int change_sphere_eval_prec(void const *ED, int new_prec)
{
sphere_eval_data_mp *BED = (sphere_eval_data_mp *)ED; // to avoid having to cast every time
BED->SLP->precision = new_prec;
// change the precision for the patch
changePatchPrec_mp(new_prec, &BED->patch);
if (new_prec != BED->curr_prec){
if (BED->verbose_level() >=8){
std::cout << color::brown();
printf("prec %ld\t-->\t%d\n",BED->curr_prec, new_prec);
std::cout << color::console_default();
}
BED->curr_prec = new_prec;
setprec_mp(BED->gamma, new_prec);
mpf_set_q(BED->gamma->r, BED->gamma_rat[0]);
mpf_set_q(BED->gamma->i, BED->gamma_rat[1]);
for (int ii=0; ii<1; ++ii){
change_prec_point_mp(BED->starting_linear[ii],new_prec);
vec_cp_mp(BED->starting_linear[ii], BED->starting_linear_full_prec[ii]);
}
for (int ii=0; ii<BED->num_static_linears; ++ii){
change_prec_point_mp(BED->static_linear[ii],new_prec);
vec_cp_mp(BED->static_linear[ii], BED->static_linear_full_prec[ii]);
}
change_prec_point_mp(BED->center, new_prec);
vec_cp_mp(BED->center, BED->center_full_prec);
setprec_mp(BED->radius, new_prec);
set_mp(BED->radius, BED->radius_full_prec);
setprec_mp(BED->two, new_prec);
set_mp(BED->two, BED->two_full_prec);
BED->randomizer()->change_prec(new_prec);
}
return 0;
}
void fmpz_poly_disc_gauss_rounding(fmpz_poly_t rop, const fmpq_poly_t x, const mpfr_t r_f, gmp_randstate_t randstate) {
mpfr_t xi; mpfr_init2(xi, mpfr_get_prec(r_f));
mpf_t xi_f; mpf_init2(xi_f, mpfr_get_prec(r_f));
mpq_t xi_q; mpq_init(xi_q);
mpz_t s_z; mpz_init(s_z);
const long n = fmpq_poly_length(x);
const size_t tau = (ceil(2*sqrt(log2((double)n))) > 3) ? ceil(2*sqrt(log2((double)n))) : 3;
fmpz_poly_zero(rop);
for(int i=0; i<n; i++) {
fmpq_poly_get_coeff_mpq(xi_q, x, i);
mpf_set_q(xi_f, xi_q);
mpfr_set_f(xi, xi_f, MPFR_RNDN);
dgs_disc_gauss_mp_t *D = dgs_disc_gauss_mp_init(r_f, xi, tau, DGS_DISC_GAUSS_UNIFORM_ONLINE);
D->call(s_z, D, randstate);
dgs_disc_gauss_mp_clear(D);
fmpz_poly_set_coeff_mpz(rop, i, s_z);
}
mpz_clear(s_z);
mpq_clear(xi_q);
mpf_clear(xi_f);
mpfr_clear(xi);
}
void
check_various (void)
{
mpf_t got;
mpq_t q;
mpf_init (got);
mpq_init (q);
/* 1/1 == 1 */
mpf_set_prec (got, 20L);
mpq_set_ui (q, 1L, 1L);
mpf_set_q (got, q);
MPF_CHECK_FORMAT (got);
ASSERT_ALWAYS (mpf_cmp_ui (got, 1L) == 0);
/* 1/(2^n+1), a case where truncating the divisor would be wrong */
mpf_set_prec (got, 500L);
mpq_set_ui (q, 1L, 1L);
mpz_mul_2exp (mpq_denref(q), mpq_denref(q), 800L);
mpz_add_ui (mpq_denref(q), mpq_denref(q), 1L);
check_one (got, q);
mpf_clear (got);
mpq_clear (q);
}
Float::Float(const Rational& r)
{
mpf_init(value);
mpq_t mpq;
r.mpqInit(mpq);
mpf_set_q(value, mpq);
mpq_clear(mpq);
}
void gmp_print_mpq(FILE* fp, const mpq_t qval)
{
mpf_t fval;
mpf_init(fval);
mpf_set_q(fval, qval);
mpf_out_str(fp, 10, 32, fval);
fprintf(fp, " = ");
mpq_out_str(fp, 10, qval);
fputc('\n', fp);
mpf_clear(fval);
}
void
check_one (mpf_ptr got, mpq_srcptr q)
{
mpf_t n, d;
mpf_set_q (got, q);
PTR(n) = PTR(&q->_mp_num);
