longrat.cc File Reference

#include <misc/auxiliary.h>
#include <omalloc/omalloc.h>
#include <factory/factory.h>
#include <misc/sirandom.h>
#include <reporter/reporter.h>
#include "rmodulon.h"
#include "longrat.h"
#include "shortfl.h"
#include "modulop.h"
#include <string.h>
#include <float.h>
#include <coeffs/coeffs.h>
#include <coeffs/numbers.h>
#include <coeffs/mpr_complex.h>

Go to the source code of this file.

Macros
#define	LINLINE
#define	nlTest(a, r)   nlDBTest(a,__FILE__,__LINE__, r)
#define	MAX_NUM_SIZE   28
#define	POW_2_28   (1L<<28)
#define	POW_2_28_32   (1L<<28)
#define	LONG   int
#define	LONGRAT_CC
#define	BYTES_PER_MP_LIMB   sizeof(mp_limb_t)
#define	MP_SMALL   1
#define	mpz_isNeg(A)   ((A)->_mp_size<0)
#define	mpz_limb_size(A)   ((A)->_mp_size)
#define	mpz_limb_d(A)   ((A)->_mp_d)
#define	MPZ_DIV(A, B, C)   mpz_tdiv_q((A),(B),(C))
#define	MPZ_EXACTDIV(A, B, C)   mpz_divexact((A),(B),(C))
#define	SSI_BASE   16

Functions
LINLINE BOOLEAN	nlEqual (number a, number b, const coeffs r)
LINLINE number	nlInit (long i, const coeffs r)
LINLINE BOOLEAN	nlIsOne (number a, const coeffs r)
LINLINE BOOLEAN	nlIsZero (number za, const coeffs r)
LINLINE number	nlCopy (number a, const coeffs r)
LINLINE number	nl_Copy (number a, const coeffs r)
LINLINE void	nlDelete (number *a, const coeffs r)
LINLINE number	nlNeg (number za, const coeffs r)
LINLINE number	nlAdd (number la, number li, const coeffs r)
LINLINE number	nlSub (number la, number li, const coeffs r)
LINLINE number	nlMult (number a, number b, const coeffs r)
LINLINE void	nlInpAdd (number &a, number b, const coeffs r)
LINLINE void	nlInpMult (number &a, number b, const coeffs r)
number	nlRInit (long i)
void	nlNormalize (number &x, const coeffs r)
number	nlGcd (number a, number b, const coeffs r)
number	nlExtGcd (number a, number b, number *s, number *t, const coeffs)
number	nlNormalizeHelper (number a, number b, const coeffs r)
BOOLEAN	nlGreater (number a, number b, const coeffs r)
BOOLEAN	nlIsMOne (number a, const coeffs r)
long	nlInt (number &n, const coeffs r)
number	nlBigInt (number &n)
number	nlMapGMP (number from, const coeffs src, const coeffs dst)
BOOLEAN	nlGreaterZero (number za, const coeffs r)
number	nlInvers (number a, const coeffs r)
number	nlDiv (number a, number b, const coeffs r)
number	nlExactDiv (number a, number b, const coeffs r)
number	nlIntDiv (number a, number b, const coeffs r)
number	nlIntMod (number a, number b, const coeffs r)
void	nlPower (number x, int exp, number *lu, const coeffs r)
const char *	nlRead (const char *s, number *a, const coeffs r)
void	nlWrite (number &a, const coeffs r)
number	nlGetDenom (number &n, const coeffs r)
number	nlGetNumerator (number &n, const coeffs r)
void	nlCoeffWrite (const coeffs r, BOOLEAN details)
number	nlChineseRemainder (number *x, number *q, int rl, const coeffs C)
number	nlFarey (number nN, number nP, const coeffs CF)
BOOLEAN	nlDBTest (number a, const char *f, const int l)
nMapFunc	nlSetMap (const coeffs src, const coeffs dst)
void	nlInpIntDiv (number &a, number b, const coeffs r)
BOOLEAN	nlDBTest (number a, char *f, int l, const coeffs r)
static number	nlShort3 (number x)
void	_nlDelete_NoImm (number *a)
number	nlShort3_noinline (number x)
void	mpz_mul_si (mpz_ptr r, mpz_srcptr s, long int si)
static number	nlMapP (number from, const coeffs src, const coeffs dst)
static number	nlMapLongR (number from, const coeffs src, const coeffs dst)
static number	nlMapR (number from, const coeffs src, const coeffs dst)
number	nlMapZ (number from, const coeffs src, const coeffs dst)
number	nlMapMachineInt (number from, const coeffs, const coeffs)
BOOLEAN	nlDBTest (number a, const char *f, const int l, const coeffs)
static CanonicalForm	nlConvSingNFactoryN (number n, const BOOLEAN setChar, const coeffs)
static number	nlConvFactoryNSingN (const CanonicalForm f, const coeffs r)
int	nlSize (number a, const coeffs)
number	nlBigInt (number &i, const coeffs r)
BOOLEAN	nlDivBy (number a, number b, const coeffs)
int	nlDivComp (number a, number b, const coeffs r)
number	nlGetUnit (number n, const coeffs r)
coeffs	nlQuot1 (number c, const coeffs r)
BOOLEAN	nlIsUnit (number a, const coeffs)
number	nlShort1 (number x)
number	nlModP (number q, const coeffs Q, const coeffs Zp)
void	nlGMP (number &i, number n, const coeffs r)
BOOLEAN	_nlEqual_aNoImm_OR_bNoImm (number a, number b)
number	_nlCopy_NoImm (number a)
number	_nlNeg_NoImm (number a)
number	_nlAdd_aNoImm_OR_bNoImm (number a, number b)
void	_nlInpAdd_aNoImm_OR_bNoImm (number &a, number b)
number	_nlSub_aNoImm_OR_bNoImm (number a, number b)
number	_nlMult_aImm_bImm_rNoImm (number a, number b)
number	_nlMult_aNoImm_OR_bNoImm (number a, number b)
number	nlCopyMap (number a, const coeffs src, const coeffs dst)
number	nlInit2 (int i, int j, const coeffs r)
	create a rational i/j (implicitly) over Q NOTE: make sure to use correct Q in debug mode More...
number	nlInit2gmp (mpz_t i, mpz_t j, const coeffs r)
	create a rational i/j (implicitly) over Q NOTE: make sure to use correct Q in debug mode More...
static void	nlMPZ (mpz_t m, number &n, const coeffs r)
static number	nlInitMPZ (mpz_t m, const coeffs)
void	nlInpGcd (number &a, number b, const coeffs r)
number	nlChineseRemainderSym (number *x, number *q, int rl, BOOLEAN sym, const coeffs CF)
static void	nlClearContent (ICoeffsEnumerator &numberCollectionEnumerator, number &c, const coeffs cf)
static void	nlClearDenominators (ICoeffsEnumerator &numberCollectionEnumerator, number &c, const coeffs cf)
char *	nlCoeffName (const coeffs r)
static char *	nlCoeffString (const coeffs r)
static void	nlWriteFd (number n, FILE *f, const coeffs)
static number	nlReadFd (s_buff f, const coeffs)
BOOLEAN	nlCoeffIsEqual (const coeffs r, n_coeffType n, void *p)
static number	nlLcm (number a, number b, const coeffs r)
static number	nlRandom (siRandProc p, number v2, number, const coeffs cf)
BOOLEAN	nlInitChar (coeffs r, void *p)

Macro Definition Documentation

#define BYTES_PER_MP_LIMB   sizeof(mp_limb_t)

Definition at line 147 of file longrat.cc.

#define LINLINE

Definition at line 25 of file longrat.cc.

#define LONG   int

Definition at line 107 of file longrat.cc.

#define LONGRAT_CC

Definition at line 134 of file longrat.cc.

#define MAX_NUM_SIZE   28

Definition at line 104 of file longrat.cc.

#define MP_SMALL   1

Definition at line 155 of file longrat.cc.

#define MPZ_DIV	(		A,
			B,
			C
	)		mpz_tdiv_q((A),(B),(C))

Definition at line 160 of file longrat.cc.

#define MPZ_EXACTDIV	(		A,
			B,
			C
	)		mpz_divexact((A),(B),(C))

Definition at line 161 of file longrat.cc.

#define mpz_isNeg

(

A

)

((A)->_mp_size<0)

Definition at line 157 of file longrat.cc.

#define mpz_limb_d

(

A

)

((A)->_mp_d)

Definition at line 159 of file longrat.cc.

#define mpz_limb_size

(

A

)

((A)->_mp_size)

Definition at line 158 of file longrat.cc.

#define nlTest	(		a,
			r
	)		nlDBTest(a,__FILE__,__LINE__, r)

Definition at line 89 of file longrat.cc.

#define POW_2_28   (1L<<28)

Definition at line 105 of file longrat.cc.

#define POW_2_28_32   (1L<<28)

Definition at line 106 of file longrat.cc.

#define SSI_BASE   16

Definition at line 2975 of file longrat.cc.

Function Documentation

number _nlAdd_aNoImm_OR_bNoImm	(	number	a,
		number	b
	)

Definition at line 1576 of file longrat.cc.

{
  number u=ALLOC_RNUMBER();
#if defined(LDEBUG)
  u->debug=123456;
#endif
  mpz_init(u->z);
  if (SR_HDL(b) & SR_INT)
  {
    number x=a;
    a=b;
    b=x;
  }
  if (SR_HDL(a) & SR_INT)
  {
    switch (b->s)
    {
      case 0:
      case 1:/* a:short, b:1 */
      {
        mpz_t x;
        mpz_init(x);
        mpz_mul_si(x,b->n,SR_TO_INT(a));
        mpz_add(u->z,b->z,x);
        mpz_clear(x);
        if (mpz_cmp_ui(u->z,(long)0)==0)
        {
          mpz_clear(u->z);
          FREE_RNUMBER(u);
          return INT_TO_SR(0);
        }
        if (mpz_cmp(u->z,b->n)==0)
        {
          mpz_clear(u->z);
          FREE_RNUMBER(u);
          return INT_TO_SR(1);
        }
        mpz_init_set(u->n,b->n);
        u->s = 0;
        break;
      }
      case 3:
      {
        if ((long)a>0L)
          mpz_add_ui(u->z,b->z,SR_TO_INT(a));
        else
          mpz_sub_ui(u->z,b->z,-SR_TO_INT(a));
        if (mpz_cmp_ui(u->z,(long)0)==0)
        {
          mpz_clear(u->z);
          FREE_RNUMBER(u);
          return INT_TO_SR(0);
        }
        u->s = 3;
        u=nlShort3(u);
        break;
      }
    }
  }
  else
  {
    switch (a->s)
    {
      case 0:
      case 1:
      {
        switch(b->s)
        {
          case 0:
          case 1:
          {
            mpz_t x;
            mpz_init(x);

            mpz_mul(x,b->z,a->n);
            mpz_mul(u->z,a->z,b->n);
            mpz_add(u->z,u->z,x);
            mpz_clear(x);

            if (mpz_cmp_ui(u->z,(long)0)==0)
            {
              mpz_clear(u->z);
              FREE_RNUMBER(u);
              return INT_TO_SR(0);
            }
            mpz_init(u->n);
            mpz_mul(u->n,a->n,b->n);
            if (mpz_cmp(u->z,u->n)==0)
            {
               mpz_clear(u->z);
               mpz_clear(u->n);
               FREE_RNUMBER(u);
               return INT_TO_SR(1);
            }
            u->s = 0;
            break;
          }
          case 3: /* a:1 b:3 */
          {
            mpz_mul(u->z,b->z,a->n);
            mpz_add(u->z,u->z,a->z);
            if (mpz_cmp_ui(u->z,(long)0)==0)
            {
              mpz_clear(u->z);
              FREE_RNUMBER(u);
              return INT_TO_SR(0);
            }
            if (mpz_cmp(u->z,a->n)==0)
            {
              mpz_clear(u->z);
              FREE_RNUMBER(u);
              return INT_TO_SR(1);
            }
            mpz_init_set(u->n,a->n);
            u->s = 0;
            break;
          }
        } /*switch (b->s) */
        break;
      }
      case 3:
      {
        switch(b->s)
        {
          case 0:
          case 1:/* a:3, b:1 */
          {
            mpz_mul(u->z,a->z,b->n);
            mpz_add(u->z,u->z,b->z);
            if (mpz_cmp_ui(u->z,(long)0)==0)
            {
              mpz_clear(u->z);
              FREE_RNUMBER(u);
              return INT_TO_SR(0);
            }
            if (mpz_cmp(u->z,b->n)==0)
            {
              mpz_clear(u->z);
              FREE_RNUMBER(u);
              return INT_TO_SR(1);
            }
            mpz_init_set(u->n,b->n);
            u->s = 0;
            break;
          }
          case 3:
          {
            mpz_add(u->z,a->z,b->z);
            if (mpz_cmp_ui(u->z,(long)0)==0)
            {
              mpz_clear(u->z);
              FREE_RNUMBER(u);
              return INT_TO_SR(0);
            }
            u->s = 3;
            u=nlShort3(u);
            break;
          }
        }
        break;
      }
    }
  }
  return u;
}

number _nlCopy_NoImm

(

number

a

)

Definition at line 1525 of file longrat.cc.

