static void test_reuse (void) { mpc_t z; mpfr_t y; int inex; mpfr_init2 (y, 2); mpc_init2 (z, 2); mpc_set_si_si (z, 0, -1, MPC_RNDNN); mpfr_neg (mpc_realref (z), mpc_realref (z), MPFR_RNDN); mpc_div_2ui (z, z, 4, MPC_RNDNN); mpfr_set_ui (y, 512, MPFR_RNDN); inex = mpc_pow_fr (z, z, y, MPC_RNDNN); if (MPC_INEX_RE(inex) != 0 || MPC_INEX_IM(inex) != 0 || mpfr_cmp_ui_2exp (mpc_realref(z), 1, -2048) != 0 || mpfr_cmp_ui (mpc_imagref(z), 0) != 0 || mpfr_signbit (mpc_imagref(z)) == 0) { printf ("Error in test_reuse, wrong ternary value or output\n"); printf ("inex=(%d %d)\n", MPC_INEX_RE(inex), MPC_INEX_IM(inex)); printf ("z="); mpc_out_str (stdout, 2, 0, z, MPC_RNDNN); printf ("\n"); exit (1); } mpfr_clear (y); mpc_clear (z); }
static PyObject * GMPy_Complex_Div_2exp(PyObject *x, PyObject *y, CTXT_Object *context) { MPC_Object *result, *tempx; unsigned long exp = 0; CHECK_CONTEXT(context); exp = c_ulong_From_Integer(y); if (exp == (unsigned long)(-1) && PyErr_Occurred()) { return NULL; } result = GMPy_MPC_New(0, 0, context); tempx = GMPy_MPC_From_Complex(x, 1, 1, context); if (!result || !tempx) { Py_XDECREF((PyObject*)result); Py_XDECREF((PyObject*)tempx); return NULL; } result->rc = mpc_div_2ui(result->c, tempx->c, exp, GET_MPC_ROUND(context)); Py_DECREF((PyObject*)tempx); GMPY_MPC_CLEANUP(result, context, "div_2exp()"); return (PyObject*)result; }
/* put in rop the value of exp(2*i*pi*k/n) rounded according to rnd */ int mpc_rootofunity (mpc_ptr rop, unsigned long n, unsigned long k, mpc_rnd_t rnd) { unsigned long g; mpq_t kn; mpfr_t t, s, c; mpfr_prec_t prec; int inex_re, inex_im; mpfr_rnd_t rnd_re, rnd_im; if (n == 0) { /* Compute exp (0 + i*inf). */ mpfr_set_nan (mpc_realref (rop)); mpfr_set_nan (mpc_imagref (rop)); return MPC_INEX (0, 0); } /* Eliminate common denominator. */ k %= n; g = gcd (k, n); k /= g; n /= g; /* Now 0 <= k < n and gcd(k,n)=1. */ /* We assume that only n=1, 2, 3, 4, 6 and 12 may yield exact results and treat them separately; n=8 is also treated here for efficiency reasons. */ if (n == 1) { /* necessarily k=0 thus we want exp(0)=1 */ MPC_ASSERT (k == 0); return mpc_set_ui_ui (rop, 1, 0, rnd); } else if (n == 2) { /* since gcd(k,n)=1, necessarily k=1, thus we want exp(i*pi)=-1 */ MPC_ASSERT (k == 1); return mpc_set_si_si (rop, -1, 0, rnd); } else if (n == 4) { /* since gcd(k,n)=1, necessarily k=1 or k=3, thus we want exp(2*i*pi/4)=i or exp(2*i*pi*3/4)=-i */ MPC_ASSERT (k == 1 || k == 3); if (k == 1) return mpc_set_ui_ui (rop, 0, 1, rnd); else return mpc_set_si_si (rop, 0, -1, rnd); } else if (n == 3 || n == 6) { MPC_ASSERT ((n == 3 && (k == 1 || k == 2)) || (n == 6 && (k == 1 || k == 5))); /* for n=3, necessarily k=1 or k=2: -1/2+/-1/2*sqrt(3)*i; for n=6, necessarily k=1 or k=5: 1/2+/-1/2*sqrt(3)*i */ inex_re = mpfr_set_si (mpc_realref (rop), (n == 3 ? -1 : 1), MPC_RND_RE (rnd)); /* inverse the rounding mode for -sqrt(3)/2 for zeta_3^2 and zeta_6^5 */ rnd_im = MPC_RND_IM (rnd); if (k != 1) rnd_im = INV_RND (rnd_im); inex_im = mpfr_sqrt_ui (mpc_imagref (rop), 3, rnd_im); mpc_div_2ui (rop, rop, 1, MPC_RNDNN); if (k != 1) { mpfr_neg (mpc_imagref (rop), mpc_imagref (rop), MPFR_RNDN); inex_im = -inex_im; } return MPC_INEX (inex_re, inex_im); } else if (n == 12) { /* necessarily k=1, 5, 7, 11: k=1: 1/2*sqrt(3) + 1/2*I k=5: -1/2*sqrt(3) + 1/2*I k=7: -1/2*sqrt(3) - 1/2*I k=11: 1/2*sqrt(3) - 1/2*I */ MPC_ASSERT (k == 1 || k == 5 || k == 7 || k == 11); /* inverse the rounding mode for -sqrt(3)/2 for zeta_12^5 and zeta_12^7 */ rnd_re = MPC_RND_RE (rnd); if (k == 5 || k == 7) rnd_re = INV_RND (rnd_re); inex_re = mpfr_sqrt_ui (mpc_realref (rop), 3, rnd_re); inex_im = mpfr_set_si (mpc_imagref (rop), k < 6 ? 1 : -1, MPC_RND_IM (rnd)); mpc_div_2ui (rop, rop, 1, MPC_RNDNN); if (k == 5 || k == 7) { mpfr_neg (mpc_realref (rop), mpc_realref (rop), MPFR_RNDN); inex_re = -inex_re; } return MPC_INEX (inex_re, inex_im); } else if (n == 8) { /* k=1, 3, 5 or 7: k=1: (1/2*I + 1/2)*sqrt(2) k=3: (1/2*I - 1/2)*sqrt(2) k=5: -(1/2*I + 1/2)*sqrt(2) k=7: -(1/2*I - 1/2)*sqrt(2) */ MPC_ASSERT (k == 1 || k == 3 || k == 5 || k == 7); rnd_re = MPC_RND_RE (rnd); if (k == 3 || k == 5) rnd_re = INV_RND (rnd_re); rnd_im = MPC_RND_IM (rnd); if (k > 4) rnd_im = INV_RND (rnd_im); inex_re = mpfr_sqrt_ui (mpc_realref (rop), 2, rnd_re); inex_im = mpfr_sqrt_ui (mpc_imagref (rop), 2, rnd_im); mpc_div_2ui (rop, rop, 1, MPC_RNDNN); if (k == 3 || k == 5) { mpfr_neg (mpc_realref (rop), mpc_realref (rop), MPFR_RNDN); inex_re = -inex_re; } if (k > 4) { mpfr_neg (mpc_imagref (rop), mpc_imagref (rop), MPFR_RNDN); inex_im = -inex_im; } return MPC_INEX (inex_re, inex_im); } prec = MPC_MAX_PREC(rop); /* For the error analysis justifying the following algorithm, see algorithms.tex. */ mpfr_init2 (t, 67); mpfr_init2 (s, 67); mpfr_init2 (c, 67); mpq_init (kn); mpq_set_ui (kn, k, n); mpq_mul_2exp (kn, kn, 1); /* kn=2*k/n < 2 */ do { prec += mpc_ceil_log2 (prec) + 5; /* prec >= 6 */ mpfr_set_prec (t, prec); mpfr_set_prec (s, prec); mpfr_set_prec (c, prec); mpfr_const_pi (t, MPFR_RNDN); mpfr_mul_q (t, t, kn, MPFR_RNDN); mpfr_sin_cos (s, c, t, MPFR_RNDN); } while ( !mpfr_can_round (c, prec - (4 - mpfr_get_exp (c)), MPFR_RNDN, MPFR_RNDZ, MPC_PREC_RE(rop) + (MPC_RND_RE(rnd) == MPFR_RNDN)) || !mpfr_can_round (s, prec - (4 - mpfr_get_exp (s)), MPFR_RNDN, MPFR_RNDZ, MPC_PREC_IM(rop) + (MPC_RND_IM(rnd) == MPFR_RNDN))); inex_re = mpfr_set (mpc_realref(rop), c, MPC_RND_RE(rnd)); inex_im = mpfr_set (mpc_imagref(rop), s, MPC_RND_IM(rnd)); mpfr_clear (t); mpfr_clear (s); mpfr_clear (c); mpq_clear (kn); return MPC_INEX(inex_re, inex_im); }