SIZ(n) = SIZ(&q->_mp_num);
EXP(n) = ABSIZ(&q->_mp_num);
PTR(d) = PTR(&q->_mp_den);
SIZ(d) = SIZ(&q->_mp_den);
EXP(d) = ABSIZ(&q->_mp_den);
if (! refmpf_validate_division ("mpf_set_q", got, n, d))
{
mp_trace_base = -16;
mpq_trace (" q", q);
abort ();
}
}
static void
check_mixed (FILE *fout)
{
int ch = 'a';
signed char sch = -1;
unsigned char uch = 1;
short sh = -1;
unsigned short ush = 1;
int i = -1;
int j = 1;
unsigned int ui = 1;
long lo = -1;
unsigned long ulo = 1;
float f = -1.25;
double d = -1.25;
long double ld = -1.25;
ptrdiff_t p = 1;
size_t sz = 1;
mpz_t mpz;
mpq_t mpq;
mpf_t mpf;
mp_rnd_t rnd = GMP_RNDN;
mp_size_t limb_size = 3;
mp_limb_t limb[3];
mpfr_t mpfr;
mpfr_prec_t prec = 53;
mpz_init (mpz);
mpz_set_ui (mpz, ulo);
mpq_init (mpq);
mpq_set_si (mpq, lo, ulo);
mpf_init (mpf);
mpf_set_q (mpf, mpq);
mpfr_init2 (mpfr, prec);
mpfr_set_f (mpfr, mpf, GMP_RNDN);
limb[0] = limb[1] = limb[2] = ~ (mp_limb_t) 0;
check_vfprintf (fout, "a. %Ra, b. %u, c. %lx%n", mpfr, ui, ulo, &j);
check_length (1, j, 22, d);
check_vfprintf (fout, "a. %c, b. %Rb, c. %u, d. %li%ln", i, mpfr, i,
lo, &ulo);
check_length (2, ulo, 36, lu);
check_vfprintf (fout, "a. %hi, b. %*f, c. %Re%hn", ush, 3, f, mpfr, &ush);
check_length (3, ush, 29, hu);
check_vfprintf (fout, "a. %hi, b. %f, c. %#.2Rf%n", sh, d, mpfr, &i);
check_length (4, i, 29, d);
check_vfprintf (fout, "a. %R*A, b. %Fe, c. %i%zn", rnd, mpfr, mpf, sz,
&sz);
check_length (5, (unsigned long) sz, 34, lu); /* no format specifier "%zu" in C89 */
check_vfprintf (fout, "a. %Pu, b. %c, c. %Zi%Zn", prec, ch, mpz, &mpz);
check_length_with_cmp (6, mpz, 17, mpz_cmp_ui (mpz, 17), Zi);
check_vfprintf (fout, "%% a. %#.0RNg, b. %Qx%Rn, c. %p", mpfr, mpq, &mpfr,
(void *) &i);
check_length_with_cmp (7, mpfr, 15, mpfr_cmp_ui (mpfr, 15), Rg);
#ifndef NPRINTF_T
check_vfprintf (fout, "%% a. %RNg, b. %Qx, c. %td%tn", mpfr, mpq, p, &p);
check_length (8, (long) p, 20, ld); /* no format specifier "%td" in C89 */
#endif
#ifndef NPRINTF_L
check_vfprintf (fout, "a. %RA, b. %Lf, c. %QX%zn", mpfr, ld, mpq, &sz);
check_length (9, (unsigned long) sz, 30, lu); /* no format specifier "%zu" in C89 */
#endif
#ifndef NPRINTF_HH
check_vfprintf (fout, "a. %hhi, b.%RA, c. %hhu%hhn", sch, mpfr, uch, &uch);
check_length (10, (unsigned int) uch, 21, u); /* no format specifier "%hhu" in C89 */
#endif
#if (__GNU_MP_VERSION * 10 + __GNU_MP_VERSION_MINOR) >= 42
/* The 'M' specifier was added in gmp 4.2.0 */
check_vfprintf (fout, "a. %Mx b. %Re%Mn", limb[0], mpfr, &limb[0]);
if (limb[0] != 14 + BITS_PER_MP_LIMB / 4 || limb[1] != ~ (mp_limb_t) 0
|| limb[2] != ~ (mp_limb_t) 0)
{
printf ("Error in test #11: mpfr_vfprintf did not print %d characters"
" as expected\n", 14 + (int) BITS_PER_MP_LIMB / 4);
exit (1);
}
limb[0] = ~ (mp_limb_t) 0;
/* we tell vfprintf that limb array is 2 cells wide
and check it doesn't go through */
check_vfprintf (fout, "a. %Re .b %Nx%Nn", mpfr, limb, limb_size, limb,
limb_size - 1);
