X-Git-Url: https://oss.titaniummirror.com/gitweb?a=blobdiff_plain;f=mpfr%2Fsin_cos.c;fp=mpfr%2Fsin_cos.c;h=4ac3bef870921fba270d4be9de295ccaac3f26ea;hb=6fed43773c9b0ce596dca5686f37ac3fc0fa11c0;hp=0000000000000000000000000000000000000000;hpb=27b11d56b743098deb193d510b337ba22dc52e5c;p=msp430-gcc.git diff --git a/mpfr/sin_cos.c b/mpfr/sin_cos.c new file mode 100644 index 00000000..4ac3bef8 --- /dev/null +++ b/mpfr/sin_cos.c @@ -0,0 +1,212 @@ +/* mpfr_sin_cos -- sine and cosine of a floating-point number + +Copyright 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009 Free Software Foundation, Inc. +Contributed by the Arenaire and Cacao 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 2.1 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.LIB. If not, 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" + +/* (y, z) <- (sin(x), cos(x)), return value is 0 iff both results are exact + ie, iff x = 0 */ +int +mpfr_sin_cos (mpfr_ptr y, mpfr_ptr z, mpfr_srcptr x, mp_rnd_t rnd_mode) +{ + mp_prec_t prec, m; + int neg, reduce; + mpfr_t c, xr; + mpfr_srcptr xx; + mp_exp_t err, expx; + int inexy, inexz; + MPFR_ZIV_DECL (loop); + MPFR_SAVE_EXPO_DECL (expo); + + MPFR_ASSERTN (y != z); + + if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x))) + { + if (MPFR_IS_NAN(x) || MPFR_IS_INF(x)) + { + MPFR_SET_NAN (y); + MPFR_SET_NAN (z); + MPFR_RET_NAN; + } + else /* x is zero */ + { + MPFR_ASSERTD (MPFR_IS_ZERO (x)); + MPFR_SET_ZERO (y); + MPFR_SET_SAME_SIGN (y, x); + /* y = 0, thus exact, but z is inexact in case of underflow + or overflow */ + return mpfr_set_ui (z, 1, rnd_mode); + } + } + + MPFR_LOG_FUNC (("x[%#R]=%R rnd=%d", x, x, rnd_mode), + ("sin[%#R]=%R cos[%#R]=%R", y, y, z, z)); + + MPFR_SAVE_EXPO_MARK (expo); + + prec = MAX (MPFR_PREC (y), MPFR_PREC (z)); + m = prec + MPFR_INT_CEIL_LOG2 (prec) + 13; + expx = MPFR_GET_EXP (x); + + /* When x is close to 0, say 2^(-k), then there is a cancellation of about + 2k bits in 1-cos(x)^2. FIXME: in that case, it would be more efficient + to compute sin(x) directly. VL: This is partly done by using + MPFR_FAST_COMPUTE_IF_SMALL_INPUT from the mpfr_sin and mpfr_cos + functions. Moreover, any overflow on m is avoided. */ + if (expx < 0) + { + /* Warning: in case y = x, and the first call to + MPFR_FAST_COMPUTE_IF_SMALL_INPUT succeeds but the second fails, + we will have clobbered the original value of x. + The workaround is to first compute z = cos(x) in that case, since + y and z are different. */ + if (y != x) + /* y and x differ, thus we can safely try to compute y first */ + { + MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, x, -2 * expx, 2, 0, rnd_mode, + { inexy = _inexact; + goto small_input; }); + if (0) + { + small_input: + /* we can go here only if we can round sin(x) */ + MPFR_FAST_COMPUTE_IF_SMALL_INPUT (z, __gmpfr_one, -2 * expx, + 1, 0, rnd_mode, + { inexz = _inexact; + goto end; }); + } + + /* if we go here, one of the two MPFR_FAST_COMPUTE_IF_SMALL_INPUT + calls failed */ + } + else /* y and x are the same variable: try to compute z first, which + necessarily