source: git/libpolys/coeffs/gnumpc.cc

/****************************************
*  Computer Algebra System SINGULAR     *
****************************************/
/*
* ABSTRACT: computations with GMP complex floating-point numbers
*
* ngc == number gnu complex
*/
#include "misc/auxiliary.h"

#include "misc/mylimits.h"
#include "reporter/reporter.h"

#include "coeffs/coeffs.h"
#include "coeffs/numbers.h"

#include "coeffs/mpr_complex.h"

#include "coeffs/gnumpc.h"
#include "coeffs/longrat.h"
#include "coeffs/gnumpfl.h"
#include "coeffs/modulop.h"
#include "coeffs/shortfl.h"

#ifdef LDEBUG
// not yet implemented
static BOOLEAN ngcDBTest(number, const char *, const int, const coeffs r)
{
  assume( getCoeffType(r) == n_long_C );

  return TRUE;
}
#endif

static number ngcParameter(int i, const coeffs r)
{
  assume( getCoeffType(r) == n_long_C );
  assume(i==1);

  if( i == 1 )
    return (number)(new gmp_complex( 0L, 1L ));

  return NULL; // new gmp_complex( )  // 0?
}

/*2
* n := i
*/
static number ngcInit (long i, const coeffs r)
{
  assume( getCoeffType(r) == n_long_C );

  gmp_complex* n= new gmp_complex( (long)i, 0L );

  return (number)n;
}

/*2
* convert number to int
*/
static long ngcInt(number &i, const coeffs r)
{
  assume( getCoeffType(r) == n_long_C );

  return ((gmp_complex*)i)->real();
}

static BOOLEAN ngcIsZero (number a, const coeffs r)
{
  assume( getCoeffType(r) == n_long_C );

  return ( ((gmp_complex*)a)->real().isZero() && ((gmp_complex*)a)->imag().isZero());
}

static int ngcSize(number n, const coeffs R)
{
  int r = (int)((gmp_complex*)n)->real();
  if (r < 0) r = -r;
  int i = (int)((gmp_complex*)n)->imag();
  if (i < 0) i = -i;
  int oneNorm = r + i;
  /* basically return the 1-norm of n;
     only if this happens to be zero although n != 0,
     return 1;
     (this code ensures that zero has the size zero) */
  if ((oneNorm == 0.0) & (ngcIsZero(n,R) == FALSE)) oneNorm = 1;
  return oneNorm;
}

/*2
* delete a
*/
static void ngcDelete (number * a, const coeffs r)
{
  assume( getCoeffType(r) == n_long_C );

  if ( *a != NULL )
  {
    delete *(gmp_complex**)a;
    *a=NULL;
  }
}

/*2
 * copy a to b
*/
static number ngcCopy(number a, const coeffs r)
{
  assume( getCoeffType(r) == n_long_C );

  gmp_complex* b= new gmp_complex( *(gmp_complex*)a );
  return (number)b;
}


/*2
* za:= - za
*/
static number ngcNeg (number a, const coeffs R)
{
  assume( getCoeffType(R) == n_long_C );

  gmp_complex* r=(gmp_complex*)a;
  (*r).neg();
  return (number)a;
}

/*
* 1/a
*/
static number ngcInvers(number a, const coeffs R)
{
  assume( getCoeffType(R) == n_long_C );

  gmp_complex* r = NULL;
  if (((gmp_complex*)a)->isZero())
  {
    WerrorS(nDivBy0);
    r = new gmp_complex( 0 );
  }
  else
  {
    r = new gmp_complex( (gmp_complex)1 / (*(gmp_complex*)a) );
  }
  return (number)r;
}

/*2
* u:= a + b
*/
static number ngcAdd (number a, number b, const coeffs R)
{
  assume( getCoeffType(R) == n_long_C );

  gmp_complex* r= new gmp_complex( (*(gmp_complex*)a) + (*(gmp_complex*)b) );
  return (number)r;
}

static void ngcInpAdd (number &a, number b, const coeffs R)
{
  assume( getCoeffType(R) == n_long_C );