if (limb[0] != 14 + 3 * BITS_PER_MP_LIMB / 4 || limb[1] != (mp_limb_t) 0
|| limb[2] != ~ (mp_limb_t) 0)
{
printf ("Error in test #12: mpfr_vfprintf did not print %d characters"
" as expected\n", 14 + (int) BITS_PER_MP_LIMB / 4);
exit (1);
}
#endif
#if defined(HAVE_LONG_LONG) && !defined(NPRINTF_LL)
{
long long llo = -1;
unsigned long long ullo = 1;
check_vfprintf (fout, "a. %Re, b. %llx%Qn", mpfr, ullo, &mpq);
check_length_with_cmp (21, mpq, 16, mpq_cmp_ui (mpq, 16, 1), Qu);
check_vfprintf (fout, "a. %lli, b. %Rf%Fn", llo, mpfr, &mpf);
check_length_with_cmp (22, mpf, 19, mpf_cmp_ui (mpf, 19), Fg);
}
#endif
#if defined(_MPFR_H_HAVE_INTMAX_T) && !defined(NPRINTF_J)
{
intmax_t im = -1;
uintmax_t uim = 1;
check_vfprintf (fout, "a. %*RA, b. %ji%Qn", 10, mpfr, im, &mpq);
check_length_with_cmp (31, mpq, 20, mpq_cmp_ui (mpq, 20, 1), Qu);
check_vfprintf (fout, "a. %.*Re, b. %jx%Fn", 10, mpfr, uim, &mpf);
check_length_with_cmp (32, mpf, 25, mpf_cmp_ui (mpf, 25), Fg);
}
#endif
mpfr_clear (mpfr);
mpf_clear (mpf);
mpq_clear (mpq);
mpz_clear (mpz);
}
static void
check_mixed (void)
{
int ch = 'a';
#ifndef NPRINTF_HH
signed char sch = -1;
unsigned char uch = 1;
#endif
short sh = -1;
unsigned short ush = 1;
int i = -1;
int j = 1;
unsigned int ui = 1;
long lo = -1;
unsigned long ulo = 1;
float f = -1.25;
double d = -1.25;
#if !defined(NPRINTF_T) || !defined(NPRINTF_L)
long double ld = -1.25;
#endif
#ifndef NPRINTF_T
ptrdiff_t p = 1, saved_p;
#endif
size_t sz = 1;
mpz_t mpz;
mpq_t mpq;
mpf_t mpf;
mpfr_rnd_t rnd = MPFR_RNDN;
mpfr_t mpfr;
mpfr_prec_t prec;
mpz_init (mpz);
mpz_set_ui (mpz, ulo);
mpq_init (mpq);
mpq_set_si (mpq, lo, ulo);
mpf_init (mpf);
mpf_set_q (mpf, mpq);
mpfr_init (mpfr);
mpfr_set_f (mpfr, mpf, MPFR_RNDN);
prec = mpfr_get_prec (mpfr);
check_vprintf ("a. %Ra, b. %u, c. %lx%n", mpfr, ui, ulo, &j);
check_length (1, j, 22, d);
check_vprintf ("a. %c, b. %Rb, c. %u, d. %li%ln", i, mpfr, i, lo, &ulo);
check_length (2, ulo, 36, lu);
check_vprintf ("a. %hi, b. %*f, c. %Re%hn", ush, 3, f, mpfr, &ush);
check_length (3, ush, 29, hu);
check_vprintf ("a. %hi, b. %f, c. %#.2Rf%n", sh, d, mpfr, &i);
check_length (4, i, 29, d);
check_vprintf ("a. %R*A, b. %Fe, c. %i%zn", rnd, mpfr, mpf, sz, &sz);
check_length (5, (unsigned long) sz, 34, lu); /* no format specifier '%zu' in C89 */
check_vprintf ("a. %Pu, b. %c, c. %RUG, d. %Zi%Zn", prec, ch, mpfr, mpz, &mpz);
check_length_with_cmp (6, mpz, 24, mpz_cmp_ui (mpz, 24), Zi);
check_vprintf ("%% a. %#.0RNg, b. %Qx%Rn c. %p",
mpfr, mpq, &mpfr, (void *) &i);
check_length_with_cmp (7, mpfr, 15, mpfr_cmp_ui (mpfr, 15), Rg);
#ifndef NPRINTF_T
saved_p = p;
check_vprintf ("%% a. %RNg, b. %Qx, c. %td%tn", mpfr, mpq, p, &p);
if (p != 20)
mpfr_fprintf (stderr, "Error in test 8, got '%% a. %RNg, b. %Qx, c. %td'\n", mpfr, mpq, saved_p);
check_length (8, (long) p, 20, ld); /* no format specifier '%td' in C89 */
#endif
#ifndef NPRINTF_L
check_vprintf ("a. %RA, b. %Lf, c. %QX%zn", mpfr, ld, mpq, &sz);
