longrat.cc File Reference

#include "misc/auxiliary.h"
#include "factory/factory.h"
#include "misc/sirandom.h"
#include "misc/prime.h"
#include "reporter/reporter.h"
#include "coeffs/coeffs.h"
#include "coeffs/numbers.h"
#include "coeffs/rmodulon.h"
#include "coeffs/longrat.h"
#include "coeffs/shortfl.h"
#include "coeffs/modulop.h"
#include "coeffs/mpr_complex.h"
#include <string.h>
#include <float.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	GCD_NORM_COND(OLD, NEW)   (mpz_size1(NEW->z)>mpz_size1(OLD->z))

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)
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	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, const char *f, int l, const coeffs r)
static number	nlShort3 (number x)
void	_nlDelete_NoImm (number *a)
number	nlShort3_noinline (number x)
static number	nlInitMPZ (mpz_t m, const coeffs)
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)
static number	nlMapGMP (number from, const coeffs, const coeffs dst)
number	nlMapZ (number from, const coeffs, const coeffs dst)
number	nlMapMachineInt (number from, const coeffs, const coeffs)
static CanonicalForm	nlConvSingNFactoryN (number n, const BOOLEAN setChar, const coeffs)
static number	nlConvFactoryNSingN (const CanonicalForm f, const coeffs r)
static number	nlMapR_BI (number from, const coeffs src, const coeffs dst)
static number	nlMapLongR_BI (number from, const coeffs src, const coeffs dst)
static number	nlMapC (number from, const coeffs src, const coeffs dst)
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 cf)
coeffs	nlQuot1 (number c, const coeffs r)
BOOLEAN	nlIsUnit (number a, const coeffs)
static int	int_extgcd (int a, int b, int *u, int *x, int *v, int *y)
number	nlShort1 (number x)
number	nlModP (number q, const coeffs, const coeffs Zp)
number	nlGetDenom (number &n, const coeffs r)
number	nlGetNumerator (number &n, const coeffs r)
BOOLEAN	_nlEqual_aNoImm_OR_bNoImm (number a, number b)
number	_nlCopy_NoImm (number a)
number	_nlNeg_NoImm (number a)
static void	nlNormalize_Gcd (number &x)
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, const coeffs)
number	nlMapQtoZ (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
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
void	nlMPZ (mpz_t m, number &n, const coeffs r)
	get numerator as mpz_t
void	nlMPZ2 (mpz_t m, number &n, const coeffs r)
	get demoninator as mpz_t
number	nlXExtGcd (number a, number b, number *s, number *t, number *u, number *v, const coeffs r)
number	nlQuotRem (number a, number b, number *r, const coeffs R)
void	nlInpGcd (number &a, number b, const coeffs r)
number	nlChineseRemainderSym (number *x, number *q, int rl, BOOLEAN sym, CFArray &inv_cache, 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)
void	nlWriteFd (number n, const ssiInfo *d, const coeffs)
static void	nlWriteFd_S (number n, const coeffs)
number	nlReadFd (const ssiInfo *d, const coeffs)
number	nlReadFd_S (char **s, 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)

Variables
VAR int	n_SwitchChinRem =0

Macro Definition Documentation

BYTES_PER_MP_LIMB

#define BYTES_PER_MP_LIMB   sizeof(mp_limb_t)

Definition at line 136 of file longrat.cc.

GCD_NORM_COND

#define GCD_NORM_COND	(		OLD,
			NEW
	)		(mpz_size1(NEW->z)>mpz_size1(OLD->z))

Definition at line 1770 of file longrat.cc.

LINLINE

#define LINLINE

Definition at line 31 of file longrat.cc.

LONG

#define LONG   int

Definition at line 105 of file longrat.cc.

LONGRAT_CC

#define LONGRAT_CC

Definition at line 133 of file longrat.cc.

MAX_NUM_SIZE

#define MAX_NUM_SIZE   28

Definition at line 102 of file longrat.cc.

MP_SMALL

#define MP_SMALL   1

Definition at line 144 of file longrat.cc.

mpz_isNeg

#define mpz_isNeg

(

A

)

((A)->_mp_size<0)

Definition at line 146 of file longrat.cc.

mpz_limb_d

#define mpz_limb_d

(

A

)

((A)->_mp_d)

Definition at line 148 of file longrat.cc.

mpz_limb_size

#define mpz_limb_size

(

A

)

((A)->_mp_size)

Definition at line 147 of file longrat.cc.

nlTest

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

Definition at line 87 of file longrat.cc.

POW_2_28

#define POW_2_28   (1L<<28)

Definition at line 103 of file longrat.cc.

POW_2_28_32

#define POW_2_28_32   (1L<<28)

Definition at line 104 of file longrat.cc.

Function Documentation

_nlAdd_aNoImm_OR_bNoImm()

number _nlAdd_aNoImm_OR_bNoImm	(	number	a,
		number	b
	)

Definition at line 1792 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_sgn1(u->z)==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;
        if (GCD_NORM_COND(b,u)) { nlNormalize_Gcd(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));
        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_sgn1(u->z)==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;
            if (GCD_NORM_COND(b,u)) { nlNormalize_Gcd(u); }
            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_sgn1(u->z)==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;
            if (GCD_NORM_COND(a,u)) { nlNormalize_Gcd(u); }
            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_sgn1(u->z)==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;
            if (GCD_NORM_COND(b,u)) { nlNormalize_Gcd(u); }
            break;
          }
          case 3:
          {
            mpz_add(u->z,a->z,b->z);
            u->s = 3;
            u=nlShort3(u);
            break;
          }
        }
        break;
      }
    }
  }
  return u;
}

_nlCopy_NoImm()

number _nlCopy_NoImm

(

number

a

)

Definition at line 1720 of file longrat.cc.

