/* mpz_bin_uiui - compute n over k.

Contributed to the GNU project by Torbjorn Granlund and Marco Bodrato.

Copyright 2010-2012 Free Software Foundation, Inc.

This file is part of the GNU MP Library.

The GNU MP Library is free software; you can redistribute it and/or modify

it under the terms of either:

  * the GNU Lesser General Public License as published by the Free

    Software Foundation; either version 3 of the License, or (at your

    option) any later version.

or

  * the GNU General Public License as published by the Free Software

    Foundation; either version 2 of the License, or (at your option) any

    later version.

or both in parallel, as here.

The GNU MP Library is distributed in the hope that it will be useful, but

WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY

or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License

for more details.

You should have received copies of the GNU General Public License and the

GNU Lesser General Public License along with the GNU MP Library.  If not,

see https://www.gnu.org/licenses/.  */

#include "gmp.h"

#include "gmp-impl.h"

#include "longlong.h"

#ifndef BIN_GOETGHELUCK_THRESHOLD

#define BIN_GOETGHELUCK_THRESHOLD  1000

#endif

#ifndef BIN_UIUI_ENABLE_SMALLDC

#define BIN_UIUI_ENABLE_SMALLDC    1

#endif

#ifndef BIN_UIUI_RECURSIVE_SMALLDC

#define BIN_UIUI_RECURSIVE_SMALLDC (GMP_NUMB_BITS > 32)

#endif

/* Algorithm:

   Accumulate chunks of factors first limb-by-limb (using one of mul0-mul8)

   which are then accumulated into mpn numbers.  The first inner loop

   accumulates divisor factors, the 2nd inner loop accumulates exactly the same

   number of dividend factors.  We avoid accumulating more for the divisor,

   even with its smaller factors, since we else cannot guarantee divisibility.

   Since we know each division will yield an integer, we compute the quotient

   using Hensel norm: If the quotient is limited by 2^t, we compute A / B mod

   2^t.

   Improvements:

   (1) An obvious improvement to this code would be to compute mod 2^t

   everywhere.  Unfortunately, we cannot determine t beforehand, unless we

   invoke some approximation, such as Stirling's formula.  Of course, we don't

   need t to be tight.  However, it is not clear that this would help much,

   our numbers are kept reasonably small already.

   (2) Compute nmax/kmax semi-accurately, without scalar division or a loop.

   Extracting the 3 msb, then doing a table lookup using cnt*8+msb as index,

   would make it both reasonably accurate and fast.  (We could use a table

   stored into a limb, perhaps.)  The table should take the removed factors of

   2 into account (those done on-the-fly in mulN).

   (3) The first time in the loop we compute the odd part of a

   factorial in kp, we might use oddfac_1 for this task.

 */

/* This threshold determines how large divisor to accumulate before we call

   bdiv.  Perhaps we should never call bdiv, and accumulate all we are told,

   since we are just basecase code anyway?  Presumably, this depends on the

   relative speed of the asymptotically fast code and this code.  */

#define SOME_THRESHOLD 20

/* Multiply-into-limb functions.  These remove factors of 2 on-the-fly.  FIXME:

   All versions of MAXFACS don't take this 2 removal into account now, meaning

   that then, shifting just adds some overhead.  (We remove factors from the

   completed limb anyway.)  */

static mp_limb_t

mul1 (mp_limb_t m)

{

  return m;

}

static mp_limb_t

mul2 (mp_limb_t m)

{

  /* We need to shift before multiplying, to avoid an overflow. */

  mp_limb_t m01 = (m | 1) * ((m + 1) >> 1);

  return m01;

}

static mp_limb_t

mul3 (mp_limb_t m)

{

  mp_limb_t m01 = (m + 0) * (m + 1) >> 1;

  mp_limb_t m2 = (m + 2);

  return m01 * m2;

}

static mp_limb_t

mul4 (mp_limb_t m)