check_length (9, (unsigned long) sz, 30, lu); /* no format specifier '%zu' in C89 */
#endif
#ifndef NPRINTF_HH
check_vprintf ("a. %hhi, b. %Ra, c. %hhu%hhn", sch, mpfr, uch, &uch);
check_length (10, (unsigned int) uch, 22, u); /* no format specifier '%hhu' in C89 */
#endif
#if defined(HAVE_LONG_LONG) && !defined(NPRINTF_LL)
{
long long llo = -1;
unsigned long long ullo = 1;
check_vprintf ("a. %Re, b. %llx%Qn", mpfr, ullo, &mpq);
check_length_with_cmp (11, mpq, 16, mpq_cmp_ui (mpq, 16, 1), Qu);
check_vprintf ("a. %lli, b. %Rf%lln", llo, mpfr, &ullo);
check_length (12, ullo, 19, llu);
}
#endif
#if defined(_MPFR_H_HAVE_INTMAX_T) && !defined(NPRINTF_J)
{
intmax_t im = -1;
uintmax_t uim = 1;
check_vprintf ("a. %*RA, b. %ji%Fn", 10, mpfr, im, &mpf);
check_length_with_cmp (31, mpf, 20, mpf_cmp_ui (mpf, 20), Fg);
check_vprintf ("a. %.*Re, b. %jx%jn", 10, mpfr, uim, &im);
check_length (32, (long) im, 25, li); /* no format specifier "%ji" in C89 */
}
#endif
mpfr_clear (mpfr);
mpf_clear (mpf);
mpq_clear (mpq);
mpz_clear (mpz);
}
//------------------------------------------------------------------------------
// Name:
//------------------------------------------------------------------------------
knumber_float::knumber_float(const knumber_fraction *value) {
mpf_init(mpf_);
mpf_set_q(mpf_, value->mpq_);
}
double
hyperd(N, K, n, k)
{
static mpq_t num, num2, den, q;
static mpq_t p2, t;
static mpf_t f;
static int first = 1;
double d;
double p;
if (first) {
mpq_init(num);
mpq_init(num2);
mpq_init(den);
mpq_init(q);
mpf_init(f);
mpq_init(p2);
mpq_init(t);
first = 0;
}
switch (hyperd_mode) {
case 0:
mP(&num, K, k);
mP(&p2, N - K, n - k);
mpq_mul(num2, num, p2);
mH(&p2, k + 1, n - k);
mpq_mul(num, num2, p2);
mP(&den, N, n);
mpq_div(q, num, den);
mpf_set_q(f, q);
d = mpf_get_d(f);
break;
case 1:
xx:
mC(&num2, K, k);
mC(&p2, N - K, n - k);
mpq_mul(num, num2, p2);
mC(&den, N, n);
mpq_div(q, num, den);
mpf_set_q(f, q);
d = mpf_get_d(f);
break;
case 2:
if (k == K || n - k == N - K || n == N) {
goto xx;
}
if (k == 0 || n - k == 0 || n == 0) {
goto xx;
}
p = (double)n / N;
d = dB(K, p, k) * dB(N - K, p, n - k) / dB(N, p, n);
if (d < 3e-14) {
goto xx;
}
break;
default:
fprintf(stderr, "internal error\n");
exit(1);
/* NOTREACHED */
}
return d;
}
/**
* @brief Setup vectors and variables
*/
MPS_PRIVATE void
mps_setup (mps_context * s)
{
int i;
mps_polynomial *p = s->active_poly;
mpf_t mptemp;
mpc_t mptempc;
if (s->DOLOG)
{
/* fprintf (s->logstr, "Goal = %5s\n", s->goal); */
/* fprintf (s->logstr, "Data type = %3s\n", s->data_type); */
fprintf (s->logstr, "Degree = %d\n", s->n);
fprintf (s->logstr, "Input prec. = %ld digits\n", (long)(s->active_poly->prec
* LOG10_2));
fprintf (s->logstr, "Output prec. = %ld digits\n", (long)(s->output_config->prec
* LOG10_2));
}
/* setup temporary vectors */
if (MPS_IS_MONOMIAL_POLY (p) && MPS_DENSITY_IS_SPARSE (s->active_poly->density))
{
mps_monomial_poly *mp = MPS_MONOMIAL_POLY (p);
for (i = 0; i <= p->degree; i++)
{
