int main()
{
slong iter;
flint_rand_t state;
flint_printf("cmpabs....");
fflush(stdout);
flint_randinit(state);
/* compare with fmpz */
{
arf_t x, y;
fmpz_t X, Y;
arf_init(x);
arf_init(y);
fmpz_init(X);
fmpz_init(Y);
for (iter = 0; iter < 100000 * arb_test_multiplier(); iter++)
{
int cmp1, cmp2;
fmpz_randtest(X, state, 1 + n_randint(state, 1000));
switch (n_randint(state, 8))
{
case 0:
fmpz_neg(Y, X);
break;
case 1:
fmpz_set(Y, X);
break;
default:
fmpz_randtest(Y, state, 1 + n_randint(state, 1000));
}
arf_set_fmpz(x, X);
arf_set_fmpz(y, Y);
cmp1 = arf_cmpabs(x, y);
cmp2 = fmpz_cmpabs(X, Y);
cmp2 = (cmp2 > 0) - (cmp2 < 0);
if (cmp1 != cmp2)
{
flint_printf("FAIL\n\n");
flint_printf("x = "); arf_debug(x); flint_printf("\n\n");
flint_printf("y = "); arf_debug(y); flint_printf("\n\n");
flint_printf("X = "); fmpz_print(X); flint_printf("\n\n");
flint_printf("Y = "); fmpz_print(Y); flint_printf("\n\n");
flint_printf("cmp1 = %d, cmp2 = %d\n\n", cmp1, cmp2);
abort();
}
}
arf_clear(x);
arf_clear(y);
fmpz_clear(X);
fmpz_clear(Y);
}
/* compare with mpfr */
for (iter = 0; iter < 100000 * arb_test_multiplier(); iter++)
{
slong bits;
arf_t x, y;
mpfr_t X, Y;
int cmp1, cmp2;
bits = 2 + n_randint(state, 200);
arf_init(x);
arf_init(y);
mpfr_init2(X, bits);
mpfr_init2(Y, bits);
arf_randtest_special(x, state, bits, 10);
arf_randtest_special(y, state, bits, 10);
arf_get_mpfr(X, x, MPFR_RNDN);
arf_get_mpfr(Y, y, MPFR_RNDN);
mpfr_abs(X, X, MPFR_RNDN);
mpfr_abs(Y, Y, MPFR_RNDN);
cmp1 = arf_cmpabs(x, y);
cmp2 = mpfr_cmp(X, Y);
if (cmp1 != cmp2)
{
flint_printf("FAIL\n\n");
flint_printf("x = "); arf_print(x); flint_printf("\n\n");
flint_printf("y = "); arf_print(y); flint_printf("\n\n");
flint_printf("cmp1 = %d, cmp2 = %d\n\n", cmp1, cmp2);
abort();
}
arf_clear(x);
arf_clear(y);
mpfr_clear(X);
mpfr_clear(Y);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
void
_fmpq_poly_revert_series_lagrange(fmpz * Qinv, fmpz_t den,
const fmpz * Q, const fmpz_t Qden, long n)
{
long i;
fmpz *R, *S, *T, *dens, *tmp;
fmpz_t Rden, Sden, Tden;
if (fmpz_is_one(Qden) && (n > 1) && fmpz_is_pm1(Q + 1))
{
_fmpz_poly_revert_series(Qinv, Q, n);
fmpz_one(den);
}
else if (n <= 2)
{
fmpz_zero(Qinv);
if (n == 2)
{
fmpz_set(Qinv + 1, Qden);
fmpz_set(den, Q + 1);
_fmpq_poly_canonicalise(Qinv, den, 2);
}
}
else
{
dens = _fmpz_vec_init(n);
R = _fmpz_vec_init(n - 1);
S = _fmpz_vec_init(n - 1);
T = _fmpz_vec_init(n - 1);
fmpz_init(Rden);
fmpz_init(Sden);
fmpz_init(Tden);
fmpz_zero(Qinv);
fmpz_one(dens);
fmpz_set(Qinv + 1, Qden);
fmpz_set(dens + 1, Q + 1);
_fmpq_poly_inv_series(R, Rden, Q + 1, Qden, n - 1);
_fmpq_poly_canonicalise(R, Rden, n - 1);
_fmpz_vec_set(S, R, n - 1);
fmpz_set(Sden, Rden);
for (i = 2; i < n; i++)
{
_fmpq_poly_mullow(T, Tden, S, Sden, n - 1, R, Rden, n - 1, n - 1);
_fmpq_poly_canonicalise(T, Tden, n - 1);
fmpz_set(Qinv + i, T + i - 1);
fmpz_mul_ui(dens + i, Tden, i);
tmp = S; S = T; T = tmp;
fmpz_swap(Sden, Tden);
}
_set_vec(Qinv, den, Qinv, dens, n);
_fmpq_poly_canonicalise(Qinv, den, n);
_fmpz_vec_clear(R, n - 1);
_fmpz_vec_clear(S, n - 1);
_fmpz_vec_clear(T, n - 1);
_fmpz_vec_clear(dens, n);
fmpz_clear(Rden);
fmpz_clear(Sden);
fmpz_clear(Tden);
}
}
int
main(void)
{
int i, result;
FLINT_TEST_INIT(state);
flint_printf("evaluate_fmpz....");
fflush(stdout);
/* Check that (f+g)(a) = f(a) + g(a) */
for (i = 0; i < 1000 * flint_test_multiplier(); i++)
{
fmpz_t a;
fmpq_poly_t f, g, h;
fmpq_t x, y;
fmpq_init(x);
fmpq_init(y);
fmpz_init(a);
fmpq_poly_init(f);
fmpq_poly_init(g);
fmpq_poly_init(h);
fmpq_poly_randtest(f, state, n_randint(state, 100), 200);
fmpq_poly_randtest(g, state, n_randint(state, 100), 200);
fmpz_randtest(a, state, n_randint(state, 100));
fmpq_poly_evaluate_fmpz(x, f, a);
fmpq_poly_evaluate_fmpz(y, g, a);
fmpq_add(x, x, y);
fmpq_poly_add(h, f, g);
fmpq_poly_evaluate_fmpz(y, h, a);
result = (fmpq_equal(x, y));
if (!result)
{
flint_printf("FAIL:\n");
flint_printf("f = "), fmpq_poly_debug(f), flint_printf("\n");
flint_printf("g = "), fmpq_poly_debug(g), flint_printf("\n");
flint_printf("a = "), fmpz_print(a), flint_printf("\n");
flint_printf("f(a) + g(a) = "), fmpq_print(x), flint_printf("\n\n");
flint_printf("(f + g)(a) = "), fmpq_print(y), flint_printf("\n\n");
abort();
}
fmpq_clear(x);
fmpq_clear(y);
fmpz_clear(a);
fmpq_poly_clear(f);
fmpq_poly_clear(g);
fmpq_poly_clear(h);
}
/* Check that (f*g)(a) = f(a) * g(a) */
for (i = 0; i < 1000 * flint_test_multiplier(); i++)
{
fmpz_t a;
fmpq_poly_t f, g;
fmpq_t x, y;
fmpq_init(x);
fmpq_init(y);
fmpz_init(a);
fmpq_poly_init(f);
fmpq_poly_init(g);
fmpq_poly_randtest(f, state, n_randint(state, 100), 200);
fmpq_poly_randtest(g, state, n_randint(state, 100), 200);
fmpz_randtest(a, state, n_randint(state, 100));
fmpq_poly_evaluate_fmpz(x, f, a);
fmpq_poly_evaluate_fmpz(y, g, a);
fmpq_mul(x, x, y);
fmpq_poly_mul(f, f, g);
fmpq_poly_evaluate_fmpz(y, f, a);
result = (fmpq_equal(x, y));
if (!result)
{
flint_printf("FAIL:\n");
fmpz_print(a), flint_printf("\n\n");
abort();
}
fmpq_clear(x);
fmpq_clear(y);
fmpz_clear(a);
fmpq_poly_clear(f);
fmpq_poly_clear(g);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
char * _padic_get_str(char * str, const padic_t op, const padic_ctx_t ctx)
{
const fmpz * u = padic_unit(op);
const long v = padic_val(op);
if (fmpz_is_zero(u))
{
if (!str)
{
str = flint_malloc(2);
}
str[0] = '0';
str[1] = '\0';
return str;
}
if (ctx->mode == PADIC_TERSE)
{
if (v == 0)
{
str = fmpz_get_str(str, 10, u);
}
else if (v > 0)
{
fmpz_t t;
fmpz_init(t);
fmpz_pow_ui(t, ctx->p, v);
fmpz_mul(t, t, u);
str = fmpz_get_str(str, 10, t);
fmpz_clear(t);
}
else /* v < 0 */
{
fmpz_t t;
fmpz_init(t);
fmpz_pow_ui(t, ctx->p, -v);
str = _fmpq_get_str(str, 10, u, t);
fmpz_clear(t);
}
}
else if (ctx->mode == PADIC_SERIES)
{
char *s;
fmpz_t x;
fmpz_t d;
long j, N;
if (fmpz_sgn(u) < 0)
{
printf("ERROR (_padic_get_str). u < 0 in SERIES mode.\n");
abort();
}
N = fmpz_clog(u, ctx->p) + v;
if (!str)
{
long b = (N - v) * (2 * fmpz_sizeinbase(ctx->p, 10)
+ z_sizeinbase(FLINT_MAX(FLINT_ABS(v), FLINT_ABS(N)), 10)
+ 5) + 1;
str = flint_malloc(b);
if (!str)
{
printf("ERROR (_padic_get_str). Memory allocation failed.\n");
abort();
}
}
s = str;
fmpz_init(d);
fmpz_init(x);
fmpz_set(x, u);
/* Unroll first step */
j = 0;
{
fmpz_mod(d, x, ctx->p); /* d = u mod p^{j+1} */
fmpz_sub(x, x, d); /* x = x - d */
fmpz_divexact(x, x, ctx->p); /* x = x / p */
if (!fmpz_is_zero(d))
{
if (j + v != 0)
{
fmpz_get_str(s, 10, d);
while (*++s != '\0') ;
*s++ = '*';
fmpz_get_str(s, 10, ctx->p);
while (*++s != '\0') ;
*s++ = '^';
