#include <coeffs/si_gmp.h>
#include <coeffs/mpr_global.h>

Data Structures
class	gmp_float

class	gmp_complex
	gmp_complex numbers based on More...

Macros
#define	ZTOF 1

#define	QTOF 2

#define	RTOF 3

#define	CTOF 4

Functions
void	setGMPFloatDigits (size_t digits, size_t rest)
	Set size of mantissa digits - the number of output digits (basis 10) the size of mantissa consists of two parts: the "output" part a and the "rest" part b. More...

char *	floatToStr (const gmp_float &r, const unsigned int oprec)

gmp_float	abs (const gmp_float &)

gmp_float	sqrt (const gmp_float &)

gmp_float	hypot (const gmp_float &, const gmp_float &)

gmp_float	sin (const gmp_float &)

gmp_float	cos (const gmp_float &)

gmp_float	log (const gmp_float &)

gmp_float	exp (const gmp_float &)

gmp_float	max (const gmp_float &, const gmp_float &)

gmp_float	numberToFloat (number num, const coeffs src)

gmp_float	numberFieldToFloat (number num, int k, const coeffs src)

gmp_complex	operator+ (const gmp_complex &a, const gmp_float b_d)

gmp_complex	operator- (const gmp_complex &a, const gmp_float b_d)

gmp_complex	operator* (const gmp_complex &a, const gmp_float b_d)

gmp_complex	operator/ (const gmp_complex &a, const gmp_float b_d)

bool	operator== (const gmp_complex &a, const gmp_complex &b)

bool	operator> (const gmp_complex &a, const gmp_complex &b)

bool	operator< (const gmp_complex &a, const gmp_complex &b)

bool	operator>= (const gmp_complex &a, const gmp_complex &b)

bool	operator<= (const gmp_complex &a, const gmp_complex &b)

gmp_float	abs (const gmp_complex &c)

gmp_complex	sqrt (const gmp_complex &x)

gmp_complex	numberToComplex (number num, const coeffs r)

char *	complexToStr (gmp_complex &c, const unsigned int oprec, const coeffs src)

bool	complexNearZero (gmp_complex *c, int digits)

Macro Definition Documentation

#define CTOF 4

Definition at line 21 of file mpr_complex.h.

#define QTOF 2

Definition at line 19 of file mpr_complex.h.

#define RTOF 3

Definition at line 20 of file mpr_complex.h.

#define ZTOF 1

Definition at line 18 of file mpr_complex.h.

Function Documentation

gmp_float abs ( const gmp_float & )

Definition at line 323 of file mpr_complex.cc.

 {
   gmp_float tmp;
   mpf_abs( *(tmp._mpfp()), *a.mpfp() );
   return tmp;
 }

gmp_float abs ( const gmp_complex & c )

inline

Definition at line 305 of file mpr_complex.h.

 {
   return hypot(c.real(),c.imag());
 }

bool complexNearZero	(	gmp_complex *	c,
		int	digits
	)

Definition at line 778 of file mpr_complex.cc.

 {
   gmp_float eps,epsm;
 
   if ( digits < 1 ) return true;
 
   eps=pow(10.0,(int)digits);
   //Print("eps: %s\n",floatToStr(eps,gmp_output_digits));
   eps=(gmp_float)1.0/eps;
   epsm=-eps;
 
   //Print("eps: %s\n",floatToStr(eps,gmp_output_digits));
 
   if ( c->real().sign() > 0 ) // +
     return (c->real() < eps && (c->imag() < eps && c->imag() > epsm));
   else // -
     return (c->real() > epsm && (c->imag() < eps && c->imag() > epsm));
 }

char* complexToStr	(	gmp_complex &	c,
		const unsigned int	oprec,
		const coeffs	src
	)

Definition at line 717 of file mpr_complex.cc.

