| version 1.2, 1999/12/21 02:47:34 |
version 1.13, 2019/03/29 01:57:46 |
|
|
| @comment $OpenXM$ |
@comment $OpenXM: OpenXM/src/asir-doc/parts/builtin/num.texi,v 1.12 2016/08/29 04:56:58 noro Exp $ |
| \BJP |
\BJP |
| @node $B?t$N1i;;(B,,, $BAH$_9~$_H!?t(B |
@node $B?t$N1i;;(B,,, $BAH$_9~$_H!?t(B |
| @section $B?t$N1i;;(B |
@section $B?t$N1i;;(B |
|
|
| * fac:: |
* fac:: |
| * igcd igcdcntl:: |
* igcd igcdcntl:: |
| * ilcm:: |
* ilcm:: |
| |
* isqrt:: |
| * inv:: |
* inv:: |
| * prime lprime:: |
* prime lprime:: |
| * random:: |
* random:: |
| * mt_save mt_load:: |
* mt_save mt_load:: |
| * nm dn:: |
* nm dn:: |
| * conj real imag:: |
* conj real imag:: |
| * eval:: |
* eval deval:: |
| * pari:: |
* pari:: |
| * setprec:: |
* setbprec setprec:: |
| * setmod:: |
* setmod:: |
| * lrandom:: |
* lrandom:: |
| |
* ntoint32 int32ton:: |
| |
* setround:: |
| |
* inttorat:: |
| @end menu |
@end menu |
| |
|
| \JP @node idiv irem,,, $B?t$N1i;;(B |
\JP @node idiv irem,,, $B?t$N1i;;(B |
|
|
| @item return |
@item return |
| \JP $B@0?t(B |
\JP $B@0?t(B |
| \EG integer |
\EG integer |
| @item i1,i2 |
@item i1 i2 |
| \JP $B@0?t(B |
\JP $B@0?t(B |
| \EG integer |
\EG integer |
| @end table |
@end table |
| Line 158 Returns 0 if the argument @var{i} is negative. |
|
| Line 162 Returns 0 if the argument @var{i} is negative. |
|
| @item return |
@item return |
| \JP $B@0?t(B |
\JP $B@0?t(B |
| \EG integer |
\EG integer |
| @item i1,i2,i |
@item i1 i2 i |
| \JP $B@0?t(B |
\JP $B@0?t(B |
| \EG integer |
\EG integer |
| @end table |
@end table |
| Line 259 In most cases @code{3} is the fastest, but there are e |
|
| Line 263 In most cases @code{3} is the fastest, but there are e |
|
| @item return |
@item return |
| \JP $B@0?t(B |
\JP $B@0?t(B |
| \EG integer |
\EG integer |
| @item i1,i2 |
@item i1 i2 |
| \JP $B@0?t(B |
\JP $B@0?t(B |
| \EG integer |
\EG integer |
| @end table |
@end table |
| Line 286 If one of argument is equal to 0, the return 0. |
|
| Line 290 If one of argument is equal to 0, the return 0. |
|
| @fref{igcd igcdcntl}, @fref{mt_save mt_load}. |
@fref{igcd igcdcntl}, @fref{mt_save mt_load}. |
| @end table |
@end table |
| |
|
| |
\JP @node isqrt,,, $B?t$N1i;;(B |
| |
\EG @node isqrt,,, Numbers |
| |
@subsection @code{isqrt} |
| |
@findex isqrt |
| |
|
| |
@table @t |
| |
@item isqrt(@var{n}) |
| |
\JP :: $BJ?J}:,$r1[$($J$$:GBg$N@0?t$r5a$a$k(B. |
| |
\EG :: The integer square root of @var{n}. |
| |
@end table |
| |
|
| |
@table @var |
| |
@item return |
| |
\JP $BHsIi@0?t(B |
| |
\EG non-negative integer |
| |
@item n |
| |
\JP $BHsIi@0?t(B |
| |
\EG non-negative integer |
| |
@end table |
| |
|
| \JP @node inv,,, $B?t$N1i;;(B |
\JP @node inv,,, $B?t$N1i;;(B |
| \EG @node inv,,, Numbers |
\EG @node inv,,, Numbers |
| @subsection @code{inv} |
@subsection @code{inv} |
| Line 301 If one of argument is equal to 0, the return 0. |
|
| Line 325 If one of argument is equal to 0, the return 0. |
|
| @item return |
@item return |
| \JP $B@0?t(B |
\JP $B@0?t(B |
| \EG integer |
\EG integer |
| @item i,m |
@item i m |
| \JP $B@0?t(B |
\JP $B@0?t(B |
| \EG integer |
\EG integer |
| @end table |
@end table |
|
|
| @findex random |
@findex random |
| |
|
| @table @t |
@table @t |
| @item radom([@var{seed}]) |
@item random([@var{seed}]) |
| \JP :: $BMp?t$r@8@.$9$k(B. |
\JP :: $BMp?t$r@8@.$9$k(B. |
| @end table |
@end table |
| |
|
| Line 481 one can trace a single random number sequence arcoss m |
|
| Line 505 one can trace a single random number sequence arcoss m |
|
| @findex lrandom |
@findex lrandom |
| |
|
| @table @t |
@table @t |
| @item lradom(@var{bit}) |
@item lrandom(@var{bit}) |
| \JP :: $BB?G\D9Mp?t$r@8@.$9$k(B. |
\JP :: $BB?G\D9Mp?t$r@8@.$9$k(B. |
| \EG :: Generates a long random number. |
\EG :: Generates a long random number. |
| @end table |
@end table |
| Line 692 These functions works also for polynomials with comple |
|