sprintf(s, "%ld", j + v);
while (*++s != '\0') ;
}
else
{
fmpz_get_str(s, 10, d);
while (*++s != '\0') ;
}
}
j++;
}
for ( ; !fmpz_is_zero(x); j++)
{
fmpz_mod(d, x, ctx->p); /* d = u mod p^{j+1} */
fmpz_sub(x, x, d); /* x = x - d */
fmpz_divexact(x, x, ctx->p); /* x = x / p */
if (!fmpz_is_zero(d))
{
if (j + v != 0)
{
*s++ = ' ';
*s++ = '+';
*s++ = ' ';
fmpz_get_str(s, 10, d);
while (*++s != '\0') ;
*s++ = '*';
fmpz_get_str(s, 10, ctx->p);
while (*++s != '\0') ;
*s++ = '^';
sprintf(s, "%ld", j + v);
while (*++s != '\0') ;
}
else
{
*s++ = ' ';
*s++ = '+';
*s++ = ' ';
fmpz_get_str(s, 10, d);
while (*++s != '\0') ;
}
}
}
fmpz_clear(x);
fmpz_clear(d);
}
else /* ctx->mode == PADIC_VAL_UNIT */
{
if (!str)
{
long b = fmpz_sizeinbase(u, 10) + fmpz_sizeinbase(ctx->p, 10)
+ z_sizeinbase(v, 10) + 4;
str = flint_malloc(b);
if (!str)
{
printf("ERROR (_padic_get_str). Memory allocation failed.\n");
abort();
}
}
if (v == 0)
{
str = fmpz_get_str(str, 10, u);
}
else if (v == 1)
{
char *s = str;
fmpz_get_str(s, 10, u);
while (*++s != '\0') ;
*s++ = '*';
fmpz_get_str(s, 10, ctx->p);
}
else
{
char *s = str;
fmpz_get_str(s, 10, u);
while (*++s != '\0') ;
*s++ = '*';
fmpz_get_str(s, 10, ctx->p);
while (*++s != '\0') ;
*s++ = '^';
sprintf(s, "%ld", v);
}
}
return str;
}
int main() {
slong n = 7;
fmpz_t mod;
fmpz* xs = _fmpz_vec_init(n);
fmpz* ys = _fmpz_vec_init(n);
fmpz_mod_poly_t res;
fmpz_poly_t res2;
fmpz_init(mod);
fmpz_set_ui(mod, 11);
fmpz_set_ui(xs, 0);
fmpz_set_ui(xs+1, 1);
fmpz_set_ui(xs+2, 2);
fmpz_set_ui(xs+3, 3);
fmpz_set_ui(xs+4, 4);
fmpz_set_ui(xs+5, 5);
fmpz_set_ui(xs+6, 6);
fmpz_set_si(ys, 5);
fmpz_set_si(ys+1, 1);
fmpz_set_si(ys+2, 4);
fmpz_set_si(ys+3, 8);
fmpz_set_si(ys+4, 4);
fmpz_set_si(ys+5, 1);
fmpz_set_si(ys+6, 5);
printf("xs :\n");
_fmpz_vec_print(xs,n);
printf("\n");
printf("ys :\n");
_fmpz_vec_print(ys,n);
printf("\n");
fmpz_mod_poly_init(res,mod);
fmpz_mod_poly_interpolate_fmpz_vec_fast(res, xs, ys, n, mod);
fmpz_poly_init(res2);
fmpz_poly_interpolate_fmpz_vec(res2, xs, ys, n);
printf("Nouvelle interpolation (f(xs) = ys) :\n");
fmpz_mod_poly_print(res);
printf("\n");
fmpz* zs = _fmpz_vec_init(n);
fmpz_poly_evaluate_fmpz_vec(zs, res2, xs, n);
fmpz* as = _fmpz_vec_init(n);
fmpz_mod_poly_evaluate_fmpz_vec(as, res, xs, n);
printf("f(xs) :\n");
_fmpz_vec_print(as,n);
printf("\n");
printf("FLINT :\n");
fmpz_poly_print(res2);
printf("\n");
printf("f(xs) :\n");
_fmpz_vec_print(zs,n);
printf("\n");
fmpz_clear(mod);
_fmpz_vec_clear(xs,n);
_fmpz_vec_clear(ys,n);
return 0;
}
int main(int argc, char *argv[])
{
slong i, len, prec, num_threads;
char * out_file;
arb_ptr z;
if (argc < 2)
{
flint_printf("keiper_li n [-prec prec] [-threads num_threads] [-out out_file]\n");
return 1;
}
len = atol(argv[1]) + 1;
prec = 1.1 * len + 50;
num_threads = 1;
out_file = NULL;
for (i = 1; i < argc; i++)
{
if (!strcmp(argv[i], "-prec"))
prec = atol(argv[i+1]);
else if (!strcmp(argv[i], "-threads"))
num_threads = atol(argv[i+1]);
else if (!strcmp(argv[i], "-out"))
out_file = argv[i+1];
}
flint_set_num_threads(num_threads);
z = _arb_vec_init(len);
keiper_li_series(z, len, prec);
for (i = 0; i < len; i++)
{
if (i <= 10 || len - i <= 10)
{
flint_printf("%wd: ", i); arb_printd(z + i, 50); flint_printf("\n");
}
}
SHOW_MEMORY_USAGE
if (out_file != NULL)
{
fmpz_t man, exp;
arf_t t;
FILE * fp = fopen(out_file, "w");
fmpz_init(man);
fmpz_init(exp);
arf_init(t);
for (i = 0; i < len; i++)
{
arf_get_fmpz_2exp(man, exp, arb_midref(z + i));
flint_fprintf(fp, "%wd ", i);
fmpz_fprint(fp, man);
flint_fprintf(fp, " ");
fmpz_fprint(fp, exp);
flint_fprintf(fp, " ");
arf_set_mag(t, arb_radref(z + i));
arf_get_fmpz_2exp(man, exp, t);
fmpz_fprint(fp, man);
flint_fprintf(fp, " ");
fmpz_fprint(fp, exp);
flint_fprintf(fp, "\n");
}
fclose(fp);
fmpz_clear(man);
fmpz_clear(exp);
arf_clear(t);
}
_arb_vec_clear(z, len);
flint_cleanup();
return 0;
}
int
arf_submul_mpz(arf_ptr z, arf_srcptr x, const mpz_t y, slong prec, arf_rnd_t rnd)
{
mp_size_t xn, yn, zn, tn, alloc;
mp_srcptr xptr, yptr, zptr;
mp_ptr tptr, tptr2;
fmpz_t texp, yexp;
slong shift;
int tsgnbit, ysgnbit, inexact;
ARF_MUL_TMP_DECL
yn = FLINT_ABS(y->_mp_size);
if (arf_is_special(x) || yn == 0 || arf_is_special(z))
{
if (arf_is_zero(z))
{
/* TODO: make more efficient */
arf_mul_mpz(z, x, y, ARF_PREC_EXACT, rnd);
return arf_neg_round(z, z, prec, rnd);
}
else if (arf_is_finite(x))
{
return arf_set_round(z, z, prec, rnd);
}
else
{
/* todo: speed up */
arf_t t;
arf_init(t);
arf_mul_mpz(t, x, y, ARF_PREC_EXACT, ARF_RND_DOWN);
inexact = arf_sub(z, z, t, prec, rnd);
arf_clear(t);
return inexact;
}
}
ARF_GET_MPN_READONLY(xptr, xn, x);
yptr = y->_mp_d;
ysgnbit = (y->_mp_size > 0);
*yexp = yn * FLINT_BITS;
ARF_GET_MPN_READONLY(zptr, zn, z);
fmpz_init(texp);
tsgnbit = ARF_SGNBIT(x) ^ ysgnbit;
alloc = tn = xn + yn;
ARF_MUL_TMP_ALLOC(tptr2, alloc)
tptr = tptr2;
ARF_MPN_MUL(tptr, xptr, xn, yptr, yn);
shift = (tptr[tn - 1] == 0) * FLINT_BITS;
tn -= (tptr[tn - 1] == 0);
_fmpz_add2_fast(texp, ARF_EXPREF(x), yexp, -shift);
shift = _fmpz_sub_small(ARF_EXPREF(z), texp);
if (shift >= 0)
inexact = _arf_add_mpn(z, zptr, zn, ARF_SGNBIT(z), ARF_EXPREF(z),
tptr, tn, tsgnbit, shift, prec, rnd);
else
inexact = _arf_add_mpn(z, tptr, tn, tsgnbit, texp,
zptr, zn, ARF_SGNBIT(z), -shift, prec, rnd);
ARF_MUL_TMP_FREE(tptr2, alloc)
fmpz_clear(texp);
return inexact;
}
int main()
{
long iter;
flint_rand_t state;
printf("get_fmpz....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 100000; iter++)
{
long bits;
fmpr_t x;
mpfr_t y;
fmpz_t z, z2;
mpz_t w;
bits = 2 + n_randint(state, 1000);
fmpr_init(x);
mpfr_init2(y, bits);
fmpz_init(z);
fmpz_init(z2);
mpz_init(w);
fmpr_randtest(x, state, bits, 10);
fmpr_get_mpfr(y, x, MPFR_RNDN);
switch (n_randint(state, 5))
{
case 0:
fmpr_get_fmpz(z, x, FMPR_RND_FLOOR);
mpfr_get_z(w, y, MPFR_RNDD);
break;
case 1:
fmpr_get_fmpz(z, x, FMPR_RND_CEIL);
mpfr_get_z(w, y, MPFR_RNDU);
break;
case 2:
fmpr_get_fmpz(z, x, FMPR_RND_DOWN);
mpfr_get_z(w, y, MPFR_RNDZ);
break;
case 3:
fmpr_get_fmpz(z, x, FMPR_RND_UP);
mpfr_get_z(w, y, MPFR_RNDA);
break;
default:
fmpr_get_fmpz(z, x, FMPR_RND_NEAR);
mpfr_get_z(w, y, MPFR_RNDN);
break;
}
fmpz_set_mpz(z2, w);
if (!fmpz_equal(z, z2))
{
printf("FAIL\n\n");
printf("x = "); fmpr_print(x); printf("\n\n");
printf("z = "); fmpz_print(z); printf("\n\n");
printf("z2 = "); fmpz_print(z2); printf("\n\n");
abort();
}
fmpr_clear(x);
mpfr_clear(y);
fmpz_clear(z);
fmpz_clear(z2);
mpz_clear(w);
}
flint_randclear(state);
