conversions.txt

数值算法库for Unix

CONVERSIONS

destination: source


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

unsigned 
int:         ZZ

unsigned 
long:        ZZ

xdouble:     int, long, ZZ, float, double, xdouble, quad_float, RR, 
             unsigned int, unsigned long, const char*

quad_float:  int, long, ZZ, float, double, xdouble, quad_float, RR, 
             unsigned int, unsigned long, const char*

RR:          int, long, ZZ, float, double, xdouble, quad_float, RR, 
             unsigned int, unsigned long, const char*

ZZ:          int, long, ZZ, float, double, xdouble, quad_float, RR, 
             unsigned int, unsigned long, const char*

ZZ_p:        long, ZZ
vec_ZZ_p:    vec_ZZ
ZZ_pX:       long, ZZ_p, ZZ, ZZX, vec_ZZ_p

zz_p:        long, ZZ
vec_zz_p:    vec_ZZ
ZZ_pX:       long, zz_p, ZZ, ZZX, vec_zz_p

vec_ZZ:      vec_ZZ_p, vec_zz_p
ZZX:         long, ZZ, ZZ_pX, zz_pX

GF2:         long, ZZ
vec_GF2:     GF2X
GF2X:        long, ZZ, GF2, vec_GF2

GF2E:        long, ZZ, GF2, GF2X

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

mat_ZZ_p:    mat_ZZ  

mat_zz_p:    mat_ZZ  

ZZ_pE:       long, ZZ, ZZ_p, ZZ_pX
ZZ_pEX:      long, ZZ, ZZ_p, ZZ_pE, ZZ_pX

zz_pE:       long, ZZ, zz_p, zz_pX
zz_pEX:      long, ZZ, zz_p, zz_pE, zz_pX


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

 [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 = to_T(a);
 
     Note that when T is 'unsigned int/long', the functional
     forms are 'to_uint' and 'to_ulong'.
 
 [2] All conversions from ZZ to signed or unsigned int or long compute 
     the result modulo 2^n, where n is the number of bits of 
     the destination type.
 
 [2] All floating point to integral conversions compute the floor
     function *exactly*.
 
 [3] 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.
 
 [4] All conversions to RR round to the current working precision.
 
 [5] All conversions from long or ZZ to one of "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.
 
 [6] All polynomial to polynomial conversions apply coefficient-wise
     conversion.
 
 [7] All vector/matrix to vector/matrix conversions apply element-wise
     conversion.
 
 [8] The GF2X/ZZ_pX/zz_pX to GF2E/ZZ_pE/zz_pE conversions reduce
     the given polynomial modulo the current modulus.
 
 [9] All conversions from the type  const char*  apply the same algorithm
     as is used for reading from an I/O stream, so 
        ZZ x = to_ZZ("999999999999999999");
     initializes the ZZ x to the integer 999999999999999999.
 
[10] The conversions to vec_ZZ from vec_ZZ_p and vec_zz_p copy the
     standard non-negative residues; likewise for the conversions
     to ZZX from ZZ_pX and zz_pX.