mp->fap[i] = 0.0;
mp->fpr[i] = 0.0;
rdpe_set (mp->dap[i], rdpe_zero);
cplx_set (mp->fpc[i], cplx_zero);
rdpe_set (mp->dpr[i], rdpe_zero);
cdpe_set (mp->dpc[i], cdpe_zero);
}
}
/* Indexes of the first (and only) cluster start from
* 0 and reach n */
mps_cluster_reset (s);
/* set input and output epsilon */
rdpe_set_2dl (s->eps_in, 1.0, 1 - s->active_poly->prec);
rdpe_set_2dl (s->eps_out, 1.0, 1 - s->output_config->prec);
/* precision of each root */
for (i = 0; i < s->n; i++)
s->root[i]->wp = 53;
/* output order info */
for (i = 0; i < s->n; i++)
s->order[i] = i;
/* reset root counts */
s->count[0] = s->count[1] = s->count[2] = 0;
/* compute DPE approximations */
if (MPS_IS_MONOMIAL_POLY (p))
{
mps_monomial_poly *mp = MPS_MONOMIAL_POLY (p);
/* init temporary mp variables */
mpf_init2 (mptemp, DBL_MANT_DIG);
mpc_init2 (mptempc, DBL_MANT_DIG);
/* main loop */
s->skip_float = false;
for (i = 0; i <= s->n; i++)
{
if (MPS_DENSITY_IS_SPARSE (s->active_poly->density) && !mp->spar[i])
continue;
if (MPS_STRUCTURE_IS_REAL (s->active_poly->structure))
{
if (MPS_STRUCTURE_IS_RATIONAL (s->active_poly->structure) ||
MPS_STRUCTURE_IS_INTEGER (s->active_poly->structure))
{
mpf_set_q (mptemp, mp->initial_mqp_r[i]);
mpf_get_rdpe (mp->dpr[i], mptemp);
/*#G GMP 2.0.2 bug begin */
if (rdpe_sgn (mp->dpr[i]) != mpq_sgn (mp->initial_mqp_r[i]))
rdpe_neg_eq (mp->dpr[i]);
/*#G GMP bug end */
}
if (MPS_STRUCTURE_IS_FP (s->active_poly->structure))
mpf_get_rdpe (mp->dpr[i], mpc_Re (mp->mfpc[i]));
cdpe_set_e (mp->dpc[i], mp->dpr[i], rdpe_zero);
/* compute dap[i] and check for float phase */
rdpe_abs (mp->dap[i], mp->dpr[i]);
rdpe_abs (mp->dap[i], mp->dpr[i]);
if (rdpe_gt (mp->dap[i], rdpe_maxd)
|| rdpe_lt (mp->dap[i], rdpe_mind))
s->skip_float = true;
}
else if (MPS_STRUCTURE_IS_COMPLEX (s->active_poly->structure))
{
if (MPS_STRUCTURE_IS_RATIONAL (s->active_poly->structure) ||
MPS_STRUCTURE_IS_INTEGER (s->active_poly->structure))
{
mpc_set_q (mptempc, mp->initial_mqp_r[i], mp->initial_mqp_i[i]);
mpc_get_cdpe (mp->dpc[i], mptempc);
/*#G GMP 2.0.2 bug begin */
if (rdpe_sgn (cdpe_Re (mp->dpc[i])) != mpq_sgn (mp->initial_mqp_r[i]))
rdpe_neg_eq (cdpe_Re (mp->dpc[i]));
if (rdpe_sgn (cdpe_Im (mp->dpc[i])) != mpq_sgn (mp->initial_mqp_i[i]))
rdpe_neg_eq (cdpe_Im (mp->dpc[i]));
/*#G GMP bug end */
}
else if (MPS_STRUCTURE_IS_FP (s->active_poly->structure))
mpc_get_cdpe (mp->dpc[i], mp->mfpc[i]);
/* compute dap[i] */
cdpe_mod (mp->dap[i], mp->dpc[i]);
if (rdpe_gt (mp->dap[i], rdpe_maxd)
|| rdpe_lt (mp->dap[i], rdpe_mind))
s->skip_float = true;
}
}
/* free temporary mp variables */
mpf_clear (mptemp);
mpc_clear (mptempc);
/* adjust input data type */
if (MPS_STRUCTURE_IS_FP (s->active_poly->structure) && s->skip_float)
s->active_poly->structure = MPS_STRUCTURE_IS_REAL (s->active_poly->structure) ?
MPS_STRUCTURE_REAL_BIGFLOAT : MPS_STRUCTURE_COMPLEX_BIGFLOAT;
/* prepare floating point vectors */
if (!s->skip_float)
for (i = 0; i <= MPS_POLYNOMIAL (p)->degree; i++)