{
  assume(!((SR_HDL(a) & SR_INT)||(a==NULL)));
  //nlTest(a, r);
  number b=ALLOC_RNUMBER();
#if defined(LDEBUG)
  b->debug=123456;
#endif
  switch (a->s)
  {
    case 0:
    case 1:
            mpz_init_set(b->n,a->n);
    case 3:
            mpz_init_set(b->z,a->z);
            break;
  }
  b->s = a->s;
  return b;
}

void _nlDelete_NoImm

(

number *

a

)

Definition at line 1546 of file longrat.cc.

{
  {
    switch ((*a)->s)
    {
      case 0:
      case 1:
        mpz_clear((*a)->n);
      case 3:
        mpz_clear((*a)->z);
#ifdef LDEBUG
        (*a)->s=2;
#endif
    }
    FREE_RNUMBER(*a); // omFreeBin((void *) *a, rnumber_bin);
  }
}

BOOLEAN _nlEqual_aNoImm_OR_bNoImm	(	number	a,
		number	b
	)

Definition at line 1478 of file longrat.cc.

{
  assume(! (SR_HDL(a) & SR_HDL(b) & SR_INT));
//  long - short
  BOOLEAN bo;
  if (SR_HDL(b) & SR_INT)
  {
    if (a->s!=0) return FALSE;
    number n=b; b=a; a=n;
  }
//  short - long
  if (SR_HDL(a) & SR_INT)
  {
    if (b->s!=0)
      return FALSE;
    if (((long)a > 0L) && (mpz_isNeg(b->z)))
      return FALSE;
    if (((long)a < 0L) && (!mpz_isNeg(b->z)))
      return FALSE;
    mpz_t  bb;
    mpz_init_set(bb,b->n);
    mpz_mul_si(bb,bb,(long)SR_TO_INT(a));
    bo=(mpz_cmp(bb,b->z)==0);
    mpz_clear(bb);
    return bo;
  }
// long - long
  if (((a->s==1) && (b->s==3))
  ||  ((b->s==1) && (a->s==3)))
    return FALSE;
  if (mpz_isNeg(a->z)&&(!mpz_isNeg(b->z)))
    return FALSE;
  if (mpz_isNeg(b->z)&&(!mpz_isNeg(a->z)))
    return FALSE;
  mpz_t  aa;
  mpz_t  bb;
  mpz_init_set(aa,a->z);
  mpz_init_set(bb,b->z);
  if (a->s<2) mpz_mul(bb,bb,a->n);
  if (b->s<2) mpz_mul(aa,aa,b->n);
  bo=(mpz_cmp(aa,bb)==0);
  mpz_clear(aa);
  mpz_clear(bb);
  return bo;
}

void _nlInpAdd_aNoImm_OR_bNoImm	(	number &	a,
		number	b
	)

Definition at line 1742 of file longrat.cc.

{
  if (SR_HDL(b) & SR_INT)
  {
    switch (a->s)
    {
      case 0:
      case 1:/* b:short, a:1 */
      {
        mpz_t x;
        mpz_init(x);
        mpz_mul_si(x,a->n,SR_TO_INT(b));
        mpz_add(a->z,a->z,x);
        mpz_clear(x);
        a->s = 0;
        a=nlShort1(a);
        break;
      }
      case 3:
      {
        if ((long)b>0L)
          mpz_add_ui(a->z,a->z,SR_TO_INT(b));
        else
          mpz_sub_ui(a->z,a->z,-SR_TO_INT(b));
        a->s = 3;
        a=nlShort3_noinline(a);
        break;
      }
    }
    return;
  }
  else if (SR_HDL(a) & SR_INT)
  {
    number u=ALLOC_RNUMBER();
    #if defined(LDEBUG)
    u->debug=123456;
    #endif
    mpz_init(u->z);
    switch (b->s)
    {
      case 0:
      case 1:/* a:short, b:1 */
      {
        mpz_t x;
        mpz_init(x);

        mpz_mul_si(x,b->n,SR_TO_INT(a));
        mpz_add(u->z,b->z,x);
        mpz_clear(x);
        // result cannot be 0, if coeffs are normalized
        mpz_init_set(u->n,b->n);
        u->s = 0;
        u=nlShort1(u);
        break;
      }
      case 3:
      {
        if ((long)a>0L)
          mpz_add_ui(u->z,b->z,SR_TO_INT(a));
        else
          mpz_sub_ui(u->z,b->z,-SR_TO_INT(a));
        // result cannot be 0, if coeffs are normalized
        u->s = 3;
        u=nlShort3_noinline(u);
        break;
      }
    }
    a=u;
  }
  else
  {
    switch (a->s)
    {
      case 0:
      case 1:
      {
        switch(b->s)
        {
          case 0:
          case 1: /* a:1 b:1 */
          {
            mpz_t x;
            mpz_t y;
            mpz_init(x);
            mpz_init(y);
            mpz_mul(x,b->z,a->n);
            mpz_mul(y,a->z,b->n);
            mpz_add(a->z,x,y);
            mpz_clear(x);
            mpz_clear(y);
            mpz_mul(a->n,a->n,b->n);
            a->s = 0;
            break;
          }
          case 3: /* a:1 b:3 */
          {
            mpz_t x;
            mpz_init(x);
            mpz_mul(x,b->z,a->n);
            mpz_add(a->z,a->z,x);
            mpz_clear(x);
            a->s = 0;
            break;
          }
        } /*switch (b->s) */
        a=nlShort1(a);
        break;
      }
      case 3:
      {
        switch(b->s)
        {
          case 0:
          case 1:/* a:3, b:1 */
          {
            mpz_t x;
            mpz_init(x);
            mpz_mul(x,a->z,b->n);
            mpz_add(a->z,b->z,x);
            mpz_clear(x);
            mpz_init_set(a->n,b->n);
            a->s = 0;
            a=nlShort1(a);
            break;
          }
          case 3:
          {
            mpz_add(a->z,a->z,b->z);
            a->s = 3;
            a=nlShort3_noinline(a);
            break;
          }
        }
        break;
      }
    }
  }
}

number _nlMult_aImm_bImm_rNoImm	(	number	a,
		number	b
	)

Definition at line 2105 of file longrat.cc.

{
  number u=ALLOC_RNUMBER();
#if defined(LDEBUG)
  u->debug=123456;
#endif
  u->s=3;
  mpz_init_set_si(u->z,SR_TO_INT(a));
  mpz_mul_si(u->z,u->z,SR_TO_INT(b));
  return u;
}

number _nlMult_aNoImm_OR_bNoImm	(	number	a,
		number	b
	)

Definition at line 2118 of file longrat.cc.

{
  assume(! (SR_HDL(a) & SR_HDL(b) & SR_INT));
  number u=ALLOC_RNUMBER();
#if defined(LDEBUG)
  u->debug=123456;
#endif
  mpz_init(u->z);
  if (SR_HDL(b) & SR_INT)
  {
    number x=a;
    a=b;
    b=x;
  }
  if (SR_HDL(a) & SR_INT)
  {
    u->s=b->s;
    if (u->s==1) u->s=0;
    if ((long)a>0L)
    {
      mpz_mul_ui(u->z,b->z,(unsigned long)SR_TO_INT(a));
    }
    else
    {
      if (a==INT_TO_SR(-1))
      {
        mpz_set(u->z,b->z);
        mpz_neg(u->z,u->z);
        u->s=b->s;
      }
      else
      {
        mpz_mul_ui(u->z,b->z,(unsigned long)-SR_TO_INT(a));
        mpz_neg(u->z,u->z);
      }
    }
    if (u->s<2)
    {
      if (mpz_cmp(u->z,b->n)==0)
      {
        mpz_clear(u->z);
        FREE_RNUMBER(u);
        return INT_TO_SR(1);
      }
      mpz_init_set(u->n,b->n);
    }
    else //u->s==3
    {
      u=nlShort3(u);
    }
  }
  else
  {
    mpz_mul(u->z,a->z,b->z);
    u->s = 0;
    if(a->s==3)
    {
      if(b->s==3)
      {
        u->s = 3;
      }
      else
      {
        if (mpz_cmp(u->z,b->n)==0)
        {
          mpz_clear(u->z);
          FREE_RNUMBER(u);
          return INT_TO_SR(1);
        }
        mpz_init_set(u->n,b->n);
      }
    }
    else
    {
      if(b->s==3)
      {
        if (mpz_cmp(u->z,a->n)==0)
        {
          mpz_clear(u->z);
          FREE_RNUMBER(u);
          return INT_TO_SR(1);
        }
        mpz_init_set(u->n,a->n);
      }
      else
      {
        mpz_init(u->n);
        mpz_mul(u->n,a->n,b->n);
        if (mpz_cmp(u->z,u->n)==0)
        {
          mpz_clear(u->z);
          mpz_clear(u->n);
          FREE_RNUMBER(u);
          return INT_TO_SR(1);
        }
      }
    }
  }
  return u;
}

number _nlNeg_NoImm

(

number

a

)

Definition at line 1564 of file longrat.cc.

{
  {
    mpz_neg(a->z,a->z);
    if (a->s==3)
    {
      a=nlShort3(a);
    }
  }
  return a;
}

number _nlSub_aNoImm_OR_bNoImm	(	number	a,
		number	b
	)

Definition at line 1881 of file longrat.cc.

