longrat.h File Reference

#include <misc/auxiliary.h>
#include <coeffs/si_gmp.h>
#include <coeffs/coeffs.h>

Go to the source code of this file.

Data Structures
struct	number
	'SR_INT' is the type of those integers small enough to fit into 29 bits. More...

Macros
#define	SR_HDL(A)   ((long)(A))
#define	SR_INT   1L
#define	INT_TO_SR(INT)   ((number) (((long)INT << 2) + SR_INT))
#define	SR_TO_INT(SR)   (((long)SR) >> 2)
#define	MP_SMALL   1

Functions
BOOLEAN	nlInitChar (coeffs, void *)
static int	nlQlogSize (number n, const coeffs r)
	only used by slimgb (tgb.cc) More...
number	nlModP (number q, const coeffs Q, const coeffs Zp)
void	nlNormalize (number &x, const coeffs r)
void	nlInpGcd (number &a, number b, const coeffs r)
void	nlDelete (number *a, const coeffs r)
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...
void	nlGMP (number &i, number n, const coeffs r)
number	nlMapGMP (number from, const coeffs src, const coeffs dst)

---

Data Structure Documentation

struct snumber

'SR_INT' is the type of those integers small enough to fit into 29 bits.

Therefor the value range of this small integers is: $-2^{28}...2^{28}-1$.

Small integers are represented by an immediate integer handle, containing the value instead of pointing to it, which has the following form:

+-------+-------+-------+-------+- - - -+-------+-------+-------+
| guard | sign  | bit   | bit   |       | bit   | tag   | tag   |
| bit   | bit   | 27    | 26    |       | 0     | 0     | 1     |
+-------+-------+-------+-------+- - - -+-------+-------+-------+

Immediate integers handles carry the tag 'SR_INT', i.e. the last bit is 1. This distuingishes immediate integers from other handles which point to structures aligned on 4 byte boundaries and therefor have last bit zero. (The second bit is reserved as tag to allow extensions of this scheme.) Using immediates as pointers and dereferencing them gives address errors.

To aid overflow check the most significant two bits must always be equal, that is to say that the sign bit of immediate integers has a guard bit.

The macros 'INT_TO_SR' and 'SR_TO_INT' should be used to convert between a small integer value and its representation as immediate integer handle.

Large integers and rationals are represented by z and n where n may be undefined (if s==3) NULL represents only deleted values

Definition at line 46 of file longrat.h.

Data Fields
int	debug
mpz_t	n
BOOLEAN	s	parameter s in number: 0 (or FALSE): not normalised rational 1 (or TRUE): normalised rational 3 : integer with n==NULL
mpz_t	z

Macro Definition Documentation

#define INT_TO_SR

(

INT

)

((number) (((long)INT << 2) + SR_INT))

Definition at line 66 of file longrat.h.

#define MP_SMALL   1

Definition at line 69 of file longrat.h.

#define SR_HDL

(

A

)

((long)(A))

Definition at line 63 of file longrat.h.

#define SR_INT   1L

Definition at line 65 of file longrat.h.

#define SR_TO_INT

(

SR

)

(((long)SR) >> 2)

Definition at line 67 of file longrat.h.

Function Documentation

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;
  }
}

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);
}

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	,
		void *
	)

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;
}

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);
  }
}

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;
}

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;
}

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);
}

static int nlQlogSize ( number  n, const coeffs  r  )

inlinestatic

only used by slimgb (tgb.cc)

Definition at line 74 of file longrat.h.

{
  assume( nCoeff_is_Q (r) );

  long nl=n_Size(n,r);
  if (nl==0L) return 0;
  if (nl==1L)
  {
    long i = SR_TO_INT (n);
    unsigned long v;
    v = (i >= 0) ? i : -i;
    int r = 0;

    while(v >>= 1)
    {
      r++;
    }
    return r + 1;
  }
  //assume denominator is 0
  number nn=(number) n;
  return mpz_sizeinbase (nn->z, 2);
}