  (*(gmp_complex*)a) += (*(gmp_complex*)b);
}

/*2
* u:= a - b
*/
static number ngcSub (number a, number b, const coeffs R)
{
  assume( getCoeffType(R) == n_long_C );

  gmp_complex* r= new gmp_complex( (*(gmp_complex*)a) - (*(gmp_complex*)b) );
  return (number)r;
}

/*2
* u := a * b
*/
static number ngcMult (number a, number b, const coeffs R)
{
  assume( getCoeffType(R) == n_long_C );

  gmp_complex* r= new gmp_complex( (*(gmp_complex*)a) * (*(gmp_complex*)b) );
  return (number)r;
}

static void ngcInpMult (number &a, number b, const coeffs R)
{
  assume( getCoeffType(R) == n_long_C );

  (*(gmp_complex*)a) *= (*(gmp_complex*)b);
}

/*2
* u := a / b
*/
static number ngcDiv (number a, number b, const coeffs r)
{
  assume( getCoeffType(r) == n_long_C );

  if (((gmp_complex*)b)->isZero())
  {
    // a/0 = error
    WerrorS(nDivBy0);
    return (number)new gmp_complex( 0 );
  }
  gmp_complex* res = new gmp_complex( (*(gmp_complex*)a) / (*(gmp_complex*)b) );
  return (number)res;
}

/*2
* u:= x ^ exp
*/
static void ngcPower ( number x, int exp, number * u, const coeffs r)
{
  assume( getCoeffType(r) == n_long_C );

  if ( exp == 0 )
  {
    gmp_complex* n = new gmp_complex(1);
    *u=(number)n;
    return;
  }
  else if ( exp == 1 )
  {
    gmp_complex* n = new gmp_complex();
    *n= *(gmp_complex*)x;
    *u=(number)n;
    return;
  }
  else if (exp == 2)
  {
    gmp_complex* n = new gmp_complex();
    *n= *(gmp_complex*)x;
    *u=(number)n;
    *(gmp_complex*)(*u) *= *(gmp_complex*)n;
    return;
  }
  if ( (exp & 1) == 1 )
  {
    ngcPower(x,exp-1,u, r);
    gmp_complex *n = new gmp_complex();
    *n=*(gmp_complex*)x;
    *(gmp_complex*)(*u) *= *(gmp_complex*)n;
    delete n;
  }
  else
  {
    number w=NULL;
    ngcPower(x,exp/2,&w, r);
    ngcPower(w,2,u, r);
    n_Delete(&w, r);
  }
}

static number ngcRePart(number a, const coeffs r)
{
  assume( getCoeffType(r) == n_long_C );

  gmp_complex* n = new gmp_complex(((gmp_complex*)a)->real());
  return (number)n;
}

static number ngcImPart(number a, const coeffs r)
{
  assume( getCoeffType(r) == n_long_C );

  gmp_complex* n = new gmp_complex(((gmp_complex*)a)->imag());
  return (number)n;
}

/*2
* za >= 0 ?
*/
static BOOLEAN ngcGreaterZero (number a, const coeffs r)
{
  assume( getCoeffType(r) == n_long_C );

  if ( ! ((gmp_complex*)a)->imag().isZero() )
    return ( abs( *(gmp_complex*)a).sign() >= 0 );
  else
    return ( ((gmp_complex*)a)->real().sign() >= 0 );
}

/*2
* a > b ?
*/
static BOOLEAN ngcGreater (number a, number b, const coeffs r)
{
  assume( getCoeffType(r) == n_long_C );

  gmp_complex *aa=(gmp_complex*)a;
  gmp_complex *bb=(gmp_complex*)b;
  return (*aa) > (*bb);
}

/*2
* a = b ?
*/
static BOOLEAN ngcEqual (number a, number b, const coeffs r)
{
  assume( getCoeffType(r) == n_long_C );

  gmp_complex *aa=(gmp_complex*)a;
  gmp_complex *bb=(gmp_complex*)b;
  return (*aa) == (*bb);
}