flint_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("add_inline....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 100000; iter++)
{
fmpz_t a, b, c, d;
fmpz_init(a);
fmpz_init(b);
fmpz_init(c);
fmpz_init(d);
fmpz_randtest(a, state, 1 + n_randint(state, 200));
fmpz_randtest(b, state, 1 + n_randint(state, 200));
fmpz_randtest(c, state, 1 + n_randint(state, 200));
fmpz_randtest(d, state, 1 + n_randint(state, 200));
fmpz_add(c, a, b);
fmpz_add_inline(d, a, b);
if (!fmpz_equal(c, d))
{
flint_printf("FAIL\n");
fmpz_print(a); flint_printf("\n\n");
fmpz_print(b); flint_printf("\n\n");
fmpz_print(c); flint_printf("\n\n");
fmpz_print(d); flint_printf("\n\n");
abort();
}
fmpz_add_inline(a, a, b);
if (!fmpz_equal(c, a))
{
flint_printf("FAIL (aliasing 1)\n");
fmpz_print(a); flint_printf("\n\n");
fmpz_print(b); flint_printf("\n\n");
fmpz_print(c); flint_printf("\n\n");
fmpz_print(d); flint_printf("\n\n");
abort();
}
fmpz_randtest(a, state, 1 + n_randint(state, 200));
fmpz_add(c, a, b);
fmpz_add_inline(b, a, b);
if (!fmpz_equal(c, b))
{
flint_printf("FAIL (aliasing 2)\n");
fmpz_print(a); flint_printf("\n\n");
fmpz_print(b); flint_printf("\n\n");
fmpz_print(c); flint_printf("\n\n");
fmpz_print(d); flint_printf("\n\n");
abort();
}
fmpz_add(d, a, a);
fmpz_add_inline(c, a, a);
if (!fmpz_equal(c, d))
{
flint_printf("FAIL (aliasing 3)\n");
fmpz_print(a); flint_printf("\n\n");
fmpz_print(b); flint_printf("\n\n");
fmpz_print(c); flint_printf("\n\n");
fmpz_print(d); flint_printf("\n\n");
abort();
}
fmpz_add(d, a, a);
fmpz_add_inline(a, a, a);
if (!fmpz_equal(d, a))
{
flint_printf("FAIL (aliasing 4)\n");
fmpz_print(a); flint_printf("\n\n");
fmpz_print(b); flint_printf("\n\n");
fmpz_print(c); flint_printf("\n\n");
fmpz_print(d); flint_printf("\n\n");
abort();
}
fmpz_clear(a);
fmpz_clear(b);
fmpz_clear(c);
fmpz_clear(d);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
void
fmpq_poly_compose_series_horner(fmpq_poly_t res,
const fmpq_poly_t poly1, const fmpq_poly_t poly2, long n)
{
long len1 = poly1->length;
long len2 = poly2->length;
long lenr;
if (len2 != 0 && !fmpz_is_zero(poly2->coeffs))
{
printf("exception: fmpq_poly_compose_series_horner: inner polynomial "
"must have zero constant term\n");
abort();
}
if (len1 == 0 || n == 0)
{
fmpq_poly_zero(res);
return;
}
if (len2 == 0 || len1 == 1)
{
fmpq_poly_fit_length(res, 1);
fmpz_set(res->coeffs, poly1->coeffs);
fmpz_set(res->den, poly1->den);
{
fmpz_t d;
fmpz_init(d);
fmpz_gcd(d, res->coeffs, res->den);
if (!fmpz_is_one(d))
{
fmpz_divexact(res->coeffs, res->coeffs, d);
fmpz_divexact(res->den, res->den, d);
}
fmpz_clear(d);
}
_fmpq_poly_set_length(res, 1);
_fmpq_poly_normalise(res);
return;
}
lenr = FLINT_MIN((len1 - 1) * (len2 - 1) + 1, n);
len1 = FLINT_MIN(len1, lenr);
len2 = FLINT_MIN(len2, lenr);
if ((res != poly1) && (res != poly2))
{
fmpq_poly_fit_length(res, lenr);
_fmpq_poly_compose_series_horner(res->coeffs, res->den,
poly1->coeffs, poly1->den, len1,
poly2->coeffs, poly2->den, len2, lenr);
_fmpq_poly_set_length(res, lenr);
_fmpq_poly_normalise(res);
}
else
{
fmpq_poly_t t;
fmpq_poly_init2(t, lenr);
_fmpq_poly_compose_series_horner(t->coeffs, t->den,
poly1->coeffs, poly1->den, len1,
poly2->coeffs, poly2->den, len2, lenr);
_fmpq_poly_set_length(t, lenr);
_fmpq_poly_normalise(t);
fmpq_poly_swap(res, t);
fmpq_poly_clear(t);
}
}
int
main(void)
{
fmpz_mat_t A, X, B, AX;
fmpz_t den;
slong i, m, n, r;
int success;
FLINT_TEST_INIT(state);
flint_printf("solve_cramer....");
fflush(stdout);
for (i = 0; i < 1000 * flint_test_multiplier(); i++)
{
m = n_randint(state, 4);
n = n_randint(state, 10);
fmpz_mat_init(A, m, m);
fmpz_mat_init(B, m, n);
fmpz_mat_init(X, m, n);
fmpz_mat_init(AX, m, n);
fmpz_init(den);
fmpz_mat_randrank(A, state, m, 1+n_randint(state, 2)*n_randint(state, 100));
fmpz_mat_randtest(B, state, 1+n_randint(state, 2)*n_randint(state, 100));
/* Dense */
if (n_randint(state, 2))
fmpz_mat_randops(A, state, 1+n_randint(state, 1 + m*m));
success = fmpz_mat_solve_cramer(X, den, A, B);
fmpz_mat_mul(AX, A, X);
fmpz_mat_scalar_divexact_fmpz(AX, AX, den);
if (!fmpz_mat_equal(AX, B) || !success)
{
flint_printf("FAIL:\n");
flint_printf("AX != B!\n");
flint_printf("A:\n"), fmpz_mat_print_pretty(A), flint_printf("\n");
flint_printf("B:\n"), fmpz_mat_print_pretty(B), flint_printf("\n");
flint_printf("X:\n"), fmpz_mat_print_pretty(X), flint_printf("\n");
flint_printf("den(X) = "), fmpz_print(den), flint_printf("\n");
flint_printf("AX:\n"), fmpz_mat_print_pretty(AX), flint_printf("\n");
abort();
}
fmpz_mat_clear(A);
fmpz_mat_clear(B);
fmpz_mat_clear(X);
fmpz_mat_clear(AX);
fmpz_clear(den);
}
/* Test singular systems */
for (i = 0; i < 1000 * flint_test_multiplier(); i++)
{
m = 1 + n_randint(state, 3);
n = 1 + n_randint(state, 10);
r = n_randint(state, m);
fmpz_mat_init(A, m, m);
fmpz_mat_init(B, m, n);
fmpz_mat_init(X, m, n);
fmpz_mat_init(AX, m, n);
fmpz_init(den);
fmpz_mat_randrank(A, state, r, 1+n_randint(state, 2)*n_randint(state, 100));
fmpz_mat_randtest(B, state, 1+n_randint(state, 2)*n_randint(state, 100));
/* Dense */
if (n_randint(state, 2))
fmpz_mat_randops(A, state, 1+n_randint(state, 1 + m*m));
success = fmpz_mat_solve_cramer(X, den, A, B);
if (!fmpz_is_zero(den) || success)
{
flint_printf("FAIL:\n");
flint_printf("singular system gave nonzero determinant\n");
abort();
}
fmpz_mat_clear(A);
fmpz_mat_clear(B);
fmpz_mat_clear(X);
fmpz_mat_clear(AX);
fmpz_clear(den);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
int
main(void)
{
int i, result;
flint_rand_t state;
printf("evaluate...");
fflush(stdout);
flint_randinit(state);
/* Check aliasing */
for (i = 0; i < 100; i++)
{
int ans1, ans2;
mpq_t a, b;
fmpz_t num, den;
fmpz_poly_q_t f;
mpq_init(a);
mpq_init(b);
fmpz_init(num);
fmpz_init(den);
fmpz_poly_q_init(f);
fmpz_poly_q_randtest(f, state, n_randint(state, 10), 10, n_randint(state, 10), 10);
fmpz_randtest(num, state, 50);
fmpz_randtest_not_zero(den, state, 50);
fmpz_get_mpz(mpq_numref(a), num);
fmpz_get_mpz(mpq_denref(a), den);
mpq_canonicalize(a);
ans1 = fmpz_poly_q_evaluate(b, f, a);
ans2 = fmpz_poly_q_evaluate(a, f, a);
result = (ans1 == ans2) && mpq_equal(a, b);
if (!result)
{
printf("FAIL:\n");
printf("f = "), fmpz_poly_q_print(f), printf("\n");
printf("num = "), fmpz_print(num), printf("\n");
printf("den = "), fmpz_print(den), printf("\n");
gmp_printf("a = %Qd\n", a);
gmp_printf("b = %Qd\n", b);
printf("ans1 = %d\n", ans1);
printf("ans2 = %d\n", ans2);
abort();
}
mpq_clear(a);
mpq_clear(b);
fmpz_clear(num);
fmpz_clear(den);
fmpz_poly_q_clear(f);
}
flint_randclear(state);
_fmpz_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}
