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support partition function of bignum n (work in progress)

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This commit is contained in:
Fredrik Johansson 2014-03-03 16:32:29 +01:00
parent 2810e26428
commit 61e0c0c2ff
3 changed files with 69 additions and 46 deletions
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6
partitions.h
View file

@ -35,9 +35,11 @@
extern "C" {
#endif
void partitions_rademacher_bound(fmpr_t b, ulong n, ulong N);
void partitions_rademacher_bound(fmpr_t b, const fmpz_t n, ulong N);
void partitions_hrr_sum_fmprb(fmprb_t x, ulong n, long N0, long N, int use_doubles);
void partitions_hrr_sum_fmprb(fmprb_t x, const fmpz_t n, long N0, long N, int use_doubles);
void partitions_fmpz_fmpz(fmpz_t p, const fmpz_t n, int use_doubles);
void partitions_fmpz_ui(fmpz_t p, ulong n);

99
partitions/hrr_sum_fmprb.c
View file

@ -70,7 +70,7 @@ partitions_remainder_bound_log2(double n, double N)
}
static long
partitions_needed_terms(ulong n)
partitions_needed_terms(double n)
{
long N;
for (N = 1; partitions_remainder_bound_log2(n, N) > 10; N++);
@ -115,7 +115,7 @@ log2_ceil(double x)
}
static long
partitions_prec_bound(ulong n, long k, long N)
partitions_prec_bound(double n, long k, long N)
{
long prec;
@ -234,24 +234,25 @@ sinh_cosh_divk_precomp(fmprb_t sh, fmprb_t ch, fmprb_t ex, long k, long prec)
void
partitions_hrr_sum_fmprb(fmprb_t x, ulong n, long N0, long N, int use_doubles)
partitions_hrr_sum_fmprb(fmprb_t x, const fmpz_t n, long N0, long N, int use_doubles)
{
trig_prod_t prod;
fmprb_t acc, C, t1, t2, t3, t4, exp1;
fmpr_t bound;
fmpz_t n24;
long k, prec, res_prec, acc_prec, guard_bits;
double Cd;
double nd, Cd;
if (n <= 2)
if (fmpz_cmp_ui(n, 2) <= 0)
{
fmprb_set_ui(x, FLINT_MAX(1, n));
return;
abort();
}
nd = fmpz_get_d(n);
/* compute initial precision */
guard_bits = 2 * FLINT_BIT_COUNT(N) + 32;
prec = partitions_remainder_bound_log2(n, N0) + guard_bits;
prec = partitions_remainder_bound_log2(nd, N0) + guard_bits;
prec = FLINT_MAX(prec, DOUBLE_PREC);
res_prec = acc_prec = prec;
@ -267,7 +268,7 @@ partitions_hrr_sum_fmprb(fmprb_t x, ulong n, long N0, long N, int use_doubles)
fmprb_zero(x);
/* n24 = 24n - 1 */
fmpz_set_ui(n24, n);
fmpz_set(n24, n);
fmpz_mul_ui(n24, n24, 24);
fmpz_sub_ui(n24, n24, 1);
@ -280,18 +281,18 @@ partitions_hrr_sum_fmprb(fmprb_t x, ulong n, long N0, long N, int use_doubles)
/* exp1 = exp(C) */
fmprb_exp(exp1, C, prec);
Cd = PI * sqrt(24*n-1) / 6;
Cd = PI * sqrt(24*nd-1) / 6;
for (k = N0; k <= N; k++)
{
trig_prod_init(prod);
arith_hrr_expsum_factored(prod, k, n % k);
arith_hrr_expsum_factored(prod, k, fmpz_fdiv_ui(n, k));
if (prod->prefactor != 0)
{
if (prec > MIN_PREC)
prec = partitions_prec_bound(n, k, N);
prec = partitions_prec_bound(nd, k, N);
prod->prefactor *= 4;
prod->sqrt_p *= 3;
@ -320,7 +321,7 @@ partitions_hrr_sum_fmprb(fmprb_t x, ulong n, long N0, long N, int use_doubles)
{
double xx, zz, xxerr;
xx = eval_trig_prod_d(prod) / (24*n - 1);
xx = eval_trig_prod_d(prod) / (24*nd - 1);
zz = Cd / k;
xx = xx * (cosh(zz) - sinh(zz) / zz);
@ -363,53 +364,69 @@ partitions_hrr_sum_fmprb(fmprb_t x, ulong n, long N0, long N, int use_doubles)
#define NUMBER_OF_SMALL_PARTITIONS 128
extern const unsigned int partitions_lookup[NUMBER_OF_SMALL_PARTITIONS];
void
partitions_fmpz_fmpz(fmpz_t p, const fmpz_t n, int use_doubles)
{
if (fmpz_cmp_ui(n, NUMBER_OF_SMALL_PARTITIONS) < 0)
{
if (fmpz_sgn(n) < 0)
fmpz_zero(p);
else
fmpz_set_ui(p, partitions_lookup[fmpz_get_ui(n)]);
}
else
{
fmprb_t x;
long N;
fmprb_init(x);
N = partitions_needed_terms(fmpz_get_d(n));
partitions_hrr_sum_fmprb(x, n, 1, N, use_doubles);
if (!fmprb_get_unique_fmpz(p, x))
{
printf("not unique!\n");
fmprb_printd(x, 50);
printf("\n");
abort();
}
fmprb_clear(x);
}
}
void
partitions_fmpz_ui(fmpz_t p, ulong n)
{
fmprb_t x;
if (n < NUMBER_OF_SMALL_PARTITIONS)
{
fmpz_set_ui(p, partitions_lookup[n]);
return;
}
fmprb_init(x);
partitions_hrr_sum_fmprb(x, n, 1, partitions_needed_terms(n), 0);
if (!fmprb_get_unique_fmpz(p, x))
else
{
printf("not unique!\n");
fmprb_printd(x, 50);
printf("\n");
abort();
fmpz_t t;
fmpz_init(t);
fmpz_set_ui(t, n);
partitions_fmpz_fmpz(p, t, 0);
fmpz_clear(t);
}
fmprb_clear(x);
}
void
partitions_fmpz_ui_using_doubles(fmpz_t p, ulong n)
{
fmprb_t x;
if (n < NUMBER_OF_SMALL_PARTITIONS)
{
fmpz_set_ui(p, partitions_lookup[n]);
return;
}
fmprb_init(x);
partitions_hrr_sum_fmprb(x, n, 1, partitions_needed_terms(n), 1);
if (!fmprb_get_unique_fmpz(p, x))
else
{
printf("not unique!\n");
fmprb_printd(x, 50);
printf("\n");
abort();
fmpz_t t;
fmpz_init(t);
fmpz_set_ui(t, n);
partitions_fmpz_fmpz(p, t, 1);
fmpz_clear(t);
}
fmprb_clear(x);
}