{
  number u=ALLOC_RNUMBER();
#if defined(LDEBUG)
  u->debug=123456;
#endif
  mpz_init(u->z);
  if (SR_HDL(a) & SR_INT)
  {
    switch (b->s)
    {
      case 0:
      case 1:/* a:short, b:1 */
      {
        mpz_t x;
        mpz_init(x);
        mpz_mul_si(x,b->n,SR_TO_INT(a));
        mpz_sub(u->z,x,b->z);
        mpz_clear(x);
        if (mpz_cmp_ui(u->z,(long)0)==0)
        {
          mpz_clear(u->z);
          FREE_RNUMBER(u);
          return INT_TO_SR(0);
        }
        if (mpz_cmp(u->z,b->n)==0)
        {
          mpz_clear(u->z);
          FREE_RNUMBER(u);
          return INT_TO_SR(1);
        }
        mpz_init_set(u->n,b->n);
        u->s = 0;
        break;
      }
      case 3:
      {
        if ((long)a>0L)
        {
          mpz_sub_ui(u->z,b->z,SR_TO_INT(a));
          mpz_neg(u->z,u->z);
        }
        else
        {
          mpz_add_ui(u->z,b->z,-SR_TO_INT(a));
          mpz_neg(u->z,u->z);
        }
        if (mpz_cmp_ui(u->z,(long)0)==0)
        {
          mpz_clear(u->z);
          FREE_RNUMBER(u);
          return INT_TO_SR(0);
        }
        u->s = 3;
        u=nlShort3(u);
        break;
      }
    }
  }
  else if (SR_HDL(b) & SR_INT)
  {
    switch (a->s)
    {
      case 0:
      case 1:/* b:short, a:1 */
      {
        mpz_t x;
        mpz_init(x);
        mpz_mul_si(x,a->n,SR_TO_INT(b));
        mpz_sub(u->z,a->z,x);
        mpz_clear(x);
        if (mpz_cmp_ui(u->z,(long)0)==0)
        {
          mpz_clear(u->z);
          FREE_RNUMBER(u);
          return INT_TO_SR(0);
        }
        if (mpz_cmp(u->z,a->n)==0)
        {
          mpz_clear(u->z);
          FREE_RNUMBER(u);
          return INT_TO_SR(1);
        }
        mpz_init_set(u->n,a->n);
        u->s = 0;
        break;
      }
      case 3:
      {
        if ((long)b>0L)
        {
          mpz_sub_ui(u->z,a->z,SR_TO_INT(b));
        }
        else
        {
          mpz_add_ui(u->z,a->z,-SR_TO_INT(b));
        }
        if (mpz_cmp_ui(u->z,(long)0)==0)
        {
          mpz_clear(u->z);
          FREE_RNUMBER(u);
          return INT_TO_SR(0);
        }
        u->s = 3;
        u=nlShort3(u);
        break;
      }
    }
  }
  else
  {
    switch (a->s)
    {
      case 0:
      case 1:
      {
        switch(b->s)
        {
          case 0:
          case 1:
          {
            mpz_t x;
            mpz_t y;
            mpz_init(x);
            mpz_init(y);
            mpz_mul(x,b->z,a->n);
            mpz_mul(y,a->z,b->n);
            mpz_sub(u->z,y,x);
            mpz_clear(x);
            mpz_clear(y);
            if (mpz_cmp_ui(u->z,(long)0)==0)
            {
              mpz_clear(u->z);
              FREE_RNUMBER(u);
              return INT_TO_SR(0);
            }
            mpz_init(u->n);
            mpz_mul(u->n,a->n,b->n);
            if (mpz_cmp(u->z,u->n)==0)
            {
              mpz_clear(u->z);
              mpz_clear(u->n);
              FREE_RNUMBER(u);
              return INT_TO_SR(1);
            }
            u->s = 0;
            break;
          }
          case 3: /* a:1, b:3 */
          {
            mpz_t x;
            mpz_init(x);
            mpz_mul(x,b->z,a->n);
            mpz_sub(u->z,a->z,x);
            mpz_clear(x);
            if (mpz_cmp_ui(u->z,(long)0)==0)
            {
              mpz_clear(u->z);
              FREE_RNUMBER(u);
              return INT_TO_SR(0);
            }
            if (mpz_cmp(u->z,a->n)==0)
            {
              mpz_clear(u->z);
              FREE_RNUMBER(u);
              return INT_TO_SR(1);
            }
            mpz_init_set(u->n,a->n);
            u->s = 0;
            break;
          }
        }
        break;
      }
      case 3:
      {
        switch(b->s)
        {
          case 0:
          case 1: /* a:3, b:1 */
          {
            mpz_t x;
            mpz_init(x);
            mpz_mul(x,a->z,b->n);
            mpz_sub(u->z,x,b->z);
            mpz_clear(x);
            if (mpz_cmp_ui(u->z,(long)0)==0)
            {
              mpz_clear(u->z);
              FREE_RNUMBER(u);
              return INT_TO_SR(0);
            }
            if (mpz_cmp(u->z,b->n)==0)
            {
              mpz_clear(u->z);
              FREE_RNUMBER(u);
              return INT_TO_SR(1);
            }
            mpz_init_set(u->n,b->n);
            u->s = 0;
            break;
          }
          case 3: /* a:3 , b:3 */
          {
            mpz_sub(u->z,a->z,b->z);
            if (mpz_cmp_ui(u->z,(long)0)==0)
            {
              mpz_clear(u->z);
              FREE_RNUMBER(u);
              return INT_TO_SR(0);
            }
            u->s = 3;
            u=nlShort3(u);
            break;
          }
        }
        break;
      }
    }
  }
  return u;
}

void mpz_mul_si	(	mpz_ptr	r,
		mpz_srcptr	s,
		long int	si
	)

Definition at line 179 of file longrat.cc.

{
  if (si>=0)
    mpz_mul_ui(r,s,si);
  else
  {
    mpz_mul_ui(r,s,-si);
    mpz_neg(r,r);
  }
}

LINLINE number nl_Copy	(	number	a,
		const coeffs	r
	)

LINLINE number nlAdd	(	number	la,
		number	li,
		const coeffs	r
	)

Definition at line 2439 of file longrat.cc.

{
  if (SR_HDL(a) & SR_HDL(b) & SR_INT)
  {
    LONG r=SR_HDL(a)+SR_HDL(b)-1L;
    if ( ((r << 1) >> 1) == r )
      return (number)(long)r;
    else
      return nlRInit(SR_TO_INT(r));
  }
  number u =  _nlAdd_aNoImm_OR_bNoImm(a, b);
  nlTest(u, R);
  return u;
}

number nlBigInt

(

number &

n

)

number nlBigInt	(	number &	i,
		const coeffs	r
	)

Definition at line 636 of file longrat.cc.

{
  nlTest(i, r);
  nlNormalize(i,r);
  if (SR_HDL(i) & SR_INT) return (i);
  if (i->s==3)
  {
    return nlCopy(i,r);
  }
  number tmp=nlRInit(1);
  MPZ_DIV(tmp->z,i->z,i->n);
  tmp=nlShort3(tmp);
  return tmp;
}

number nlChineseRemainder	(	number *	x,
		number *	q,
		int	rl,
		const coeffs	C
	)

Definition at line 2772 of file longrat.cc.

{
  return nlChineseRemainderSym(x,q,rl,TRUE,C);
}

number nlChineseRemainderSym	(	number *	x,
		number *	q,
		int	rl,
		BOOLEAN	sym,
		const coeffs	CF
	)

Definition at line 2741 of file longrat.cc.

{
  setCharacteristic( 0 ); // only in char 0
  Off(SW_RATIONAL);
  CFArray X(rl), Q(rl);
  int i;
  for(i=rl-1;i>=0;i--)
  {
    X[i]=CF->convSingNFactoryN(x[i],FALSE,CF); // may be larger MAX_INT
    Q[i]=CF->convSingNFactoryN(q[i],FALSE,CF); // may be larger MAX_INT
  }
  CanonicalForm xnew,qnew;
  chineseRemainder(X,Q,xnew,qnew);
  number n=CF->convFactoryNSingN(xnew,CF);
  if (sym)
  {
    number p=CF->convFactoryNSingN(qnew,CF);
    number p2=nlIntDiv(p,nlInit(2, CF),CF);
    if (nlGreater(n,p2,CF))
    {
       number n2=nlSub(n,p,CF);
       nlDelete(&n,CF);
       n=n2;
    }
    nlDelete(&p2,CF);
    nlDelete(&p,CF);
  }
  nlNormalize(n,CF);
  return n;
}

static void nlClearContent ( ICoeffsEnumerator &  numberCollectionEnumerator, number &  c, const coeffs  cf  )

static

Definition at line 2777 of file longrat.cc.

{
  assume(cf != NULL);

  numberCollectionEnumerator.Reset();

  if( !numberCollectionEnumerator.MoveNext() ) // empty zero polynomial?
  {
    c = nlInit(1, cf);
    return;
  }

  // all coeffs are given by integers!!!

  // part 1, find a small candidate for gcd
  number cand1,cand;
  int s1,s;
  s=2147483647; // max. int

  const BOOLEAN lc_is_pos=nlGreaterZero(numberCollectionEnumerator.Current(),cf);

  int normalcount = 0;
  do
  {
    number& n = numberCollectionEnumerator.Current();
    nlNormalize(n, cf); ++normalcount;
    cand1 = n;

    if (SR_HDL(cand1)&SR_INT) { cand=cand1; break; }
    assume(cand1->s==3); // all coeffs should be integers // ==0?!! after printing
    s1=mpz_size1(cand1->z);
    if (s>s1)
    {
      cand=cand1;
      s=s1;
    }
  } while (numberCollectionEnumerator.MoveNext() );

//  assume( nlGreaterZero(cand,cf) ); // cand may be a negative integer!

  cand=nlCopy(cand,cf);
  // part 2: compute gcd(cand,all coeffs)

  numberCollectionEnumerator.Reset();

  while (numberCollectionEnumerator.MoveNext() )
  {
    number& n = numberCollectionEnumerator.Current();

    if( (--normalcount) <= 0)
      nlNormalize(n, cf);

    nlInpGcd(cand, n, cf);
    assume( nlGreaterZero(cand,cf) );

    if(nlIsOne(cand,cf))
    {
      c = cand;

      if(!lc_is_pos)
      {
        // make the leading coeff positive
        c = nlNeg(c, cf);
        numberCollectionEnumerator.Reset();

        while (numberCollectionEnumerator.MoveNext() )
        {
          number& nn = numberCollectionEnumerator.Current();
          nn = nlNeg(nn, cf);
        }
      }
      return;
    }
  }

  // part3: all coeffs = all coeffs / cand
  if (!lc_is_pos)
    cand = nlNeg(cand,cf);

  c = cand;
  numberCollectionEnumerator.Reset();

  while (numberCollectionEnumerator.MoveNext() )
  {
    number& n = numberCollectionEnumerator.Current();
    number t=nlIntDiv(n, cand, cf); // simple integer exact division, no ratios to remain
    nlDelete(&n, cf);
    n = t;
  }
}

static void nlClearDenominators ( ICoeffsEnumerator &  numberCollectionEnumerator, number &  c, const coeffs  cf  )

static

Definition at line 2868 of file longrat.cc.

{
  assume(cf != NULL);

  numberCollectionEnumerator.Reset();

  if( !numberCollectionEnumerator.MoveNext() ) // empty zero polynomial?
  {
    c = nlInit(1, cf);
//    assume( n_GreaterZero(c, cf) );
    return;
  }

  // all coeffs are given by integers after returning from this routine

  // part 1, collect product of all denominators /gcds
  number cand;
  cand=ALLOC_RNUMBER();
#if defined(LDEBUG)
  cand->debug=123456;
#endif
  cand->s=3;

  int s=0;

  const BOOLEAN lc_is_pos=nlGreaterZero(numberCollectionEnumerator.Current(),cf);

  do
  {
    number& cand1 = numberCollectionEnumerator.Current();

    if (!(SR_HDL(cand1)&SR_INT))
    {
      nlNormalize(cand1, cf);
      if ((!(SR_HDL(cand1)&SR_INT)) // not a short int
      && (cand1->s==1))             // and is a normalised rational
      {
        if (s==0) // first denom, we meet
        {
          mpz_init_set(cand->z, cand1->n); // cand->z = cand1->n
          s=1;
        }
        else // we have already something
        {
          mpz_lcm(cand->z, cand->z, cand1->n);
        }
      }
    }
  }
  while (numberCollectionEnumerator.MoveNext() );


  if (s==0) // nothing to do, all coeffs are already integers
  {
//    mpz_clear(tmp);
    FREE_RNUMBER(cand);
    if (lc_is_pos)
      c=nlInit(1,cf);
    else
    {
      // make the leading coeff positive
      c=nlInit(-1,cf);

      // TODO: incorporate the following into the loop below?
      numberCollectionEnumerator.Reset();
      while (numberCollectionEnumerator.MoveNext() )
      {
        number& n = numberCollectionEnumerator.Current();
        n = nlNeg(n, cf);
      }
    }
//    assume( n_GreaterZero(c, cf) );
    return;
  }

  cand = nlShort3(cand);

  // part2: all coeffs = all coeffs * cand
  // make the lead coeff positive
  numberCollectionEnumerator.Reset();

  if (!lc_is_pos)
    cand = nlNeg(cand, cf);

  c = cand;

  while (numberCollectionEnumerator.MoveNext() )
  {
    number &n = numberCollectionEnumerator.Current();
    nlInpMult(n, cand, cf);
  }

}

BOOLEAN nlCoeffIsEqual	(	const coeffs	r,
		n_coeffType	n,
		void *	p
	)

Definition at line 3085 of file longrat.cc.

{
  /* test, if r is an instance of nInitCoeffs(n,parameter) */
  /* if parameter is not needed */
  if (n==r->type)
  {
    if ((p==NULL)&&(r->cfDiv==nlDiv)) return TRUE;
    if ((p!=NULL)&&(r->cfDiv!=nlDiv)) return TRUE;
  }
  return FALSE;
}

char* nlCoeffName

(

const coeffs

r

)

Definition at line 2962 of file longrat.cc.