| Line 716 These functions works also for polynomials with comple |
|
| [2,11,(2-11*@@i)] |
[2,11,(2-11*@@i)] |
| @end example |
@end example |
| |
|
| \JP @node eval,,, $B?t$N1i;;(B |
\JP @node eval deval ,,, $B?t$N1i;;(B |
| \EG @node eval,,, Numbers |
\EG @node eval deval,,, Numbers |
| @subsection @code{eval} |
@subsection @code{eval}, @code{deval} |
| @findex eval |
@findex eval |
| |
@findex deval |
| @cindex PARI |
@cindex PARI |
| |
|
| @table @t |
@table @t |
| @item eval(@var{obj}[,@var{prec}]) |
@item eval(@var{obj}[,@var{prec}]) |
| |
@item deval(@var{obj}) |
| \JP :: @var{obj} $B$NCM$NI>2A(B. |
\JP :: @var{obj} $B$NCM$NI>2A(B. |
| \EG :: Evaluate @var{obj} numerically. |
\EG :: Evaluate @var{obj} numerically. |
| @end table |
@end table |
| Line 721 These functions works also for polynomials with comple |
|
| Line 747 These functions works also for polynomials with comple |
|
| @item |
@item |
| @var{obj} $B$K4^$^$l$kH!?t$NCM$r2DG=$J8B$jI>2A$9$k(B. |
@var{obj} $B$K4^$^$l$kH!?t$NCM$r2DG=$J8B$jI>2A$9$k(B. |
| @item |
@item |
| $B7W;;$O(B @b{PARI} (@xref{pari}) $B$,9T$&(B. |
@code{deval} $B$OG\@:EYIbF0>.?t$r7k2L$H$7$F(B |
| |
@code{eval} $B$N>l9g(B, $BM-M}?t$O$=$N$^$^;D$k(B. |
| @item |
@item |
| |
@code{eval} $B$K$*$$$F$O(B, $B7W;;$O(B @b{MPFR} $B%i%$%V%i%j$,9T$&(B. |
| |
@code{deval} $B$K$*$$$F$O(B, $B7W;;$O(B C $B?t3X%i%$%V%i%j$N4X?t$rMQ$$$F9T$&(B. |
| |
@item |
| |
@code{deval} $B$OJ#AG?t$O07$($J$$(B. |
| |
@item |
| |
@code{eval} $B$K$*$$$F$O(B, |
| @var{prec} $B$r;XDj$7$?>l9g(B, $B7W;;$O(B, 10 $B?J(B @var{prec} $B7eDxEY$G9T$o$l$k(B. |
@var{prec} $B$r;XDj$7$?>l9g(B, $B7W;;$O(B, 10 $B?J(B @var{prec} $B7eDxEY$G9T$o$l$k(B. |
| @var{prec} $B$N;XDj$,$J$$>l9g(B, $B8=:_@_Dj$5$l$F$$$k@:EY$G9T$o$l$k(B. |
@var{prec} $B$N;XDj$,$J$$>l9g(B, $B8=:_@_Dj$5$l$F$$$k@:EY$G9T$o$l$k(B. |
| (@xref{setprec}) |
(@xref{setbprec setprec}.) |
| @item |
@item |
| @table @t |
@table @t |
| @item $B07$($kH!?t$O(B, $B<!$NDL$j(B. |
@item $B07$($kH!?t$O(B, $B<!$NDL$j(B. |
| Line 740 These functions works also for polynomials with comple |
|
| Line 773 These functions works also for polynomials with comple |
|
| @code{exp}, @code{log}, @code{pow(a,b) (a^b)} |
@code{exp}, @code{log}, @code{pow(a,b) (a^b)} |
| @end table |
@end table |
| @item |
@item |
| $B0J2<$N5-9f$r?t$H$7$FI>2A$G$-$k(B. |
$B0J2<$N5-9f$r?t$H$7$FI>2A$G$-$k(B. $B$?$@$7(B @code{@@i} $B$r07$($k$N$O(B |
| |
@code{eval}, @code{deval} $B$N$_$G$"$k(B. |
| @table @t |
@table @t |
| @item @@i |
@item @@i |
| $B5u?tC10L(B |
$B5u?tC10L(B |
| Line 755 These functions works also for polynomials with comple |
|
| Line 789 These functions works also for polynomials with comple |
|
| Evaluates the value of the functions contained in @var{obj} as far as |
Evaluates the value of the functions contained in @var{obj} as far as |
| possible. |
possible. |
| @item |
@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 |
@item |
| |
In @code{eval} the computation is done |
| |
by @b{MPFR} library. 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 |
When @var{prec} is specified, computation will be performed with a |
| precision of about @var{prec}-digits. |
precision of about @var{prec}-digits. |
| If @var{prec} is not specified, computation is performed with the |
If @var{prec} is not specified, computation is performed with the |
| precision set currently. (@xref{setprec}) |
precision set currently. (@xref{setbprec setprec}.) |
| @item |
@item |
| Currently available numerical functions are listed below. |
Currently available numerical functions are listed below. |
| Note they are only a small part of whole @b{PARI} functions. |
|
| |
|
| @table @t |
@table @t |
| @code{sin}, @code{cos}, @code{tan}, |
@code{sin}, @code{cos}, @code{tan}, |
| Line 776 Note they are only a small part of whole @b{PARI} func |
|
| Line 816 Note they are only a small part of whole @b{PARI} func |
|
| @code{exp}, @code{log}, @code{pow(a,b) (a^b)} |
