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version 1.14, 2015/08/18 02:54:05 version 1.15, 2016/08/22 05:38:27
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 %% $OpenXM: OpenXM/doc/OpenXM-specs/cmo-basic1.tex,v 1.13 2005/03/04 03:49:47 takayama Exp $  %% $OpenXM: OpenXM/doc/OpenXM-specs/cmo-basic1.tex,v 1.14 2015/08/18 02:54:05 noro Exp $
 //&jp \section{ 数, 多項式 の  CMO 表現 }  //&jp \section{ 数, 多項式 の  CMO 表現 }
 //&eg \section{ CMOexpressions for numbers and polynomials }  //&eg \section{ CMOexpressions for numbers and polynomials }
 \label{sec:basic1}  \label{sec:basic1}
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 #define     CMO_RATIONAL       34  #define     CMO_RATIONAL       34
 #define     CMO_COMPLEX       35  #define     CMO_COMPLEX       35
   
   #define     CMO_BIGFLOAT32    52
   
 #define     CMO_INDETERMINATE  60  #define     CMO_INDETERMINATE  60
 #define     CMO_TREE           61  #define     CMO_TREE           61
Line 73  ZZ, QQ, Zero, Rational, Indeterminate $\in$ CMObject/B
Line 74  ZZ, QQ, Zero, Rational, Indeterminate $\in$ CMObject/B
 & & \mbox{ --- 有理数 $a/b$ を表す. } \\  & & \mbox{ --- 有理数 $a/b$ を表す. } \\
 \mbox{Rational}        &:& ({\tt CMO\_RATIONAL}, {\sl CMObject}\, {\rm a}, {\sl CMObject}\, {\rm b}) \\  \mbox{Rational}        &:& ({\tt CMO\_RATIONAL}, {\sl CMObject}\, {\rm a}, {\sl CMObject}\, {\rm b}) \\
 & & \mbox{ ---  $a/b$ を表す. } \\  & & \mbox{ ---  $a/b$ を表す. } \\
 \mbox{Bigfloat}         &:& ({\tt CMO\_BIGFLOAT},  \mbox{Bigfloat32}         &:& ({\tt CMO\_BIGFLOAT32},
 {\sl int32}\, {\rm sign}, {\sl int32}\, {\rm prec}, {\sl int64}\, {\rm exp},  {\sl int32}\, {\rm prec}, {\sl int32}\, {\rm sign}, {\sl int32}\, {\rm exp},
 {\sl int32}\, \mbox{a[1]}, \ldots , {\sl int32}\, \mbox{a[$\lfloor \frac{{\rm prec}+31}{32} \rfloor$]} ) \\  {\sl int32}\, \mbox{a[1]}, \ldots , {\sl int32}\, \mbox{a[k]} ) \\
 &:& \mbox{ --- bigfloat をあらわす. a[i] についてはあとで説明}\\  &:& \mbox{ --- bigfloat をあらわす. a[i], k についてはあとで説明}\\
 \mbox{Complex}        &:& ({\tt CMO\_COMPLEX}, {\sl CMObject}\, {\rm re}, {\sl CMObject}\, {\rm im}) \\  \mbox{Complex}        &:& ({\tt CMO\_COMPLEX}, {\sl CMObject}\, {\rm re}, {\sl CMObject}\, {\rm im}) \\
 & & \mbox{ ---  $a+b\sqrt{-1}$ を表す. } \\  & & \mbox{ ---  $a+b\sqrt{-1}$ を表す. } \\
 \mbox{Indeterminate}        &:& ({\tt CMO\_INDETERMINATE}, {\sl Cstring}\, {\rm v}) \\  \mbox{Indeterminate}        &:& ({\tt CMO\_INDETERMINATE}, {\sl Cstring}\, {\rm v}) \\
Line 103  ZZ, QQ, Zero, Rational, Indeterminate $\in$ CMObject/B
Line 104  ZZ, QQ, Zero, Rational, Indeterminate $\in$ CMObject/B
 & & \mbox{ --- Rational number $a/b$. } \\  & & \mbox{ --- Rational number $a/b$. } \\
 \mbox{Rational}        &:& ({\tt CMO\_RATIONAL}, {\sl CMObject}\, {\rm a}, {\sl CMObject}\, {\rm b}) \\  \mbox{Rational}        &:& ({\tt CMO\_RATIONAL}, {\sl CMObject}\, {\rm a}, {\sl CMObject}\, {\rm b}) \\
 & & \mbox{ ---  Rational expression $a/b$. } \\  & & \mbox{ ---  Rational expression $a/b$. } \\
 \mbox{Bigfloat}         &:& ({\tt CMO\_BIGFLOAT},  \mbox{Bigfloat32}         &:& ({\tt CMO\_BIGFLOAT32},
 {\sl int32}\, {\rm sign}, {\sl int32}\, {\rm prec}, {\sl int64}\, {\rm exp},  {\sl int32}\, {\rm prec}, {\sl int32}\, {\rm sign}, {\sl int32}\, {\rm exp},
 {\sl int32}\, \mbox{a[1]}, \ldots , {\sl int32}\, \mbox{a[$\lfloor \frac{{\rm prec}+31}{32} \rfloor$]} ) \\  {\sl int32}\, \mbox{a[1]}, \ldots , {\sl int32}\, \mbox{a[k]} ) \\
 &:& \mbox{ --- bignfloat. The meaning of a[i] will be explained later.}\\  &:& \mbox{ --- bigfloat. The meaning of a[i], k will be explained later.}\\
 \mbox{Complex}        &:& ({\tt CMO\_COMPLEX}, {\sl CMObject}\, {\rm re}, {\sl CMObject}\, {\rm im}) \\  \mbox{Complex}        &:& ({\tt CMO\_COMPLEX}, {\sl CMObject}\, {\rm re}, {\sl CMObject}\, {\rm im}) \\
 & & \mbox{ ---  Complex number $a+b\sqrt{-1}$. } \\  & & \mbox{ ---  Complex number $a+b\sqrt{-1}$. } \\
 \mbox{Indeterminate}        &:& ({\tt CMO\_INDETERMINATE}, {\sl Cstring}\, {\rm v}) \\  \mbox{Indeterminate}        &:& ({\tt CMO\_INDETERMINATE}, {\sl Cstring}\, {\rm v}) \\
Line 747  $\in$ CMObject/MachineDouble \\
Line 748  $\in$ CMObject/MachineDouble \\
 \bigbreak  \bigbreak
   