{

  mp_limb_t m01 = (m + 0) * (m + 1) >> 1;

  mp_limb_t m23 = (m + 2) * (m + 3) >> 1;

  return m01 * m23;

}

static mp_limb_t

mul5 (mp_limb_t m)

{

  mp_limb_t m012 = (m + 0) * (m + 1) * (m + 2) >> 1;

  mp_limb_t m34 = (m + 3) * (m + 4) >> 1;

  return m012 * m34;

}

static mp_limb_t

mul6 (mp_limb_t m)

{

  mp_limb_t m01 = (m + 0) * (m + 1);

  mp_limb_t m23 = (m + 2) * (m + 3);

  mp_limb_t m45 = (m + 4) * (m + 5) >> 1;

  mp_limb_t m0123 = m01 * m23 >> 3;

  return m0123 * m45;

}

static mp_limb_t

mul7 (mp_limb_t m)

{

  mp_limb_t m01 = (m + 0) * (m + 1);

  mp_limb_t m23 = (m + 2) * (m + 3);

  mp_limb_t m456 = (m + 4) * (m + 5) * (m + 6) >> 1;

  mp_limb_t m0123 = m01 * m23 >> 3;

  return m0123 * m456;

}

static mp_limb_t

mul8 (mp_limb_t m)

{

  mp_limb_t m01 = (m + 0) * (m + 1);

  mp_limb_t m23 = (m + 2) * (m + 3);

  mp_limb_t m45 = (m + 4) * (m + 5);

  mp_limb_t m67 = (m + 6) * (m + 7);

  mp_limb_t m0123 = m01 * m23 >> 3;

  mp_limb_t m4567 = m45 * m67 >> 3;

  return m0123 * m4567;

}

typedef mp_limb_t (* mulfunc_t) (mp_limb_t);

static const mulfunc_t mulfunc[] = {mul1,mul2,mul3,mul4,mul5,mul6,mul7,mul8};

#define M (numberof(mulfunc))

/* Number of factors-of-2 removed by the corresponding mulN function.  */

static const unsigned char tcnttab[] = {0, 1, 1, 2, 2, 4, 4, 6};

#if 1

/* This variant is inaccurate but share the code with other functions.  */

#define MAXFACS(max,l)							\

  do {									\

    (max) = log_n_max (l);						\

  } while (0)

#else

/* This variant is exact(?) but uses a loop.  It takes the 2 removal

 of mulN into account.  */

static const unsigned long ftab[] =

#if GMP_NUMB_BITS == 64

  /* 1 to 8 factors per iteration */

  {CNST_LIMB(0xffffffffffffffff),CNST_LIMB(0x100000000),0x32cbfe,0x16a0b,0x24c4,0xa16,0x34b,0x1b2 /*,0xdf,0x8d */};

#endif

#if GMP_NUMB_BITS == 32

  /* 1 to 7 factors per iteration */

  {0xffffffff,0x10000,0x801,0x16b,0x71,0x42,0x26 /* ,0x1e */};

#endif

#define MAXFACS(max,l)							\

  do {									\

    int __i;								\

    for (__i = numberof (ftab) - 1; l > ftab[__i]; __i--)		\

      ;									\

    (max) = __i + 1;							\

  } while (0)

#endif

/* Entry i contains (i!/2^t)^(-1) where t is chosen such that the parenthesis

   is an odd integer. */

static const mp_limb_t facinv[] = { ONE_LIMB_ODD_FACTORIAL_INVERSES_TABLE };

static void

mpz_bdiv_bin_uiui (mpz_ptr r, unsigned long int n, unsigned long int k)

{

  int nmax, kmax, nmaxnow, numfac;

  mp_ptr np, kp;

  mp_size_t nn, kn, alloc;

  mp_limb_t i, j, t, iii, jjj, cy, dinv;

  mp_bitcnt_t i2cnt, j2cnt;

  int cnt;

  mp_size_t maxn;

  TMP_DECL;

  ASSERT (k > ODD_FACTORIAL_TABLE_LIMIT);

