/* set f to the rational q */ int mpfr_set_q (mpfr_ptr f, mpq_srcptr q, mp_rnd_t rnd) { mpz_srcptr num, den; mpfr_t n, d; int inexact; mp_prec_t prec; MPFR_CLEAR_FLAGS (f); num = mpq_numref (q); if (mpz_cmp_ui (num, 0) == 0) { MPFR_SET_ZERO (f); MPFR_SET_POS (f); MPFR_RET (0); } den = mpq_denref (q); mpfr_save_emin_emax (); prec = mpz_sizeinbase (num, 2); if (prec < MPFR_PREC_MIN) prec = MPFR_PREC_MIN; mpfr_init2 (n, prec); if (mpfr_set_z (n, num, GMP_RNDZ)) /* result is exact unless overflow */ { mpfr_clear (n); mpfr_restore_emin_emax (); MPFR_SET_NAN (f); MPFR_RET_NAN; } prec = mpz_sizeinbase(den, 2); if (prec < MPFR_PREC_MIN) prec = MPFR_PREC_MIN; mpfr_init2 (d, prec); if (mpfr_set_z (d, den, GMP_RNDZ)) /* result is exact unless overflow */ { mpfr_clear (d); mpfr_clear (n); mpfr_restore_emin_emax (); MPFR_SET_NAN (f); MPFR_RET_NAN; } inexact = mpfr_div (f, n, d, rnd); mpfr_clear (n); mpfr_clear (d); MPFR_RESTORE_RET (inexact, f, rnd); }
int mpfr_cos (mpfr_ptr y, mpfr_srcptr x, mp_rnd_t rnd_mode) { int K0, K, precy, m, k, l; int inexact; mpfr_t r, s; mp_limb_t *rp, *sp; mp_size_t sm; mp_exp_t exps, cancel = 0; TMP_DECL (marker); if (MPFR_UNLIKELY(MPFR_IS_SINGULAR(x))) { if (MPFR_IS_NAN(x) || MPFR_IS_INF(x)) { MPFR_SET_NAN(y); MPFR_RET_NAN; } else { MPFR_ASSERTD(MPFR_IS_ZERO(x)); return mpfr_set_ui (y, 1, GMP_RNDN); } } mpfr_save_emin_emax (); precy = MPFR_PREC(y); K0 = __gmpfr_isqrt(precy / 2); /* Need K + log2(precy/K) extra bits */ m = precy + 3 * (K0 + 2 * MAX(MPFR_GET_EXP (x), 0)) + 3; TMP_MARK(marker); sm = (m + BITS_PER_MP_LIMB - 1) / BITS_PER_MP_LIMB; MPFR_TMP_INIT(rp, r, m, sm); MPFR_TMP_INIT(sp, s, m, sm); for (;;) { mpfr_mul (r, x, x, GMP_RNDU); /* err <= 1 ulp */ /* we need that |r| < 1 for mpfr_cos2_aux, i.e. up(x^2)/2^(2K) < 1 */ K = K0 + MAX (MPFR_GET_EXP (r), 0); mpfr_div_2ui (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); MPFR_SET_ONE (r); for (k = 0; k < K; k++) { mpfr_mul (s, s, s, GMP_RNDU); /* err <= 2*olderr */ mpfr_mul_2ui (s, s, 1, GMP_RNDU); /* err <= 4*olderr */ mpfr_sub (s, s, r, 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; l = (l + 1) >> 1) k++; /* now the error is bounded by 2^(k-m) = 2^(EXP(s)-err) */ exps = MPFR_GET_EXP(s); if (MPFR_LIKELY(mpfr_can_round (s, exps + m - k, GMP_RNDN, GMP_RNDZ, precy + (rnd_mode == GMP_RNDN)))) break; m += BITS_PER_MP_LIMB; if (exps < cancel) { m += cancel - exps; cancel = exps; } sm = (m + BITS_PER_MP_LIMB - 1) / BITS_PER_MP_LIMB; MPFR_TMP_INIT(rp, r, m, sm); MPFR_TMP_INIT(sp, s, m, sm); } mpfr_restore_emin_emax (); inexact = mpfr_set (y, s, rnd_mode); /* FIXME: Dont' need check range? */ TMP_FREE(marker); return inexact; }