 {
   const char * complex_parameter = "I";
   int N = 1; // strlen(complex_parameter);
 
   if (nCoeff_is_long_C(src))
   {
     complex_parameter = n_ParameterNames(src)[0];
     N = strlen(complex_parameter);
   }
 
   assume( complex_parameter != NULL && N > 0);
 
   char *out,*in_imag,*in_real;
 
   c.SmallToZero();
   if ( !c.imag().isZero() )
   {
 
     in_real=floatToStr( c.real(), oprec );         // get real part
     in_imag=floatToStr( abs(c.imag()), oprec );    // get imaginary part
 
     if (nCoeff_is_long_C(src))
     {
       int len=(strlen(in_real)+strlen(in_imag)+7+N)*sizeof(char);
       out=(char*)omAlloc(len);
       memset(out,0,len);
       if (  !c.real().isZero() )  // (-23-i*5.43) or (15.1+i*5.3)
         sprintf(out,"(%s%s%s*%s)",in_real,c.imag().sign()>=0?"+":"-",complex_parameter,in_imag);
       else // (-i*43) or (i*34)
       {
         if (c.imag().isOne())
           sprintf(out,"%s", complex_parameter);
         else if (c.imag().isMOne())
           sprintf(out,"-%s", complex_parameter);
         else
           sprintf(out,"(%s%s*%s)",c.imag().sign()>=0?"":"-", complex_parameter,in_imag);
       }
     }
     else
     {
       int len=(strlen(in_real)+strlen(in_imag)+9) * sizeof(char);
       out=(char*)omAlloc( len );
       memset(out,0,len);
       if ( !c.real().isZero() )
         sprintf(out,"(%s%s%s)",in_real,c.imag().sign()>=0?"+I*":"-I*",in_imag);
       else
         sprintf(out,"(%s%s)",c.imag().sign()>=0?"I*":"-I*",in_imag);
     }
     omFree( (void *) in_real );
     omFree( (void *) in_imag );
   }
   else
   {
     out= floatToStr( c.real(), oprec );
   }
 
   return out;
 }

gmp_float cos ( const gmp_float & )

Definition at line 340 of file mpr_complex.cc.

 {
   gmp_float tmp( cos((double)a) );
   return tmp;
 }

gmp_float exp ( const gmp_float & )

Definition at line 359 of file mpr_complex.cc.

 {
   gmp_float tmp( exp((double)a) );
   return tmp;
 }

char* floatToStr	(	const gmp_float &	r,
		const unsigned int	oprec
	)

Definition at line 591 of file mpr_complex.cc.

 {
 #if 1
   mp_exp_t exponent;
   int size,insize;
   char *nout,*out,*in;
 
   insize= (oprec+2) * sizeof(char) + 10;
   in= (char*)omAlloc( insize );
 
   mpf_get_str(in,&exponent,10,oprec,*(r.mpfp()));
 
   if ( (exponent > 0)
   && (exponent < (int)oprec)
   && (strlen(in)-(in[0]=='-'?1:0) == oprec) )
   {
     omFree( (void *) in );
     insize= (exponent+oprec+2) * sizeof(char) + 10;
     in= (char*)omAlloc( insize );
     int newprec= exponent+oprec;
     mpf_get_str(in,&exponent,10,newprec,*(r.mpfp()));
   }
   nout= nicifyFloatStr( in, exponent, oprec, &size, SIGN_EMPTY );
   omFree( (void *) in );
   out= (char*)omAlloc( (strlen(nout)+1) * sizeof(char) );
   strcpy( out, nout );
   omFree( (void *) nout );
 
   return out;
 #else
   // for testing purpose...
   char *out= (char*)omAlloc( (1024) * sizeof(char) );
   sprintf(out,"% .10f",(double)r);
   return out;
 #endif
 }

gmp_float hypot	(	const gmp_float &	,
		const gmp_float &
	)

Definition at line 350 of file mpr_complex.cc.

 {
 #if 1
   return ( sqrt( (a*a) + (b*b) ) );
 #else
   gmp_float tmp( hypot( (double)a, (double)b ) );
   return tmp;
 #endif
 }

gmp_float log ( const gmp_float & )

Definition at line 345 of file mpr_complex.cc.