int
main(void)
{
int i, result;
flint_rand_t state;
printf("div_basecase....");
fflush(stdout);
flint_randinit(state);
/* Compare to divrem_basecase */
for (i = 0; i < 5000; i++)
{
fmpz_t p;
fmpz_mod_poly_t a, b, q, q2, r2;
fmpz_init(p);
fmpz_randtest_unsigned(p, state, 2 * FLINT_BITS);
fmpz_add_ui(p, p, 2);
fmpz_mod_poly_init(a, p);
fmpz_mod_poly_init(b, p);
fmpz_mod_poly_init(q, p);
fmpz_mod_poly_init(q2, p);
fmpz_mod_poly_init(r2, p);
fmpz_mod_poly_randtest(a, state, n_randint(state, 100));
fmpz_mod_poly_randtest_not_zero(b, state, n_randint(state, 100) + 1);
{
fmpz_t d;
fmpz *leadB = fmpz_mod_poly_lead(b);
fmpz_init(d);
fmpz_gcd(d, p, leadB);
while (!fmpz_is_one(d))
{
fmpz_divexact(leadB, leadB, d);
fmpz_gcd(d, p, leadB);
}
fmpz_clear(d);
}
fmpz_mod_poly_div_basecase(q, a, b);
fmpz_mod_poly_divrem_basecase(q2, r2, a, b);
result = (fmpz_mod_poly_equal(q, q2));
if (!result)
{
printf("FAIL:\n");
printf("p = "), fmpz_print(p), printf("\n\n");
printf("a = "), fmpz_mod_poly_print(a), printf("\n\n");
printf("b = "), fmpz_mod_poly_print(b), printf("\n\n");
printf("q = "), fmpz_mod_poly_print(q), printf("\n\n");
printf("q2 = "), fmpz_mod_poly_print(q2), printf("\n\n");
printf("r2 = "), fmpz_mod_poly_print(r2), printf("\n\n");
abort();
}
fmpz_mod_poly_clear(a);
fmpz_mod_poly_clear(b);
fmpz_mod_poly_clear(q);
fmpz_mod_poly_clear(q2);
fmpz_mod_poly_clear(r2);
fmpz_clear(p);
}
/* Alias a and q */
for (i = 0; i < 500; i++)
{
fmpz_t p;
fmpz_mod_poly_t a, b, q;
fmpz_init(p);
fmpz_randtest_unsigned(p, state, 2 * FLINT_BITS);
fmpz_add_ui(p, p, 2);
fmpz_mod_poly_init(a, p);
fmpz_mod_poly_init(b, p);
fmpz_mod_poly_init(q, p);
fmpz_mod_poly_randtest(a, state, n_randint(state, 100));
fmpz_mod_poly_randtest_not_zero(b, state, n_randint(state, 100) + 1);
{
fmpz_t d;
fmpz *leadB = fmpz_mod_poly_lead(b);
fmpz_init(d);
fmpz_gcd(d, p, leadB);
while (!fmpz_is_one(d))
{
fmpz_divexact(leadB, leadB, d);
fmpz_gcd(d, p, leadB);
}
fmpz_clear(d);
}
fmpz_mod_poly_div_basecase(q, a, b);
fmpz_mod_poly_div_basecase(a, a, b);
result = (fmpz_mod_poly_equal(q, a));
if (!result)
{
printf("FAIL:\n");
printf("p = "), fmpz_print(p), printf("\n\n");
printf("a = "), fmpz_mod_poly_print(a), printf("\n\n");
printf("b = "), fmpz_mod_poly_print(b), printf("\n\n");
printf("q = "), fmpz_mod_poly_print(q), printf("\n\n");
abort();
}
fmpz_mod_poly_clear(a);
fmpz_mod_poly_clear(b);
fmpz_mod_poly_clear(q);
fmpz_clear(p);
}
/* Alias b and q */
for (i = 0; i < 500; i++)
{
fmpz_t p;
fmpz_mod_poly_t a, b, q;
fmpz_init(p);
fmpz_randtest_unsigned(p, state, 2 * FLINT_BITS);
fmpz_add_ui(p, p, 2);
fmpz_mod_poly_init(a, p);
fmpz_mod_poly_init(b, p);
fmpz_mod_poly_init(q, p);
fmpz_mod_poly_randtest(a, state, n_randint(state, 100));
fmpz_mod_poly_randtest_not_zero(b, state, n_randint(state, 100) + 1);
{
fmpz_t d;
fmpz *leadB = fmpz_mod_poly_lead(b);
fmpz_init(d);
fmpz_gcd(d, p, leadB);
while (!fmpz_is_one(d))
{
fmpz_divexact(leadB, leadB, d);
fmpz_gcd(d, p, leadB);
}
fmpz_clear(d);
}
fmpz_mod_poly_div_basecase(q, a, b);
fmpz_mod_poly_div_basecase(b, a, b);
result = (fmpz_mod_poly_equal(q, b));
if (!result)
{
printf("FAIL:\n");
printf("p = "), fmpz_print(p), printf("\n\n");
printf("a = "), fmpz_mod_poly_print(a), printf("\n\n");
printf("b = "), fmpz_mod_poly_print(b), printf("\n\n");
printf("q = "), fmpz_mod_poly_print(q), printf("\n\n");
abort();
}
fmpz_mod_poly_clear(a);
fmpz_mod_poly_clear(b);
fmpz_mod_poly_clear(q);
fmpz_clear(p);
}
flint_randclear(state);
_fmpz_cleanup();
printf("PASS\n");
return 0;
}
int main()
{
flint_rand_t state;
flint_printf("digits_round_inplace....");
fflush(stdout);
flint_randinit(state);
{
char s[30];
slong i, j, len, n;
mp_bitcnt_t shift;
fmpz_t inp, out, err, t;
arf_rnd_t rnd;
fmpz_init(inp);
fmpz_init(out);
fmpz_init(err);
fmpz_init(t);
for (i = 0; i < 100000 * arb_test_multiplier(); i++)
{
len = 1 + n_randint(state, 20);
n = 1 + n_randint(state, 20);
s[0] = (n_randint(state, 9) + '1');
for (j = 1; j < len; j++)
s[j] = (n_randint(state, 10) + '0');
s[len] = '\0';
fmpz_set_str(inp, s, 10);
switch (n_randint(state, 3))
{
case 0:
rnd = ARF_RND_DOWN;
break;
case 1:
rnd = ARF_RND_UP;
break;
default:
rnd = ARF_RND_NEAR;
break;
}
_arb_digits_round_inplace(s, &shift, err, n, rnd);
fmpz_set_str(out, s, 10);
fmpz_set_ui(t, 10);
fmpz_pow_ui(t, t, shift);
fmpz_mul(t, t, out);
fmpz_add(t, t, err);
if (!fmpz_equal(t, inp) || (rnd == ARF_RND_UP && fmpz_sgn(err) > 0))
{
flint_printf("FAIL!\n");
flint_printf("inp = "); fmpz_print(inp); flint_printf("\n\n");
flint_printf("shift = %wd\n\n", shift);
flint_printf("err = "); fmpz_print(err); flint_printf("\n\n");
flint_printf("out = "); fmpz_print(out); flint_printf("\n\n");
flint_printf(" t = "); fmpz_print(t); flint_printf("\n\n");
abort();
}
}
fmpz_clear(inp);
fmpz_clear(out);
fmpz_clear(err);
fmpz_clear(t);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
/* todo: use log(1-z) when this is better? would also need to
adjust strategy in the main function */
void
acb_hypgeom_dilog_bernoulli(acb_t res, const acb_t z, slong prec)
{
acb_t s, w, w2;
slong n, k;
fmpz_t c, d;
mag_t m, err;
double lm;
int real;
acb_init(s);
acb_init(w);
acb_init(w2);
fmpz_init(c);
fmpz_init(d);
mag_init(m);
mag_init(err);
real = 0;
if (acb_is_real(z))
{
arb_sub_ui(acb_realref(w), acb_realref(z), 1, 30);
real = arb_is_nonpositive(acb_realref(w));
}
acb_log(w, z, prec);
acb_get_mag(m, w);
/* for k >= 4, the terms are bounded by (|w| / (2 pi))^k */
mag_set_ui_2exp_si(err, 2670177, -24); /* upper bound for 1/(2pi) */
mag_mul(err, err, m);
lm = mag_get_d_log2_approx(err);
if (lm < -0.25)
{
n = prec / (-lm) + 1;
n = FLINT_MAX(n, 4);
mag_geom_series(err, err, n);
BERNOULLI_ENSURE_CACHED(n)
acb_mul(w2, w, w, prec);
for (k = n - (n % 2 == 0); k >= 3; k -= 2)
{
fmpz_mul_ui(c, fmpq_denref(bernoulli_cache + k - 1), k - 1);
fmpz_mul_ui(d, c, (k + 1) * (k + 2));
acb_mul(s, s, w2, prec);
acb_mul_fmpz(s, s, c, prec);
fmpz_mul_ui(c, fmpq_numref(bernoulli_cache + k - 1), (k + 1) * (k + 2));
acb_sub_fmpz(s, s, c, prec);
acb_div_fmpz(s, s, d, prec);
}
acb_mul(s, s, w, prec);
acb_mul_2exp_si(s, s, 1);
acb_sub_ui(s, s, 3, prec);
acb_mul(s, s, w2, prec);
acb_mul_2exp_si(s, s, -1);
acb_const_pi(w2, prec);
acb_addmul(s, w2, w2, prec);
acb_div_ui(s, s, 6, prec);
acb_neg(w2, w);
acb_log(w2, w2, prec);
acb_submul(s, w2, w, prec);
acb_add(res, s, w, prec);
acb_add_error_mag(res, err);
if (real)
arb_zero(acb_imagref(res));
}
else
{
acb_indeterminate(res);
}
acb_clear(s);
acb_clear(w);
acb_clear(w2);
fmpz_clear(c);
fmpz_clear(d);