{
  assume(!(SR_HDL(a) & SR_INT));
  //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); /*no break*/
    case 3:
            mpz_init_set(b->z,a->z);
            break;
  }
  b->s = a->s;
  return b;
}

_nlDelete_NoImm()

void _nlDelete_NoImm

(

number *

a

)

Definition at line 1741 of file longrat.cc.

{
  {
    switch ((*a)->s)
    {
      case 0:
      case 1:
        mpz_clear((*a)->n); /*no break*/
      case 3:
        mpz_clear((*a)->z);
    }
    #ifdef LDEBUG
    memset(*a,0,sizeof(**a));
    #endif
    FREE_RNUMBER(*a); // omFreeBin((void *) *a, rnumber_bin);
  }
}

_nlEqual_aNoImm_OR_bNoImm()

BOOLEAN _nlEqual_aNoImm_OR_bNoImm	(	number	a,
		number	b
	)

Definition at line 1673 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(bb);
    mpz_mul_si(bb,b->n,(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;
}

_nlInpAdd_aNoImm_OR_bNoImm()

void _nlInpAdd_aNoImm_OR_bNoImm	(	number &	a,
		number	b
	)

Definition at line 1950 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);
        nlNormalize_Gcd(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;
        if (GCD_NORM_COND(b,u)) { nlNormalize_Gcd(u); }
        else { 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;
            if (GCD_NORM_COND(b,a)) { nlNormalize_Gcd(a); }
            else { a=nlShort1(a);}
            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;
            if (GCD_NORM_COND(b,a)) { nlNormalize_Gcd(a); }
            else { a=nlShort1(a);}
            break;
          }
        } /*switch (b->s) */
        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;
            if (GCD_NORM_COND(b,a)) { nlNormalize_Gcd(a); }
            else { a=nlShort1(a);}
            break;
          }
          case 3:
          {
            mpz_add(a->z,a->z,b->z);
            a->s = 3;
            a=nlShort3_noinline(a);
            break;
          }
        }
        break;
      }
    }
  }
}

_nlMult_aImm_bImm_rNoImm()

number _nlMult_aImm_bImm_rNoImm	(	number	a,
		number	b
	)

Definition at line 2304 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;
}

_nlMult_aNoImm_OR_bNoImm()

number _nlMult_aNoImm_OR_bNoImm	(	number	a,
		number	b
	)

Definition at line 2317 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);
      if (GCD_NORM_COND(b,u)) { nlNormalize_Gcd(u); }
    }
    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);
        if (GCD_NORM_COND(b,u)) { nlNormalize_Gcd(u); }
      }
    }
    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);
        if (GCD_NORM_COND(a,u)) { nlNormalize_Gcd(u); }
      }
      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);
        }
        if (GCD_NORM_COND(a,u)) { nlNormalize_Gcd(u); }
      }
    }
  }
  return u;
}

_nlNeg_NoImm()

number _nlNeg_NoImm

(

number

a

)

Definition at line 1759 of file longrat.cc.

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

_nlSub_aNoImm_OR_bNoImm()

number _nlSub_aNoImm_OR_bNoImm	(	number	a,
		number	b
	)

Definition at line 2093 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_sgn1(u->z)==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;
        if (GCD_NORM_COND(b,u)) { nlNormalize_Gcd(u); }
        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);
        }
        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_sgn1(u->z)==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;
        if (GCD_NORM_COND(a,u)) { nlNormalize_Gcd(u); }
        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));
        }
        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_sgn1(u->z)==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;
            if (GCD_NORM_COND(a,u)) { nlNormalize_Gcd(u); }
            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_sgn1(u->z)==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;
            if (GCD_NORM_COND(a,u)) { nlNormalize_Gcd(u); }
            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_sgn1(u->z)==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;
            if (GCD_NORM_COND(b,u)) { nlNormalize_Gcd(u); }
            break;
          }
          case 3: /* a:3 , b:3 */
          {
            mpz_sub(u->z,a->z,b->z);
            u->s = 3;
            u=nlShort3(u);
            break;
          }
        }
        break;
      }
    }
  }
  return u;
}

int_extgcd()

static int int_extgcd ( int  a, int  b, int *  u, int *  x, int *  v, int *  y  )

static

Definition at line 1410 of file longrat.cc.

{
  int q, r;
  if (a==0)
  {
    *u = 0;
    *v = 1;
    *x = -1;
    *y = 0;
    return b;
  }
  if (b==0)
  {
    *u = 1;
    *v = 0;
    *x = 0;
    *y = 1;
    return a;
  }
  *u=1;
  *v=0;
  *x=0;
  *y=1;
  do
  {
    q = a/b;
    r = a%b;
    assume (q*b+r == a);
    a = b;
    b = r;
 
    r = -(*v)*q+(*u);
    (*u) =(*v);
    (*v) = r;
 
    r = -(*y)*q+(*x);
    (*x) = (*y);
    (*y) = r;
  } while (b);
 
  return a;
}

mpz_mul_si()

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

Definition at line 177 of file longrat.cc.