 {
   gmp_float tmp( log((double)a) );
   return tmp;
 }

gmp_float max	(	const gmp_float &	,
		const gmp_float &
	)

Definition at line 364 of file mpr_complex.cc.

 {
   gmp_float tmp;
   a > b ? tmp= a : tmp= b;
   return tmp;
 }

gmp_float numberFieldToFloat	(	number	num,
		int	k,
		const coeffs	src
	)

Definition at line 440 of file mpr_complex.cc.

 {
   gmp_float r;
 
   switch (k)
   {
   case QTOF:
     if ( num != NULL )
     {
       if (SR_HDL(num) & SR_INT)
       {
         r = gmp_float(SR_TO_INT(num));
       }
       else
       {
         if ( num->s == 0 )
         {
           nlNormalize( num, src ); // FIXME? TODO? // extern void     nlNormalize(number &x, const coeffs r); // FIXME
         }
         if (SR_HDL(num) & SR_INT)
         {
           r = gmp_float(SR_TO_INT(num));
         }
         else
         {
           if ( num->s != 3 )
           {
             r= num->z;
             r/= (gmp_float)num->n;
           }
           else
           {
             r= num->z;
           }
         }
       }
     }
     else
     {
       r= 0.0;
     }
     break;
   case RTOF:
     r= *(gmp_float*)num;
     break;
   case CTOF:
     WerrorS("Can not map from field C to field R!");
     break;
   case ZTOF:
   default:
     WerrorS("Ground field not implemented!");
   } // switch
 
   return r;
 }

gmp_complex numberToComplex	(	number	num,
		const coeffs	r
	)

inline

Definition at line 312 of file mpr_complex.h.

 {
   if (nCoeff_is_long_C(r))
   {
     return *(gmp_complex*)num;
   }
   else
   {
     return gmp_complex( numberToFloat(num, r) );
   }
 }

gmp_float numberToFloat	(	number	num,
		const coeffs	src
	)

Definition at line 374 of file mpr_complex.cc.

 {
   gmp_float r;
 
   if ( nCoeff_is_Q(src) )
   {
     if ( num != NULL )
     {
       if (SR_HDL(num) & SR_INT)
       {
         //n_Print(num, src);printf("\n");
         int nn = SR_TO_INT(num);
         if((long)nn == SR_TO_INT(num))
             r = SR_TO_INT(num);
         else
             r = gmp_float(SR_TO_INT(num));
         //int dd = 20;
         //gmp_printf("\nr = %.*Ff\n",dd,*r.mpfp());
         //getchar();
       }
       else
       {
         if ( num->s == 0 )
         {
           nlNormalize( num, src ); // FIXME? TODO? // extern void     nlNormalize(number &x, const coeffs r); // FIXME
         }
         if (SR_HDL(num) & SR_INT)
         {
           r= SR_TO_INT(num);
         }
         else
         {
           if ( num->s != 3 )
           {
             r= num->z;
             r/= (gmp_float)num->n;
           }
           else
           {
             r= num->z;
           }
         }
       }
     }
     else
     {
       r= 0.0;
     }
   }
   else if (nCoeff_is_long_R(src) || nCoeff_is_long_C(src))
   {
     r= *(gmp_float*)num;
   }
   else if ( nCoeff_is_R(src) )
   {
     // Add some code here :-)
     WerrorS("Ground field not implemented!");
   }
   else
   {
     WerrorS("Ground field not implemented!");
   }
 
   return r;
 }

gmp_complex operator*	(	const gmp_complex &	a,
		const gmp_float	b_d
	)

inline

Definition at line 255 of file mpr_complex.h.

 {
   return gmp_complex( a.r * b_d, a.i * b_d );
 }

gmp_complex operator+	(	const gmp_complex &	a,
		const gmp_float	b_d
	)

inline

Definition at line 247 of file mpr_complex.h.

 {
   return gmp_complex( a.r + b_d, a.i );
 }

gmp_complex operator-	(	const gmp_complex &	a,
		const gmp_float	b_d
	)

inline

Definition at line 251 of file mpr_complex.h.

