CONVERSIONS

notation:

   typedef unsigned int  uint;
   typedef unsigned long ulong;
   typedef const char *  cstr;


destination: source


int:         int, long, uint, ulong, ZZ, float, double, xdouble, quad_float, RR
             GF2, zz_p, ZZ_p

long:        int, long, uint, ulong, ZZ, float, double, xdouble, quad_float, RR
             GF2, zz_p, ZZ_p

uint:        int, long, uint, ulong, ZZ, float, double, xdouble, quad_float, RR
             GF2, zz_p, ZZ_p

ulong:       int, long, uint, ulong, ZZ, float, double, xdouble, quad_float, RR
             GF2, zz_p, ZZ_p

ZZ:          int, long, uint, ulong, ZZ, float, double, xdouble, quad_float, RR, cstr 
             GF2, zz_p, ZZ_p

float:       int, long, uint, ulong, ZZ, float, double, xdouble, quad_float, RR

double:      int, long, uint, ulong, ZZ, float, double, xdouble, quad_float, RR

xdouble:     int, long, uint, ulong, ZZ, float, double, xdouble, RR, cstr

quad_float:  int, long, uint, ulong, ZZ, float, double, quad_float, RR, cstr

RR:          int, long, uint, ulong, ZZ, float, double, xdouble, quad_float, 
             RR, cstr


ZZ_p:        long, ZZ, ZZ_p

ZZ_pX:       long, ZZ, ZZ_p; ZZX, ZZ_pX; ZZ_pE; vec_ZZ_p 

zz_p:        long, ZZ, zz_p

zz_pX:       long, ZZ, zz_p; ZZX, zz_pX; zz_pE; vec_zz_p

ZZX:         long, ZZ; ZZX, GF2X, zz_pX, ZZ_pX; vec_ZZ 

GF2:         long, ZZ, GF2

GF2X:        long, ZZ, GF2; ZZX, GF2X; GF2E; vec_GF2

GF2E:        long, ZZ, GF2, GF2E; GF2X

GF2EX:       long, ZZ, GF2, GF2E; ZZX, GF2X, GF2EX; vec_GF2E

ZZ_pE:       long, ZZ, ZZ_p, ZZ_pE; ZZ_pX

ZZ_pEX:      long, ZZ, ZZ_p, ZZ_pE; ZZX, ZZ_pX, ZZ_pEX; vec_ZZ_pE

zz_pE:       long, ZZ, zz_p, zz_pE; zz_pX

zz_pEX:      long, ZZ, zz_p, zz_pE; ZZX, zz_pX, zz_pEX; vec_zz_pE

vec_ZZ:      ZZX
vec_ZZ_p:    ZZ_pX
vec_zz_p:    zz_pX
vec_GF2:     GF2X
vec_ZZ_pE:   ZZ_pEX
vec_zz_pE:   zz_pEX
vec_GF2E:    GF2EX


********** NOTES ***********

nomenclature:

  - integral types: int, long, uint, ulong, ZZ
  - bounded integral types: int, long, uint, ulong
  - floating point types: float, double, xdouble, quad_float, RR


 [1] All conversion operators come in procedural or functional
     form.  To convert  a  of type S to  x  of type T, you can write
        conv(x, a);
     or
        x = conv<T>(a);

     E.g., conv<int>(a), conv<ZZ>(a), conv< Vec<ZZ_p> >, etc.

     The notation conv<T>(a) was introduced in NTL v6.  Prior to
     this, the notation to_T(a) was used.  For backard compatibility,
     the various "to_T" functions have been retained; however, their
     use is dicouraged.  Also note that new conversions have been 
     added in v6 for which there is no corresponding "to_T" function:
     for these, one must use the new "conv<T>" notation.

     Note that conv<T> is implemented as a template function:

        template<class T, class S> T conv(const S& a) 
        { T x; conv(x, a); return x; }

     Thus, the call conv<T>(a) always resolves to the procedure call
     conv(x, a).  Modern C++ compilers do a pretty good job implementing
     the "named return value optimization", so this should not create too
     any unnecessary temporary objects.

 [2] In addition to the conversions listed, for generic vector types, 
     a template conversion operator is provided:

        template<class T, class S> 
        void conv(Vec<T>& x, const Vec<S>& a) {
           long n = a.length();
           x.SetLength(n);
           for (long i = 0; i < n; i++)
              conv(x[i], a[i]);
        }

     This provides component-wise conversion.  This, if there is a conversion
     provided from S to T, then there is automatically a conversion provided
     from Vec<S> to Vec<T>.

     Note that because of the simple implementation, this input a is not allowed 
     to alias the output x.

     Similarly, for generic matrix types Mat<T>, a template conversion 
     operator provides component-wise conversion.  Again, the input may not
     alias the output.

 [3] All conversions from an integral type to a bounded integral type
     compute the result modulo 2^n, where n is the number of bits of the 
     destination type:  no overflow occurs.
 
 [4] All floating point to signed integral conversions compute the floor
     function *exactly*, unless the destination type is int or long
     and overflow occurs, in which case the result is undefined.
     An exception: converting an RR x to int or long will always
     yield floor(x) modulo 2^n, where n is the number of bits
     in the destination type. 

 [5] Conversions from floating point to unsigned int and unsigned long 
     are done via conversions to signed long: if the conversion to long
     overflows, the result is undefined; otherwise, the result
     is computed modulo 2^n, where n is the number of bits in
     the destination type.
 
 [6] The ZZ to double conversion routine is very precise:
     the result is the nearest double, breaking ties using the 
     "round to even" rule.  Overflow results in +/- Infinity.
     All this assumes the underlying floating point adheres to
     the IEEE standard.
 
 [7] All conversions to RR round to the current working precision:
     even converting an RR to an RR.

 
 [8] All conversions from long or ZZ to one of the "mod p" types
        ZZ_p, ZZ_pX, ZZ_pE, ZZ_pEX,
        zz_p, zz_pX, zz_pE, zz_pEX,
        GF2, GF2X, GF2E, GF2EX
     yield the the residue class modulo p (or 2).
 
 [9] All polynomial-to-polynomial conversions apply coefficient-wise
     conversion.  Note that as a rule, if a conversion S to T
     is provided, then there is a corresponding conversion from
     the polynomial ring S[X] to the polynomial ring T[X].

[10] All polynomial/vector conversions simply copy from/to the coefficient
     vector of the polynomial.
 
[11] The GF2X/ZZ_pX/zz_pX to GF2E/ZZ_pE/zz_pE conversions reduce
     the given polynomial modulo the current modulus; the reverse
     conversions yield the standard representative (smallest degree polynomial).

[12] Conversions from GF2, zz_p or ZZ_p to any integral type yeld 
     the standard representative (least non-negative) of the given residue class.
 
[13] All conversions from the type cstr apply the same algorithm
     as is used for reading from an I/O stream, so 
        ZZ x = conv<ZZ>("999999999999999999");
     initializes the ZZ x to the integer 999999999999999999.
 