{
if (MPS_DENSITY_IS_SPARSE (s->active_poly->density) || !mp->spar[i])
continue;
if (MPS_STRUCTURE_IS_REAL (s->active_poly->structure))
{
mp->fpr[i] = rdpe_get_d (mp->dpr[i]);
mp->fap[i] = fabs (mp->fpr[i]);
cplx_set_d (mp->fpc[i], mp->fpr[i], 0.0);
}
else
{
cdpe_get_x (mp->fpc[i], mp->dpc[i]);
mp->fap[i] = cplx_mod (mp->fpc[i]);
}
}
}
}
static void compute_pi(int prec) {
//Chudnovsky brothers' Ramanujan formula
//http://www.cs.uwaterloo.ca/~alopez-o/math-faq/mathtext/node12.html
mpz_t k1, k2, k4, k5, d;
unsigned int k3 = 640320;
unsigned int k6 = 53360;
mpz_t z0, z1, z2;
mpq_t p, q;
mpf_t f1;
int toggle = 1;
int n;
//converges fast: each term gives over 47 bits
int nlimit = prec / 47 + 1;
mpz_init(k1);
mpz_init(k2);
mpz_init(k4);
mpz_init(k5);
mpz_init(d);
mpz_init(z0);
mpz_init(z1);
mpz_init(z2);
mpq_init(q);
mpq_init(p);
mpf_init(f1);
mpz_set_str(k1, "545140134", 10);
mpz_set_str(k2, "13591409", 10);
mpz_set_str(k4, "100100025", 10);
mpz_set_str(k5, "327843840", 10);
mpz_mul(d, k4, k5);
mpz_mul_2exp(d, d, 3);
mpq_set_ui(p, 0, 1);
for (n=0; n<nlimit; n++) {
mpz_fac_ui(z0, 6*n);
mpz_mul_ui(z1, k1, n);
mpz_add(z1, z1, k2);
mpz_mul(z0, z0, z1);
mpz_fac_ui(z1, 3*n);
mpz_fac_ui(z2, n);
mpz_pow_ui(z2, z2, 3);
mpz_mul(z1, z1, z2);
mpz_pow_ui(z2, d, n);
mpz_mul(z1, z1, z2);
mpz_set(mpq_numref(q), z0);
mpz_set(mpq_denref(q), z1);
mpq_canonicalize(q);
if (toggle) {
mpq_add(p, p, q);
} else {
mpq_sub(p, p, q);
}
toggle = !toggle;
}
mpq_inv(q, p);
mpz_mul_ui(mpq_numref(q), mpq_numref(q), k6);
mpq_canonicalize(q);
mpf_set_q(pi, q);
mpf_sqrt_ui(f1, k3);
mpf_mul(pi, pi, f1);
//mpf_out_str(stdout, 0, 14 * nlimit, pi);
//printf("\n");
mpz_clear(k1);
mpz_clear(k2);
mpz_clear(k4);
mpz_clear(k5);
mpz_clear(d);
mpz_clear(z0);
mpz_clear(z1);
mpz_clear(z2);
mpq_clear(q);
mpq_clear(p);
mpf_clear(f1);
}
static void
check_set (void)
{
long int lo;
mpz_t mpz;
mpq_t mpq;
mpf_t mpf;
mpfr_t fr;
mpc_t x, z;
mpfr_prec_t prec;
mpz_init (mpz);
mpq_init (mpq);
mpf_init2 (mpf, 1000);
mpfr_init2 (fr, 1000);
mpc_init2 (x, 1000);
mpc_init2 (z, 1000);
mpz_set_ui (mpz, 0x4217);
mpq_set_si (mpq, -1, 0x4321);
mpf_set_q (mpf, mpq);
for (prec = 2; prec <= 1000; prec++)
{
unsigned long int u = (unsigned long int) prec;
mpc_set_prec (z, prec);
mpfr_set_prec (fr, prec);
lo = -prec;
mpfr_set_d (fr, 1.23456789, GMP_RNDN);
mpc_set_d (z, 1.23456789, MPC_RNDNN);
if (mpfr_cmp (MPC_RE(z), fr) != 0 || mpfr_cmp_si (MPC_IM(z), 0) != 0)
PRINT_ERROR ("mpc_set_d", prec, z);
#if defined _MPC_H_HAVE_COMPLEX
mpc_set_dc (z, I*1.23456789+1.23456789, MPC_RNDNN);
if (mpfr_cmp (MPC_RE(z), fr) != 0 || mpfr_cmp (MPC_IM(z), fr) != 0)
PRINT_ERROR ("mpc_set_c", prec, z);
#endif
mpc_set_ui (z, u, MPC_RNDNN);
if (mpfr_cmp_ui (MPC_RE(z), u) != 0
|| mpfr_cmp_ui (MPC_IM(z), 0) != 0)
PRINT_ERROR ("mpc_set_ui", prec, z);
mpc_set_d_d (z, 1.23456789, 1.23456789, MPC_RNDNN);
if (mpfr_cmp (MPC_RE(z), fr) != 0 || mpfr_cmp (MPC_IM(z), fr) != 0)
PRINT_ERROR ("mpc_set_d_d", prec, z);
