CONVERSIONS
notation:
typedef unsigned int uint;
typedef unsigned long ulong;
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
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
quad_float: int, long, uint, ulong, ZZ, float, double, quad_float, RR
RR: int, long, uint, ulong, ZZ, float, double, xdouble, quad_float, RR
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(a);
E.g., conv(a), conv(a), conv< Vec >, etc.
The notation conv(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" notation.
Note that conv is implemented as a template function:
template T conv(const S& a)
{ T x; conv(x, a); return x; }
Thus, the call conv(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, there is a generic conversion
from a C-strings (i.e., const char *) to any type T, which is
implemented using templates using the input operator >> for type T.
So, for example, you can write
ZZ x = conv("99999999999999999999999");
Vec v;
conv(v, "[1 2 3]");
If the input fails, the conversion operation will raise an error.
[3] In addition to the conversions listed, for generic vector types,
a template conversion operator is provided:
template
void conv(Vec& x, const Vec~~& 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~~~~ to Vec.
Note that because of the simple implementation, this input a is not
allowed to alias any components of the output x. However, a and x could
be the same.
Similarly, for generic matrix types Mat, a template conversion
operator provides component-wise conversion. Again, the input may not
alias the output.
[4] 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.
[5] 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.
[6] 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.
[7] 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.
[8] All conversions to RR round to the current working precision:
even converting an RR to an RR.
[9] 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).
[10] 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].
[11] All polynomial/vector conversions simply copy from/to the coefficient
vector of the polynomial.
[12] 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).
[13] Conversions from GF2, zz_p or ZZ_p to any integral type yeld
the standard representative (least non-negative) of the given residue class.
~~