10
partitions/rademacher_bound.c
View file

@ -38,15 +38,17 @@ _fmpr_sinh(fmpr_t y, const fmpr_t x, long prec)
/* Equation (1.8) in the paper */
void
partitions_rademacher_bound(fmpr_t b, ulong n, ulong N)
partitions_rademacher_bound(fmpr_t b, const fmpz_t n, ulong N)
{
fmpr_t A, B, C, t, u;
fmpz_t n1;
fmpr_init(A);
fmpr_init(B);
fmpr_init(C);
fmpr_init(t);
fmpr_init(u);
fmpz_init(n1);
/* bound for 44*pi^2/(225*sqrt(3)) */
fmpr_set_si_2exp_si(A, 18695160, -24);
@ -63,12 +65,13 @@ partitions_rademacher_bound(fmpr_t b, ulong n, ulong N)
/* B * sqrt(N/(n-1)) */
fmpr_set_ui(t, N);
fmpr_div_ui(t, t, n - 1, FMPRB_RAD_PREC, FMPR_RND_UP);
fmpz_sub_ui(n1, n, 1);
fmpr_div_fmpz(t, t, n1, FMPRB_RAD_PREC, FMPR_RND_UP);
fmpr_sqrt(t, t, FMPRB_RAD_PREC, FMPR_RND_UP);
fmpr_mul(t, B, t, FMPRB_RAD_PREC, FMPR_RND_UP);
/* sinh(C*sqrt(n)/N) */
fmpr_sqrt_ui(u, n, FMPRB_RAD_PREC, FMPR_RND_UP);
fmpr_sqrt_fmpz(u, n, FMPRB_RAD_PREC, FMPR_RND_UP);
fmpr_div_ui(u, u, N, FMPRB_RAD_PREC, FMPR_RND_UP);
fmpr_mul(u, C, u, FMPRB_RAD_PREC, FMPR_RND_UP);
@ -83,5 +86,6 @@ partitions_rademacher_bound(fmpr_t b, ulong n, ulong N)
fmpr_clear(C);
fmpr_clear(t);
fmpr_clear(u);
fmpz_clear(n1);
}