 \begin{verbatim}  \begin{verbatim}
 #define CMO_BIGFLOAT   50  
 #define CMO_IEEE_DOUBLE_FLOAT 51  #define CMO_IEEE_DOUBLE_FLOAT 51
 \end{verbatim}  \end{verbatim}
   
Line 779  when the engine starts.
Line 779  when the engine starts.
   
 */  */
   
 \noindent  \subsection{Bigfloat32}
 Group CMObject/Bigfloat requires CMObject/Primitive, CMObject/Basic.\\  /*&jp
 Bigfloat  int32 を基本とした bigfloat の表現方法について述べる.
 $\in$ CMObject/Bigfloat \\  この形式は mpfr を 32bit CPU で使用した時の内部表現と共通である.
   */
   /*&eg
   This subsection describes our format for bigfloat in terms of the int32.
   This format is identical to the internal format of mpfr on 32 bit CPU's.
   */
   Ref: {\tt OpenXM/src/mpfr/bfsize/bfsize.c}
   
 \begin{eqnarray*}  \begin{verbatim}
 \mbox{Bigfloat} &:&  #define     CMO_BIGFLOAT32          52
 \mbox{({\tt CMO\_BIGFLOAT}, } \\  \end{verbatim}
 & & \quad \mbox{ {\sl ZZ} a , {\sl ZZ} e})\\  
 & & \mbox{ --- $a \times 2^e$. } \\  
 \end{eqnarray*}  /*&jp
   Bigfloat32 は次の形式の int32 の配列である.
   */
   /*&eg
   The bigfloat32 is an array of int32 numbers of the following format.
   */
   
   \begin{center}
   {\sl int32}\, {\rm prec}, {\sl int32}\, {\rm sign}, {\sl int32}\, {\rm exp},
   {\sl int32}\, \mbox{a[1]}, \ldots , {\sl int32}\, \mbox{a[k]}
   \end{center}
   
   /*&jp
   p=prec は精度, s=sign は符号(1 が正の数,  -1 (2の補数表現)が負の数) ,
   E=exp は指数部で, 上のデータは数
   $$ s (a[k]/B + a[k-1]/B^2 + ... + a[1]/B^k) 2^E  $$
   を表す.
   ここで $B=2^{32}$,
   $k = \lceil p/32 \rceil$
   である.
   */
   /*&eg
   p=prec is the precision, s=sign is the sign(1 means positive,  -1 (expressed by two's complement) is nevative),
   E=exp is the exponent, and the data above expresses the number
   $$ s (a[k]/B + a[k-1]/B^2 + ... + a[1]/B^k) 2^E.  $$
   Here, $B=2^{32}$,
   $k = \lceil p/32 \rceil$.
   */
   
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