mag_clear(m);
mag_clear(err);
}
int
main(void)
{
int i, result;
flint_rand_t state;
printf("derivative....");
fflush(stdout);
flint_randinit(state);
/* Check aliasing */
for (i = 0; i < 10000; i++)
{
fmpz_t p;
fmpz_mod_poly_t a, b, c;
fmpz_init(p);
fmpz_randtest_unsigned(p, state, 2 * FLINT_BITS);
fmpz_add_ui(p, p, 2);
fmpz_mod_poly_init(a, p);
fmpz_mod_poly_init(b, p);
fmpz_mod_poly_init(c, p);
fmpz_mod_poly_randtest(a, state, n_randint(state, 100));
fmpz_mod_poly_set(b, a);
fmpz_mod_poly_derivative(c, b);
fmpz_mod_poly_derivative(b, b);
result = (fmpz_mod_poly_equal(b, c));
if (!result)
{
printf("FAIL (alias):\n");
fmpz_mod_poly_print(a), printf("\n\n");
fmpz_mod_poly_print(b), printf("\n\n");
fmpz_mod_poly_print(c), printf("\n\n");
abort();
}
fmpz_mod_poly_clear(a);
fmpz_mod_poly_clear(b);
fmpz_mod_poly_clear(c);
fmpz_clear(p);
}
/* Check constants have derivative zero */
for (i = 0; i < 10000; i++)
{
fmpz_t p;
fmpz_mod_poly_t a, b;
fmpz_init(p);
fmpz_randtest_unsigned(p, state, 2 * FLINT_BITS);
fmpz_add_ui(p, p, 2);
fmpz_mod_poly_init(a, p);
fmpz_mod_poly_init(b, p);
fmpz_mod_poly_randtest(a, state, n_randint(state, 2));
fmpz_mod_poly_derivative(b, a);
result = (b->length == 0);
if (!result)
{
printf("FAIL (da == 0):\n");
fmpz_mod_poly_print(a), printf("\n\n");
fmpz_mod_poly_print(b), printf("\n\n");
abort();
}
fmpz_mod_poly_clear(a);
fmpz_mod_poly_clear(b);
fmpz_clear(p);
}
/* Check (f g)' = f' g + f g' */
for (i = 0; i < 10000; i++)
{
fmpz_t p;
fmpz_mod_poly_t a, b, c, d, lhs, rhs;
fmpz_init(p);
fmpz_randtest_unsigned(p, state, 2 * FLINT_BITS);
fmpz_add_ui(p, p, 2);
fmpz_mod_poly_init(a, p);
fmpz_mod_poly_init(b, p);
fmpz_mod_poly_init(c, p);
fmpz_mod_poly_init(d, p);
fmpz_mod_poly_init(lhs, p);
fmpz_mod_poly_init(rhs, p);
fmpz_mod_poly_randtest(a, state, n_randint(state, 100));
fmpz_mod_poly_randtest(b, state, n_randint(state, 100));
fmpz_mod_poly_mul(lhs, a, b);
fmpz_mod_poly_derivative(lhs, lhs);
fmpz_mod_poly_derivative(c, a);
fmpz_mod_poly_derivative(d, b);
fmpz_mod_poly_mul(c, c, b);
fmpz_mod_poly_mul(d, a, d);
fmpz_mod_poly_add(rhs, c, d);
result = fmpz_mod_poly_equal(lhs, rhs);
if (!result)
{
printf("FAIL (Leibniz):\n");
printf("a = "), fmpz_mod_poly_print(a), printf("\n\n");
printf("b = "), fmpz_mod_poly_print(b), printf("\n\n");
printf("(ab)' = "), fmpz_mod_poly_print(lhs), printf("\n\n");
printf("a'b + ab' = "), fmpz_mod_poly_print(rhs), printf("\n\n");
abort();
}
fmpz_mod_poly_clear(a);
fmpz_mod_poly_clear(b);
fmpz_mod_poly_clear(c);
fmpz_mod_poly_clear(d);
fmpz_mod_poly_clear(lhs);
fmpz_mod_poly_clear(rhs);
fmpz_clear(p);
}
flint_randclear(state);
_fmpz_cleanup();
printf("PASS\n");
return 0;
}
int main()
{
long iter;
flint_rand_t state;
printf("set_round_ui_2exp_fmpz....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 100000; iter++)
{
long prec, ret1, ret2;
fmpz_t man, exp;
fmpr_t x, y;
mp_limb_t lo;
fmpr_rnd_t rnd;
int negative;
fmpz_init(man);
fmpz_init(exp);
fmpr_init(x);
fmpr_init(y);
prec = 2 + n_randint(state, 1000);
if (n_randint(state, 10) == 0)
prec = FMPR_PREC_EXACT;
negative = n_randint(state, 2);
lo = n_randtest(state);
fmpz_randtest(exp, state, 1 + n_randint(state, 100));
if (negative)
fmpz_neg_ui(man, lo);
else
fmpz_set_ui(man, lo);
switch (n_randint(state, 4))
{
case 0: rnd = FMPR_RND_DOWN; break;
case 1: rnd = FMPR_RND_UP; break;
case 2: rnd = FMPR_RND_FLOOR; break;
default: rnd = FMPR_RND_CEIL; break;
}
ret1 = fmpr_set_round_ui_2exp_fmpz(x, lo, exp, negative, prec, rnd);
fmpr_set_fmpz_2exp(y, man, exp);
ret2 = fmpr_set_round(y, y, prec, rnd);
if (!fmpr_equal(x, y) || ret1 != ret2 ||
!fmpr_check_ulp(x, ret1, prec) || !fmpr_check_ulp(y, ret2, prec))
{
printf("FAIL\n\n");
printf("prec: %ld\n", prec);
printf("man = "); fmpz_print(man); printf("\n\n");
printf("exp = "); fmpz_print(exp); printf("\n\n");
printf("x = "); fmpr_print(x); printf("\n\n");
printf("y = "); fmpr_print(y); printf("\n\n");
printf("ret1 = %ld, ret2 = %ld\n\n", ret1, ret2);
abort();
}
fmpz_clear(man);
fmpz_clear(exp);
fmpr_clear(x);
fmpr_clear(y);
}
flint_randclear(state);
flint_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}
int
main(void)
{
int i, result;
FLINT_TEST_INIT(state);
flint_printf("pow_trunc....");
fflush(stdout);
/* Check aliasing */
for (i = 0; i < 10000; i++)
{
fmpz_mod_poly_t a, b, c;
fmpz_t p;
slong e, trunc;
fmpz_init(p);
fmpz_randtest_unsigned(p, state, 2 * FLINT_BITS);
fmpz_add_ui(p, p, 2);
fmpz_mod_poly_init(a, p);
fmpz_mod_poly_init(b, p);
fmpz_mod_poly_init(c, p);
fmpz_mod_poly_randtest(a, state, n_randint(state, 30));
e = n_randint(state, 20);
trunc = n_randint(state, 30);
fmpz_mod_poly_set(c, a);
fmpz_mod_poly_pow_trunc(b, a, e, trunc);
fmpz_mod_poly_pow_trunc(c, c, e, trunc);
result = (fmpz_mod_poly_equal(b, c));
if (!result)
{
flint_printf("FAIL aliasing:\n");
flint_printf("a->length = %wd, p = %wu, exp = %wd, trunc = %wd\n",
a->length, a->p, e, trunc);
flint_printf("a:\n"); fmpz_mod_poly_print(a), flint_printf("\n\n");
flint_printf("b:\n"); fmpz_mod_poly_print(b), flint_printf("\n\n");
flint_printf("c:\n"); fmpz_mod_poly_print(c), flint_printf("\n\n");
abort();
}
fmpz_clear(p);
fmpz_mod_poly_clear(a);
fmpz_mod_poly_clear(b);
fmpz_mod_poly_clear(c);
}
/* Check powering against naive method */
for (i = 0; i < 10000; i++)
{
fmpz_mod_poly_t a, b, c;
fmpz_t p;
slong e, trunc;
fmpz_init(p);
fmpz_randtest_unsigned(p, state, 2 * FLINT_BITS);
fmpz_add_ui(p, p, 2);
fmpz_mod_poly_init(a, p);
fmpz_mod_poly_init(b, p);
fmpz_mod_poly_init(c, p);
fmpz_mod_poly_randtest(a, state, n_randint(state, 30));
e = n_randint(state, 20);
trunc = n_randint(state, 30);
fmpz_mod_poly_pow_trunc(b, a, e, trunc);
fmpz_mod_poly_pow(c, a, e);
fmpz_mod_poly_truncate(c, trunc);
result = (fmpz_mod_poly_equal(b, c)
|| (a->length == 0 && e == 0 && c->length == 1 && c->coeffs[0] == 1));
if (!result)
{
flint_printf("FAIL:\n");
flint_printf("a->length = %wd, p = %wu, exp = %wd, trunc = %wd\n",
a->length, a->p, e, trunc);
flint_printf("a:\n"); fmpz_mod_poly_print(a), flint_printf("\n\n");
flint_printf("b:\n"); fmpz_mod_poly_print(b), flint_printf("\n\n");
flint_printf("c:\n"); fmpz_mod_poly_print(c), flint_printf("\n\n");
abort();
}
fmpz_clear(p);
fmpz_mod_poly_clear(a);
fmpz_mod_poly_clear(b);
fmpz_mod_poly_clear(c);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
int
arf_submul(arf_ptr z, arf_srcptr x, arf_srcptr y, slong prec, arf_rnd_t rnd)
{
mp_size_t xn, yn, zn, tn, alloc;
mp_srcptr xptr, yptr, zptr;
mp_ptr tptr, tptr2;
fmpz_t texp;
slong shift;
int tsgnbit, inexact;
ARF_MUL_TMP_DECL