{
  if (r->cfDiv==nlDiv) return (char*)"QQ";
  else                 return (char*)"ZZ";
}

static char* nlCoeffString ( const coeffs  r )

static

Definition at line 2968 of file longrat.cc.

{
  //return omStrDup(nlCoeffName(r));
  if (r->cfDiv==nlDiv) return omStrDup("0");
  else                 return omStrDup("integer");
}

void nlCoeffWrite	(	const coeffs	r,
		BOOLEAN	details
	)

Definition at line 2733 of file longrat.cc.

{
  if (r->is_field)
  PrintS("//   characteristic : 0\n");
  else
  PrintS("//   coeff. ring is : Integers\n");
}

static number nlConvFactoryNSingN ( const CanonicalForm  f, const coeffs  r  )

static

Definition at line 378 of file longrat.cc.

{
  if (f.isImm())
  {
    return nlInit(f.intval(),r);
  }
  else
  {
    number z = ALLOC_RNUMBER(); //Q!? // (number)omAllocBin(rnumber_bin);
#if defined(LDEBUG)
    z->debug=123456;
#endif
    gmp_numerator( f, z->z );
    if ( f.den().isOne() )
      z->s = 3;
    else
    {
      gmp_denominator( f, z->n );
      z->s = 0;
    }
    nlNormalize(z,r);
    return z;
  }
}

static CanonicalForm nlConvSingNFactoryN ( number  n, const BOOLEAN  setChar, const coeffs    )

static

Definition at line 340 of file longrat.cc.

{
  if (setChar) setCharacteristic( 0 );

  CanonicalForm term;
  if ( SR_HDL(n) & SR_INT )
  {
    long nn=SR_TO_INT(n);
    term = nn;
  }
  else
  {
    if ( n->s == 3 )
    {
      mpz_t dummy;
      long lz=mpz_get_si(n->z);
      if (mpz_cmp_si(n->z,lz)==0) term=lz;
      else
      {
        mpz_init_set( dummy,n->z );
        term = make_cf( dummy );
      }
    }
    else
    {
      // assume s==0 or s==1
      mpz_t num, den;
      On(SW_RATIONAL);
      mpz_init_set( num, n->z );
      mpz_init_set( den, n->n );
      term = make_cf( num, den, ( n->s != 1 ));
    }
  }
  return term;
}

LINLINE number nlCopy	(	number	a,
		const coeffs	r
	)

Definition at line 2391 of file longrat.cc.

{
  if ((SR_HDL(a) & SR_INT)||(a==NULL))
  {
    return a;
  }
  return _nlCopy_NoImm(a);
}

number nlCopyMap	(	number	a,
		const coeffs	src,
		const coeffs	dst
	)

Definition at line 2222 of file longrat.cc.

{
  if ((SR_HDL(a) & SR_INT)||(a==NULL))
  {
    return a;
  }
  return _nlCopy_NoImm(a);
}

BOOLEAN nlDBTest	(	number	a,
		const char *	f,
		const int	l
	)

BOOLEAN nlDBTest	(	number	a,
		char *	f,
		int	l,
		const coeffs	r
	)

BOOLEAN nlDBTest	(	number	a,
		const char *	f,
		const int	l,
		const coeffs
	)

Definition at line 248 of file longrat.cc.

{
  if (a==NULL)
  {
    Print("!!longrat: NULL in %s:%d\n",f,l);
    return FALSE;
  }
  //if ((int)a==1) Print("!! 0x1 as number ? %s %d\n",f,l);
  if ((((long)a)&3L)==3L)
  {
    Print(" !!longrat:ptr(3) in %s:%d\n",f,l);
    return FALSE;
  }
  if ((((long)a)&3L)==1L)
  {
    if (((((LONG)(long)a)<<1)>>1)!=((LONG)(long)a))
    {
      Print(" !!longrat:arith:%lx in %s:%d\n",(long)a, f,l);
      return FALSE;
    }
    return TRUE;
  }
  /* TODO: If next line is active, then computations in algebraic field
           extensions over Q will throw a lot of assume violations although
           everything is computed correctly and no seg fault appears.
           Maybe the test is not appropriate in this case. */
  omCheckIf(omCheckAddrSize(a,sizeof(*a)), return FALSE);
  if (a->debug!=123456)
  {
    Print("!!longrat:debug:%d in %s:%d\n",a->debug,f,l);
    a->debug=123456;
    return FALSE;
  }
  if ((a->s<0)||(a->s>4))
  {
    Print("!!longrat:s=%d in %s:%d\n",a->s,f,l);
    return FALSE;
  }
  /* TODO: If next line is active, then computations in algebraic field
           extensions over Q will throw a lot of assume violations although
           everything is computed correctly and no seg fault appears.
           Maybe the test is not appropriate in this case. */
  //omCheckAddrSize(a->z[0]._mp_d,a->z[0]._mp_alloc*BYTES_PER_MP_LIMB);
  if (a->z[0]._mp_alloc==0)
    Print("!!longrat:z->alloc=0 in %s:%d\n",f,l);

  if (a->s<2)
  {
    if ((a->n[0]._mp_d[0]==0)&&(a->n[0]._mp_alloc<=1))
    {
      Print("!!longrat: n==0 in %s:%d\n",f,l);
      return FALSE;
    }
    /* TODO: If next line is active, then computations in algebraic field
             extensions over Q will throw a lot of assume violations although
             everything is computed correctly and no seg fault appears.
             Maybe the test is not appropriate in this case. */
    //omCheckIf(omCheckAddrSize(a->n[0]._mp_d,a->n[0]._mp_alloc*BYTES_PER_MP_LIMB), return FALSE);
    if (a->z[0]._mp_alloc==0)
      Print("!!longrat:n->alloc=0 in %s:%d\n",f,l);
    if ((mpz_size1(a->n) ==1) && (mpz_cmp_si(a->n,(long)1)==0))
    {
      Print("!!longrat:integer as rational in %s:%d\n",f,l);
      mpz_clear(a->n); a->s=3;
      return FALSE;
    }
    else if (mpz_isNeg(a->n))
    {
      Print("!!longrat:div. by negative in %s:%d\n",f,l);
      mpz_neg(a->z,a->z);
      mpz_neg(a->n,a->n);
      return FALSE;
    }
    return TRUE;
  }
  //if (a->s==2)
  //{
  //  Print("!!longrat:s=2 in %s:%d\n",f,l);
  //  return FALSE;
  //}
  if (mpz_size1(a->z)>MP_SMALL) return TRUE;
  LONG ui=(LONG)mpz_get_si(a->z);
  if ((((ui<<3)>>3)==ui)
  && (mpz_cmp_si(a->z,(long)ui)==0))
  {
    Print("!!longrat:im int %d in %s:%d\n",ui,f,l);
    return FALSE;
  }
  return TRUE;
}

LINLINE void nlDelete	(	number *	a,
		const coeffs	r
	)

Definition at line 2404 of file longrat.cc.

{
  if (*a!=NULL)
  {
    nlTest(*a, r);
    if ((SR_HDL(*a) & SR_INT)==0)
    {
      _nlDelete_NoImm(a);
    }
    *a=NULL;
  }
}

number nlDiv	(	number	a,
		number	b,
		const coeffs	r
	)

Definition at line 965 of file longrat.cc.

{
  if (nlIsZero(b,r))
  {
    WerrorS(nDivBy0);
    return INT_TO_SR(0);
  }
  number u;
// ---------- short / short ------------------------------------
  if (SR_HDL(a) & SR_HDL(b) & SR_INT)
  {
    LONG i=SR_TO_INT(a);
    LONG j=SR_TO_INT(b);
    if (j==1L) return a;
    if ((i==-POW_2_28) && (j== -1L))
    {
      return nlRInit(POW_2_28);
    }
    LONG r=i%j;
    if (r==0)
    {
      return INT_TO_SR(i/j);
    }
    u=ALLOC_RNUMBER();
    u->s=0;
    #if defined(LDEBUG)
    u->debug=123456;
    #endif
    mpz_init_set_si(u->z,(long)i);
    mpz_init_set_si(u->n,(long)j);
  }
  else
  {
    u=ALLOC_RNUMBER();
    u->s=0;
    #if defined(LDEBUG)
    u->debug=123456;
    #endif
    mpz_init(u->z);
// ---------- short / long ------------------------------------
    if (SR_HDL(a) & SR_INT)
    {
      // short a / (z/n) -> (a*n)/z
      if (b->s<2)
      {
        mpz_mul_si(u->z,b->n,SR_TO_INT(a));
      }
      else
      // short a / long z -> a/z
      {
        mpz_set_si(u->z,SR_TO_INT(a));
      }
      if (mpz_cmp(u->z,b->z)==0)
      {
        mpz_clear(u->z);
        FREE_RNUMBER(u);
        return INT_TO_SR(1);
      }
      mpz_init_set(u->n,b->z);
    }
// ---------- long / short ------------------------------------
    else if (SR_HDL(b) & SR_INT)
    {
      mpz_set(u->z,a->z);
      // (z/n) / b -> z/(n*b)
      if (a->s<2)
      {
        mpz_init_set(u->n,a->n);
        if ((long)b>0L)
          mpz_mul_ui(u->n,u->n,SR_TO_INT(b));
        else
        {
          mpz_mul_ui(u->n,u->n,-SR_TO_INT(b));
          mpz_neg(u->z,u->z);
        }
      }
      else
      // long z / short b -> z/b
      {
        //mpz_set(u->z,a->z);
        mpz_init_set_si(u->n,SR_TO_INT(b));
      }
    }
// ---------- long / long ------------------------------------
    else
    {
      mpz_set(u->z,a->z);
      mpz_init_set(u->n,b->z);
      if (a->s<2) mpz_mul(u->n,u->n,a->n);
      if (b->s<2) mpz_mul(u->z,u->z,b->n);
    }
  }
  if (mpz_isNeg(u->n))
  {
    mpz_neg(u->z,u->z);
    mpz_neg(u->n,u->n);
  }
  if (mpz_cmp_si(u->n,(long)1)==0)
  {
    mpz_clear(u->n);
    u->s=3;
    u=nlShort3(u);
  }
  nlTest(u, r);
  return u;
}

BOOLEAN nlDivBy	(	number	a,
		number	b,
		const coeffs
	)

Definition at line 909 of file longrat.cc.

{
  if (SR_HDL(a) & SR_HDL(b) & SR_INT)
  {
    return ((SR_TO_INT(a) % SR_TO_INT(b))==0);
  }
  if (SR_HDL(b) & SR_INT)
  {
    return (mpz_divisible_ui_p(a->z,SR_TO_INT(b))!=0);
  }
  if (SR_HDL(a) & SR_INT) return FALSE;
  return mpz_divisible_p(a->z, b->z) != 0;
}

int nlDivComp	(	number	a,
		number	b,
		const coeffs	r
	)

Definition at line 923 of file longrat.cc.

{
  if (nlDivBy(a, b, r))
  {
    if (nlDivBy(b, a, r)) return 2;
    return -1;
  }
  if (nlDivBy(b, a, r)) return 1;
  return 0;
}

LINLINE BOOLEAN nlEqual	(	number	a,
		number	b,
		const coeffs	r
	)

Definition at line 2335 of file longrat.cc.

{
  nlTest(a, r);
  nlTest(b, r);
// short - short
  if (SR_HDL(a) & SR_HDL(b) & SR_INT) return a==b;
  return _nlEqual_aNoImm_OR_bNoImm(a, b);
}

number nlExactDiv	(	number	a,
		number	b,
		const coeffs	r
	)

Definition at line 733 of file longrat.cc.