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

nl_Copy()

LINLINE number nl_Copy	(	number	a,
		const coeffs	r
	)

nlAdd()

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

Definition at line 2672 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;
}

nlBigInt() [1/2]

number nlBigInt	(	number &	i,
		const coeffs	r
	)

Definition at line 772 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_tdiv_q(tmp->z,i->z,i->n);
  tmp=nlShort3(tmp);
  return tmp;
}

nlBigInt() [2/2]

number nlBigInt

(

number &

n

)

nlChineseRemainderSym()

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

Definition at line 3075 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;
  if (n_SwitchChinRem)
    chineseRemainder(X,Q,xnew,qnew);
  else
    chineseRemainderCached(X,Q,xnew,qnew,inv_cache);
  number n=CF->convFactoryNSingN(xnew,CF);
  if (sym)
  {
    number p=CF->convFactoryNSingN(qnew,CF);
    number p2;
    if (getCoeffType(CF) == n_Q) p2=nlIntDiv(p,nlInit(2, CF),CF);
    else                         p2=CF->cfDiv(p,CF->cfInit(2, CF),CF);
    if (CF->cfGreater(n,p2,CF))
    {
       number n2=CF->cfSub(n,p,CF);
       CF->cfDelete(&n,CF);
       n=n2;
    }
    CF->cfDelete(&p2,CF);
    CF->cfDelete(&p,CF);
  }
  CF->cfNormalize(n,CF);
  return n;
}

nlClearContent()

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

static

Definition at line 3119 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=nlExactDiv(n, cand, cf); // simple integer exact division, no ratios to remain
    nlDelete(&n, cf);
    n = t;
  }
}

nlClearDenominators()

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

static

Definition at line 3210 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);
  }
 
}

nlCoeffIsEqual()

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

Definition at line 3523 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;
}

nlCoeffName()

char * nlCoeffName

(

const coeffs

r

)

Definition at line 3304 of file longrat.cc.

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

nlConvFactoryNSingN()

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

static

Definition at line 365 of file longrat.cc.

{
  if (f.isImm())
  {
    return nlInit(f.intval(),r);
  }
  else
  {
    number z = ALLOC_RNUMBER();
#if defined(LDEBUG)
    z->debug=123456;
#endif
    gmp_numerator( f, z->z );
    if ( f.den().isOne() )
    {
      z->s = 3;
      z=nlShort3(z);
    }
    else
    {
      gmp_denominator( f, z->n );
      z->s = 1;
    }
    return z;
  }
}

nlConvSingNFactoryN()

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

static

Definition at line 327 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;
}

nlCopy()

LINLINE number nlCopy	(	number	a,
		const coeffs	r
	)

Definition at line 2624 of file longrat.cc.

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

nlCopyMap()

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

Definition at line 2425 of file longrat.cc.

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

nlDBTest() [1/2]

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

nlDBTest() [2/2]

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

Definition at line 235 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,1L)==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;
}

nlDelete()

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

Definition at line 2637 of file longrat.cc.

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

nlDiv()

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

Definition at line 1140 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,1L)==0)
  {
    mpz_clear(u->n);
    u->s=3;
    u=nlShort3(u);
  }
  nlTest(u, r);
  return u;
}

nlDivBy()

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

Definition at line 1077 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;
}

nlDivComp()

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

Definition at line 1091 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;
}

nlEqual()

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

Definition at line 2568 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);
}

nlExactDiv()

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

Definition at line 870 of file longrat.cc.

{
  if (b==INT_TO_SR(0))
  {
    WerrorS(nDivBy0);
    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 aa=NULL;
  number bb=NULL;
  if (SR_HDL(a) & SR_INT)
  {
    aa=nlRInit(SR_TO_INT(a));
    a=aa;
  }
  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;
  assume(a->s==3);
  assume(b->s==3);
  mpz_divexact(u->z,a->z,b->z);
  if (aa!=NULL)
  {
    mpz_clear(aa->z);
#if defined(LDEBUG)
    aa->debug=654324;
#endif
    FREE_RNUMBER(aa); // omFreeBin((void *)aa, rnumber_bin);
  }
  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;
}

nlExtGcd()

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

Definition at line 3019 of file longrat.cc.

{
  mpz_ptr 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;
  #ifdef LDEBUG
  g->debug=123456;
  (*s)->debug=123456;
  (*t)->debug=123456;
  #endif
  if (SR_HDL(a) & SR_INT)
  {
    aa=(mpz_ptr)omAlloc(sizeof(mpz_t));
    mpz_init_set_si(aa,SR_TO_INT(a));
  }
  else
  {
    aa=a->z;
  }
  if (SR_HDL(b) & SR_INT)
  {
    bb=(mpz_ptr)omAlloc(sizeof(mpz_t));
    mpz_init_set_si(bb,SR_TO_INT(b));
  }
  else
  {
    bb=b->z;
  }
  mpz_gcdext(g->z,(*s)->z,(*t)->z,aa,bb);
  g=nlShort3(g);
  (*s)=nlShort3((*s));
  (*t)=nlShort3((*t));
  if (SR_HDL(a) & SR_INT)
  {
    mpz_clear(aa);
    omFreeSize(aa, sizeof(mpz_t));
  }
  if (SR_HDL(b) & SR_INT)
  {
    mpz_clear(bb);
    omFreeSize(bb, sizeof(mpz_t));
  }
  return g;
}

nlFarey()

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

Definition at line 2948 of file longrat.cc.