@code{exp}, @code{log}, @code{pow(a,b) (a^b)} |
| @end table |
@end table |
| @item |
@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 |
@table @t |
| @item @@i |
@item @@i |
| unit of imaginary number |
unit of imaginary number |
| Line 798 Napier's number (@t{exp}(1)) |
|
| Line 839 Napier's number (@t{exp}(1)) |
|
| 0.86602540378443864674620506632 |
0.86602540378443864674620506632 |
| [121] eval(sin(@@pi/3)-3^(1/2)/2,50); |
[121] eval(sin(@@pi/3)-3^(1/2)/2,50); |
| -2.78791084448179148471 E-58 |
-2.78791084448179148471 E-58 |
| |
[122] eval(1/2); |
| |
1/2 |
| |
[123] deval(sin(1)^2+cos(1)^2); |
| |
1 |
| @end example |
@end example |
| |
|
| @table @t |
@table @t |
| \JP @item $B;2>H(B |
\JP @item $B;2>H(B |
| \EG @item References |
\EG @item References |
| @fref{ctrl}, @fref{setprec}, @fref{pari}. |
@fref{ctrl}, @fref{setbprec setprec}. |
| @end table |
@end table |
| |
|
| \JP @node pari,,, $B?t$N1i;;(B |
\JP @node pari,,, $B?t$N1i;;(B |
| Line 846 Napier's number (@t{exp}(1)) |
|
| Line 891 Napier's number (@t{exp}(1)) |
|
| $BH!?tCM$NI>2A$r9bB.$K9T$&$3$H$,$G$-$k(B. @b{PARI} $B$OB>$N%W%m%0%i%`$+$i(B |
$BH!?tCM$NI>2A$r9bB.$K9T$&$3$H$,$G$-$k(B. @b{PARI} $B$OB>$N%W%m%0%i%`$+$i(B |
| $B%5%V%k!<%A%s%i%$%V%i%j$H$7$FMQ$$$k$3$H$,$G$-(B, $B$^$?(B, @samp{gp} $B$H$$$&(B |
$B%5%V%k!<%A%s%i%$%V%i%j$H$7$FMQ$$$k$3$H$,$G$-(B, $B$^$?(B, @samp{gp} $B$H$$$&(B |
| @b{PARI}$B%i%$%V%i%j$N%$%s%?%U%'!<%9$K$h$j(B UNIX $B$N%"%W%j%1!<%7%g%s$H$7$F(B |
@b{PARI}$B%i%$%V%i%j$N%$%s%?%U%'!<%9$K$h$j(B UNIX $B$N%"%W%j%1!<%7%g%s$H$7$F(B |
| $BMxMQ$9$k$3$H$b$G$-$k(B. $B8=:_$N%P!<%8%g%s$O(B @b{2.0.17beta} $B$G$$$/$D$+$N(B ftp |
$BMxMQ$9$k$3$H$b$G$-$k(B. |
| site ($B$?$H$($P(B @code{ftp://megrez.ceremab.u-bordeaux.fr/pub/pari}) |
|
| $B$+$i(B anonymous ftp $B$G$-$k(B. |
|
| @item |
@item |
| $B:G8e$N0z?t(B @var{prec} $B$G7W;;@:EY$r;XDj$G$-$k(B. |
$B:G8e$N0z?t(B @var{prec} $B$G7W;;@:EY$r;XDj$G$-$k(B. |
| @var{prec} $B$r>JN,$7$?>l9g(B @code{setprec()} $B$G;XDj$7$?@:EY$H$J$k(B. |
@var{prec} $B$r>JN,$7$?>l9g(B @code{setprec()} $B$G;XDj$7$?@:EY$H$J$k(B. |
| Line 870 function evaluations as well as arithmetic operations |
|
| Line 913 function evaluations as well as arithmetic operations |
|
| speed. It can also be used from other external programs as a library. |
speed. It can also be used from other external programs as a library. |
| It provides a language interface named @samp{gp} to its library, which |
It provides a language interface named @samp{gp} to its library, which |
| enables a user to use @b{PARI} as a calculator which runs on UNIX. |
enables a user to use @b{PARI} as a calculator which runs on UNIX. |
| The current version is @b{2.0.17beta}. It can be obtained by several ftp |
|
| sites. (For example, @code{ftp://megrez.ceremab.u-bordeaux.fr/pub/pari}.) |
|
| @item |
@item |
| The last argument (optional) @var{int} specifies the precision in digits |
The last argument (optional) @var{int} specifies the precision in digits |
| for bigfloat operation. |
for bigfloat operation. |
| Line 960 For details of individual functions, refer to the @b{P |
|
| Line 1001 For details of individual functions, refer to the @b{P |
|
| @code{lngamma}, |
@code{lngamma}, |
| @code{logagm}, |
@code{logagm}, |
| @code{mat}, |
@code{mat}, |
| @code{matinvr}, |
|
| @code{matrixqz2}, |
@code{matrixqz2}, |
| @code{matrixqz3}, |
@code{matrixqz3}, |
| @code{matsize}, |
@code{matsize}, |
| Line 1019 For details of individual functions, refer to the @b{P |
|
| Line 1059 For details of individual functions, refer to the @b{P |
|
| |
|
| \BJP |
\BJP |
| @item |
@item |
| @b{Asir} $B$GMQ$$$F$$$k$N$O(B @b{PARI} $B$N$[$s$N0lIt$N5!G=$G$"$k$,(B, $B:#8e(B |
@b{Asir} $B$GMQ$$$F$$$k$N$O(B @b{PARI} $B$N$[$s$N0lIt$N5!G=$G$"$k(B. |
| $B$h$jB?$/$N5!G=$,MxMQ$G$-$k$h$&2~NI$9$kM=Dj$G$"$k(B. |
|
| \E |
\E |
| \BEG |
\BEG |
| @item |
@item |
| @b{Asir} currently uses only a very small subset of @b{PARI}. |