{
  if (b==INT_TO_SR(0))
  {
    WerrorS(nDivBy0);
    return INT_TO_SR(0);
  }
  if (a==INT_TO_SR(0))
    return INT_TO_SR(0);
  number u;
  if (SR_HDL(a) & SR_HDL(b) & SR_INT)
  {
    /* the small int -(1<<28) divided by -1 is the large int (1<<28)   */
    if ((a==INT_TO_SR(-(POW_2_28)))&&(b==INT_TO_SR(-1L)))
    {
      return nlRInit(POW_2_28);
    }
    long aa=SR_TO_INT(a);
    long bb=SR_TO_INT(b);
    return INT_TO_SR(aa/bb);
  }
  number bb=NULL;
  if (SR_HDL(b) & SR_INT)
  {
    bb=nlRInit(SR_TO_INT(b));
    b=bb;
  }
  u=ALLOC_RNUMBER();
#if defined(LDEBUG)
  u->debug=123456;
#endif
  mpz_init(u->z);
  /* u=a/b */
  u->s = 3;
  MPZ_EXACTDIV(u->z,a->z,b->z);
  if (bb!=NULL)
  {
    mpz_clear(bb->z);
#if defined(LDEBUG)
    bb->debug=654324;
#endif
    FREE_RNUMBER(bb); // omFreeBin((void *)bb, rnumber_bin);
  }
  u=nlShort3(u);
  nlTest(u, r);
  return u;
}

number nlExtGcd	(	number	a,
		number	b,
		number *	s,
		number *	t,
		const coeffs
	)

Definition at line 2699 of file longrat.cc.

{
  mpz_t aa,bb;
  *s=ALLOC_RNUMBER();
  mpz_init((*s)->z); (*s)->s=3;
  (*t)=ALLOC_RNUMBER();
  mpz_init((*t)->z); (*t)->s=3;
  number g=ALLOC_RNUMBER();
  mpz_init(g->z); g->s=3;
  if (SR_HDL(a) & SR_INT)
  {
    mpz_init_set_si(aa,SR_TO_INT(a));
  }
  else
  {
    mpz_init_set(aa,a->z);
  }
  if (SR_HDL(b) & SR_INT)
  {
    mpz_init_set_si(bb,SR_TO_INT(b));
  }
  else
  {
    mpz_init_set(bb,b->z);
  }
  mpz_gcdext(g->z,(*s)->z,(*t)->z,aa,bb);
  mpz_clear(aa);
  mpz_clear(bb);
  (*s)=nlShort3((*s));
  (*t)=nlShort3((*t));
  g=nlShort3(g);
  return g;
}

number nlFarey	(	number	nN,
		number	nP,
		const coeffs	CF
	)

Definition at line 2630 of file longrat.cc.

{
  mpz_t tmp; mpz_init(tmp);
  mpz_t A,B,C,D,E,N,P;
  if (SR_HDL(nN) & SR_INT) mpz_init_set_si(N,SR_TO_INT(nN));
  else                     mpz_init_set(N,nN->z);
  if (SR_HDL(nP) & SR_INT) mpz_init_set_si(P,SR_TO_INT(nP));
  else                     mpz_init_set(P,nP->z);
  assume(!mpz_isNeg(P));
  if (mpz_isNeg(N))  mpz_add(N,N,P);
  mpz_init_set_si(A,(long)0);
  mpz_init_set_ui(B,(unsigned long)1);
  mpz_init_set_si(C,(long)0);
  mpz_init(D);
  mpz_init_set(E,P);
  number z=INT_TO_SR(0);
  while(mpz_cmp_si(N,(long)0)!=0)
  {
    mpz_mul(tmp,N,N);
    mpz_add(tmp,tmp,tmp);
    if (mpz_cmp(tmp,P)<0)
    {
       if (mpz_isNeg(B))
       {
         mpz_neg(B,B);
         mpz_neg(N,N);
       }
       // check for gcd(N,B)==1
       mpz_gcd(tmp,N,B);
       if (mpz_cmp_ui(tmp,1)==0)
       {
         // return N/B
         z=ALLOC_RNUMBER();
         #ifdef LDEBUG
         z->debug=123456;
         #endif
         mpz_init_set(z->z,N);
         mpz_init_set(z->n,B);
         z->s = 0;
         nlNormalize(z,r);
       }
       else
       {
         // return nN (the input) instead of "fail"
         z=nlCopy(nN,r);
       }
       break;
    }
    //mpz_mod(D,E,N);
    //mpz_div(tmp,E,N);
    mpz_divmod(tmp,D,E,N);
    mpz_mul(tmp,tmp,B);
    mpz_sub(C,A,tmp);
    mpz_set(E,N);
    mpz_set(N,D);
    mpz_set(A,B);
    mpz_set(B,C);
  }
  mpz_clear(tmp);
  mpz_clear(A);
  mpz_clear(B);
  mpz_clear(C);
  mpz_clear(D);
  mpz_clear(E);
  mpz_clear(N);
  mpz_clear(P);
  return z;
}

number nlGcd	(	number	a,
		number	b,
		const coeffs	r
	)

Definition at line 1165 of file longrat.cc.

{
  number result;
  nlTest(a, r);
  nlTest(b, r);
  //nlNormalize(a);
  //nlNormalize(b);
  if ((a==INT_TO_SR(1L))||(a==INT_TO_SR(-1L))
  ||  (b==INT_TO_SR(1L))||(b==INT_TO_SR(-1L)))
    return INT_TO_SR(1L);
  if (a==INT_TO_SR(0)) /* gcd(0,b) ->b */
    return nlCopy(b,r);
  if (b==INT_TO_SR(0)) /* gcd(a,0) -> a */
    return nlCopy(a,r);
  if (SR_HDL(a) & SR_HDL(b) & SR_INT)
  {
    long i=SR_TO_INT(a);
    long j=SR_TO_INT(b);
    if((i==0L)||(j==0L))
      return INT_TO_SR(1);
    long l;
    i=ABS(i);
    j=ABS(j);
    do
    {
      l=i%j;
      i=j;
      j=l;
    } while (l!=0L);
    if (i==POW_2_28)
      result=nlRInit(POW_2_28);
    else
     result=INT_TO_SR(i);
    nlTest(result,r);
    return result;
  }
  if (((!(SR_HDL(a) & SR_INT))&&(a->s<2))
  ||  ((!(SR_HDL(b) & SR_INT))&&(b->s<2))) return INT_TO_SR(1);
  if (SR_HDL(a) & SR_INT)
  {
    LONG aa=ABS(SR_TO_INT(a));
    unsigned long t=mpz_gcd_ui(NULL,b->z,(long)aa);
    if (t==POW_2_28)
      result=nlRInit(POW_2_28);
    else
     result=INT_TO_SR(t);
  }
  else
  if (SR_HDL(b) & SR_INT)
  {
    LONG bb=ABS(SR_TO_INT(b));
    unsigned long t=mpz_gcd_ui(NULL,a->z,(long)bb);
    if (t==POW_2_28)
      result=nlRInit(POW_2_28);
    else
     result=INT_TO_SR(t);
  }
  else
  {
    result=ALLOC0_RNUMBER();
    mpz_init(result->z);
    mpz_gcd(result->z,a->z,b->z);
    result->s = 3;
  #ifdef LDEBUG
    result->debug=123456;
  #endif
    result=nlShort3(result);
  }
  nlTest(result, r);
  return result;
}

number nlGetDenom	(	number &	n,
		const coeffs	r
	)

Definition at line 1418 of file longrat.cc.

{
  if (!(SR_HDL(n) & SR_INT))
  {
    if (n->s==0)
    {
      nlNormalize(n,r);
    }
    if (!(SR_HDL(n) & SR_INT))
    {
      if (n->s!=3)
      {
        number u=ALLOC_RNUMBER();
        u->s=3;
#if defined(LDEBUG)
        u->debug=123456;
#endif
        mpz_init_set(u->z,n->n);
        u=nlShort3_noinline(u);
        return u;
      }
    }
  }
  return INT_TO_SR(1);
}

number nlGetNumerator	(	number &	n,
		const coeffs	r
	)

Definition at line 1447 of file longrat.cc.

{
  if (!(SR_HDL(n) & SR_INT))
  {
    if (n->s==0)
    {
      nlNormalize(n,r);
    }
    if (!(SR_HDL(n) & SR_INT))
    {
      number u=ALLOC_RNUMBER();
#if defined(LDEBUG)
      u->debug=123456;
#endif
      u->s=3;
      mpz_init_set(u->z,n->z);
      if (n->s!=3)
      {
        u=nlShort3_noinline(u);
      }
      return u;
    }
  }
  return n; // imm. int
}

number nlGetUnit	(	number	n,
		const coeffs	r
	)

Definition at line 934 of file longrat.cc.

{
  if (nlGreaterZero(n, r))
    return INT_TO_SR(1);
  else
    return INT_TO_SR(-1);
}

void nlGMP	(	number &	i,
		number	n,
		const coeffs	r
	)

Definition at line 1397 of file longrat.cc.

{
  // Hier brauche ich einfach die GMP Zahl
  nlTest(i, r);
  nlNormalize(i, r);
  if (SR_HDL(i) & SR_INT)
  {
    mpz_set_si((mpz_ptr) n, SR_TO_INT(i));
    return;
  }
  if (i->s!=3)
  {
     WarnS("Omitted denominator during coefficient mapping !");
  }
  mpz_set((mpz_ptr) n, i->z);
}

BOOLEAN nlGreater	(	number	a,
		number	b,
		const coeffs	r
	)

Definition at line 1138 of file longrat.cc.

{
  nlTest(a, r);
  nlTest(b, r);
  number re;
  BOOLEAN rr;
  re=nlSub(a,b,r);
  rr=(!nlIsZero(re,r)) && (nlGreaterZero(re,r));
  nlDelete(&re,r);
  return rr;
}

BOOLEAN nlGreaterZero	(	number	za,
		const coeffs	r
	)

Definition at line 1128 of file longrat.cc.

{
  nlTest(a, r);
  if (SR_HDL(a) & SR_INT) return SR_HDL(a)>1L /* represents number(0) */;
  return (!mpz_isNeg(a->z));
}

LINLINE number nlInit	(	long	i,
		const coeffs	r
	)

Definition at line 2344 of file longrat.cc.

{
  number n;
  #if MAX_NUM_SIZE == 60
  if (((i << 3) >> 3) == i) n=INT_TO_SR(i);
  else                      n=nlRInit(i);
  #else
  LONG ii=(LONG)i;
  if ( (((long)ii==i) && ((ii << 3) >> 3) == ii )) n=INT_TO_SR(ii);
  else                                             n=nlRInit(i);
  #endif
  nlTest(n, r);
  return n;
}

number nlInit2	(	int	i,
		int	j,
		const coeffs	r
	)

create a rational i/j (implicitly) over Q NOTE: make sure to use correct Q in debug mode

Definition at line 2282 of file longrat.cc.

{
  number z=ALLOC_RNUMBER();
#if defined(LDEBUG)
  z->debug=123456;
#endif
  mpz_init_set_si(z->z,(long)i);
  mpz_init_set_si(z->n,(long)j);
  z->s = 0;
  nlNormalize(z,r);
  return z;
}

number nlInit2gmp	(	mpz_t	i,
		mpz_t	j,
		const coeffs	r
	)

create a rational i/j (implicitly) over Q NOTE: make sure to use correct Q in debug mode

Definition at line 2295 of file longrat.cc.

{
  number z=ALLOC_RNUMBER();
#if defined(LDEBUG)
  z->debug=123456;
#endif
  mpz_init_set(z->z,i);
  mpz_init_set(z->n,j);
  z->s = 0;
  nlNormalize(z,r);
  return z;
}

BOOLEAN nlInitChar	(	coeffs	r,
		void *	p
	)

Definition at line 3121 of file longrat.cc.