if (arf_is_special(x) || arf_is_special(y) || arf_is_special(z))
{
if (arf_is_zero(z))
{
return arf_neg_mul(z, x, y, prec, rnd);
}
else if (arf_is_finite(x) && arf_is_finite(y))
{
return arf_set_round(z, z, prec, rnd);
}
else
{
/* todo: speed up */
arf_t t;
arf_init(t);
arf_mul(t, x, y, ARF_PREC_EXACT, ARF_RND_DOWN);
inexact = arf_sub(z, z, t, prec, rnd);
arf_clear(t);
return inexact;
}
}
tsgnbit = ARF_SGNBIT(x) ^ ARF_SGNBIT(y) ^ 1;
ARF_GET_MPN_READONLY(xptr, xn, x);
ARF_GET_MPN_READONLY(yptr, yn, y);
ARF_GET_MPN_READONLY(zptr, zn, z);
fmpz_init(texp);
_fmpz_add2_fast(texp, ARF_EXPREF(x), ARF_EXPREF(y), 0);
shift = _fmpz_sub_small(ARF_EXPREF(z), texp);
alloc = tn = xn + yn;
ARF_MUL_TMP_ALLOC(tptr2, alloc)
tptr = tptr2;
ARF_MPN_MUL(tptr, xptr, xn, yptr, yn);
tn -= (tptr[0] == 0);
tptr += (tptr[0] == 0);
if (shift >= 0)
inexact = _arf_add_mpn(z, zptr, zn, ARF_SGNBIT(z), ARF_EXPREF(z),
tptr, tn, tsgnbit, shift, prec, rnd);
else
inexact = _arf_add_mpn(z, tptr, tn, tsgnbit, texp,
zptr, zn, ARF_SGNBIT(z), -shift, prec, rnd);
ARF_MUL_TMP_FREE(tptr2, alloc)
fmpz_clear(texp);
return inexact;
}
/**
* Testing the flexibility of large index sets with a smaller kappa
*/
int test_jigsaw_indices(const size_t lambda, const size_t kappa, const size_t gamma, aes_randstate_t randstate) {
printf("lambda: %d, kappa: %d, gamma: %d", (int) lambda, (int) kappa, (int) gamma);
gghlite_sk_t self;
gghlite_flag_t flags = GGHLITE_FLAGS_QUIET;
gghlite_jigsaw_init_gamma(self, lambda, kappa, gamma, flags, randstate);
fmpz_t p; fmpz_init(p);
fmpz_poly_oz_ideal_norm(p, self->g, self->params->n, 0);
/* partitioning of the universe set */
int partition[GAMMA];
for (int i = 0; i < gamma; i++) {
partition[i] = rand() % kappa;
}
fmpz_t a[kappa];
fmpz_t acc; fmpz_init(acc);
fmpz_set_ui(acc, 1);
for(size_t k=0; k<kappa; k++) {
fmpz_init(a[k]);
fmpz_randm_aes(a[k], randstate, p);
fmpz_mul(acc, acc, a[k]);
fmpz_mod(acc, acc, p);
}
gghlite_clr_t e[kappa];
gghlite_enc_t u[kappa];
for(size_t k=0; k<kappa; k++) {
gghlite_clr_init(e[k]);
gghlite_enc_init(u[k], self->params);
}
gghlite_enc_t left;
gghlite_enc_init(left, self->params);
gghlite_enc_set_ui0(left, 1, self->params);
for(size_t k=0; k<kappa; k++) {
fmpz_poly_set_coeff_fmpz(e[k], 0, a[k]);
const int i = (gghlite_sk_is_symmetric(self)) ? 0 : k;
int group[GAMMA];
memset(group, 0, GAMMA * sizeof(int));
for (int j = 0; j < gamma; j++) {
if (partition[j] == k) {
group[j] = 1;
}
}
gghlite_enc_set_gghlite_clr(u[k], self, e[k], 1, group, 1);
gghlite_enc_mul(left, self->params, left, u[k]);
}
gghlite_enc_t rght;
gghlite_enc_init(rght, self->params);
gghlite_enc_set_ui0(rght, 1, self->params);
fmpz_poly_t tmp; fmpz_poly_init(tmp);
fmpz_poly_set_coeff_fmpz(tmp, 0, acc);
gghlite_enc_set_gghlite_clr0(rght, self, tmp);
for(size_t k=0; k<gamma; k++) {
gghlite_enc_mul(rght, self->params, rght, self->z_inv[k]);
}
gghlite_enc_sub(rght, self->params, rght, left);
int status = 1 - gghlite_enc_is_zero(self->params, rght);
for(size_t i=0; i<kappa; i++) {
fmpz_clear(a[i]);
gghlite_clr_clear(e[i]);
gghlite_enc_clear(u[i]);
}
gghlite_enc_clear(left);
gghlite_enc_clear(rght);
gghlite_clr_clear(tmp);
fmpz_clear(p);
gghlite_sk_clear(self, 1);
if (status == 0)
printf(" PASS\n");
else
printf(" FAIL\n");
return status;
}
void
_arith_cos_minpoly(fmpz * coeffs, slong d, ulong n)
{
slong i, j;
fmpz * alpha;
fmpz_t half;
mpfr_t t, u;
mp_bitcnt_t prec;
slong exp;
if (n <= MAX_32BIT)
{
for (i = 0; i <= d; i++)
fmpz_set_si(coeffs + i, lookup_table[n - 1][i]);
return;
}
/* Direct formula for odd primes > 3 */
if (n_is_prime(n))
{
slong s = (n - 1) / 2;
switch (s % 4)
{
case 0:
fmpz_set_si(coeffs, WORD(1));
fmpz_set_si(coeffs + 1, -s);
break;
case 1:
fmpz_set_si(coeffs, WORD(1));
fmpz_set_si(coeffs + 1, s + 1);
break;
case 2:
fmpz_set_si(coeffs, WORD(-1));
fmpz_set_si(coeffs + 1, s);
break;
case 3:
fmpz_set_si(coeffs, WORD(-1));
fmpz_set_si(coeffs + 1, -s - 1);
break;
}
for (i = 2; i <= s; i++)
{
slong b = (s - i) % 2;
fmpz_mul2_uiui(coeffs + i, coeffs + i - 2, s+i-b, s+2-b-i);
fmpz_divexact2_uiui(coeffs + i, coeffs + i, i, i-1);
fmpz_neg(coeffs + i, coeffs + i);
}
return;
}
prec = magnitude_bound(d) + 5 + FLINT_BIT_COUNT(d);
alpha = _fmpz_vec_init(d);
fmpz_init(half);
mpfr_init2(t, prec);
mpfr_init2(u, prec);
fmpz_one(half);
fmpz_mul_2exp(half, half, prec - 1);
mpfr_const_pi(t, prec);
mpfr_div_ui(t, t, n, MPFR_RNDN);
for (i = j = 0; j < d; i++)
{
if (n_gcd(n, i) == 1)
{
mpfr_mul_ui(u, t, 2 * i, MPFR_RNDN);
mpfr_cos(u, u, MPFR_RNDN);
mpfr_neg(u, u, MPFR_RNDN);
exp = mpfr_get_z_2exp(_fmpz_promote(alpha + j), u);
_fmpz_demote_val(alpha + j);
fmpz_mul_or_div_2exp(alpha + j, alpha + j, exp + prec);
j++;
}
}
balanced_product(coeffs, alpha, d, prec);
/* Scale and round */
for (i = 0; i < d + 1; i++)
{
slong r = d;
if ((n & (n - 1)) == 0)
r--;
fmpz_mul_2exp(coeffs + i, coeffs + i, r);
fmpz_add(coeffs + i, coeffs + i, half);
fmpz_fdiv_q_2exp(coeffs + i, coeffs + i, prec);
}
fmpz_clear(half);
mpfr_clear(t);
mpfr_clear(u);
_fmpz_vec_clear(alpha, d);
}
int test_jigsaw(const size_t lambda, const size_t kappa, int symmetric, aes_randstate_t randstate) {
printf("λ: %4zu, κ: %2zu, symmetric: %d …", lambda, kappa, symmetric);
gghlite_sk_t self;
gghlite_flag_t flags = GGHLITE_FLAGS_QUIET;
if (symmetric)
gghlite_init(self, lambda, kappa, kappa, 0x0, flags | GGHLITE_FLAGS_GOOD_G_INV, randstate);
else
gghlite_jigsaw_init(self, lambda, kappa, flags, randstate);
fmpz_t p; fmpz_init(p);
fmpz_poly_oz_ideal_norm(p, self->g, self->params->n, 0);
fmpz_t a[kappa];
fmpz_t acc; fmpz_init(acc);
fmpz_set_ui(acc, 1);
for(size_t k=0; k<kappa; k++) {
fmpz_init(a[k]);
fmpz_randm_aes(a[k], randstate, p);
fmpz_mul(acc, acc, a[k]);
fmpz_mod(acc, acc, p);
}
gghlite_clr_t e[kappa];
gghlite_enc_t u[kappa];
for(size_t k=0; k<kappa; k++) {
gghlite_clr_init(e[k]);
gghlite_enc_init(u[k], self->params);
}
gghlite_enc_t left;
gghlite_enc_init(left, self->params);
gghlite_enc_set_ui0(left, 1, self->params);
for(size_t k=0; k<kappa; k++) {
fmpz_poly_set_coeff_fmpz(e[k], 0, a[k]);
const int i = (gghlite_sk_is_symmetric(self)) ? 0 : k;
int group[GAMMA];
memset(group, 0, GAMMA * sizeof(int));
group[i] = 1;
gghlite_enc_set_gghlite_clr(u[k], self, e[k], 1, group, 1);
gghlite_enc_mul(left, self->params, left, u[k]);
}
gghlite_enc_t rght;
gghlite_enc_init(rght, self->params);
gghlite_enc_set_ui0(rght, 1, self->params);
fmpz_poly_t tmp; fmpz_poly_init(tmp);
fmpz_poly_set_coeff_fmpz(tmp, 0, acc);
gghlite_enc_set_gghlite_clr0(rght, self, tmp);
for(size_t k=0; k<kappa; k++) {