{
  mpz_t A,B,C,D,E,N,P,tmp;
  if (SR_HDL(nP) & SR_INT) mpz_init_set_si(P,SR_TO_INT(nP));
  else                     mpz_init_set(P,nP->z);
  const mp_bitcnt_t bits=2*(mpz_size1(P)+1)*GMP_LIMB_BITS;
  mpz_init2(N,bits);
  if (SR_HDL(nN) & SR_INT) mpz_set_si(N,SR_TO_INT(nN));
  else                     mpz_set(N,nN->z);
  assume(!mpz_isNeg(P));
  if (mpz_isNeg(N))  mpz_add(N,N,P);
  mpz_init2(A,bits); mpz_set_ui(A,0L);
  mpz_init2(B,bits); mpz_set_ui(B,1L);
  mpz_init2(C,bits); mpz_set_ui(C,0L);
  mpz_init2(D,bits);
  mpz_init2(E,bits); mpz_set(E,P);
  mpz_init2(tmp,bits);
  number z=INT_TO_SR(0);
  while(mpz_sgn1(N)!=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
         memcpy(z->z,N,sizeof(mpz_t));
         memcpy(z->n,B,sizeof(mpz_t));
         z->s = 0;
         nlNormalize(z,r);
       }
       else
       {
         // return nN (the input) instead of "fail"
         z=nlCopy(nN,r);
         mpz_clear(B);
         mpz_clear(N);
       }
       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(C);
  mpz_clear(D);
  mpz_clear(E);
  mpz_clear(P);
  return z;
}

nlGcd()

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

Definition at line 1340 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);
    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();
    result->s = 3;
  #ifdef LDEBUG
    result->debug=123456;
  #endif
    mpz_init(result->z);
    mpz_gcd(result->z,a->z,b->z);
    result=nlShort3(result);
  }
  nlTest(result, r);
  return result;
}

nlGetDenom()

number nlGetDenom	(	number &	n,
		const coeffs	r
	)

Definition at line 1613 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);
}

nlGetNumerator()

number nlGetNumerator	(	number &	n,
		const coeffs	r
	)

Definition at line 1642 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
}

nlGetUnit()

number nlGetUnit	(	number	n,
		const coeffs	cf
	)

Definition at line 1102 of file longrat.cc.

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

nlGreater()

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

Definition at line 1313 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;
}

nlGreaterZero()

BOOLEAN nlGreaterZero	(	number	za,
		const coeffs	r
	)

Definition at line 1303 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));
}

nlInit()

LINLINE number nlInit	(	long	i,
		const coeffs	r
	)

Definition at line 2577 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;
}

nlInit2()

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 2515 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;
}

nlInit2gmp()

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 2528 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;
}

nlInitChar()

BOOLEAN nlInitChar	(	coeffs	r,
		void *	p
	)

Definition at line 3559 of file longrat.cc.

{
  r->is_domain=TRUE;
  r->rep=n_rep_gap_rat;
 
  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;
  r->cfExactDiv= nlExactDiv;
  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->cfXExtGcd=nlXExtGcd;
    r->cfQuotRem=nlQuotRem;
  }
  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->cfWriteFd_S=nlWriteFd_S;
  r->cfReadFd=nlReadFd;
  r->cfReadFd_S=nlReadFd_S;
 
  //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;
}

nlInitMPZ()

static number nlInitMPZ ( mpz_t  m, const coeffs    )

static

Definition at line 164 of file longrat.cc.

{
  number z = ALLOC_RNUMBER();
  z->s = 3;
  #ifdef LDEBUG
  z->debug=123456;
  #endif
  mpz_init_set(z->z, m);
  z=nlShort3(z);
  return z;
}

nlInpAdd()

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

Definition at line 2690 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);
  }
}

nlInpGcd()

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

Definition at line 2913 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);
  }
}

nlInpIntDiv()

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

Definition at line 2928 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
  {
    mpz_t rr;
    mpz_init(rr);
    mpz_mod(rr,a->z,b->z);
    mpz_sub(a->z,a->z,rr);
    mpz_clear(rr);
    mpz_divexact(a->z,a->z,b->z);
    a=nlShort3_noinline(a);
  }
}

nlInpMult()

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

Definition at line 2756 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;
    }
  }
}

nlInt()

long nlInt	(	number &	n,
		const coeffs	r
	)

Definition at line 740 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_tdiv_q(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;
}

nlIntDiv()

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

Definition at line 935 of file longrat.cc.

{
  if (b==INT_TO_SR(0))
  {
    WerrorS(nDivBy0);
    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);
    LONG rr=aa%bb;
    if (rr<0) rr+=ABS(bb);
    LONG cc=(aa-rr)/bb;
    return INT_TO_SR(cc);
  }
  number aa=NULL;
  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);
      }
    }
    aa=nlRInit(SR_TO_INT(a));
    a=aa;
  }
  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);
  /* u=u/b */
  mpz_t rr;
  mpz_init(rr);
  mpz_mod(rr,a->z,b->z);
  u->s = 3;
  mpz_init(u->z);
  mpz_sub(u->z,a->z,rr);
  mpz_clear(rr);
  mpz_divexact(u->z,u->z,b->z);
  if (aa!=NULL)
  {
    mpz_clear(aa->z);
#if defined(LDEBUG)
    aa->debug=654324;
#endif
    FREE_RNUMBER(aa);
  }
  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;
}

nlIntMod()

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

Definition at line 1016 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 aa=SR_TO_INT(a);
    LONG bb=SR_TO_INT(b);
    LONG c=aa % bb;
    if (c<0) c+=ABS(bb);
    return INT_TO_SR(c);
  }
  if (SR_HDL(a) & SR_INT)
  {
    LONG ai=SR_TO_INT(a);
    mpz_t aa;
    mpz_init_set_si(aa, ai);
    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;
}

nlInvers()

number nlInvers	(	number	a,
		const coeffs	r
	)

