mode); + /* inexact cannot be 0, since this would mean that c was representable + within the target precision, but in that case mpfr_can_round will fail */ + + mpfr_clear (c); + mpfr_clear (xr); + + MPFR_SAVE_EXPO_FREE (expo); + return mpfr_check_range (y, inexact, rnd_mode); +} |