  TMP_MARK;

  maxn = 1 + n / GMP_NUMB_BITS;    /* absolutely largest result size (limbs) */

  /* FIXME: This allocation might be insufficient, but is usually way too

     large.  */

  alloc = SOME_THRESHOLD - 1 + MAX (3 * maxn / 2, SOME_THRESHOLD);

  alloc = MIN (alloc, k) + 1;

  np = TMP_ALLOC_LIMBS (alloc);

  kp = TMP_ALLOC_LIMBS (SOME_THRESHOLD + 1);

  MAXFACS (nmax, n);

  ASSERT (nmax <= M);

  MAXFACS (kmax, k);

  ASSERT (kmax <= M);

  ASSERT (k >= M);

  i = n - k + 1;

  np[0] = 1; nn = 1;

  i2cnt = 0;				/* total low zeros in dividend */

  j2cnt = __gmp_fac2cnt_table[ODD_FACTORIAL_TABLE_LIMIT / 2 - 1];

					/* total low zeros in divisor */

  numfac = 1;

  j = ODD_FACTORIAL_TABLE_LIMIT + 1;

  jjj = ODD_FACTORIAL_TABLE_MAX;

  ASSERT (__gmp_oddfac_table[ODD_FACTORIAL_TABLE_LIMIT] == ODD_FACTORIAL_TABLE_MAX);

  while (1)

    {

      kp[0] = jjj;				/* store new factors */

      kn = 1;

      t = k - j + 1;

      kmax = MIN (kmax, t);

      while (kmax != 0 && kn < SOME_THRESHOLD)

	{

	  jjj = mulfunc[kmax - 1] (j);

	  j += kmax;				/* number of factors used */

	  count_trailing_zeros (cnt, jjj);	/* count low zeros */

	  jjj >>= cnt;				/* remove remaining low zeros */

	  j2cnt += tcnttab[kmax - 1] + cnt;	/* update low zeros count */

	  cy = mpn_mul_1 (kp, kp, kn, jjj);	/* accumulate new factors */

	  kp[kn] = cy;

	  kn += cy != 0;

	  t = k - j + 1;

	  kmax = MIN (kmax, t);

	}

      numfac = j - numfac;

      while (numfac != 0)

	{

	  nmaxnow = MIN (nmax, numfac);

	  iii = mulfunc[nmaxnow - 1] (i);

	  i += nmaxnow;				/* number of factors used */

	  count_trailing_zeros (cnt, iii);	/* count low zeros */

	  iii >>= cnt;				/* remove remaining low zeros */

	  i2cnt += tcnttab[nmaxnow - 1] + cnt;	/* update low zeros count */

	  cy = mpn_mul_1 (np, np, nn, iii);	/* accumulate new factors */

	  np[nn] = cy;

	  nn += cy != 0;

	  numfac -= nmaxnow;

	}

      ASSERT (nn < alloc);

      binvert_limb (dinv, kp[0]);

      nn += (np[nn - 1] >= kp[kn - 1]);

      nn -= kn;

      mpn_sbpi1_bdiv_q (np, np, nn, kp, MIN(kn,nn), -dinv);

      if (kmax == 0)

	break;

      numfac = j;

      jjj = mulfunc[kmax - 1] (j);

      j += kmax;				/* number of factors used */

      count_trailing_zeros (cnt, jjj);		/* count low zeros */

      jjj >>= cnt;				/* remove remaining low zeros */

      j2cnt += tcnttab[kmax - 1] + cnt;		/* update low zeros count */

    }

  /* Put back the right number of factors of 2.  */

  cnt = i2cnt - j2cnt;

  if (cnt != 0)

    {

      ASSERT (cnt < GMP_NUMB_BITS); /* can happen, but not for intended use */

      cy = mpn_lshift (np, np, nn, cnt);

      np[nn] = cy;

      nn += cy != 0;

    }

  nn -= np[nn - 1] == 0;	/* normalisation */

  kp = MPZ_NEWALLOC (r, nn);