Definition at line 790 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_ui(n->z,1L);
      mpz_init_set_si(n->n,(long)SR_TO_INT(a));
    }
    else
    {
      mpz_init_set_si(n->z,-1L);
      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
  {
    mpz_init_set(n->n,a->z);
    switch (a->s)
    {
      case 0:
      case 1:
              n->s=a->s;
              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_ui(n->n,1L)==0)
              {
                mpz_clear(n->n);
                n->s=3;
                n=nlShort3(n);
              }
              break;
      case 3:
              // i.e. |a| > 2^...
              n->s=1;
              if (mpz_isNeg(n->n)) /* && n->s<2*/
              {
                mpz_neg(n->n,n->n);
                mpz_init_set_si(n->z,-1L);
              }
              else
              {
                mpz_init_set_ui(n->z,1L);
              }
              break;
    }
  }
  nlTest(n, r);
  return n;
}

nlIsMOne()

BOOLEAN nlIsMOne	(	number	a,
		const coeffs	r
	)

Definition at line 1328 of file longrat.cc.

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

nlIsOne()

LINLINE BOOLEAN nlIsOne	(	number	a,
		const coeffs	r
	)

Definition at line 2595 of file longrat.cc.

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

nlIsUnit()

BOOLEAN nlIsUnit	(	number	a,
		const coeffs
	)

Definition at line 1131 of file longrat.cc.

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

nlIsZero()

LINLINE BOOLEAN nlIsZero	(	number	za,
		const coeffs	r
	)

Definition at line 2604 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,0L)==0)
  {
    printf("gmp-0 in nlIsZero\n");
    dErrorBreak();
    return TRUE;
  }
  return FALSE;
  #else
  return (a==NULL)|| (a==INT_TO_SR(0));
  #endif
}

nlLcm()

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

static

Definition at line 3535 of file longrat.cc.

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

nlMapC()

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

static

Definition at line 545 of file longrat.cc.

{
  assume( getCoeffType(src) == n_long_C );
  if ( ! ((gmp_complex*)from)->imag().isZero() )
    return INT_TO_SR(0);
 
  if (dst->is_field==FALSE) /* ->ZZ */
  {
    char *s=floatToStr(((gmp_complex*)from)->real(),src->float_len);
    mpz_t z;
    mpz_init(z);
    char *ss=nEatLong(s,z);
    if (*ss=='\0')
    {
      omFree(s);
      number n=nlInitMPZ(z,dst);
      mpz_clear(z);
      return n;
    }
    omFree(s);
    mpz_clear(z);
    WarnS("conversion problem in CC -> ZZ mapping");
    return INT_TO_SR(0);
  }
 
  mpf_t *f = ((gmp_complex*)from)->real()._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;
 
  void* (*allocfunc) (size_t);
  mp_get_memory_functions (&allocfunc,NULL, NULL);
  if (e<0)
  {
    al = dest->_mp_size = size;
    if (al<2) al = 2;
    dd = (mp_ptr)allocfunc(sizeof(mp_limb_t)*al);
    for (i=0;i<size;i++) dd[i] = qp[i];
    bl = 1-e;
    nn = (mp_ptr)allocfunc(sizeof(mp_limb_t)*bl);
    memset(nn,0,sizeof(mp_limb_t)*bl);
    nn[bl-1] = 1;
    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)allocfunc(sizeof(mp_limb_t)*al);
    memset(dd,0,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) mpz_neg(dest,dest);
 
  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;
}

nlMapGMP()

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

inlinestatic

Definition at line 205 of file longrat.cc.

{
  return nlInitMPZ((mpz_ptr)from,dst);
}

nlMapLongR()

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

static

Definition at line 432 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;
 
  void* (*allocfunc) (size_t);
  mp_get_memory_functions (&allocfunc,NULL, NULL);
  if (e<0)
  {
    al = dest->_mp_size = size;
    if (al<2) al = 2;
    dd = (mp_ptr)allocfunc(sizeof(mp_limb_t)*al);
    for (i=0;i<size;i++) dd[i] = qp[i];
    bl = 1-e;
    nn = (mp_ptr)allocfunc(sizeof(mp_limb_t)*bl);
    memset(nn,0,sizeof(mp_limb_t)*bl);
    nn[bl-1] = 1;
    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)allocfunc(sizeof(mp_limb_t)*al);
    memset(dd,0,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) mpz_neg(dest,dest);
 
  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;
}

nlMapLongR_BI()

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

static

Definition at line 512 of file longrat.cc.

{
  assume( getCoeffType(src) == n_long_R );
 
  gmp_float *ff=(gmp_float*)from;
  if (mpf_fits_slong_p(ff->t))
  {
    long l=mpf_get_si(ff->t);
    return nlInit(l,dst);
  }
  char *out=floatToStr(*(gmp_float*)from, src->float_len);
  char *p=strchr(out,'.');
  *p='\0';
  number res;
  res = ALLOC_RNUMBER();
#if defined(LDEBUG)
  res->debug=123456;
#endif
  res->s=3;
  mpz_init(res->z);
  if (out[0]=='-')
  {
    mpz_set_str(res->z,out+1,10);
    res=nlNeg(res,dst);
  }
  else
  {
    mpz_set_str(res->z,out,10);
  }
  omFree( (void *)out );
  return res;
}

nlMapMachineInt()

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

Definition at line 222 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;
}

nlMapP()

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

static

Definition at line 189 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;
}

nlMapQtoZ()

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

Definition at line 2434 of file longrat.cc.