 {
   return gmp_complex( a.r - b_d, a.i );
 }

gmp_complex operator/	(	const gmp_complex &	a,
		const gmp_float	b_d
	)

inline

Definition at line 259 of file mpr_complex.h.

 {
   return gmp_complex( a.r / b_d, a.i / b_d );
 }

bool operator<	(	const gmp_complex &	a,
		const gmp_complex &	b
	)

inline

Definition at line 273 of file mpr_complex.h.

 {
   return ( a.real() < b.real() );
 }

bool operator<=	(	const gmp_complex &	a,
		const gmp_complex &	b
	)

inline

Definition at line 281 of file mpr_complex.h.

 {
   return ( a.real() <= b.real() );
 }

bool operator==	(	const gmp_complex &	a,
		const gmp_complex &	b
	)

inline

Definition at line 265 of file mpr_complex.h.

 {
   return ( b.real() == a.real() ) && ( b.imag() == a.imag() );
 }

bool operator>	(	const gmp_complex &	a,
		const gmp_complex &	b
	)

inline

Definition at line 269 of file mpr_complex.h.

 {
   return ( a.real() > b.real() );
 }

bool operator>=	(	const gmp_complex &	a,
		const gmp_complex &	b
	)

inline

Definition at line 277 of file mpr_complex.h.

 {
   return ( a.real() >= b.real() );
 }

void setGMPFloatDigits	(	size_t	digits,
		size_t	rest
	)

Set size of mantissa digits - the number of output digits (basis 10) the size of mantissa consists of two parts: the "output" part a and the "rest" part b.

According to the GMP-precision digits is recomputed to bits (basis 2). Two numbers a, b are equal if | a - b | < | a | * 0.1^digits . In this case we have a - b = 0 . The epsilon e is e=0.1^(digits+rest) with 1+e != 1, but 1+0.1*e = 1.

Definition at line 62 of file mpr_complex.cc.

 {
   size_t bits = 1 + (size_t) ((float)digits * 3.5);
   size_t rb = 1 + (size_t) ((float)rest * 3.5);
   size_t db = bits+rb;
   gmp_output_digits= digits;
   mpf_set_default_prec( db );
   if (diff!=NULL) delete diff;
   diff=new gmp_float(0.0);
   mpf_set_prec(*diff->_mpfp(),32);
   if (gmpRel!=NULL) delete gmpRel;
   gmpRel=new gmp_float(0.0);
   mpf_set_prec(*gmpRel->_mpfp(),32);
   mpf_set_d(*gmpRel->_mpfp(),0.1);
   mpf_pow_ui(*gmpRel->_mpfp(),*gmpRel->_mpfp(),digits);
 }

gmp_float sin ( const gmp_float & )

Definition at line 335 of file mpr_complex.cc.

 {
   gmp_float tmp( sin((double)a) );
   return tmp;
 }

gmp_float sqrt ( const gmp_float & )

Definition at line 329 of file mpr_complex.cc.

 {
   gmp_float tmp;
   mpf_sqrt( *(tmp._mpfp()), *a.mpfp() );
   return tmp;
 }

gmp_complex sqrt ( const gmp_complex & x )

Definition at line 689 of file mpr_complex.cc.

 {
   gmp_float r = abs(x);
   gmp_float nr, ni;
   if (r == (gmp_float) 0.0)
   {
     nr = ni = r;
   }
   else if ( x.real() > (gmp_float)0)
   {
     nr = sqrt((gmp_float)0.5 * (r + x.real()));
     ni = x.imag() / nr / (gmp_float)2;
   }
   else
   {
     ni = sqrt((gmp_float)0.5 * (r - x.real()));
     if (x.imag() < (gmp_float)0)
     {
       ni = - ni;
     }
     nr = x.imag() / ni / (gmp_float)2;
   }
   gmp_complex tmp(nr, ni);
   return tmp;
 }

Data Structures

Macros

Functions

Macro Definition Documentation

Function Documentation