  SIZ(r) = nn;

  MPN_COPY (kp, np, nn);

  TMP_FREE;

}

static void

mpz_smallk_bin_uiui (mpz_ptr r, unsigned long int n, unsigned long int k)

{

  int nmax, numfac;

  mp_ptr rp;

  mp_size_t rn, alloc;

  mp_limb_t i, iii, cy;

  mp_bitcnt_t i2cnt, cnt;

  count_leading_zeros (cnt, (mp_limb_t) n);

  cnt = GMP_LIMB_BITS - cnt;

  alloc = cnt * k / GMP_NUMB_BITS + 3;	/* FIXME: ensure rounding is enough. */

  rp = MPZ_NEWALLOC (r, alloc);

  MAXFACS (nmax, n);

  nmax = MIN (nmax, M);

  i = n - k + 1;

  nmax = MIN (nmax, k);

  rp[0] = mulfunc[nmax - 1] (i);

  rn = 1;

  i += nmax;				/* number of factors used */

  i2cnt = tcnttab[nmax - 1];		/* low zeros count */

  numfac = k - nmax;

  while (numfac != 0)

    {

      nmax = MIN (nmax, numfac);

      iii = mulfunc[nmax - 1] (i);

      i += nmax;			/* number of factors used */

      i2cnt += tcnttab[nmax - 1];	/* update low zeros count */

      cy = mpn_mul_1 (rp, rp, rn, iii);	/* accumulate new factors */

      rp[rn] = cy;

      rn += cy != 0;

      numfac -= nmax;

    }

  ASSERT (rn < alloc);

  mpn_pi1_bdiv_q_1 (rp, rp, rn, __gmp_oddfac_table[k], facinv[k - 2],

		    __gmp_fac2cnt_table[k / 2 - 1] - i2cnt);

  /* A two-fold, branch-free normalisation is possible :*/

  /* rn -= rp[rn - 1] == 0; */

  /* rn -= rp[rn - 1] == 0; */

  MPN_NORMALIZE_NOT_ZERO (rp, rn);

  SIZ(r) = rn;

}

/* Algorithm:

   Plain and simply multiply things together.

   We tabulate factorials (k!/2^t)^(-1) mod B (where t is chosen such

   that k!/2^t is odd).

*/

static mp_limb_t

bc_bin_uiui (unsigned int n, unsigned int k)

{

  return ((__gmp_oddfac_table[n] * facinv[k - 2] * facinv[n - k - 2])

    << (__gmp_fac2cnt_table[n / 2 - 1] - __gmp_fac2cnt_table[k / 2 - 1] - __gmp_fac2cnt_table[(n-k) / 2 - 1]))

    & GMP_NUMB_MASK;

}

/* Algorithm:

   Recursively exploit the relation

   bin(n,k) = bin(n,k>>1)*bin(n-k>>1,k-k>>1)/bin(k,k>>1) .

   Values for binomial(k,k>>1) that fit in a limb are precomputed

   (with inverses).

*/

/* bin2kk[i - ODD_CENTRAL_BINOMIAL_OFFSET] =

   binomial(i*2,i)/2^t (where t is chosen so that it is odd). */

static const mp_limb_t bin2kk[] = { ONE_LIMB_ODD_CENTRAL_BINOMIAL_TABLE };

/* bin2kkinv[i] = bin2kk[i]^-1 mod B */

static const mp_limb_t bin2kkinv[] = { ONE_LIMB_ODD_CENTRAL_BINOMIAL_INVERSE_TABLE };

/* bin2kk[i] = binomial((i+MIN_S)*2,i+MIN_S)/2^t. This table contains the t values. */

static const unsigned char fac2bin[] = { CENTRAL_BINOMIAL_2FAC_TABLE };

static void

mpz_smallkdc_bin_uiui (mpz_ptr r, unsigned long int n, unsigned long int k)

