Integer ZZ

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Integer ZZ

#define     CMO_ZZ          20

We describe the bignum (multi-precision integer) representation CMO_ZZ in OpenXM. The format is similar to that in GNU MP. (cf. plugin/cmo-gmp.c in the kan/sm1 distribution). CMO_ZZ is defined as follows.

int32 CMO_ZZ int32 f int32 b₀ $\cdots$ int32 b_n

f is a 32bit integer. $b_0, \ldots, b_n$ are unsigned 32bit integers. |f| is equal to n+1. The sign of f represents that of the above integer to be expressed. As stated in Section 2, a negative 32bit integer is represented by two's complement.

In OpenXM the above CMO represents the following integer. ( R = 2³².)

$\begin{displaymath}\mbox{sgn}(f)\times (b_0 R^{0}+ b_1 R^{1} + \cdots + b_{n-1}R^{n-1} + b_n R^n). \end{displaymath}$

Example: If we express int32 by the network byte order, a CMO_ZZ 14 is expressed by

$\begin{displaymath}\mbox{(CMO\_ZZ, 1, 0, 0, 0, e)}, \end{displaymath}$

The corresponding byte sequence is

$\begin{displaymath}\mbox{\tt00 00 00 14 00 00 00 01 00 00 00 0e} \end{displaymath}$

Note that CMO_ZZ 0 is expressed by (CMO_ZZ, 00,00,00,00).

Next: Distributed polynomial Dpolynomial Up: CMOexpressions for numbers and Previous: Zero

Nobuki Takayama 平成14年1月21日