===================================================================
RCS file: /home/cvs/OpenXM/src/asir-doc/parts/builtin/num.texi,v
retrieving revision 1.2
retrieving revision 1.7
diff -u -p -r1.2 -r1.7
--- OpenXM/src/asir-doc/parts/builtin/num.texi	1999/12/21 02:47:34	1.2
+++ OpenXM/src/asir-doc/parts/builtin/num.texi	2002/09/03 01:50:59	1.7
@@ -1,4 +1,4 @@
-@comment $OpenXM$
+@comment $OpenXM: OpenXM/src/asir-doc/parts/builtin/num.texi,v 1.6 2002/08/08 05:24:37 noro Exp $
 \BJP
 @node 数の演算,,, 組み込み函数
 @section 数の演算
@@ -19,11 +19,12 @@
 * mt_save mt_load::
 * nm dn::
 * conj real imag::
-* eval::
+* eval deval::
 * pari::
 * setprec::
 * setmod::
 * lrandom::
+* ntoint32 int32ton::
 @end menu
 
 \JP @node idiv irem,,, 数の演算
@@ -418,7 +419,7 @@ function
 @findex random
 
 @table @t
-@item radom([@var{seed}])
+@item random([@var{seed}])
 \JP :: 乱数を生成する. 
 @end table
 
@@ -481,7 +482,7 @@ one can trace a single random number sequence arcoss m
 @findex lrandom
 
 @table @t
-@item lradom(@var{bit})
+@item lrandom(@var{bit})
 \JP :: 多倍長乱数を生成する. 
 \EG :: Generates a long random number.
 @end table
@@ -692,14 +693,16 @@ These functions works also for polynomials with comple
 [2,11,(2-11*@@i)]
 @end example
 
-\JP @node eval,,, 数の演算
-\EG @node eval,,, Numbers
-@subsection @code{eval}
+\JP @node eval deval ,,, 数の演算
+\EG @node eval deval,,, Numbers
+@subsection @code{eval}, @code{deval}
 @findex eval
+@findex deval
 @cindex PARI
 
 @table @t
 @item eval(@var{obj}[,@var{prec}])
+@item deval(@var{obj})
 \JP :: @var{obj} の値の評価. 
 \EG :: Evaluate @var{obj} numerically.
 @end table
@@ -721,11 +724,18 @@ These functions works also for polynomials with comple
 @item
 @var{obj} に含まれる函数の値を可能な限り評価する. 
 @item
-計算は @b{PARI} (@xref{pari}) が行う. 
+@code{deval} は倍精度浮動小数を結果として 
+@code{eval} の場合, 有理数はそのまま残る. 
 @item
+@code{eval} においては, 計算は @b{PARI} (@ref{pari}) が行う. 
+@code{deval} においては, 計算は C 数学ライブラリの関数を用いて行う. 
+@item
+@code{deval} は複素数は扱えない. 
+@item
+@code{eval} においては, 
 @var{prec} を指定した場合, 計算は, 10 進 @var{prec} 桁程度で行われる. 
 @var{prec} の指定がない場合, 現在設定されている精度で行われる. 
-(@xref{setprec})
+(@xref{setprec}.)
 @item
 @table @t
 @item 扱える函数は, 次の通り. 
@@ -740,7 +750,8 @@ These functions works also for polynomials with comple
 @code{exp}, @code{log}, @code{pow(a,b) (a^b)}
 @end table
 @item
-以下の記号を数として評価できる. 
+以下の記号を数として評価できる. ただし @code{@@i} を扱えるのは
+@code{eval}, @code{deval} のみである.
 @table @t
 @item @@i
 虚数単位
@@ -755,12 +766,19 @@ These functions works also for polynomials with comple
 Evaluates the value of the functions contained in @var{obj} as far as
 possible.
 @item
-The computation is done by @b{PARI} (@xref{pari}).
+@code{deval} returns
+double float. Rational numbers remain unchanged in results from @code{eval}.
 @item
+In @code{eval} the computation is done 
+by @b{PARI}. (@xref{pari}.) In @code{deval} the computation is
+done by the C math library.
+@item
+@code{deval} cannot handle complex numbers.
+@item
 When @var{prec} is specified, computation will be performed with a
 precision of about @var{prec}-digits.
 If @var{prec} is not specified, computation is performed with the
-precision set currently. (@xref{setprec})
+precision set currently. (@xref{setprec}.)
 @item
 Currently available numerical functions are listed below.
 Note they are only a small part of whole @b{PARI} functions.
@@ -776,7 +794,8 @@ Note they are only a small part of whole @b{PARI} func
 @code{exp}, @code{log}, @code{pow(a,b) (a^b)}
 @end table
 @item
-Symbols for special values are as the followings.
+Symbols for special values are as the followings. Note that
+@code{@@i} cannot be handled by @code{deval}.
 @table @t
 @item @@i
 unit of imaginary number
@@ -798,6 +817,10 @@ Napier's number (@t{exp}(1))
 0.86602540378443864674620506632
 [121] eval(sin(@@pi/3)-3^(1/2)/2,50);
 -2.78791084448179148471 E-58
+[122] eval(1/2);
+1/2
+[123] deval(sin(1)^2+cos(1)^2);
+1
 @end example
 
