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Diffstat (limited to 'mpfr/cos.c')
| -rw-r--r-- | mpfr/cos.c | 137 |
1 files changed, 137 insertions, 0 deletions
diff --git a/mpfr/cos.c b/mpfr/cos.c new file mode 100644 index 000000000..02461cedc --- /dev/null +++ b/mpfr/cos.c @@ -0,0 +1,137 @@ +/* mpfr_cos -- cosine of a floating-point number + +Copyright (C) 2001 Free Software Foundation. + +This file is part of the MPFR Library. + +The 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 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 MPFR Library; see the file COPYING.LIB. If not, write to +the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, +MA 02111-1307, USA. */ + +#include <stdio.h> +#include "gmp.h" +#include "gmp-impl.h" +#include "mpfr.h" +#include "mpfr-impl.h" + +static int mpfr_cos2_aux _PROTO ((mpfr_ptr, mpfr_srcptr)); + +int +mpfr_cos (mpfr_ptr y, mpfr_srcptr x, mp_rnd_t rnd_mode) +{ + int K, precy, m, k, l, inexact; + mpfr_t r, s; + + if (MPFR_IS_NAN(x) || MPFR_IS_INF(x)) + { + MPFR_SET_NAN(y); + return 1; + } + + if (!MPFR_NOTZERO(x)) + { + mpfr_set_ui (y, 1, GMP_RNDN); + return 0; + } + + precy = MPFR_PREC(y); + + K = _mpfr_isqrt(precy / 2); + if (MPFR_EXP(x) > 0) + K += MPFR_EXP(x); + /* we need at least K + log2(precy/K) extra bits */ + m = precy + 3 * K + 3; + + mpfr_init2 (r, m); + mpfr_init2 (s, m); + + do + { + mpfr_mul (r, x, x, GMP_RNDU); /* err <= 1 ulp */ + mpfr_div_2exp (r, r, 2 * K, GMP_RNDN); /* r = (x/2^K)^2, err <= 1 ulp */ + + /* s <- 1 - r/2! + ... + (-1)^l r^l/(2l)! */ + l = mpfr_cos2_aux (s, r); + + for (k = 0; k < K; k++) + { + mpfr_mul (s, s, s, GMP_RNDU); /* err <= 2*olderr */ + mpfr_mul_2exp (s, s, 1, GMP_RNDU); /* err <= 4*olderr */ + mpfr_sub_ui (s, s, 1, GMP_RNDN); + } + + /* absolute error on s is bounded by (2l+1/3)*2^(2K-m) */ + for (k = 2 * K, l = 2 * l + 1; l > 1; k++, l = (l + 1) >> 1); + /* now the error is bounded by 2^(k-m) = 2^(EXP(s)-err) */ + + l = mpfr_can_round (s, MPFR_EXP(s) + m - k, GMP_RNDN, rnd_mode, precy); + + if (l == 0) + { + m += BITS_PER_MP_LIMB; + mpfr_set_prec (r, m); + mpfr_set_prec (s, m); + } + } + while (l == 0); + + inexact = mpfr_set (y, s, rnd_mode); + + mpfr_clear (r); + mpfr_clear (s); + + return inexact; +} + +/* s <- 1 - r/2! + r^2/4! + ... + (-1)^l r^l/(2l)! + ... + Assumes |r| < 1. + Returns the index l0 of the last term (-1)^l r^l/(2l)!. + The absolute error on s is at most 2 * l0 * 2^(-m). +*/ +static int +mpfr_cos2_aux (mpfr_ptr s, mpfr_srcptr r) +{ + unsigned int l, b = 2; + int prec_t, m = MPFR_PREC(s); + mpfr_t t; + + MPFR_ASSERTN (MPFR_EXP(r) <= 0); + mpfr_init2 (t, m); + mpfr_set_ui (t, 1, GMP_RNDN); + mpfr_set_ui(s, 1, GMP_RNDN); + + for (l = 1; MPFR_EXP(t) >= -m; l++) + { + mpfr_mul (t, t, r, GMP_RNDU); /* err <= (3l-1) ulp */ + mpfr_div_ui (t, t, (2*l-1)*(2*l), GMP_RNDU); /* err <= 3l ulp */ + if (l % 2 == 0) + mpfr_add (s, s, t, GMP_RNDD); + else + mpfr_sub (s, s, t, GMP_RNDD); + MPFR_ASSERTN (MPFR_EXP(s) == 0); /* check 1/2 <= s < 1 */ + /* err(s) <= l * 2^(-m) */ + if (3 * l > (1 << b)) + b++; + /* now 3l <= 2^b, we want 3l*ulp(t) <= 2^(-m) + i.e. b+EXP(t)-PREC(t) <= -m */ + prec_t = m + MPFR_EXP(t) + b; + if (prec_t > 0) + mpfr_round (t, GMP_RNDN, prec_t); + } + + mpfr_clear (t); + + return l; +} + |