{
  if ((SR_HDL(a) & SR_INT)||(a==NULL))
  {
    return a;
  }
  if (a->s==3) return _nlCopy_NoImm(a);
  number a0=a;
  BOOLEAN a1=FALSE;
  if (a->s==0) { a0=_nlCopy_NoImm(a); a1=TRUE; }
  number b1=nlGetNumerator(a0,src);
  number b2=nlGetDenom(a0,src);
  number b=nlIntDiv(b1,b2,dst);
  nlDelete(&b1,src);
  nlDelete(&b2,src);
  if (a1)  _nlDelete_NoImm(&a0);
  return b;
}

nlMapR()

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

static

Definition at line 392 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;
}

nlMapR_BI()

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

static

Definition at line 422 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);
  long l=long(f);
  return nlInit(l,dst);
}

nlMapZ()

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

Definition at line 210 of file longrat.cc.

{
  if (SR_HDL(from) & SR_INT)
  {
    return from;
  }
  return nlInitMPZ((mpz_ptr)from,dst);
}

nlModP()

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

Definition at line 1572 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;
}

nlMPZ()

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

get numerator as mpz_t

Definition at line 2790 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);
}

nlMPZ2()

void nlMPZ2	(	mpz_t	m,
		number &	n,
		const coeffs	r
	)

get demoninator as mpz_t

Definition at line 2798 of file longrat.cc.

{
  nlTest(n, r);
  nlNormalize(n, r);
  if (SR_HDL(n) & SR_INT) mpz_init_set_si(m,1); /* small int*/
  else if (n->s==3)       mpz_init_set_si(m,1); /* large int*/
  else                    mpz_init_set(m, (mpz_ptr)n->n);
}

nlMult()

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

Definition at line 2708 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;
 
}

nlNeg()

LINLINE number nlNeg	(	number	za,
		const coeffs	r
	)

Definition at line 2653 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;
 
}

nlNormalize()

void nlNormalize	(	number &	x,
		const coeffs	r
	)

Definition at line 1481 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,1L)==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,1L)!=0)
      {
        mpz_divexact(x->z,x->z,gcd);
        mpz_divexact(x->n,x->n,gcd);
        if (mpz_cmp_si(x->n,1L)==0)
        {
          mpz_clear(x->n);
          x->s=3;
          x=nlShort3_noinline(x);
        }
      }
      mpz_clear(gcd);
    }
  }
  nlTest(x, r);
}

nlNormalize_Gcd()

static void nlNormalize_Gcd ( number &  x )

static

Definition at line 1772 of file longrat.cc.

{
  mpz_t gcd;
  mpz_init(gcd);
  mpz_gcd(gcd,x->z,x->n);
  x->s=1;
  if (mpz_cmp_si(gcd,1L)!=0)
  {
    mpz_divexact(x->z,x->z,gcd);
    mpz_divexact(x->n,x->n,gcd);
    if (mpz_cmp_si(x->n,1L)==0)
    {
      mpz_clear(x->n);
      x->s=3;
      x=nlShort3_noinline(x);
    }
  }
  mpz_clear(gcd);
}

nlNormalizeHelper()

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

Definition at line 1525 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,1L)!=0)
  {
    mpz_t bt;
    mpz_init(bt);
    mpz_divexact(bt,b->n,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;
}

nlPower()

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

Definition at line 1250 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,1L)==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
}

nlQuot1()

coeffs nlQuot1	(	number	c,
		const coeffs	r
	)

Definition at line 1108 of file longrat.cc.

{
  long ch = r->cfInt(c, r);
  int p=IsPrime(ch);
  coeffs rr=NULL;
  if (((long)p)==ch)
  {
    rr = nInitChar(n_Zp,(void*)ch);
  }
  else
  {
    mpz_t dummy;
    mpz_init_set_ui(dummy, ch);
    ZnmInfo info;
    info.base = dummy;
    info.exp = (unsigned long) 1;
    rr = nInitChar(n_Zn, (void*)&info);
    mpz_clear(dummy);
  }
  return(rr);
}

nlQuotRem()

number nlQuotRem	(	number	a,
		number	b,
		number *	r,
		const coeffs	R
	)

Definition at line 2860 of file longrat.cc.

{
  assume(SR_TO_INT(b)!=0);
  if (SR_HDL(a) & SR_HDL(b) & SR_INT)
  {
    if (r!=NULL)
      *r = INT_TO_SR(SR_TO_INT(a) % SR_TO_INT(b));
    return INT_TO_SR(SR_TO_INT(a)/SR_TO_INT(b));
  }
  else if (SR_HDL(a) & SR_INT)
  {
    // -2^xx / 2^xx
    if ((a==INT_TO_SR(-(POW_2_28)))&&(b==INT_TO_SR(-1L)))
    {
      if (r!=NULL) *r=INT_TO_SR(0);
      return nlRInit(POW_2_28);
    }
    //a is small, b is not, so q=0, r=a
    if (r!=NULL)
      *r = a;
    return INT_TO_SR(0);
  }
  else if (SR_HDL(b) & SR_INT)
  {
    unsigned long rr;
    mpz_t qq;
    mpz_init(qq);
    mpz_t rrr;
    mpz_init(rrr);
    rr = mpz_divmod_ui(qq, rrr, a->z, (unsigned long)ABS(SR_TO_INT(b)));
    mpz_clear(rrr);
 
    if (r!=NULL)
      *r = INT_TO_SR(rr);
    if (SR_TO_INT(b)<0)
    {
      mpz_neg(qq, qq);
    }
    return nlInitMPZ(qq,R);
  }
  mpz_t qq,rr;
  mpz_init(qq);
  mpz_init(rr);
  mpz_divmod(qq, rr, a->z, b->z);
  if (r!=NULL)
    *r = nlInitMPZ(rr,R);
  else
  {
    mpz_clear(rr);
  }
  return nlInitMPZ(qq,R);
}

nlRandom()