{
  r->is_domain=TRUE;
  r->rep=n_rep_gap_rat;

  //const int ch = (int)(long)(p);

  r->nCoeffIsEqual=nlCoeffIsEqual;
  //r->cfKillChar = ndKillChar; /* dummy */
  r->cfCoeffString=nlCoeffString;
  r->cfCoeffName=nlCoeffName;

  r->cfInitMPZ = nlInitMPZ;
  r->cfMPZ  = nlMPZ;

  r->cfMult  = nlMult;
  r->cfSub   = nlSub;
  r->cfAdd   = nlAdd;
  if (p==NULL) /* Q */
  {
    r->is_field=TRUE;
    r->cfDiv   = nlDiv;
    //r->cfGcd  = ndGcd_dummy;
    r->cfSubringGcd  = nlGcd;
  }
  else /* Z: coeffs_BIGINT */
  {
    r->is_field=FALSE;
    r->cfDiv   = nlIntDiv;
    r->cfIntMod= nlIntMod;
    r->cfGcd  = nlGcd;
    r->cfDivBy=nlDivBy;
    r->cfDivComp = nlDivComp;
    r->cfIsUnit = nlIsUnit;
    r->cfGetUnit = nlGetUnit;
    r->cfQuot1 = nlQuot1;
    r->cfLcm = nlLcm;
  }
  r->cfExactDiv= nlExactDiv;
  r->cfInit = nlInit;
  r->cfSize  = nlSize;
  r->cfInt  = nlInt;

  r->cfChineseRemainder=nlChineseRemainderSym;
  r->cfFarey=nlFarey;
  r->cfInpNeg   = nlNeg;
  r->cfInvers= nlInvers;
  r->cfCopy  = nlCopy;
  r->cfRePart = nlCopy;
  //r->cfImPart = ndReturn0;
  r->cfWriteLong = nlWrite;
  r->cfRead = nlRead;
  r->cfNormalize=nlNormalize;
  r->cfGreater = nlGreater;
  r->cfEqual = nlEqual;
  r->cfIsZero = nlIsZero;
  r->cfIsOne = nlIsOne;
  r->cfIsMOne = nlIsMOne;
  r->cfGreaterZero = nlGreaterZero;
  r->cfPower = nlPower;
  r->cfGetDenom = nlGetDenom;
  r->cfGetNumerator = nlGetNumerator;
  r->cfExtGcd = nlExtGcd; // only for ring stuff and Z
  r->cfNormalizeHelper  = nlNormalizeHelper;
  r->cfDelete= nlDelete;
  r->cfSetMap = nlSetMap;
  //r->cfName = ndName;
  r->cfInpMult=nlInpMult;
  r->cfInpAdd=nlInpAdd;
  r->cfCoeffWrite=nlCoeffWrite;

  r->cfClearContent = nlClearContent;
  r->cfClearDenominators = nlClearDenominators;

#ifdef LDEBUG
  // debug stuff
  r->cfDBTest=nlDBTest;
#endif
  r->convSingNFactoryN=nlConvSingNFactoryN;
  r->convFactoryNSingN=nlConvFactoryNSingN;

  r->cfRandom=nlRandom;

  // io via ssi
  r->cfWriteFd=nlWriteFd;
  r->cfReadFd=nlReadFd;

  // the variables: general stuff (required)
  r->nNULL = INT_TO_SR(0);
  //r->type = n_Q;
  r->ch = 0;
  r->has_simple_Alloc=FALSE;
  r->has_simple_Inverse=FALSE;

  // variables for this type of coeffs:
  // (none)
  return FALSE;
}

static number nlInitMPZ ( mpz_t  m, const coeffs    )

static

Definition at line 2566 of file longrat.cc.

{
  number z = ALLOC_RNUMBER();
  mpz_init_set(z->z, m);
  mpz_init_set_ui(z->n, 1);
  z->s = 3;
  return z;
}

LINLINE void nlInpAdd	(	number &	a,
		number	b,
		const coeffs	r
	)

Definition at line 2457 of file longrat.cc.

{
  // a=a+b
  if (SR_HDL(a) & SR_HDL(b) & SR_INT)
  {
    LONG r=SR_HDL(a)+SR_HDL(b)-1L;
    if ( ((r << 1) >> 1) == r )
      a=(number)(long)r;
    else
      a=nlRInit(SR_TO_INT(r));
  }
  else
  {
    _nlInpAdd_aNoImm_OR_bNoImm(a,b);
    nlTest(a,r);
  }
}

void nlInpGcd	(	number &	a,
		number	b,
		const coeffs	r
	)

Definition at line 2576 of file longrat.cc.

{
  if ((SR_HDL(b)|SR_HDL(a))&SR_INT)
  {
    number n=nlGcd(a,b,r);
    nlDelete(&a,r);
    a=n;
  }
  else
  {
    mpz_gcd(a->z,a->z,b->z);
    a=nlShort3_noinline(a);
  }
}

void nlInpIntDiv	(	number &	a,
		number	b,
		const coeffs	r
	)

Definition at line 2591 of file longrat.cc.

{
  if ((SR_HDL(b)|SR_HDL(a))&SR_INT)
  {
    number n=nlIntDiv(a,b, r);
    nlDelete(&a,r);
    a=n;
  }
  else
  {
    if (mpz_isNeg(a->z))
    {
      if (mpz_isNeg(b->z))
      {
        mpz_add(a->z,a->z,b->z);
      }
      else
      {
        mpz_sub(a->z,a->z,b->z);
      }
      mpz_add_ui(a->z,a->z,1);
    }
    else
    {
      if (mpz_isNeg(b->z))
      {
        mpz_sub(a->z,a->z,b->z);
      }
      else
      {
        mpz_add(a->z,a->z,b->z);
      }
      mpz_sub_ui(a->z,a->z,1);
    }
    MPZ_DIV(a->z,a->z,b->z);
    a=nlShort3_noinline(a);
  }
}

LINLINE void nlInpMult	(	number &	a,
		number	b,
		const coeffs	r
	)

Definition at line 2523 of file longrat.cc.

{
  number aa=a;
  if (((SR_HDL(b)|SR_HDL(aa))&SR_INT))
  {
    number n=nlMult(aa,b,r);
    nlDelete(&a,r);
    a=n;
  }
  else
  {
    mpz_mul(aa->z,a->z,b->z);
    if (aa->s==3)
    {
      if(b->s!=3)
      {
        mpz_init_set(a->n,b->n);
        a->s=0;
      }
    }
    else
    {
      if(b->s!=3)
      {
        mpz_mul(a->n,a->n,b->n);
      }
      a->s=0;
    }
  }
}

long nlInt	(	number &	n,
		const coeffs	r
	)

Definition at line 604 of file longrat.cc.

{
  nlTest(i, r);
  nlNormalize(i,r);
  if (SR_HDL(i) & SR_INT)
  {
    return SR_TO_INT(i);
  }
  if (i->s==3)
  {
    if(mpz_size1(i->z)>MP_SMALL) return 0;
    long ul=mpz_get_si(i->z);
    if (mpz_cmp_si(i->z,ul)!=0) return 0;
    return ul;
  }
  mpz_t tmp;
  long ul;
  mpz_init(tmp);
  MPZ_DIV(tmp,i->z,i->n);
  if(mpz_size1(tmp)>MP_SMALL) ul=0;
  else
  {
    ul=mpz_get_si(tmp);
    if (mpz_cmp_si(tmp,ul)!=0) ul=0;
  }
  mpz_clear(tmp);
  return ul;
}

number nlIntDiv	(	number	a,
		number	b,
		const coeffs	r
	)

Definition at line 784 of file longrat.cc.

{
  if (b==INT_TO_SR(0))
  {
    WerrorS(nDivBy0);
    return INT_TO_SR(0);
  }
  if (a==INT_TO_SR(0))
    return INT_TO_SR(0);
  number u;
  if (SR_HDL(a) & SR_HDL(b) & SR_INT)
  {
    /* the small int -(1<<28) divided by -1 is the large int (1<<28)   */
    if ((a==INT_TO_SR(-(POW_2_28)))&&(b==INT_TO_SR(-1L)))
    {
      return nlRInit(POW_2_28);
    }
    long aa=SR_TO_INT(a);
    long bb=SR_TO_INT(b);
    return INT_TO_SR(aa/bb);
  }
  if (SR_HDL(a) & SR_INT)
  {
    /* the small int -(1<<28) divided by 2^28 is 1   */
    if (a==INT_TO_SR(-(POW_2_28)))
    {
      if(mpz_cmp_si(b->z,(POW_2_28))==0)
      {
        return INT_TO_SR(-1);
      }
    }
    /* a is a small and b is a large int: -> 0 */
    return INT_TO_SR(0);
  }
  number bb=NULL;
  if (SR_HDL(b) & SR_INT)
  {
    bb=nlRInit(SR_TO_INT(b));
    b=bb;
  }
  u=ALLOC_RNUMBER();
#if defined(LDEBUG)
  u->debug=123456;
#endif
  assume(a->s==3);
  assume(b->s==3);
  mpz_init_set(u->z,a->z);
  /* u=u/b */
  u->s = 3;
  MPZ_DIV(u->z,u->z,b->z);
  if (bb!=NULL)
  {
    mpz_clear(bb->z);
#if defined(LDEBUG)
    bb->debug=654324;
#endif
    FREE_RNUMBER(bb);
  }
  u=nlShort3(u);
  nlTest(u,r);
  return u;
}

number nlIntMod	(	number	a,
		number	b,
		const coeffs	r
	)

Definition at line 850 of file longrat.cc.

{
  if (b==INT_TO_SR(0))
  {
    WerrorS(nDivBy0);
    return INT_TO_SR(0);
  }
  if (a==INT_TO_SR(0))
    return INT_TO_SR(0);
  number u;
  if (SR_HDL(a) & SR_HDL(b) & SR_INT)
  {
    LONG bb=SR_TO_INT(b);
    LONG c=SR_TO_INT(a) % bb;
    return INT_TO_SR(c);
  }
  if (SR_HDL(a) & SR_INT)
  {
    mpz_t aa;
    mpz_init(aa);
    mpz_set_si(aa, SR_TO_INT(a));
    u=ALLOC_RNUMBER();
#if defined(LDEBUG)
    u->debug=123456;
#endif
    u->s = 3;
    mpz_init(u->z);
    mpz_mod(u->z,aa,b->z);
    mpz_clear(aa);
    u=nlShort3(u);
    nlTest(u,r);
    return u;
  }
  number bb=NULL;
  if (SR_HDL(b) & SR_INT)
  {
    bb=nlRInit(SR_TO_INT(b));
    b=bb;
  }
  u=ALLOC_RNUMBER();
#if defined(LDEBUG)
  u->debug=123456;
#endif
  mpz_init(u->z);
  u->s = 3;
  mpz_mod(u->z,a->z,b->z);
  if (bb!=NULL)
  {
    mpz_clear(bb->z);
#if defined(LDEBUG)
    bb->debug=654324;
#endif
    FREE_RNUMBER(bb);
  }
  u=nlShort3(u);
  nlTest(u,r);
  return u;
}

number nlInvers	(	number	a,
		const coeffs	r
	)

Definition at line 654 of file longrat.cc.

{
  nlTest(a, r);
  number n;
  if (SR_HDL(a) & SR_INT)
  {
    if ((a==INT_TO_SR(1L)) || (a==INT_TO_SR(-1L)))
    {
      return a;
    }
    if (nlIsZero(a,r))
    {
      WerrorS(nDivBy0);
      return INT_TO_SR(0);
    }
    n=ALLOC_RNUMBER();
#if defined(LDEBUG)
    n->debug=123456;
#endif
    n->s=1;
    if ((long)a>0L)
    {
      mpz_init_set_si(n->z,(long)1);
      mpz_init_set_si(n->n,(long)SR_TO_INT(a));
    }
    else
    {
      mpz_init_set_si(n->z,(long)-1);
      mpz_init_set_si(n->n,(long)-SR_TO_INT(a));
    }
    nlTest(n, r);
    return n;
  }
  n=ALLOC_RNUMBER();
#if defined(LDEBUG)
  n->debug=123456;
#endif
  {
    n->s=a->s;
    mpz_init_set(n->n,a->z);
    switch (a->s)
    {
      case 0:
      case 1:
              mpz_init_set(n->z,a->n);
              if (mpz_isNeg(n->n)) /* && n->s<2*/
              {
                mpz_neg(n->z,n->z);
                mpz_neg(n->n,n->n);
              }
              if (mpz_cmp_si(n->n,(long)1)==0)
              {
                mpz_clear(n->n);
                n->s=3;
                n=nlShort3(n);
              }
              break;
      case 3:
              n->s=1;
              if (mpz_isNeg(n->n)) /* && n->s<2*/
              {
                mpz_neg(n->n,n->n);
                mpz_init_set_si(n->z,(long)-1);
              }
              else
              {
                mpz_init_set_si(n->z,(long)1);
              }
              break;
    }
  }
  nlTest(n, r);
  return n;
}

BOOLEAN nlIsMOne	(	number	a,
		const coeffs	r
	)

Definition at line 1153 of file longrat.cc.