{

  mp_ptr rp;

  mp_size_t rn;

  unsigned long int hk;

  hk = k >> 1;

  if ((! BIN_UIUI_RECURSIVE_SMALLDC) || hk <= ODD_FACTORIAL_TABLE_LIMIT)

    mpz_smallk_bin_uiui (r, n, hk);

  else

    mpz_smallkdc_bin_uiui (r, n, hk);

  k -= hk;

  n -= hk;

  if (n <= ODD_FACTORIAL_EXTTABLE_LIMIT) {

    mp_limb_t cy;

    rn = SIZ (r);

    rp = MPZ_REALLOC (r, rn + 1);

    cy = mpn_mul_1 (rp, rp, rn, bc_bin_uiui (n, k));

    rp [rn] = cy;

    rn += cy != 0;

  } else {

    mp_limb_t buffer[ODD_CENTRAL_BINOMIAL_TABLE_LIMIT + 3];

    mpz_t t;

    ALLOC (t) = ODD_CENTRAL_BINOMIAL_TABLE_LIMIT + 3;

    PTR (t) = buffer;

    if ((! BIN_UIUI_RECURSIVE_SMALLDC) || k <= ODD_FACTORIAL_TABLE_LIMIT)

      mpz_smallk_bin_uiui (t, n, k);

    else

      mpz_smallkdc_bin_uiui (t, n, k);

    mpz_mul (r, r, t);

    rp = PTR (r);

    rn = SIZ (r);

  }

  mpn_pi1_bdiv_q_1 (rp, rp, rn, bin2kk[k - ODD_CENTRAL_BINOMIAL_OFFSET],

		    bin2kkinv[k - ODD_CENTRAL_BINOMIAL_OFFSET],

		    fac2bin[k - ODD_CENTRAL_BINOMIAL_OFFSET] - (k != hk));

  /* A two-fold, branch-free normalisation is possible :*/

  /* rn -= rp[rn - 1] == 0; */

  /* rn -= rp[rn - 1] == 0; */

  MPN_NORMALIZE_NOT_ZERO (rp, rn);

  SIZ(r) = rn;

}

/* mpz_goetgheluck_bin_uiui(RESULT, N, K) -- Set RESULT to binomial(N,K).

 *

 * Contributed to the GNU project by Marco Bodrato.

 *

 * Implementation of the algorithm by P. Goetgheluck, "Computing

 * Binomial Coefficients", The American Mathematical Monthly, Vol. 94,

 * No. 4 (April 1987), pp. 360-365.

 *

 * Acknowledgment: Peter Luschny did spot the slowness of the previous

 * code and suggested the reference.

 */

/* TODO: Remove duplicated constants / macros / static functions...

 */

/*************************************************************/

/* Section macros: common macros, for swing/fac/bin (&sieve) */

/*************************************************************/

#define FACTOR_LIST_APPEND(PR, MAX_PR, VEC, I)			\

  if ((PR) > (MAX_PR)) {					\

    (VEC)[(I)++] = (PR);					\

    (PR) = 1;							\

  }

#define FACTOR_LIST_STORE(P, PR, MAX_PR, VEC, I)		\

  do {								\

    if ((PR) > (MAX_PR)) {					\

      (VEC)[(I)++] = (PR);					\

      (PR) = (P);						\

    } else							\

      (PR) *= (P);						\

  } while (0)

#define LOOP_ON_SIEVE_CONTINUE(prime,end,sieve)			\

    __max_i = (end);						\

								\

    do {							\

      ++__i;							\

      if (((sieve)[__index] & __mask) == 0)			\

	{							\

	  (prime) = id_to_n(__i)

#define LOOP_ON_SIEVE_BEGIN(prime,start,end,off,sieve)		\

  do {								\

    mp_limb_t __mask, __index, __max_i, __i;			\

								\

    __i = (start)-(off);					\

    __index = __i / GMP_LIMB_BITS;				\

    __mask = CNST_LIMB(1) << (__i % GMP_LIMB_BITS);		\

    __i += (off);						\

								\

    LOOP_ON_SIEVE_CONTINUE(prime,end,sieve)