const int i = (gghlite_sk_is_symmetric(self)) ? 0 : k;
gghlite_enc_mul(rght, self->params, rght, self->z_inv[i]);
}
gghlite_enc_sub(rght, self->params, rght, left);
int status = 1 - gghlite_enc_is_zero(self->params, rght);
for(size_t i=0; i<kappa; i++) {
fmpz_clear(a[i]);
gghlite_clr_clear(e[i]);
gghlite_enc_clear(u[i]);
}
gghlite_enc_clear(left);
gghlite_enc_clear(rght);
gghlite_clr_clear(tmp);
fmpz_clear(p);
gghlite_sk_clear(self, 1);
if (status == 0)
printf(" PASS\n");
else
printf(" FAIL\n");
return status;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("isolate_roots....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 40; iter++)
{
slong m, r, a, b, maxdepth, maxeval, maxfound, prec, i, j, num;
arf_interval_ptr blocks;
int * info;
arf_interval_t interval;
arb_t t;
fmpz_t nn;
prec = 2 + n_randint(state, 50);
m = n_randint(state, 80);
r = 1 + n_randint(state, 80);
a = m - r;
b = m + r;
maxdepth = 1 + n_randint(state, 60);
maxeval = 1 + n_randint(state, 5000);
maxfound = 1 + n_randint(state, 100);
arf_interval_init(interval);
arb_init(t);
fmpz_init(nn);
arf_set_si(&interval->a, a);
arf_set_si(&interval->b, b);
num = arb_calc_isolate_roots(&blocks, &info, sin_pi2_x, NULL,
interval, maxdepth, maxeval, maxfound, prec);
/* check that all roots are accounted for */
for (i = a; i <= b; i++)
{
if (i % 2 == 0)
{
int found = 0;
for (j = 0; j < num; j++)
{
arf_interval_get_arb(t, blocks + j, ARF_PREC_EXACT);
if (arb_contains_si(t, i))
{
found = 1;
break;
}
}
if (!found)
{
flint_printf("FAIL: missing root %wd\n", i);
flint_printf("a = %wd, b = %wd, maxdepth = %wd, maxeval = %wd, maxfound = %wd, prec = %wd\n",
a, b, maxdepth, maxeval, maxfound, prec);
for (j = 0; j < num; j++)
{
arf_interval_printd(blocks + j, 15);
flint_printf(" %d \n", info[i]);
}
abort();
}
}
}
/* check that all reported single roots are good */
for (i = 0; i < num; i++)
{
if (info[i] == 1)
{
/* b contains unique 2n -> b/2 contains unique n */
arf_interval_get_arb(t, blocks + i, ARF_PREC_EXACT);
arb_mul_2exp_si(t, t, -1);
if (!arb_get_unique_fmpz(nn, t))
{
flint_printf("FAIL: bad root %wd\n", i);
flint_printf("a = %wd, b = %wd, maxdepth = %wd, maxeval = %wd, maxfound = %wd, prec = %wd\n",
a, b, maxdepth, maxeval, maxfound, prec);
for (j = 0; j < num; j++)
{
arf_interval_printd(blocks + j, 15);
flint_printf(" %d \n", info[i]);
}
abort();
}
}
}
_arf_interval_vec_clear(blocks, num);
flint_free(info);
arf_interval_clear(interval);
arb_clear(t);
fmpz_clear(nn);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main(int argc, char *argv[])
{
ulong r, s, p, prec, s_prec;
ulong i, m, lambda, char1, char2;
fmpz_poly_t eis, eta, eta_r;
fmpz_t p1, c1, c2, ss1, ss, pp, ppl, pplc;
// input r, s, and the precision desired
if (argc == 4) {
r = atol(argv[1]);
s = atol(argv[2]);
prec = atol(argv[3]);
prec = n_nextprime(prec, 1) - 1;
}
if (argc != 4) {
printf("usage: shimura_coeffs r s n\n");
return EXIT_FAILURE;
}
// Compute the weight of the form f_r_s
lambda = r / 2 + s;
//printf("%d\n", lambda);
// This is the necessary precision of the input
s_prec = (prec + r) * prec * r / 24;
//printf("Necessary precision: %d terms\n", s_prec);
// First compute eta
//printf("Computing eta\n");
fmpz_poly_init(eta);
eta_series(&eta, s_prec);
// Next compute eta^r
//printf("Computing eta^%d\n", r);
fmpz_poly_init(eta_r);
fmpz_poly_pow_trunc(eta_r, eta, r, s_prec);
fmpz_poly_clear(eta);
// Next compute E_s
//printf("Computing E_%d\n", s);
fmpz_poly_init(eis);
if(s != 0) {
eis_series(&eis, s, s_prec);
}
//printf("Computing coefficients\n");
// Instead of computing the product, we will compute each coefficient as
// needed. This is potentially slower, but saves memory.
//
fmpz_init(p1);
fmpz_init(c1);
fmpz_init(c2);
fmpz_init(ss);
fmpz_init(ss1);
// compute alpha(p^2*r)
p = 2;
m = r*p*p;
while(p <= prec) {
fmpz_set_ui(ss1, 0);
if(s != 0) {
for(i = r; i <= m; i += 24) {
if((m - i) % 24 == 0) {
fmpz_poly_get_coeff_fmpz(c1, eta_r, (i - r) / 24);
fmpz_poly_get_coeff_fmpz(c2, eis, (m - i) / 24);
fmpz_addmul(ss1, c1, c2);
}
}
}
else {
if((m - r) % 24 == 0)
fmpz_poly_get_coeff_fmpz(ss1, eta_r, (m - r) / 24);
}
/*
if(p == 199) {
fmpz_print(ss1);
printf("\n");
}
*/
// compute character X12(p)
char1 = n_jacobi(12, p);
// compute character ((-1)^(lambda) * n | p)
if(lambda % 2 == 0) {
char2 = n_jacobi(r, p);
}
else {
char2 = n_jacobi(-r, p);
}
// compute p^(lambda - 1)
fmpz_set_ui(pp, p);
fmpz_pow_ui(ppl, pp, lambda - 1);
fmpz_mul_si(pplc, ppl, char1*char2);
fmpz_add(ss, ss1, pplc);
printf("%d:\t", p);
fmpz_print(ss);
printf("\n");
p = n_nextprime(p, 1);
m = r*p*p;
}
fmpz_clear(p1);
fmpz_clear(c1);
fmpz_clear(c2);
fmpz_clear(ss);
fmpz_clear(ss1);
return EXIT_SUCCESS;
}
void fmpz_mod_poly_divrem_f(fmpz_t f, fmpz_mod_poly_t Q, fmpz_mod_poly_t R,
const fmpz_mod_poly_t A, const fmpz_mod_poly_t B)
{
const slong lenA = A->length;
const slong lenB = B->length;
const slong lenQ = lenA - lenB + 1;
fmpz *q, *r;
fmpz_t invB;
fmpz_init(invB);
fmpz_gcdinv(f, invB, fmpz_poly_lead(B), &(B->p));
if (!fmpz_is_one(f))
{
fmpz_clear(invB);
return;
}
if (lenA < lenB)
{
fmpz_mod_poly_set(R, A);
fmpz_mod_poly_zero(Q);
fmpz_clear(invB);
return;
}
if (Q == A || Q == B)
{
q = _fmpz_vec_init(lenQ);
}
else
{
fmpz_mod_poly_fit_length(Q, lenQ);
q = Q->coeffs;
}
if (R == A || R == B)
{
r = _fmpz_vec_init(lenA);
}
else
{
fmpz_mod_poly_fit_length(R, lenA);
r = R->coeffs;
}
_fmpz_mod_poly_divrem_divconquer(q, r, A->coeffs, lenA,
B->coeffs, lenB, invB, &(B->p));
if (Q == A || Q == B)
{
_fmpz_vec_clear(Q->coeffs, Q->alloc);
Q->coeffs = q;
Q->alloc = lenQ;
Q->length = lenQ;
}
else
{
_fmpz_mod_poly_set_length(Q, lenQ);
}
if (R == A || R == B)
{
_fmpz_vec_clear(R->coeffs, R->alloc);
R->coeffs = r;
R->alloc = lenA;
R->length = lenA;
}
_fmpz_mod_poly_set_length(R, lenB - 1);
_fmpz_mod_poly_normalise(R);
fmpz_clear(invB);
}
void eis_series(fmpz_poly_t *eis, ulong k, ulong prec)
{
ulong i, p, ee, p_pow, ind;
fmpz_t last, last_m1, mult, fp, t_coeff, term, term_m1;
long bern_fac[15] = {0, 0, 0, 0, 240, 0, -504, 0, 480, 0, -264, 0, 0, 0, -24};
// Now, we compute the eisenstein series
// First, compute primes by sieving.
// allocate memory for the array.
/*
char *primes;
primes = calloc(prec + 1, sizeof(char));
for(i = 0; i <= prec; i++) {
primes[i] = 1;
}
primes[0] = 0;
primes[1] = 0;
p = 2;
while(p*p <= prec) {
j = p*p;
while(j <= prec) {
primes[j] = 0;
j += p;
}
p += 1;
while(primes[p] != 1)
p += 1;
}
*/
// Now, create the eisenstein series.
// We build up each coefficient using the multiplicative properties of the
// divisor sum function.