@b{Asir} currently uses only a very small subset of @b{PARI}. |
| We will improve @b{Asir} so that it can provide more functions of |
|
| @b{PARI}. |
|
| \E |
\E |
| @end itemize |
@end itemize |
| |
|
| Line 1045 We will improve @b{Asir} so that it can provide more f |
|
| Line 1082 We will improve @b{Asir} so that it can provide more f |
|
| @table @t |
@table @t |
| \JP @item $B;2>H(B |
\JP @item $B;2>H(B |
| \EG @item References |
\EG @item References |
| @fref{setprec}. |
@fref{setbprec setprec}. |
| @end table |
@end table |
| |
|
| \JP @node setprec,,, $B?t$N1i;;(B |
\JP @node setbprec setprec,,, $B?t$N1i;;(B |
| \EG @node setprec,,, Numbers |
\EG @node setbprec setprec,,, Numbers |
| @subsection @code{setprec} |
@subsection @code{setbprec}, @code{setprec} |
| |
@findex setbprec |
| @findex setprec |
@findex setprec |
| @cindex PARI |
|
| |
|
| @table @t |
@table @t |
| @item setprec([@var{n}]) |
@item setbprec([@var{n}]) |
| \JP :: @b{bigfloat} $B$N7e?t$r(B @var{n} $B7e$K@_Dj$9$k(B. |
@itemx setprec([@var{n}]) |
| \EG :: Sets the precision for @b{bigfloat} operations to @var{n} digits. |
\JP :: @b{setbprec}, @b{setprec} $B$O(B @b{bigfloat} $B$N@:EY$r$=$l$>$l(B 2 $B?J(B, 10$B?J(B @var{n} $B7e$K@_Dj$9$k(B. |
| |
\EG :: @b{setbprec}, @b{setprec} set the precision for @b{bigfloat} operations to @var{n} bits, @var{n} digits respectively. |
| @end table |
@end table |
| |
|
| @table @var |
@table @var |
| Line 1075 We will improve @b{Asir} so that it can provide more f |
|
| Line 1113 We will improve @b{Asir} so that it can provide more f |
|
| $B0z?t$,$"$k>l9g(B, @b{bigfloat} $B$N7e?t$r(B @var{n} $B7e$K@_Dj$9$k(B. |
$B0z?t$,$"$k>l9g(B, @b{bigfloat} $B$N7e?t$r(B @var{n} $B7e$K@_Dj$9$k(B. |
| $B0z?t$N$"$k$J$7$K$+$+$o$i$:(B, $B0JA0$K@_Dj$5$l$F$$$?CM$rJV$9(B. |
$B0z?t$N$"$k$J$7$K$+$+$o$i$:(B, $B0JA0$K@_Dj$5$l$F$$$?CM$rJV$9(B. |
| @item |
@item |
| @b{bigfloat} $B$N7W;;$O(B @b{PARI} (@xref{pari}) $B$K$h$C$F9T$o$l$k(B. |
@b{bigfloat} $B$N7W;;$O(B @b{MPFR} $B%i%$%V%i%j$K$h$C$F9T$o$l$k(B. |
| @item |
@item |
| @b{bigfloat} $B$G$N7W;;$KBP$7M-8z$G$"$k(B. |
@b{bigfloat} $B$G$N7W;;$KBP$7M-8z$G$"$k(B. |
| @b{bigfloat} $B$N(B flag $B$r(B on $B$K$9$kJ}K!$O(B, @code{ctrl} $B$r;2>H(B. |
@b{bigfloat} $B$N(B flag $B$r(B on $B$K$9$kJ}K!$O(B, @code{ctrl} $B$r;2>H(B. |
| Line 1085 We will improve @b{Asir} so that it can provide more f |
|
| Line 1123 We will improve @b{Asir} so that it can provide more f |
|
| \E |
\E |
| \BEG |
\BEG |
| @item |
@item |
| When an argument is given, it |
When an argument @var{n} is given, these functions |
| sets the precision for @b{bigfloat} operations to @var{n} digits. |
set the precision for @b{bigfloat} operations to @var{n} bits or @var{n} digits. |
| The return value is always the previous precision in digits regardless of |
The return value is always the previous precision regardless of |
| the existence of an argument. |
the existence of an argument. |
| |
|
| @item |
@item |
| @b{Bigfloat} operations are done by @b{PARI}. (@xref{pari}) |
@b{Bigfloat} operations are done by @b{MPFR} library. |
| @item |
@item |
| This is effective for computations in @b{bigfloat}. |
This is effective for computations in @b{bigfloat}. |
| Refer to @code{ctrl()} for turning on the `@b{bigfloat} flag.' |
Refer to @code{ctrl()} for turning on the `@b{bigfloat} flag.' |
| Line 1104 Therefore, it is safe to specify a larger value. |
|
| Line 1142 Therefore, it is safe to specify a larger value. |
|
| |
|
| @example |
@example |
| [1] setprec(); |
[1] setprec(); |
| 9 |
15 |
| [2] setprec(100); |
[2] setprec(100); |
| 9 |
15 |
| [3] setprec(100); |
[3] setprec(100); |
| 96 |
99 |
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[4] setbprec(); |
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332 |
| @end example |
@end example |
| |
|
| @table @t |
@table @t |
| \JP @item $B;2>H(B |
\JP @item $B;2>H(B |
| @fref{ctrl}, @fref{eval}, @fref{pari}. |