#define LOOP_ON_SIEVE_STOP					\

	}							\

      __mask = __mask << 1 | __mask >> (GMP_LIMB_BITS-1);	\

      __index += __mask & 1;					\

    }  while (__i <= __max_i)					\

#define LOOP_ON_SIEVE_END					\

    LOOP_ON_SIEVE_STOP;						\

  } while (0)

/*********************************************************/

/* Section sieve: sieving functions and tools for primes */

/*********************************************************/

#if WANT_ASSERT

static mp_limb_t

bit_to_n (mp_limb_t bit) { return (bit*3+4)|1; }

#endif

/* id_to_n (x) = bit_to_n (x-1) = (id*3+1)|1*/

static mp_limb_t

id_to_n  (mp_limb_t id)  { return id*3+1+(id&1;; }

/* n_to_bit (n) = ((n-1)&(-CNST_LIMB(2)))/3U-1 */

static mp_limb_t

n_to_bit (mp_limb_t n) { return ((n-5)|1)/3U; }

static mp_size_t

primesieve_size (mp_limb_t n) { return n_to_bit(n) / GMP_LIMB_BITS + 1; }

/*********************************************************/

/* Section binomial: fast binomial implementation        */

/*********************************************************/

#define COUNT_A_PRIME(P, N, K, PR, MAX_PR, VEC, I)	\

  do {							\

    mp_limb_t __a, __b, __prime, __ma,__mb;		\

    __prime = (P);					\

    __a = (N); __b = (K); __mb = 0;			\

    FACTOR_LIST_APPEND(PR, MAX_PR, VEC, I);		\

    do {						\

      __mb += __b % __prime; __b /= __prime;		\

      __ma = __a % __prime; __a /= __prime;		\

      if (__ma < __mb) {				\

        __mb = 1; (PR) *= __prime;			\

      } else  __mb = 0;					\

    } while (__a >= __prime);				\

  } while (0)

#define SH_COUNT_A_PRIME(P, N, K, PR, MAX_PR, VEC, I)	\

  do {							\

    mp_limb_t __prime;					\

    __prime = (P);					\

    if (((N) % __prime) < ((K) % __prime)) {		\

      FACTOR_LIST_STORE (__prime, PR, MAX_PR, VEC, I);	\

    }							\

  } while (0)

/* Returns an approximation of the sqare root of x.  *

 * It gives: x <= limb_apprsqrt (x) ^ 2 < x * 9/4    */

static mp_limb_t

limb_apprsqrt (mp_limb_t x)

{

  int s;

  ASSERT (x > 2);

  count_leading_zeros (s, x - 1);

  s = GMP_LIMB_BITS - 1 - s;

  return (CNST_LIMB(1) << (s >> 1)) + (CNST_LIMB(1) << ((s - 1) >> 1));

}

static void

mpz_goetgheluck_bin_uiui (mpz_ptr r, unsigned long int n, unsigned long int k)

{

  mp_limb_t *sieve, *factors, count;

  mp_limb_t prod, max_prod, j;

  TMP_DECL;

  ASSERT (BIN_GOETGHELUCK_THRESHOLD >= 13);

  ASSERT (n >= 25);

  TMP_MARK;

  sieve = TMP_ALLOC_LIMBS (primesieve_size (n));

  count = gmp_primesieve (sieve, n) + 1;

  factors = TMP_ALLOC_LIMBS (count / log_n_max (n) + 1);

  max_prod = GMP_NUMB_MAX / n;

  /* Handle primes = 2, 3 separately. */

  popc_limb (count, n - k);

  popc_limb (j, k);

  count += j;

  popc_limb (j, n);

  count -= j;

  prod = CNST_LIMB(1) << count;

  j = 0;

  COUNT_A_PRIME (3, n, k, prod, max_prod, factors, j);

  /* Accumulate prime factors from 5 to n/2 */

    {

      mp_limb_t s;