mpc_set_si (z, lo, MPC_RNDNN);
if (mpfr_cmp_si (MPC_RE(z), lo) != 0 || mpfr_cmp_ui (MPC_IM(z), 0) != 0)
PRINT_ERROR ("mpc_set_si", prec, z);
mpfr_set_ld (fr, 1.23456789L, GMP_RNDN);
mpc_set_ld_ld (z, 1.23456789L, 1.23456789L, MPC_RNDNN);
if (mpfr_cmp (MPC_RE(z), fr) != 0 || mpfr_cmp (MPC_IM(z), fr) != 0)
PRINT_ERROR ("mpc_set_ld_ld", prec, z);
#if defined _MPC_H_HAVE_COMPLEX
mpc_set_ldc (z, I*1.23456789L+1.23456789L, MPC_RNDNN);
if (mpfr_cmp (MPC_RE(z), fr) != 0 || mpfr_cmp (MPC_IM(z), fr) != 0)
PRINT_ERROR ("mpc_set_lc", prec, z);
#endif
mpc_set_ui_ui (z, u, u, MPC_RNDNN);
if (mpfr_cmp_ui (MPC_RE(z), u) != 0
|| mpfr_cmp_ui (MPC_IM(z), u) != 0)
PRINT_ERROR ("mpc_set_ui_ui", prec, z);
mpc_set_ld (z, 1.23456789L, MPC_RNDNN);
mpfr_clear_flags ();
if (mpfr_cmp (MPC_RE(z), fr) != 0
|| mpfr_cmp_ui (MPC_IM(z), 0) != 0
|| mpfr_erangeflag_p())
PRINT_ERROR ("mpc_set_ld", prec, z);
mpc_set_prec (x, prec);
mpfr_set_ui(fr, 1, GMP_RNDN);
mpfr_div_ui(fr, fr, 3, GMP_RNDN);
mpfr_set(MPC_RE(x), fr, GMP_RNDN);
mpfr_set(MPC_IM(x), fr, GMP_RNDN);
mpc_set (z, x, MPC_RNDNN);
mpfr_clear_flags (); /* mpc_cmp set erange flag when an operand is a
NaN */
if (mpc_cmp (z, x) != 0 || mpfr_erangeflag_p())
{
printf ("Error in mpc_set for prec = %lu\n",
(unsigned long int) prec);
MPC_OUT(z);
MPC_OUT(x);
exit (1);
}
mpc_set_si_si (z, lo, lo, MPC_RNDNN);
if (mpfr_cmp_si (MPC_RE(z), lo) != 0
|| mpfr_cmp_si (MPC_IM(z), lo) != 0)
PRINT_ERROR ("mpc_set_si_si", prec, z);
mpc_set_fr (z, fr, MPC_RNDNN);
mpfr_clear_flags ();
if (mpfr_cmp (MPC_RE(z), fr) != 0
|| mpfr_cmp_ui (MPC_IM(z), 0) != 0
|| mpfr_erangeflag_p())
PRINT_ERROR ("mpc_set_fr", prec, z);
mpfr_set_z (fr, mpz, GMP_RNDN);
mpc_set_z_z (z, mpz, mpz, MPC_RNDNN);
mpfr_clear_flags ();
if (mpfr_cmp (MPC_RE(z), fr) != 0
|| mpfr_cmp (MPC_IM(z), fr) != 0
|| mpfr_erangeflag_p())
PRINT_ERROR ("mpc_set_z_z", prec, z);
mpc_set_fr_fr (z, fr, fr, MPC_RNDNN);
mpfr_clear_flags ();
if (mpfr_cmp (MPC_RE(z), fr) != 0
|| mpfr_cmp (MPC_IM(z), fr) != 0
|| mpfr_erangeflag_p())
PRINT_ERROR ("mpc_set_fr_fr", prec, z);
mpc_set_z (z, mpz, MPC_RNDNN);
mpfr_clear_flags ();
if (mpfr_cmp (MPC_RE(z), fr) != 0
|| mpfr_cmp_ui (MPC_IM(z), 0) != 0
|| mpfr_erangeflag_p())
PRINT_ERROR ("mpc_set_z", prec, z);
mpfr_set_q (fr, mpq, GMP_RNDN);
mpc_set_q_q (z, mpq, mpq, MPC_RNDNN);
mpfr_clear_flags ();
if (mpfr_cmp (MPC_RE(z), fr) != 0
|| mpfr_cmp (MPC_IM(z), fr) != 0
|| mpfr_erangeflag_p())
PRINT_ERROR ("mpc_set_q_q", prec, z);
mpc_set_ui_fr (z, u, fr, MPC_RNDNN);
mpfr_clear_flags ();
if (mpfr_cmp_ui (MPC_RE (z), u) != 0
|| mpfr_cmp (MPC_IM (z), fr) != 0
|| mpfr_erangeflag_p ())
PRINT_ERROR ("mpc_set_ui_fr", prec, z);
mpc_set_fr_ui (z, fr, u, MPC_RNDNN);
mpfr_clear_flags ();
if (mpfr_cmp (MPC_RE (z), fr) != 0
|| mpfr_cmp_ui (MPC_IM (z), u) != 0
|| mpfr_erangeflag_p())
PRINT_ERROR ("mpc_set_fr_ui", prec, z);
mpc_set_q (z, mpq, MPC_RNDNN);
mpfr_clear_flags ();
if (mpfr_cmp (MPC_RE(z), fr) != 0
|| mpfr_cmp_ui (MPC_IM(z), 0) != 0
|| mpfr_erangeflag_p())