@fref{ctrl}, @fref{eval deval}. |
| @end table |
@end table |
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|
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\JP @node setround,,, $B?t$N1i;;(B |
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\EG @node setround,,, Numbers |
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@subsection @code{setround} |
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@findex setround |
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|
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@table @t |
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@item setround([@var{mode}]) |
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\JP :: @b{bigfloat} $B$N4]$a%b!<%I$r(B @var{mode} $B$K@_Dj$9$k(B. |
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\EG :: Sets the rounding mode @var{mode}. |
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@end table |
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|
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@table @var |
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@item return |
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\JP $B@0?t(B |
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\EG integer |
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@item mode |
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\JP $B@0?t(B |
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\EG integer |
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@end table |
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|
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@itemize @bullet |
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\BJP |
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@item |
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$B0z?t$,$"$k>l9g(B, @b{bigfloat} $B$N4]$a%b!<%I$r(B @var{mode} $B$K@_Dj$9$k(B. |
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$B0z?t$N$"$k$J$7$K$+$+$o$i$:(B, $B0JA0$K@_Dj$5$l$F$$$?CM$rJV$9(B. |
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$B4]$a%b!<%I$N0UL#$O<!$N$H$*$j(B. |
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@table @code |
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@item 0 |
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Round to nearest |
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@item 1 |
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Round toward 0 |
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@item 2 |
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Round toward +infinity |
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@item 3 |
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Round toward -infinity |
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@end table |
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@item |
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@b{bigfloat} $B$G$N7W;;$KBP$7M-8z$G$"$k(B. |
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@b{bigfloat} $B$N(B flag $B$r(B on $B$K$9$kJ}K!$O(B, @code{ctrl} $B$r;2>H(B. |
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\E |
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\BEG |
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@item |
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When an argument @var{mode} is given, these functions |
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set the rounding mode for @b{bigfloat} operations to @var{mode}. |
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The return value is always the previous rounding mode regardless of |
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the existence of an argument. |
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The meanings of rounding modes are as follows |
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@table @code |
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@item 0 |