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

static

Definition at line 3545 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;
}

nlRead()

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

Definition at line 31 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 = nEatLong((char *)s, z);
    if (*s == '/')
    {
      mpz_init(n);
      (*a)->s = 0;
      s++;
      s = nEatLong((char *)s, n);
      if (mpz_cmp_si(n,0L)==0)
      {
        WerrorS(nDivBy0);
        mpz_clear(n);
        (*a)->s = 3;
      }
      else if (mpz_cmp_si(n,1L)==0)
      {
        mpz_clear(n);
        (*a)->s=3;
      }
    }
    if (mpz_cmp_si(z,0L)==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;
}

nlReadFd()

number nlReadFd	(	const ssiInfo *	d,
		const coeffs
	)

Definition at line 3405 of file longrat.cc.

{
  int sub_type=-1;
  sub_type=s_readint(d->f_read);
  switch(sub_type)
  {
     case 0:
     case 1:
       {// read mpz_t, mpz_t
         number n=nlRInit(0);
         mpz_init(n->n);
         s_readmpz(d->f_read,n->z);
         s_readmpz(d->f_read,n->n);
         n->s=sub_type;
         return n;
       }
 
     case 3:
       {// read mpz_t
         number n=nlRInit(0);
         s_readmpz(d->f_read,n->z);
         n->s=3; /*sub_type*/
         #if SIZEOF_LONG == 8
         n=nlShort3(n);
         #endif
         return n;
       }
     case 4:
       {
         LONG dd=s_readlong(d->f_read);
         return INT_TO_SR(dd);
       }
     case 5:
     case 6:
       {// read raw mpz_t, mpz_t
         number n=nlRInit(0);
         mpz_init(n->n);
         s_readmpz_base (d->f_read,n->z, SSI_BASE);
         s_readmpz_base (d->f_read,n->n, SSI_BASE);
         n->s=sub_type-5;
         return n;
       }
     case 8:
       {// read raw mpz_t
         number n=nlRInit(0);
         s_readmpz_base (d->f_read,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;
}

nlReadFd_S()

number nlReadFd_S	(	char **	s,
		const coeffs
	)

Definition at line 3464 of file longrat.cc.

{
  int sub_type=-1;
  sub_type=s_readint_S(s);
  switch(sub_type)
  {
     case 0:
     case 1:
       {// read mpz_t, mpz_t
         number n=nlRInit(0);
         mpz_init(n->n);
         s_readmpz_S(s,n->z);
         s_readmpz_S(s,n->n);
         n->s=sub_type;
         return n;
       }
 
     case 3:
       {// read mpz_t
         number n=nlRInit(0);
         s_readmpz_S(s,n->z);
         n->s=3; /*sub_type*/
         #if SIZEOF_LONG == 8
         n=nlShort3(n);
         #endif
         return n;
       }
     case 4:
       {
         long dd=s_readlong_S(s);
         return INT_TO_SR(dd);
       }
     case 5:
     case 6:
       {// read raw mpz_t, mpz_t
         number n=nlRInit(0);
         mpz_init(n->n);
         s_readmpz_base_S (s,n->z, SSI_BASE);
         s_readmpz_base_S (s,n->n, SSI_BASE);
         n->s=sub_type-5;
         return n;
       }
     case 8:
       {// read raw mpz_t
         number n=nlRInit(0);
         s_readmpz_base_S (s,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;
}

nlRInit()

number nlRInit

(

long

i

)

Definition at line 2501 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;
}

nlSetMap()

nMapFunc nlSetMap	(	const coeffs	src,
		const coeffs	dst
	)

Definition at line 2453 of file longrat.cc.

{
  if (src->rep==n_rep_gap_rat)  /*Q, coeffs_BIGINT */
  {
    if ((src->is_field==dst->is_field) /* Q->Q, Z->Z*/
    || (src->is_field==FALSE))         /* Z->Q */
      return nlCopyMap;
    return nlMapQtoZ;        /* Q->Z */
  }
  if ((src->rep==n_rep_int) && nCoeff_is_Zp(src))
  {
    return nlMapP;
  }
  if ((src->rep==n_rep_float) && nCoeff_is_R(src))
  {
    if (dst->is_field) /* R -> Q */
      return nlMapR;
    else
      return nlMapR_BI; /* R -> bigint */
  }
  if ((src->rep==n_rep_gmp_float) && nCoeff_is_long_R(src))
  {
    if (dst->is_field)
      return nlMapLongR; /* long R -> Q */
    else
      return nlMapLongR_BI;
  }
  if (nCoeff_is_long_C(src))
  {
    return nlMapC; /* C -> Q */
  }
  if (src->rep==n_rep_gmp) // nCoeff_is_Z(src) || nCoeff_is_Ring_PtoM(src) || nCoeff_is_Zn(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;
  }
  return NULL;
}

nlShort1()

number nlShort1

(

number

x

)

Definition at line 1460 of file longrat.cc.