PRINT_ERROR ("mpc_set_q", prec, z);
mpfr_set_f (fr, mpf, GMP_RNDN);
mpc_set_f_f (z, mpf, mpf, MPC_RNDNN);
mpfr_clear_flags ();
if (mpfr_cmp (MPC_RE(z), fr) != 0
|| mpfr_cmp (MPC_IM(z), fr) != 0
|| mpfr_erangeflag_p())
PRINT_ERROR ("mpc_set_f_f", prec, z);
mpc_set_f (z, mpf, MPC_RNDNN);
mpfr_clear_flags ();
if (mpfr_cmp (MPC_RE(z), fr) != 0
|| mpfr_cmp_ui (MPC_IM(z), 0) != 0
|| mpfr_erangeflag_p())
PRINT_ERROR ("mpc_set_f", prec, z);
mpc_set_f_si (z, mpf, lo, MPC_RNDNN);
mpfr_clear_flags ();
if (mpfr_cmp (MPC_RE (z), fr) != 0
|| mpfr_cmp_si (MPC_IM (z), lo) != 0
|| mpfr_erangeflag_p ())
PRINT_ERROR ("mpc_set_f", prec, z);
mpc_set_nan (z);
if (!mpfr_nan_p (MPC_RE(z)) || !mpfr_nan_p (MPC_IM(z)))
PRINT_ERROR ("mpc_set_nan", prec, z);
#ifdef _MPC_H_HAVE_INTMAX_T
{
uintmax_t uim = (uintmax_t) prec;
intmax_t im = (intmax_t) prec;
mpc_set_uj (z, uim, MPC_RNDNN);
if (mpfr_cmp_ui (MPC_RE(z), u) != 0
|| mpfr_cmp_ui (MPC_IM(z), 0) != 0)
PRINT_ERROR ("mpc_set_uj", prec, z);
mpc_set_sj (z, im, MPC_RNDNN);
if (mpfr_cmp_ui (MPC_RE(z), u) != 0
|| mpfr_cmp_ui (MPC_IM(z), 0) != 0)
PRINT_ERROR ("mpc_set_sj (1)", prec, z);
mpc_set_uj_uj (z, uim, uim, MPC_RNDNN);
if (mpfr_cmp_ui (MPC_RE(z), u) != 0
|| mpfr_cmp_ui (MPC_IM(z), u) != 0)
PRINT_ERROR ("mpc_set_uj_uj", prec, z);
mpc_set_sj_sj (z, im, im, MPC_RNDNN);
if (mpfr_cmp_ui (MPC_RE(z), u) != 0
|| mpfr_cmp_ui (MPC_IM(z), u) != 0)
PRINT_ERROR ("mpc_set_sj_sj (1)", prec, z);
im = LONG_MAX;
if (sizeof (intmax_t) == 2 * sizeof (unsigned long))
im = 2 * im * im + 4 * im + 1; /* gives 2^(2n-1)-1 from 2^(n-1)-1 */
mpc_set_sj (z, im, MPC_RNDNN);
if (mpfr_get_sj (MPC_RE(z), GMP_RNDN) != im ||
mpfr_cmp_ui (MPC_IM(z), 0) != 0)
PRINT_ERROR ("mpc_set_sj (2)", im, z);
mpc_set_sj_sj (z, im, im, MPC_RNDNN);
if (mpfr_get_sj (MPC_RE(z), GMP_RNDN) != im ||
mpfr_get_sj (MPC_IM(z), GMP_RNDN) != im)
PRINT_ERROR ("mpc_set_sj_sj (2)", im, z);
}
#endif /* _MPC_H_HAVE_INTMAX_T */
#if defined _MPC_H_HAVE_COMPLEX
{
double _Complex c = 1.0 - 2.0*I;
long double _Complex lc = c;
mpc_set_dc (z, c, MPC_RNDNN);
if (mpc_get_dc (z, MPC_RNDNN) != c)
PRINT_ERROR ("mpc_get_c", prec, z);
mpc_set_ldc (z, lc, MPC_RNDNN);
if (mpc_get_ldc (z, MPC_RNDNN) != lc)
PRINT_ERROR ("mpc_get_lc", prec, z);
}
#endif
}
mpz_clear (mpz);
mpq_clear (mpq);
mpf_clear (mpf);
mpfr_clear (fr);
mpc_clear (x);
mpc_clear (z);
}
void w3j(mpf_t w, long j1, long j2, long j3, long m1, long m2, long m3)
{
mpq_t delta_sq,r;
mpz_t i;
mpf_t h;
mpq_init(delta_sq);
mpq_init(r);
mpz_init(i);
mpf_init(h);
mpq_set_si(r,0,1);
if(m1+m2+m3!=0) return;
if((iabs(m1)>j1) || (iabs(m2)>j2) || (iabs(m3)>j3)) return;
if((j3<iabs(j1-j2)) || ((j1+j2)<j3)) return;
w3j_Delta_sq(delta_sq, j1, j2, j3);
w3j_intterm(i, j1, j2, j3, m1, m2, m3);
if(iabs(j1-j2-m3)%2 == 1) mpz_neg(i,i);
w3j_sqrt_sq(r, j1, j2, j3, m1, m2, m3);
mpq_mul(r,r,delta_sq);
mpf_set_q(w,r);
mpf_sqrt(w,w);
mpf_set_z(h,i);
mpf_mul(w,w,h);
mpf_clear(h);
mpz_clear(i);
mpq_clear(r);
mpq_clear(delta_sq);
}