{
#ifdef LDEBUG
  if (a==NULL) return FALSE;
  nlTest(a, r);
#endif
  return  (a==INT_TO_SR(-1L));
}

LINLINE BOOLEAN nlIsOne	(	number	a,
		const coeffs	r
	)

Definition at line 2362 of file longrat.cc.

{
#ifdef LDEBUG
  if (a==NULL) return FALSE;
  nlTest(a, r);
#endif
  return (a==INT_TO_SR(1));
}

BOOLEAN nlIsUnit	(	number	a,
		const coeffs
	)

Definition at line 956 of file longrat.cc.

{
  return ((SR_HDL(a) & SR_INT) && (ABS(SR_TO_INT(a))==1));
}

LINLINE BOOLEAN nlIsZero	(	number	za,
		const coeffs	r
	)

Definition at line 2371 of file longrat.cc.

{
  #if 0
  if (a==INT_TO_SR(0)) return TRUE;
  if ((SR_HDL(a) & SR_INT)||(a==NULL)) return FALSE;
  if (mpz_cmp_si(a->z,(long)0)==0)
  {
    printf("gmp-0 in nlIsZero\n");
    dErrorBreak();
    return TRUE;
  }
  return FALSE;
  #else
  return (a==INT_TO_SR(0));
  #endif
}

static number nlLcm ( number  a, number  b, const coeffs  r  )

static

Definition at line 3097 of file longrat.cc.

{
  number g=nlGcd(a,b,r);
  number n1=nlMult(a,b,r);
  number n2=nlDiv(n1,g,r);
  nlDelete(&g,r);
  nlDelete(&n1,r);
  return n2;
}

number nlMapGMP	(	number	from,
		const coeffs	src,
		const coeffs	dst
	)

Definition at line 208 of file longrat.cc.

{
  number z=ALLOC_RNUMBER();
#if defined(LDEBUG)
  z->debug=123456;
#endif
  mpz_init_set(z->z,(mpz_ptr) from);
  //mpz_init_set_ui(&z->n,1);
  z->s = 3;
  z=nlShort3(z);
  return z;
}

static number nlMapLongR ( number  from, const coeffs  src, const coeffs  dst  )

static

Definition at line 433 of file longrat.cc.

{
  assume( getCoeffType(src) == n_long_R );

  gmp_float *ff=(gmp_float*)from;
  mpf_t *f=ff->_mpfp();
  number res;
  mpz_ptr dest,ndest;
  int size, i,negative;
  int e,al,bl;
  mp_ptr qp,dd,nn;

  size = (*f)[0]._mp_size;
  if (size == 0)
    return INT_TO_SR(0);
  if(size<0)
  {
    negative = 1;
    size = -size;
  }
  else
    negative = 0;

  qp = (*f)[0]._mp_d;
  while(qp[0]==0)
  {
    qp++;
    size--;
  }

  e=(*f)[0]._mp_exp-size;
  res = ALLOC_RNUMBER();
#if defined(LDEBUG)
  res->debug=123456;
#endif
  dest = res->z;

  if (e<0)
  {
    al = dest->_mp_size = size;
    if (al<2) al = 2;
    dd = (mp_ptr)omAlloc(sizeof(mp_limb_t)*al);
    for (i=0;i<size;i++) dd[i] = qp[i];
    bl = 1-e;
    nn = (mp_ptr)omAlloc(sizeof(mp_limb_t)*bl);
    nn[bl-1] = 1;
    for (i=bl-2;i>=0;i--) nn[i] = 0;
    ndest = res->n;
    ndest->_mp_d = nn;
    ndest->_mp_alloc = ndest->_mp_size = bl;
    res->s = 0;
  }
  else
  {
    al = dest->_mp_size = size+e;
    if (al<2) al = 2;
    dd = (mp_ptr)omAlloc(sizeof(mp_limb_t)*al);
    for (i=0;i<size;i++) dd[i+e] = qp[i];
    for (i=0;i<e;i++) dd[i] = 0;
    res->s = 3;
  }

  dest->_mp_d = dd;
  dest->_mp_alloc = al;
  if (negative) dest->_mp_size = -dest->_mp_size;

  if (res->s==0)
    nlNormalize(res,dst);
  else if (mpz_size1(res->z)<=MP_SMALL)
  {
    // res is new, res->ref is 1
    res=nlShort3(res);
  }
  nlTest(res, dst);
  return res;
}

number nlMapMachineInt	(	number	from,
		const coeffs	,
		const coeffs
	)

Definition at line 233 of file longrat.cc.

{
  number z=ALLOC_RNUMBER();
#if defined(LDEBUG)
  z->debug=123456;
#endif
  mpz_init_set_ui(z->z,(unsigned long) from);
  z->s = 3;
  z=nlShort3(z);
  return z;
}

static number nlMapP ( number  from, const coeffs  src, const coeffs  dst  )

static

Definition at line 191 of file longrat.cc.

{
  assume( getCoeffType(src) == n_Zp );

  number to = nlInit(npInt(from,src), dst); // FIXME? TODO? // extern long     npInt         (number &n, const coeffs r);

  return to;
}

static number nlMapR ( number  from, const coeffs  src, const coeffs  dst  )

static

Definition at line 403 of file longrat.cc.

{
  assume( getCoeffType(src) == n_R );

  double f=nrFloat(from); // FIXME? TODO? // extern float   nrFloat(number n);
  if (f==0.0) return INT_TO_SR(0);
  int f_sign=1;
  if (f<0.0)
  {
    f_sign=-1;
    f=-f;
  }
  int i=0;
  mpz_t h1;
  mpz_init_set_ui(h1,1);
  while((FLT_RADIX*f) < DBL_MAX && i<DBL_MANT_DIG)
  {
    f*=FLT_RADIX;
    mpz_mul_ui(h1,h1,FLT_RADIX);
    i++;
  }
  number re=nlRInit(1);
  mpz_set_d(re->z,f);
  memcpy(&(re->n),&h1,sizeof(h1));
  re->s=0; /* not normalized */
  if(f_sign==-1) re=nlNeg(re,dst);
  nlNormalize(re,dst);
  return re;
}

number nlMapZ	(	number	from,
		const coeffs	src,
		const coeffs	dst
	)

Definition at line 221 of file longrat.cc.

{
  if (SR_HDL(from) & SR_INT)
  {
    return from;
  }
  return nlMapGMP(from,src,dst);
}

number nlModP	(	number	q,
		const coeffs	Q,
		const coeffs	Zp
	)

Definition at line 1355 of file longrat.cc.

{
  const int p = n_GetChar(Zp);
  assume( p > 0 );

  const long P = p;
  assume( P > 0 );

  // embedded long within q => only long numerator has to be converted
  // to int (modulo char.)
  if (SR_HDL(q) & SR_INT)
  {
    long i = SR_TO_INT(q);
    return n_Init( i, Zp );
  }

  const unsigned long PP = p;

  // numerator modulo char. should fit into int
  number z = n_Init( static_cast<long>(mpz_fdiv_ui(q->z, PP)), Zp );

  // denominator != 1?
  if (q->s!=3)
  {
    // denominator modulo char. should fit into int
    number n = n_Init( static_cast<long>(mpz_fdiv_ui(q->n, PP)), Zp );

    number res = n_Div( z, n, Zp );

    n_Delete(&z, Zp);
    n_Delete(&n, Zp);

    return res;
  }

  return z;
}

static void nlMPZ ( mpz_t  m, number &  n, const coeffs  r  )

static

Definition at line 2557 of file longrat.cc.

{
  nlTest(n, r);
  nlNormalize(n, r);
  if (SR_HDL(n) & SR_INT) mpz_init_set_si(m, SR_TO_INT(n));     /* n fits in an int */
  else             mpz_init_set(m, (mpz_ptr)n->z);
}

LINLINE number nlMult	(	number	a,
		number	b,
		const coeffs	r
	)

Definition at line 2475 of file longrat.cc.

{
  nlTest(a, R);
  nlTest(b, R);
  if (a==INT_TO_SR(0)) return INT_TO_SR(0);
  if (b==INT_TO_SR(0)) return INT_TO_SR(0);
  if (SR_HDL(a) & SR_HDL(b) & SR_INT)
  {
    LONG r=(LONG)((unsigned LONG)(SR_HDL(a)-1L))*((unsigned LONG)(SR_HDL(b)>>1));
    if ((r/(SR_HDL(b)>>1))==(SR_HDL(a)-1L))
    {
      number u=((number) ((r>>1)+SR_INT));
      if (((((LONG)SR_HDL(u))<<1)>>1)==SR_HDL(u)) return (u);
      return nlRInit(SR_HDL(u)>>2);
    }
    number u = _nlMult_aImm_bImm_rNoImm(a, b);
    nlTest(u, R);
    return u;

  }
  number u = _nlMult_aNoImm_OR_bNoImm(a, b);
  nlTest(u, R);
  return u;

}

LINLINE number nlNeg	(	number	za,
		const coeffs	r
	)

Definition at line 2420 of file longrat.cc.

{
  nlTest(a, R);
  if(SR_HDL(a) &SR_INT)
  {
    LONG r=SR_TO_INT(a);
    if (r==(-(POW_2_28))) a=nlRInit(POW_2_28);
    else               a=INT_TO_SR(-r);
    return a;
  }
  a = _nlNeg_NoImm(a);
  nlTest(a, R);
  return a;

}

void nlNormalize	(	number &	x,
		const coeffs	r
	)

Definition at line 1264 of file longrat.cc.

{
  if ((SR_HDL(x) & SR_INT) ||(x==NULL))
    return;
  if (x->s==3)
  {
    x=nlShort3_noinline(x);
    nlTest(x,r);
    return;
  }
  else if (x->s==0)
  {
    if (mpz_cmp_si(x->n,(long)1)==0)
    {
      mpz_clear(x->n);
      x->s=3;
      x=nlShort3(x);
    }
    else
    {
      mpz_t gcd;
      mpz_init(gcd);
      mpz_gcd(gcd,x->z,x->n);
      x->s=1;
      if (mpz_cmp_si(gcd,(long)1)!=0)
      {
        MPZ_EXACTDIV(x->z,x->z,gcd);
        MPZ_EXACTDIV(x->n,x->n,gcd);
        if (mpz_cmp_si(x->n,(long)1)==0)
        {
          mpz_clear(x->n);
          x->s=3;
          x=nlShort3_noinline(x);
        }
      }
      mpz_clear(gcd);
    }
  }
  nlTest(x, r);
}

number nlNormalizeHelper	(	number	a,
		number	b,
		const coeffs	r
	)

Definition at line 1308 of file longrat.cc.

{
  number result;
  nlTest(a, r);
  nlTest(b, r);
  if ((SR_HDL(b) & SR_INT)
  || (b->s==3))
  {
    // b is 1/(b->n) => b->n is 1 => result is a
    return nlCopy(a,r);
  }
  result=ALLOC_RNUMBER();
#if defined(LDEBUG)
  result->debug=123456;
#endif
  result->s=3;
  mpz_t gcd;
  mpz_init(gcd);
  mpz_init(result->z);
  if (SR_HDL(a) & SR_INT)
    mpz_gcd_ui(gcd,b->n,ABS(SR_TO_INT(a)));
  else
    mpz_gcd(gcd,a->z,b->n);
  if (mpz_cmp_si(gcd,(long)1)!=0)
  {
    mpz_t bt;
    mpz_init_set(bt,b->n);
    MPZ_EXACTDIV(bt,bt,gcd);
    if (SR_HDL(a) & SR_INT)
      mpz_mul_si(result->z,bt,SR_TO_INT(a));
    else
      mpz_mul(result->z,bt,a->z);
    mpz_clear(bt);
  }
  else
    if (SR_HDL(a) & SR_INT)
      mpz_mul_si(result->z,b->n,SR_TO_INT(a));
    else
      mpz_mul(result->z,b->n,a->z);
  mpz_clear(gcd);
  result=nlShort3(result);
  nlTest(result, r);
  return result;
}

void nlPower	(	number	x,
		int	exp,
		number *	lu,
		const coeffs	r
	)

Definition at line 1075 of file longrat.cc.