{
  assume(x->s<2);
  if (mpz_sgn1(x->z)==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;
}

nlShort3()

static number nlShort3 ( number  x )

inlinestatic

Definition at line 109 of file longrat.cc.

{
  assume(x->s==3);
  if (mpz_sgn1(x->z)==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;
}

nlShort3_noinline()

number nlShort3_noinline

(

number

x

)

Definition at line 159 of file longrat.cc.

{
  return nlShort3(x);
}

nlSize()

int nlSize	(	number	a,
		const coeffs
	)

Definition at line 711 of file longrat.cc.

{
  if (a==INT_TO_SR(0))
     return 0; /* rational 0*/
  if (SR_HDL(a) & SR_INT)
     return 1; /* immediate 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;
}

nlSub()

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

Definition at line 2738 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;
 
}

nlWrite()

void nlWrite	(	number	a,
		const coeffs	r
	)

Definition at line 90 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
  {
    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);
  }
}

nlWriteFd()

void nlWriteFd	(	number	n,
		const ssiInfo *	d,
		const coeffs
	)

Definition at line 3310 of file longrat.cc.

{
  if(SR_HDL(n) & SR_INT)
  {
    #if SIZEOF_LONG == 4
    fprintf(d->f_write,"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(d->f_write,"4 %d ",nnn);
    }
    else
    {
      mpz_t tmp;
      mpz_init_set_si(tmp,nn);
      fputs("8 ",d->f_write);
      mpz_out_str (d->f_write,SSI_BASE, tmp);
      fputc(' ',d->f_write);
      mpz_clear(tmp);
    }
    #endif
  }
  else if (n->s<2)
  {
    //gmp_fprintf(f,"%d %Zd %Zd ",n->s,n->z,n->n);
    fprintf(d->f_write,"%d ",n->s+5); // 5 or 6
    mpz_out_str (d->f_write,SSI_BASE, n->z);
    fputc(' ',d->f_write);
    mpz_out_str (d->f_write,SSI_BASE, n->n);
    fputc(' ',d->f_write);
 
    //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 ",d->f_write);
    mpz_out_str (d->f_write,SSI_BASE, n->z);
    fputc(' ',d->f_write);
 
    //if (d->f_debug!=NULL) gmp_fprintf(d->f_debug,"number: gmp \"%Zd\" ",n->z);
  }
}

nlWriteFd_S()

static void nlWriteFd_S ( number  n, const coeffs    )

static

Definition at line 3356 of file longrat.cc.

{
  if(SR_HDL(n) & SR_INT)
  {
    #if SIZEOF_LONG == 4
    StringAppend("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;
      StringAppend("4 %d ",nnn);
    }
    else
    {
      char str[30];// n< 2^64
      mpz_t tmp;
      mpz_init_set_si(tmp,nn);
      StringAppendS("8 ");
      mpz_get_str (str,SSI_BASE, tmp);
      StringAppend("%s ",str);
      mpz_clear(tmp);
    }
    #endif
  }
  else if (n->s<2)
  {
    int l=mpz_sizeinbase(n->z,SSI_BASE);
    int l2=mpz_sizeinbase(n->n,SSI_BASE);
    if (l2>l) l=l2;
    char *str=(char*)omAlloc(l+2);
    StringAppend("%d ",n->s+5); // 5 or 6
    mpz_get_str (str,SSI_BASE, n->z);
    StringAppend("%s ",str);
    mpz_get_str (str,SSI_BASE, n->n);
    StringAppend("%s ",str);
    omFreeSize(str,l+2);
  }
  else /*n->s==3*/
  {
    int l=mpz_sizeinbase(n->z,SSI_BASE);
    char *str=(char*)omAlloc(l+2);
    StringAppendS("8 ");
    mpz_get_str (str,SSI_BASE, n->z);
    StringAppend("%s ",str);
    omFreeSize(str,l+2);
  }
}

nlXExtGcd()

number nlXExtGcd	(	number	a,
		number	b,
		number *	s,
		number *	t,
		number *	u,
		number *	v,
		const coeffs	r
	)

Definition at line 2808 of file longrat.cc.

{
  if (SR_HDL(a) & SR_HDL(b) & SR_INT)
  {
    int uu, vv, x, y;
    int g = int_extgcd(SR_TO_INT(a), SR_TO_INT(b), &uu, &vv, &x, &y);
    *s = INT_TO_SR(uu);
    *t = INT_TO_SR(vv);
    *u = INT_TO_SR(x);
    *v = INT_TO_SR(y);
    return INT_TO_SR(g);
  }
  else
  {
    mpz_t aa, bb;
    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_t erg; mpz_t bs; mpz_t bt;
    mpz_init(erg);
    mpz_init(bs);
    mpz_init(bt);
 
    mpz_gcdext(erg, bs, bt, aa, bb);
 
    mpz_div(aa, aa, erg);
    *u=nlInitMPZ(bb,r);
    *u=nlNeg(*u,r);
    *v=nlInitMPZ(aa,r);
 
    mpz_clear(aa);
    mpz_clear(bb);
 
    *s = nlInitMPZ(bs,r);
    *t = nlInitMPZ(bt,r);
    return nlInitMPZ(erg,r);
  }
}

Variable Documentation

n_SwitchChinRem

VAR int n_SwitchChinRem =0

Definition at line 3074 of file longrat.cc.