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Round to nearest |
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@item 1 |
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Round toward 0 |
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@item 2 |
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Round toward +infinity |
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@item 3 |
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Round toward -infinity |
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@end table |
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|
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@item |
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This is effective for computations in @b{bigfloat}. |
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Refer to @code{ctrl()} for turning on the `@b{bigfloat} flag.' |
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\E |
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@end itemize |
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|
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@example |
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[1] setprec(); |
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15 |
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[2] setprec(100); |
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15 |
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[3] setprec(100); |
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99 |
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[4] setbprec(); |
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332 |
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@end example |
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|
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@table @t |
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\JP @item $B;2>H(B |
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@fref{ctrl}, @fref{eval deval}. |
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@end table |
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|
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|
| \JP @node setmod,,, $B?t$N1i;;(B |
\JP @node setmod,,, $B?t$N1i;;(B |
| \EG @node setmod,,, Numbers |
\EG @node setmod,,, Numbers |
| @subsection @code{setmod} |
@subsection @code{setmod} |
| Line 1177 return to toplevel |
|
| Line 1298 return to toplevel |
|
| \EG @fref{dp_mod dp_rat}, @fref{Types of numbers}. |
\EG @fref{dp_mod dp_rat}, @fref{Types of numbers}. |
| @end table |
@end table |
| |
|
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\JP @node ntoint32 int32ton,,, $B?t$N1i;;(B |
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\EG @node ntoint32 int32ton,,, Numbers |
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@subsection @code{ntoint32}, @code{int32ton} |
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@findex ntoint32 |
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@findex int32ton |
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|
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@table @t |
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@item ntoint32(@var{n}) |
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@itemx int32ton(@var{int32}) |
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\JP :: $BHsIi@0?t$HId9f$J$7(B 32bit $B@0?t$N4V$N7?JQ49(B. |
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\EG :: Type-conversion between a non-negative integer and an unsigned 32bit integer. |
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@end table |
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|
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@table @var |
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@item return |
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\JP $BId9f$J$7(B 32bit $B@0?t$^$?$OHsIi@0?t(B |