{
  *u = INT_TO_SR(0); // 0^e, e!=0
  if (exp==0)
    *u= INT_TO_SR(1);
  else if (!nlIsZero(x,r))
  {
    nlTest(x, r);
    number aa=NULL;
    if (SR_HDL(x) & SR_INT)
    {
      aa=nlRInit(SR_TO_INT(x));
      x=aa;
    }
    else if (x->s==0)
      nlNormalize(x,r);
    *u=ALLOC_RNUMBER();
#if defined(LDEBUG)
    (*u)->debug=123456;
#endif
    mpz_init((*u)->z);
    mpz_pow_ui((*u)->z,x->z,(unsigned long)exp);
    if (x->s<2)
    {
      if (mpz_cmp_si(x->n,(long)1)==0)
      {
        x->s=3;
        mpz_clear(x->n);
      }
      else
      {
        mpz_init((*u)->n);
        mpz_pow_ui((*u)->n,x->n,(unsigned long)exp);
      }
    }
    (*u)->s = x->s;
    if ((*u)->s==3) *u=nlShort3(*u);
    if (aa!=NULL)
    {
      mpz_clear(aa->z);
      FREE_RNUMBER(aa);
    }
  }
#ifdef LDEBUG
  if (exp<0) Print("nlPower: neg. exp. %d\n",exp);
  nlTest(*u, r);
#endif
}

coeffs nlQuot1	(	number	c,
		const coeffs	r
	)

Definition at line 942 of file longrat.cc.

{
  long ch = r->cfInt(c, r);
  mpz_ptr dummy;
  dummy = (mpz_ptr) omAlloc(sizeof(mpz_t));
  mpz_init_set_ui(dummy, ch);
  ZnmInfo info;
  info.base = dummy;
  info.exp = (unsigned long) 1;
  coeffs rr = nInitChar(n_Zn, (void*)&info);
  return(rr);
}

static number nlRandom ( siRandProc  p, number  v2, number  , const coeffs  cf  )

static

Definition at line 3107 of file longrat.cc.

{
  number a=nlInit(p(),cf);
  if (v2!=NULL)
  {
    number b=nlInit(p(),cf);
    number c=nlDiv(a,b,cf);
    nlDelete(&b,cf);
    nlDelete(&a,cf);
    a=c;
  }
  return a;
}

const char* nlRead	(	const char *	s,
		number *	a,
		const coeffs	r
	)

Definition at line 57 of file longrat0.cc.

{
  if (*s<'0' || *s>'9')
  {
    *a = INT_TO_SR(1); /* nlInit(1) */
    return s;
  }
  *a=(number)ALLOC_RNUMBER();
  {
    (*a)->s = 3;
#if defined(LDEBUG)
    (*a)->debug=123456;
#endif
    mpz_ptr z=(*a)->z;
    mpz_ptr n=(*a)->n;
    mpz_init(z);
    s = nlEatLong((char *)s, z);
    if (*s == '/')
    {
      mpz_init(n);
      (*a)->s = 0;
      s++;
      s = nlEatLong((char *)s, n);
      if (mpz_cmp_si(n,(long)0)==0)
      {
        WerrorS(nDivBy0);
        mpz_clear(n);
        (*a)->s = 3;
      }
      else if (mpz_cmp_si(n,(long)1)==0)
      {
        mpz_clear(n);
        (*a)->s=3;
      }
    }
    if (mpz_cmp_si(z,(long)0)==0)
    {
      mpz_clear(z);
      FREE_RNUMBER(*a);
      *a=INT_TO_SR(0);
    }
    else
    if ((*a)->s==3)
    {
      number nlShort3_noinline(number x);
      *a=nlShort3_noinline(*a);
    }
    else
    {
      number aa=*a;
      nlNormalize(aa,r); // FIXME? TODO? // extern void     nlNormalize(number &x, const coeffs r);
      *a=aa;
    }
  }
  return s;
}

static number nlReadFd ( s_buff  f, const coeffs    )

static

Definition at line 3023 of file longrat.cc.

{
  int sub_type=-1;
  sub_type=s_readint(f);
  switch(sub_type)
  {
     case 0:
     case 1:
       {// read mpz_t, mpz_t
         number n=nlRInit(0);
         mpz_init(n->n);
         s_readmpz(f,n->z);
         s_readmpz(f,n->n);
         n->s=sub_type;
         return n;
       }

     case 3:
       {// read mpz_t
         number n=nlRInit(0);
         s_readmpz(f,n->z);
         n->s=3; /*sub_type*/
         #if SIZEOF_LONG == 8
         n=nlShort3(n);
         #endif
         return n;
       }
     case 4:
       {
         LONG dd=s_readlong(f);
         //#if SIZEOF_LONG == 8
         return INT_TO_SR(dd);
         //#else
         //return nlInit(dd,NULL);
         //#endif
       }
     case 5:
     case 6:
       {// read raw mpz_t, mpz_t
         number n=nlRInit(0);
         mpz_init(n->n);
         s_readmpz_base (f,n->z, SSI_BASE);
         s_readmpz_base (f,n->n, SSI_BASE);
         n->s=sub_type-5;
         return n;
       }
     case 8:
       {// read raw mpz_t
         number n=nlRInit(0);
         s_readmpz_base (f,n->z, SSI_BASE);
         n->s=sub_type=3; /*subtype-5*/
         #if SIZEOF_LONG == 8
         n=nlShort3(n);
         #endif
         return n;
       }

     default: Werror("error in reading number: invalid subtype %d",sub_type);
              return NULL;
  }
  return NULL;
}

number nlRInit

(

long

i

)

Definition at line 2268 of file longrat.cc.

{
  number z=ALLOC_RNUMBER();
#if defined(LDEBUG)
  z->debug=123456;
#endif
  mpz_init_set_si(z->z,i);
  z->s = 3;
  return z;
}

nMapFunc nlSetMap	(	const coeffs	src,
		const coeffs	dst
	)

Definition at line 2231 of file longrat.cc.

{
  if (src->rep==n_rep_gap_rat)  /*Q, coeffs_BIGINT */
  {
    return ndCopyMap;
  }
  if ((src->rep==n_rep_int) && nCoeff_is_Zp(src))
  {
    return nlMapP;
  }
  if ((src->rep==n_rep_float) && nCoeff_is_R(src))
  {
    return nlMapR;
  }
  if ((src->rep==n_rep_gmp_float) && nCoeff_is_long_R(src))
  {
    return nlMapLongR; /* long R -> Q */
  }
#ifdef HAVE_RINGS
  if (src->rep==n_rep_gmp) // nCoeff_is_Ring_Z(src) || nCoeff_is_Ring_PtoM(src) || nCoeff_is_Ring_ModN(src))
  {
    return nlMapGMP;
  }
  if (src->rep==n_rep_gap_gmp)
  {
    return nlMapZ;
  }
  if ((src->rep==n_rep_int) && nCoeff_is_Ring_2toM(src))
  {
    return nlMapMachineInt;
  }
#endif
  return NULL;
}

number nlShort1

(

number

x

)

Definition at line 1243 of file longrat.cc.

{
  assume(x->s<2);
  if (mpz_cmp_ui(x->z,(long)0)==0)
  {
    _nlDelete_NoImm(&x);
    return INT_TO_SR(0);
  }
  if (x->s<2)
  {
    if (mpz_cmp(x->z,x->n)==0)
    {
      _nlDelete_NoImm(&x);
      return INT_TO_SR(1);
    }
  }
  return x;
}

static number nlShort3 ( number  x )

inlinestatic

Definition at line 110 of file longrat.cc.

{
  assume(x->s==3);
  if (mpz_cmp_ui(x->z,(long)0)==0)
  {
    mpz_clear(x->z);
    FREE_RNUMBER(x);
    return INT_TO_SR(0);
  }
  if (mpz_size1(x->z)<=MP_SMALL)
  {
    LONG ui=mpz_get_si(x->z);
    if ((((ui<<3)>>3)==ui)
    && (mpz_cmp_si(x->z,(long)ui)==0))
    {
      mpz_clear(x->z);
      FREE_RNUMBER(x);
      return INT_TO_SR(ui);
    }
  }
  return x;
}

number nlShort3_noinline

(

number

x

)

Definition at line 172 of file longrat.cc.

{
  return nlShort3(x);
}

int nlSize	(	number	a,
		const coeffs
	)

Definition at line 575 of file longrat.cc.

{
  if (a==INT_TO_SR(0))
     return 0; /* rational 0*/
  if (SR_HDL(a) & SR_INT)
     return 1; /* immidiate int */
  int s=a->z[0]._mp_alloc;
//  while ((s>0) &&(a->z._mp_d[s]==0L)) s--;
//#if SIZEOF_LONG == 8
//  if (a->z._mp_d[s] < (unsigned long)0x100000000L) s=s*2-1;
//  else s *=2;
//#endif
//  s++;
  if (a->s<2)
  {
    int d=a->n[0]._mp_alloc;
//    while ((d>0) && (a->n._mp_d[d]==0L)) d--;
//#if SIZEOF_LONG == 8
//    if (a->n._mp_d[d] < (unsigned long)0x100000000L) d=d*2-1;
//    else d *=2;
//#endif
    s+=d;
  }
  return s;
}

LINLINE number nlSub	(	number	la,
		number	li,
		const coeffs	r
	)

Definition at line 2505 of file longrat.cc.

{
  if (SR_HDL(a) & SR_HDL(b) & SR_INT)
  {
    LONG r=SR_HDL(a)-SR_HDL(b)+1;
    if ( ((r << 1) >> 1) == r )
    {
      return (number)(long)r;
    }
    else
      return nlRInit(SR_TO_INT(r));
  }
  number u = _nlSub_aNoImm_OR_bNoImm(a, b);
  nlTest(u, r);
  return u;

}

void nlWrite	(	number &	a,
		const coeffs	r
	)

Definition at line 117 of file longrat0.cc.

{
  char *s,*z;
  if (SR_HDL(a) & SR_INT)
  {
    StringAppend("%ld",SR_TO_INT(a));
  }
  else if (a==NULL)
  {
    StringAppendS("o");
  }
  else
  {
    if (a->s==0)
    {
      nlNormalize(a,r); // FIXME? TODO? // extern void     nlNormalize(number &x, const coeffs r);
      nlWrite(a,r);
      return;
    }
    int l=mpz_sizeinbase(a->z,10);
    if (a->s<2) l=si_max(l,(int)mpz_sizeinbase(a->n,10));
    l+=2;
    s=(char*)omAlloc(l);
    z=mpz_get_str(s,10,a->z);
    StringAppendS(z);
    if (a->s!=3)
    {
      StringAppendS("/");
      z=mpz_get_str(s,10,a->n);
      StringAppendS(z);
    }
    omFreeSize((void *)s,l);
  }
}

static void nlWriteFd ( number  n, FILE *  f, const coeffs    )

static

Definition at line 2977 of file longrat.cc.

{
  if(SR_HDL(n) & SR_INT)
  {
    #if SIZEOF_LONG == 4
    fprintf(f,"4 %ld ",SR_TO_INT(n));
    #else
    long nn=SR_TO_INT(n);
    if ((nn<POW_2_28_32)&&(nn>= -POW_2_28_32))
    {
      int nnn=(int)nn;
      fprintf(f,"4 %d ",nnn);
    }
    else
    {
      mpz_t tmp;
      mpz_init_set_si(tmp,nn);
      fputs("8 ",f);
      mpz_out_str (f,SSI_BASE, tmp);
      fputc(' ',f);
      mpz_clear(tmp);
    }
    #endif
  }
  else if (n->s<2)
  {
    //gmp_fprintf(f,"%d %Zd %Zd ",n->s,n->z,n->n);
    fprintf(f,"%d ",n->s+5);
    mpz_out_str (f,SSI_BASE, n->z);
    fputc(' ',f);
    mpz_out_str (f,SSI_BASE, n->n);
    fputc(' ',f);

    //if (d->f_debug!=NULL) gmp_fprintf(d->f_debug,"number: s=%d gmp/gmp \"%Zd %Zd\" ",n->s,n->z,n->n);
  }
  else /*n->s==3*/
  {
    //gmp_fprintf(d->f_write,"3 %Zd ",n->z);
    fputs("8 ",f);
    mpz_out_str (f,SSI_BASE, n->z);
    fputc(' ',f);

    //if (d->f_debug!=NULL) gmp_fprintf(d->f_debug,"number: gmp \"%Zd\" ",n->z);
  }
}