fmpz_poly_set_coeff_si(*eis, 0, 1);
for(i = 1; i <= prec; i++)
fmpz_poly_set_coeff_si(*eis, i, bern_fac[k]);
fmpz_init(last);
fmpz_init(last_m1);
fmpz_init(mult);
fmpz_init(fp);
fmpz_init(t_coeff);
fmpz_init(term);
fmpz_init(term_m1);
ee = k - 1;
p = 2;
while(p <= prec) {
p_pow = p;
fmpz_set_ui(fp, p);
fmpz_pow_ui(mult, fp, ee);
fmpz_pow_ui(term, mult, 2);
fmpz_set(last, mult);
while(p_pow <= prec) {
ind = p_pow;
fmpz_sub_ui(term_m1, term, 1);
fmpz_sub_ui(last_m1, last, 1);
while(ind <= prec) {
fmpz_poly_get_coeff_fmpz(t_coeff, *eis, ind);
fmpz_mul(t_coeff, t_coeff, term_m1);
fmpz_divexact(t_coeff, t_coeff, last_m1);
fmpz_poly_set_coeff_fmpz(*eis, ind, t_coeff);
ind += p_pow;
}
p_pow *= p;
fmpz_set(last, term);
fmpz_mul(term, term, mult);
}
p = n_nextprime(p, 1);
}
fmpz_clear(last);
fmpz_clear(last_m1);
fmpz_clear(mult);
fmpz_clear(fp);
fmpz_clear(t_coeff);
fmpz_clear(term);
fmpz_clear(term_m1);
}
void
_fmpq_poly_revert_series_lagrange_fast(fmpz * Qinv, fmpz_t den,
const fmpz * Q, const fmpz_t Qden, slong n)
{
slong i, j, k, m;
fmpz *R, *Rden, *S, *T, *dens, *tmp;
fmpz_t Sden, Tden, t;
if (fmpz_is_one(Qden) && (n > 1) && fmpz_is_pm1(Q + 1))
{
_fmpz_poly_revert_series(Qinv, Q, n);
fmpz_one(den);
return;
}
if (n <= 2)
{
fmpz_zero(Qinv);
if (n == 2)
{
fmpz_set(Qinv + 1, Qden);
fmpz_set(den, Q + 1);
_fmpq_poly_canonicalise(Qinv, den, 2);
}
return;
}
m = n_sqrt(n);
fmpz_init(t);
dens = _fmpz_vec_init(n);
R = _fmpz_vec_init((n - 1) * m);
S = _fmpz_vec_init(n - 1);
T = _fmpz_vec_init(n - 1);
Rden = _fmpz_vec_init(m);
fmpz_init(Sden);
fmpz_init(Tden);
fmpz_zero(Qinv);
fmpz_one(dens);
_fmpq_poly_inv_series(Ri(1), Rdeni(1), Q + 1, Qden, n - 1);
_fmpq_poly_canonicalise(Ri(1), Rdeni(1), n - 1);
for (i = 2; i <= m; i++)
{
_fmpq_poly_mullow(Ri(i), Rdeni(i), Ri(i-1), Rdeni(i-1), n - 1,
Ri(1), Rdeni(1), n - 1, n - 1);
_fmpq_poly_canonicalise(Ri(i), Rdeni(i), n - 1);
}
for (i = 1; i < m; i++)
{
fmpz_set(Qinv + i, Ri(i) + i - 1);
fmpz_mul_ui(dens + i, Rdeni(i), i);
}
_fmpz_vec_set(S, Ri(m), n - 1);
fmpz_set(Sden, Rdeni(m));
for (i = m; i < n; i += m)
{
fmpz_set(Qinv + i, S + i - 1);
fmpz_mul_ui(dens + i, Sden, i);
for (j = 1; j < m && i + j < n; j++)
{
fmpz_mul(t, S + 0, Ri(j) + i + j - 1);
for (k = 1; k <= i + j - 1; k++)
fmpz_addmul(t, S + k, Ri(j) + i + j - 1 - k);
fmpz_set(Qinv + i + j, t);
fmpz_mul(dens + i + j, Sden, Rdeni(j));
fmpz_mul_ui(dens + i + j, dens + i + j, i + j);
}
if (i + 1 < n)
{
_fmpq_poly_mullow(T, Tden, S, Sden, n - 1,
Ri(m), Rdeni(m), n - 1, n - 1);
_fmpq_poly_canonicalise(T, Tden, n - 1);
fmpz_swap(Tden, Sden);
tmp = S; S = T; T = tmp;
}
}
_set_vec(Qinv, den, Qinv, dens, n);
_fmpq_poly_canonicalise(Qinv, den, n);
fmpz_clear(t);
_fmpz_vec_clear(dens, n);
_fmpz_vec_clear(R, (n - 1) * m);
_fmpz_vec_clear(S, n - 1);
_fmpz_vec_clear(T, n - 1);
_fmpz_vec_clear(Rden, m);
fmpz_clear(Sden);
fmpz_clear(Tden);
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("zeta_nzeros_gram....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 130 + 20 * arb_test_multiplier(); iter++)
{
arb_t t, x;
fmpz_t N, n;
slong prec1, prec2;
arb_init(t);
arb_init(x);
fmpz_init(n);
fmpz_init(N);
if (iter < 130)
{
fmpz_set_si(n, iter - 1);
}
else
{
fmpz_randtest_unsigned(n, state, 20);
fmpz_add_ui(n, n, 129);
}
prec1 = 2 + n_randtest(state) % 100;
prec2 = 2 + n_randtest(state) % 100;
acb_dirichlet_zeta_nzeros_gram(N, n);
acb_dirichlet_gram_point(t, n, NULL, NULL, prec1);
acb_dirichlet_zeta_nzeros(x, t, prec2);
if (!arb_contains_fmpz(x, N))
{
flint_printf("FAIL: containment\n\n");
flint_printf("n = "); fmpz_print(n);
flint_printf(" prec1 = %wd prec2 = %wd\n\n", prec1, prec2);
flint_printf("N = "); fmpz_print(N); flint_printf("\n\n");
flint_printf("t = "); arb_printn(t, 100, 0); flint_printf("\n\n");
flint_printf("x = "); arb_printn(x, 100, 0); flint_printf("\n\n");
flint_abort();
}
arb_clear(t);
arb_clear(x);
fmpz_clear(n);
fmpz_clear(N);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int
main(int argc, char** argv)
{
double s[nalgs];
int c, n, lenf, leng, len, ext, reps = 0;
fmpz_t p, temp;
TEMPLATE(T, poly_t) f, g, h;
TEMPLATE(T, ctx_t) ctx;
FLINT_TEST_INIT(state);
fmpz_init(p);
fmpz_set_str(p, argv[1], 10);
fmpz_init(temp);
fmpz_set_str(temp, argv[2], 10);
ext = fmpz_get_si(temp);
lenf = atol(argv[3]);
leng = atol(argv[4]);
len = atol(argv[5]);
TEMPLATE(T, ctx_init)(ctx, p, ext, "a");
TEMPLATE(T, poly_init)(f, ctx);
TEMPLATE(T, poly_init)(g, ctx);
TEMPLATE(T, poly_init)(h, ctx);
for (c = 0; c < nalgs; c++)
{
s[c] = 0.0;
}
for (n = 0; n < ncases; n++)
{
double t[nalgs];
int l, loops = 1;
/*
Construct random elements of fq
*/
{
TEMPLATE(T, poly_randtest_monic)(f, state, lenf, ctx);
TEMPLATE(T, poly_randtest_monic)(g, state, leng, ctx);
}
loop:
t[0] = 0.0;
init_clock(0);
prof_start();
for (l = 0; l < loops; l++)
{
TEMPLATE(T, poly_mullow_classical)(h, f, g, len, ctx);
}
prof_stop();
t[0] += get_clock(0);
t[1] = 0.0;
init_clock(0);
prof_start();
for (l = 0; l < loops; l++)
{
TEMPLATE(T, poly_mullow_KS)(h, f, g, len, ctx);
}
prof_stop();
t[1] += get_clock(0);
for (c = 0; c < nalgs; c++)
if (t[c] * FLINT_CLOCK_SCALE_FACTOR <= cpumin)
{
loops *= 10;
goto loop;
}
for (c = 0; c < nalgs; c++)
s[c] += t[c];
reps += loops;
}
for (c = 0; c < nalgs; c++)
{
flint_printf("%20f ", s[c] / (double) reps);
fflush(stdout);
}
printf("\n");
TEMPLATE(T, poly_clear)(h, ctx);
TEMPLATE(T, poly_clear)(f, ctx);
TEMPLATE(T, poly_clear)(g, ctx);
TEMPLATE(T, ctx_clear)(ctx);
fmpz_clear(p);
fmpz_clear(temp);
FLINT_TEST_CLEANUP(state);
return 0;
}
int
main(void)
{
fmpz_mat_t A, X, B, AX, AXm, Bm;
fmpz_t mod;
slong i, m, n, r;
int success;
FLINT_TEST_INIT(state);
flint_printf("solve_dixon....");
fflush(stdout);
for (i = 0; i < 100 * flint_test_multiplier(); i++)
{
m = n_randint(state, 20);
n = n_randint(state, 20);
fmpz_mat_init(A, m, m);
fmpz_mat_init(B, m, n);
fmpz_mat_init(Bm, m, n);
fmpz_mat_init(X, m, n);
fmpz_mat_init(AX, m, n);
fmpz_mat_init(AXm, m, n);
fmpz_init(mod);
fmpz_mat_randrank(A, state, m, 1+n_randint(state, 2)*n_randint(state, 100));
fmpz_mat_randtest(B, state, 1+n_randint(state, 2)*n_randint(state, 100));
/* Dense */
if (n_randint(state, 2))
fmpz_mat_randops(A, state, 1+n_randint(state, 1 + m*m));
success = fmpz_mat_solve_dixon(X, mod, A, B);
fmpz_mat_set(AXm, X);
fmpz_mat_mul(AX, A, AXm);
fmpz_mat_scalar_mod_fmpz(AXm, AX, mod);
fmpz_mat_scalar_mod_fmpz(Bm, B, mod);
if (!fmpz_mat_equal(AXm, Bm) || !success)
{
flint_printf("FAIL:\n");
flint_printf("AX != B!\n");
flint_printf("A:\n"), fmpz_mat_print_pretty(A), flint_printf("\n");
flint_printf("B:\n"), fmpz_mat_print_pretty(B), flint_printf("\n");
flint_printf("X:\n"), fmpz_mat_print_pretty(X), flint_printf("\n");
flint_printf("mod = "), fmpz_print(mod), flint_printf("\n");
flint_printf("AX:\n"), fmpz_mat_print_pretty(AX), flint_printf("\n");
abort();
}
fmpz_mat_clear(A);
fmpz_mat_clear(B);
fmpz_mat_clear(Bm);
fmpz_mat_clear(X);
fmpz_mat_clear(AX);
fmpz_mat_clear(AXm);
fmpz_clear(mod);
}
/* Test singular systems */
for (i = 0; i < 100 * flint_test_multiplier(); i++)
{
m = 1 + n_randint(state, 10);
n = 1 + n_randint(state, 10);
r = n_randint(state, m);
fmpz_mat_init(A, m, m);
fmpz_mat_init(B, m, n);
fmpz_mat_init(X, m, n);
fmpz_init(mod);
fmpz_mat_randrank(A, state, r, 1+n_randint(state, 2)*n_randint(state, 100));
fmpz_mat_randtest(B, state, 1+n_randint(state, 2)*n_randint(state, 100));
/* Dense */
if (n_randint(state, 2))
fmpz_mat_randops(A, state, 1+n_randint(state, 1 + m*m));
if (fmpz_mat_solve_dixon(X, mod, A, B) != 0)
{
flint_printf("FAIL:\n");
flint_printf("singular system, returned nonzero\n");
abort();
}
fmpz_mat_clear(A);
fmpz_mat_clear(B);
fmpz_mat_clear(X);
fmpz_clear(mod);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