/*2
* a == 1 ?
*/
static BOOLEAN ngcIsOne (number a, const coeffs r)
{
  assume( getCoeffType(r) == n_long_C );

  return (((gmp_complex*)a)->real().isOne() && ((gmp_complex*)a)->imag().isZero());
  //return (((gmp_complex*)a)->real().isOne());
}

/*2
* a == -1 ?
*/
static BOOLEAN ngcIsMOne (number a, const coeffs r)
{
  assume( getCoeffType(r) == n_long_C );

  return (((gmp_complex*)a)->real().isMOne() && ((gmp_complex*)a)->imag().isZero());
  //return (((gmp_complex*)a)->real().isMOne());
}

/*2
* extracts the number a from s, returns the rest
*/
static const char * ngcRead (const char * s, number * a, const coeffs r)
{
  assume( getCoeffType(r) == n_long_C );
  const char * const complex_parameter = n_ParameterNames(r)[0];
  assume( complex_parameter != NULL );
  const int N = strlen(complex_parameter);

  if ((*s >= '0') && (*s <= '9'))
  {
    gmp_float *re=NULL;
    s=ngfRead(s,(number *)&re, r); // FIXME? TODO? // extern const char *   ngfRead (const char *s, number *a, const coeffs r);
    gmp_complex *aa=new gmp_complex(*re);
    *a=(number)aa;
    delete re;
  }
  else if (strncmp(s, complex_parameter, N)==0)
  {
    s += N;
    gmp_complex *aa=new gmp_complex(0L,1L);
    *a=(number)aa;
  }
  else
  {
    *a=(number) new gmp_complex(1L);
  }
  return s;
}



/*2
* write a floating point number
*/
static void ngcWrite (number a, const coeffs r)
{
  assume( getCoeffType(r) == n_long_C );

  if (a==NULL)
    StringAppendS("0");
  else
  {
    char *out;
    out= complexToStr(*(gmp_complex*)a, r->float_len, r);
    StringAppendS(out);
    //    omFreeSize((void *)out, (strlen(out)+1)* sizeof(char) );
    omFree( (void *)out );
  }
}

static BOOLEAN ngcCoeffIsEqual (const coeffs r, n_coeffType n, void * parameter)
{
  if (n==n_long_C)
  {
    LongComplexInfo* p = (LongComplexInfo *)(parameter);

    if ((p==NULL)
      && (SHORT_REAL_LENGTH==r->float_len)
      && (SHORT_REAL_LENGTH==r->float_len2)
      && (strcmp("i",n_ParameterNames(r)[0]) == 0)
      )
        return TRUE;
    if ((p!=NULL) &&
        (p->float_len == r->float_len) &&
        (p->float_len2 == r->float_len2)
       )
      if (strcmp(p->par_name, n_ParameterNames(r)[0]) == 0)
        return (TRUE);
  }
  return (FALSE);
}

static void ngcKillChar(coeffs r)
{
  char** p = (char**)n_ParameterNames(r);

  const int P = n_NumberOfParameters(r);

  for( int i = 1; i <= P; i++ )
    if (p[i-1] != NULL)
      omFree( (ADDRESS)p[i-1] );

  omFreeSize((ADDRESS)p, P * sizeof(char*));
}

static char* ngcCoeffName(const coeffs r)
{
  STATIC_VAR char ngcCoeffName_buf[40];
  const char *p=n_ParameterNames(r)[0];
  sprintf(ngcCoeffName_buf,"complex,%d,%d,%s",r->float_len,r->float_len2,p);
  return ngcCoeffName_buf;
}

static void ngcCoeffWrite  (const coeffs r, BOOLEAN /*details*/)
{
  Print("real[%s](complex:%d digits, additional %d digits)/(%s^2+1)",n_ParameterNames(r)[0],
        r->float_len, r->float_len2, n_ParameterNames(r)[0]);  /* long C */
}

static number ngcMapQ(number from, const coeffs aRing, const coeffs r)
{
  assume( getCoeffType(r) == n_long_C );
  assume( aRing->rep == n_rep_gap_rat);

  if ( from != NULL )
  {
    gmp_complex *res=new gmp_complex(numberFieldToFloat(from,QTOF));
    return (number)res;
  }
  else
    return NULL;
}