      {

	mp_limb_t prime;

	s = limb_apprsqrt(n);

	s = n_to_bit (s);

	LOOP_ON_SIEVE_BEGIN (prime, n_to_bit (5), s, 0,sieve);

	COUNT_A_PRIME (prime, n, k, prod, max_prod, factors, j);

	LOOP_ON_SIEVE_END;

	s++;

      }

      ASSERT (max_prod <= GMP_NUMB_MAX / 2);

      max_prod <<= 1;

      ASSERT (bit_to_n (s) * bit_to_n (s) > n);

      ASSERT (s <= n_to_bit (n >> 1));

      {

	mp_limb_t prime;

	LOOP_ON_SIEVE_BEGIN (prime, s, n_to_bit (n >> 1), 0,sieve);

	SH_COUNT_A_PRIME (prime, n, k, prod, max_prod, factors, j);

	LOOP_ON_SIEVE_END;

      }

      max_prod >>= 1;

    }

  /* Store primes from (n-k)+1 to n */

  ASSERT (n_to_bit (n - k) < n_to_bit (n));

    {

      mp_limb_t prime;

      LOOP_ON_SIEVE_BEGIN (prime, n_to_bit (n - k) + 1, n_to_bit (n), 0,sieve);

      FACTOR_LIST_STORE (prime, prod, max_prod, factors, j);

      LOOP_ON_SIEVE_END;

    }

  if (LIKELY (j != 0))

    {

      factors[j++] = prod;

      mpz_prodlimbs (r, factors, j);

    }

  else

    {

      PTR (r)[0] = prod;

      SIZ (r) = 1;

    }

  TMP_FREE;

}

#undef COUNT_A_PRIME

#undef SH_COUNT_A_PRIME

#undef LOOP_ON_SIEVE_END

#undef LOOP_ON_SIEVE_STOP

#undef LOOP_ON_SIEVE_BEGIN

#undef LOOP_ON_SIEVE_CONTINUE

/*********************************************************/

/* End of implementation of Goetgheluck's algorithm      */

/*********************************************************/

void

mpz_bin_uiui (mpz_ptr r, unsigned long int n, unsigned long int k)

{

  if (UNLIKELY (n < k)) {

    SIZ (r) = 0;

#if BITS_PER_ULONG > GMP_NUMB_BITS

  } else if (UNLIKELY (n > GMP_NUMB_MAX)) {

    mpz_t tmp;

    mpz_init_set_ui (tmp, n);

    mpz_bin_ui (r, tmp, k);

    mpz_clear (tmp);

#endif

  } else {

    ASSERT (n <= GMP_NUMB_MAX);

    /* Rewrite bin(n,k) as bin(n,n-k) if that is smaller. */

    k = MIN (k, n - k);

    if (k < 2) {

      PTR(r)[0] = k ? n : 1; /* 1 + ((-k) & (n-1)); */

      SIZ(r) = 1;

    } else if (n <= ODD_FACTORIAL_EXTTABLE_LIMIT) { /* k >= 2, n >= 4 */

      PTR(r)[0] = bc_bin_uiui (n, k);

      SIZ(r) = 1;

    } else if (k <= ODD_FACTORIAL_TABLE_LIMIT)

      mpz_smallk_bin_uiui (r, n, k);

    else if (BIN_UIUI_ENABLE_SMALLDC &&

	     k <= (BIN_UIUI_RECURSIVE_SMALLDC ? ODD_CENTRAL_BINOMIAL_TABLE_LIMIT : ODD_FACTORIAL_TABLE_LIMIT)* 2)

      mpz_smallkdc_bin_uiui (r, n, k);

    else if (ABOVE_THRESHOLD (k, BIN_GOETGHELUCK_THRESHOLD) &&

	     k > (n >> 4)) /* k > ODD_FACTORIAL_TABLE_LIMIT */

      mpz_goetgheluck_bin_uiui (r, n, k);

    else

      mpz_bdiv_bin_uiui (r, n, k);

  }

}