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\EG unsigned 32bit integer or non-negative integer |
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@item n |
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\JP 2^32 $BL$K~$NHsIi@0?t(B |
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\EG non-negative interger less than 2^32 |
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@item int32 |
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\JP $BId9f$J$7(B 32bit $B@0?t(B |
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\EG unsigned 32bit integer |
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@end table |
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|
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@itemize @bullet |
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\BJP |
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@item $BHsIi@0?t(B ($B<1JL;R(B 1) $B$NId9f$J$7(B 32bit $B@0?t(B ($B<1JL;R(B 10) $B$X$NJQ49(B, |
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$B$^$?$O$=$N5UJQ49$r9T$&(B. |
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@item 32bit $B@0?t$O(B @b{OpenXM} $B$N4pK\9=@.MWAG$G$"$j(B, $B@0?t$r$=$N7?$GAw?.(B |
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$B$9$kI,MW$,$"$k>l9g$KMQ$$$k(B. |
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\E |
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\BEG |
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@item These functions do conversions between non-negative |
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integers (the type id 1) and unsigned 32bit integers (the type id 10). |
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@item An unsigned 32bit integer is a fundamental construct of @b{OpenXM} |
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and one often has to send an integer to a server as an unsigned 32bit |
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integer. These functions are used in such a case. |
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\E |
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@end itemize |
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|
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@table @t |
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\JP @item $B;2>H(B |
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\EG @item References |
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\JP @fref{$BJ,;67W;;(B}, @fref{$B?t$N7?(B}. |
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\EG @fref{Distributed computation}, @fref{Types of numbers}. |
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@end table |
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|
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\JP @node inttorat,,, $B?t$N1i;;(B |
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\EG @node inttorat,,, Numbers |
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@subsection @code{inttorat} |
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@findex inttorat |
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|
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@table @t |
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@item inttorat(@var{a},@var{m},@var{b}) |
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\JP :: $B@0?t(B-$BM-M}?tJQ49$r9T$&(B. |
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\EG :: Perform the rational reconstruction. |
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@end table |
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|
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@table @var |
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@item return |
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\JP $B%j%9%H$^$?$O(B 0 |
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\EG list or 0 |