static number ngcMapZ(number from, const coeffs aRing, const coeffs r)
{
  assume( getCoeffType(r) == n_long_C );
  assume( aRing->rep == n_rep_gap_gmp);

  if ( from != NULL )
  {
    if (SR_HDL(from) & SR_INT)
    {
      gmp_float f_i= gmp_float(SR_TO_INT(from));
      gmp_complex *res=new gmp_complex(f_i);
      return (number)res;
    }
    gmp_float f_i=(mpz_ptr)from;
    gmp_complex *res=new gmp_complex(f_i);
    return (number)res;
  }
  else
    return NULL;
}

static number ngcMapLongR(number from, const coeffs aRing, const coeffs r)
{
  assume( getCoeffType(r) == n_long_C );
  assume( getCoeffType(aRing) == n_long_R );

  if ( from != NULL )
  {
    gmp_complex *res=new gmp_complex(*((gmp_float *)from));
    return (number)res;
  }
  else
    return NULL;
}

static number ngcMapR(number from, const coeffs aRing, const coeffs r)
{
  assume( getCoeffType(r) == n_long_C );
  assume( getCoeffType(aRing) == n_R );

  if ( from != NULL )
  {
    gmp_complex *res=new gmp_complex((double)nrFloat(from));
    return (number)res;
  }
  else
    return NULL;
}

static number ngcMapP(number from, const coeffs aRing, const coeffs r)
{
  assume( getCoeffType(r) == n_long_C );
  assume( getCoeffType(aRing) ==  n_Zp );

  if ( from != NULL )
    return ngcInit(npInt(from, aRing), r); // FIXME? TODO? // extern int     npInt         (number &n, const coeffs r);
  else
    return NULL;
}

static number ngcCopyMap(number from, const coeffs aRing, const coeffs r)
{
  assume( getCoeffType(r) == n_long_C );
  assume( getCoeffType(aRing) ==  n_long_C );

  gmp_complex* b = NULL;

  if ( from !=  NULL )
  {
    b = new gmp_complex( *(gmp_complex*)from );
  }
  return (number)b;
}

static number ngcInitMPZ(mpz_t m, const coeffs)
{
  gmp_float mm(m);
  gmp_complex* res = new gmp_complex(mm);
  return (number)res;
}


static nMapFunc ngcSetMap(const coeffs src, const coeffs dst)
{
  assume( getCoeffType(dst) == n_long_C );

  if (src->rep==n_rep_gap_rat) /* Q, Z*/
  {
    return ngcMapQ;
  }
  if (src->rep==n_rep_gap_gmp) /* Z */
  {
    return ngcMapZ;
  }
  if ((src->rep==n_rep_gmp_float) && nCoeff_is_long_R(src))
  {
    return ngcMapLongR;
  }
  if ((src->rep==n_rep_gmp_complex) && nCoeff_is_long_C(src))
  {
    return ngcCopyMap;
  }
  if ((src->rep==n_rep_float) && nCoeff_is_R(src))
  {
    return ngcMapR;
  }
  if ((src->rep==n_rep_int) && nCoeff_is_Zp(src))
  {
    return ngcMapP;
  }
  return NULL;
}

BOOLEAN ngcInitChar(coeffs n, void* parameter)
{
  assume( getCoeffType(n) == n_long_C );
  n->is_field=TRUE;
  n->is_domain=TRUE;
  n->rep=n_rep_gmp_complex;

  n->cfKillChar = ngcKillChar;
  n->ch = 0;
  n->cfCoeffName=ngcCoeffName;
  n->cfCoeffWrite = ngcCoeffWrite;