differs */ + { + MPFR_FAST_COMPUTE_IF_SMALL_INPUT (z, __gmpfr_one, -2 * expx, + 1, 0, rnd_mode, + { inexz = _inexact; + goto small_input2; }); + if (0) + { + small_input2: + /* we can go here only if we can round cos(x) */ + MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, x, -2 * expx, 2, 0, + rnd_mode, + { inexy = _inexact; + goto end; }); + } + } + m += 2 * (-expx); + } + + mpfr_init (c); + mpfr_init (xr); + + MPFR_ZIV_INIT (loop, m); + for (;;) + { + /* the following is copied from sin.c */ + if (expx >= 2) /* reduce the argument */ + { + reduce = 1; + mpfr_set_prec (c, expx + m - 1); + mpfr_set_prec (xr, m); + mpfr_const_pi (c, GMP_RNDN); + mpfr_mul_2ui (c, c, 1, GMP_RNDN); + mpfr_remainder (xr, x, c, GMP_RNDN); + mpfr_div_2ui (c, c, 1, GMP_RNDN); + if (MPFR_SIGN (xr) > 0) + mpfr_sub (c, c, xr, GMP_RNDZ); + else + mpfr_add (c, c, xr, GMP_RNDZ); + if (MPFR_IS_ZERO(xr) || MPFR_EXP(xr) < (mp_exp_t) 3 - (mp_exp_t) m + || MPFR_EXP(c) < (mp_exp_t) 3 - (mp_exp_t) m) + goto next_step; + xx = xr; + } + else /* the input argument is already reduced */ + { + reduce = 0; + xx = x; + } + + neg = MPFR_IS_NEG (xx); /* gives sign of sin(x) */ + mpfr_set_prec (c, m); + mpfr_cos (c, xx, GMP_RNDZ); + /* If no argument reduction was performed, the error is at most ulp(c), + otherwise it is at most ulp(c) + 2^(2-m). Since |c| < 1, we have + ulp(c) <= 2^(-m), thus the error is bounded by 2^(3-m) in that later + case. */ + if (reduce == 0) + err = m; + else + err = MPFR_GET_EXP (c) + (mp_exp_t) (m - 3); + if (!mpfr_can_round (c, err, GMP_RNDN, rnd_mode, + MPFR_PREC (z) + (rnd_mode == GMP_RNDN))) + goto next_step; + + /* we can't set z now, because in case z = x, and the mpfr_can_round() + call below fails, we will have clobbered the input */ + mpfr_set_prec (xr, MPFR_PREC(c)); + mpfr_swap (xr, c); /* save the approximation of the cosine in xr */ + mpfr_sqr (c, xr, GMP_RNDU); + mpfr_ui_sub (c, 1, c, GMP_RNDN); + err = 2 + (- MPFR_GET_EXP (c)) / 2; + mpfr_sqrt (c, c, GMP_RNDN); + if (neg) + MPFR_CHANGE_SIGN (c); + + /* the absolute error on c is at most 2^(err-m), which we must put + in the form 2^(EXP(c)-err). If there was an argument reduction, + we need to add 2^(2-m); since err >= 2, the error is bounded by + 2^(err+1-m) in that case. */ + err = MPFR_GET_EXP (c) + (mp_exp_t) m - (err + reduce); + if (mpfr_can_round (c, err, GMP_RNDN, rnd_mode, + MPFR_PREC (y) + (rnd_mode == GMP_RNDN))) + break; + /* check for huge cancellation */ + if (err < (mp_exp_t) MPFR_PREC (y)) + m += MPFR_PREC (y) - err; + /* Check if near 1 */ + if (MPFR_GET_EXP (c) == 1 + && MPFR_MANT (c)[MPFR_LIMB_SIZE (c)-1] == MPFR_LIMB_HIGHBIT) + m += m; + + next_step: + MPFR_ZIV_NEXT (loop, m); + mpfr_set_prec (c, m); + } + MPFR_ZIV_FREE (loop); + + inexy = mpfr_set (y, c, rnd_mode); + inexz = mpfr_set (z, xr, rnd_mode); + + mpfr_clear (c); + mpfr_clear (xr); + + end: + /* FIXME: update the underflow flag if need be. */ + MPFR_SAVE_EXPO_FREE (expo); + mpfr_check_range (y, inexy, rnd_mode); + mpfr_check_range (z, inexz, rnd_mode); + MPFR_RET (1); /* Always inexact */ +}