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@item a |
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@itemx m |
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@itemx b |
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\JP $B@0?t(B |
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\EG integer |
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@end table |
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|
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@itemize @bullet |
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\BJP |
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@item |
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$B@0?t(B @var{a} $B$KBP$7(B, @var{xa=y} mod @var{m} $B$rK~$?$9@5@0?t(B @var{x}, $B@0?t(B @var{y} |
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(@var{x}, @var{|y|} < @var{b}, @var{GCD(x,y)=1}) $B$r5a$a$k(B. |
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@item |
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$B$3$N$h$&$J(B @var{x}, @var{y} $B$,B8:_$9$k$J$i(B @var{[y,x]} $B$rJV$7(B, $BB8:_$7$J$$>l9g$K$O(B 0 $B$rJV$9(B. |
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@item |
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@var{b} $B$r(B @var{floor(sqrt(m/2))} $B$H<h$l$P(B, @var{x}, @var{y} $B$OB8:_$9$l$P0l0U$G$"$k(B. |
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@var{floor(sqrt(m/2))} $B$O(B @code{isqrt(floor(m/2))} $B$G7W;;$G$-$k(B. |
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@end itemize |
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\E |
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\BEG |
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@item |
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For an integer @var{a}, find a positive integer @var{x} and an intger @var{y} satisfying |
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@var{xa=y} mod @var{m}, @var{x}, @var{|y|} < @var{b} and @var{GCD(x,y)=1}. |
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@item |
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If such @var{x}, @var{y} exist then a list @var{[y,x]} is returned. Otherwise 0 is returned. |
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@item |
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If @var{b} is set to @var{floor(sqrt(M/2))}, then @var{x} and @var{y} are unique if they |
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exist. @var{floor(sqrt(M/2))} can be computed by @code{floor} and @code{isqrt}. |
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@end itemize |
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\E |
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|
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@example |
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[2121] M=lprime(0)*lprime(1); |
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9996359931312779 |
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[2122] B=isqrt(floor(M/2)); |
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70697807 |
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[2123] A=234234829304; |
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234234829304 |
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[2124] inttorat(A,M,B); |
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[-20335178,86975031] |
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@end example |
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|
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@table @t |
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\JP @item $B;2>H(B |
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\EG @item References |
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@fref{floor}, @fref{isqrt}. |
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@end table |
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