  n->cfDelete  = ngcDelete;
  //n->cfNormalize=ndNormalize;
  n->cfInit    = ngcInit;
  n->cfInitMPZ = ngcInitMPZ;
  n->cfInt     = ngcInt;
  n->cfAdd     = ngcAdd;
  n->cfInpAdd  = ngcInpAdd;
  n->cfSub     = ngcSub;
  n->cfMult    = ngcMult;
  n->cfInpMult = ngcInpMult;
  n->cfDiv     = ngcDiv;
  n->cfExactDiv= ngcDiv;
  n->cfInpNeg     = ngcNeg;
  n->cfInvers  = ngcInvers;
  n->cfCopy   = ngcCopy;
  n->cfGreater = ngcGreater;
  n->cfEqual   = ngcEqual;
  n->cfIsZero  = ngcIsZero;
  n->cfIsOne   = ngcIsOne;
  n->cfIsMOne  = ngcIsMOne;
  n->cfGreaterZero = ngcGreaterZero;
  n->cfSize    = ngcSize;

  n->cfWriteLong  = ngcWrite;
  n->cfWriteShort = ngcWrite;

  n->cfRead    = ngcRead;
  n->cfPower   = ngcPower;
  n->cfSetMap = ngcSetMap;
  n->cfRePart  = ngcRePart;
  n->cfImPart  = ngcImPart;
    // cfSize  = ndSize;
#ifdef LDEBUG
  n->cfDBTest  = ngcDBTest; // not yet implemented: ngcDBTest
#endif

  n->nCoeffIsEqual = ngcCoeffIsEqual;

  n->cfSetChar=ngcSetChar;

/*
  //r->cfInitChar=nlInitChar;
  r->cfKillChar=NULL;

  r->cfMult  = nlMult;
  r->cfSub   = nlSub;
  r->cfAdd   = nlAdd;
  r->cfDiv   = nlDiv;
  r->cfIntMod= nlIntMod;
  r->cfExactDiv= nlExactDiv;
  r->cfInit = nlInit;
  r->cfSize  = nlSize;
  r->cfInt  = nlInt;
  r->cfDivComp = NULL; // only for ring stuff
  r->cfIsUnit = NULL; // only for ring stuff
  r->cfGetUnit = NULL; // only for ring stuff
  r->cfExtGcd = NULL; // only for ring stuff
  r->cfInpNeg   = nlNeg;
  r->cfInvers= nlInvers;
  r->cfCopy  = nl_Copy;
  r->cfRePart = nl_Copy;
  r->cfImPart = ndReturn0;
  r->cfWriteLong = nlWrite;
  r->cfRead = nlRead;
  r->cfNormalize=nlNormalize;
  r->cfGreater = nlGreater;
  r->cfDivBy = NULL; // only for ring stuff
  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->cfGcd  = nlGcd;
  r->cfLcm  = nlLcm;
  r->cfDelete= nlDelete;
  r->cfSetMap = nlSetMap;
  r->cfName = ndName;
  r->cfInpMult=nlInpMult;
#ifdef LDEBUG
  // debug stuff
  r->cfDBTest=nlDBTest;
#endif

  // the variables:
  r->type = n_Q;
  r->ch = 0;
  r->has_simple_Alloc=FALSE;
  r->has_simple_Inverse=FALSE;
*/

  n->iNumberOfParameters = 1;
  n->cfParameter = ngcParameter;

  char ** pParameterNames = (char **) omAlloc0(sizeof(char *));

  if( parameter != NULL)
  {
    LongComplexInfo* p = (LongComplexInfo*)parameter;
    pParameterNames[0] = omStrDup(p->par_name);
    // fix wrong parameters:
    if (p->float_len<SHORT_REAL_LENGTH) p->float_len=SHORT_REAL_LENGTH;
    n->float_len = p->float_len;
    n->float_len2 = p->float_len2;

  } else // default values, just for testing!
  {
    pParameterNames[0] = omStrDup("i");
    n->float_len = SHORT_REAL_LENGTH;
    n->float_len2 = SHORT_REAL_LENGTH;
  }

  assume( pParameterNames != NULL );
  assume( pParameterNames[0] != NULL );

  n->pParameterNames = (const char**)pParameterNames;

  // NOTE: n->complex_parameter was replaced by n_ParameterNames(n)[0]
  // TODO: nfKillChar MUST destroy n->pParameterNames[0] (0-term. string) && n->pParameterNames (array of size 1)

  return FALSE;
}

void ngcSetChar(const coeffs r)
{
  setGMPFloatDigits(r->float_len, r->float_len2);
}