 @table @t
@@ -960,7 +983,6 @@ For details of individual functions, refer to the @b{P
 @code{lngamma},
 @code{logagm},
 @code{mat},
-@code{matinvr},
 @code{matrixqz2},
 @code{matrixqz3},
 @code{matsize},
@@ -1075,7 +1097,7 @@ We will improve @b{Asir} so that it can provide more f
 引数がある場合, @b{bigfloat} の桁数を @var{n} 桁に設定する. 
 引数のあるなしにかかわらず, 以前に設定されていた値を返す. 
 @item
-@b{bigfloat} の計算は @b{PARI} (@xref{pari}) によって行われる. 
+@b{bigfloat} の計算は @b{PARI} (@ref{pari}) によって行われる. 
 @item
 @b{bigfloat} での計算に対し有効である. 
 @b{bigfloat} の flag を on にする方法は, @code{ctrl} を参照. 
@@ -1091,7 +1113,7 @@ The return value is always the previous precision in d
 the existence of an argument.
 
 @item
-@b{Bigfloat} operations are done by @b{PARI}. (@xref{pari})
+@b{Bigfloat} operations are done by @b{PARI}. (@xref{pari}.)
 @item
 This is effective for computations in @b{bigfloat}.
 Refer to @code{ctrl()} for turning on the `@b{bigfloat} flag.'
@@ -1113,7 +1135,7 @@ Therefore, it is safe to specify a larger value.
 
 @table @t
 \JP @item 参照
-@fref{ctrl}, @fref{eval}, @fref{pari}.
+@fref{ctrl}, @fref{eval deval}, @fref{pari}.
 @end table
 
 \JP @node setmod,,, 数の演算
@@ -1177,3 +1199,50 @@ return to toplevel
 \EG @fref{dp_mod dp_rat}, @fref{Types of numbers}.
 @end table
 
+\JP @node ntoint32 int32ton,,, 数の演算
+\EG @node ntoint32 int32ton,,, Numbers
+@subsection @code{ntoint32}, @code{int32ton}
+@findex ntoint32
+@findex int32ton
+
+@table @t
+@item ntoint32(@var{n})
+@itemx int32ton(@var{int32})
+\JP :: 非負整数と符号なし 32bit 整数の間の型変換. 
+\EG :: Type-conversion between a non-negative integer and an unsigned 32bit integer.
+@end table
+
+@table @var
+@item return
+\JP 符号なし 32bit 整数または非負整数
+\EG unsigned 32bit integer or non-negative integer
+@item n
+\JP 2^32 未満の非負整数
+\EG non-negative interger less than 2^32
+@item int32
+\JP 符号なし 32bit 整数
+\EG unsigned 32bit integer
+@end table
+
+@itemize @bullet
+\BJP
+@item 非負整数 (識別子 1) の符号なし 32bit 整数 (識別子 10) への変換, 
+またはその逆変換を行う. 
+@item 32bit 整数は @b{OpenXM} の基本構成要素であり, 整数をその型で送信
+する必要がある場合に用いる. 
+\E
+\BEG
+@item These functions do conversions between non-negative 
+integers (the type id 1) and unsigned 32bit integers (the type id 10).
+@item An unsigned 32bit integer is a fundamental construct of @b{OpenXM}
+and one often has to send an integer to a server as an unsigned 32bit
+integer. These functions are used in such a case.
+\E
+@end itemize
+
+@table @t
+\JP @item 参照
+\EG @item References
+\JP @fref{分散計算}, @fref{数の型}.
+\EG @fref{Distributed computation}, @fref{Types of numbers}.
+@end table