| version 1.11, 2016/03/22 07:25:14 |
version 1.13, 2019/03/29 01:57:46 |
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| @comment $OpenXM: OpenXM/src/asir-doc/parts/builtin/num.texi,v 1.10 2003/12/20 20:02:28 ohara Exp $ |
@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 |
|
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| * conj real imag:: |
* conj real imag:: |
| * eval deval:: |
* eval deval:: |
| * pari:: |
* pari:: |
| * setprec:: |
* setbprec setprec:: |
| * setmod:: |
* setmod:: |
| * lrandom:: |
* lrandom:: |
| * ntoint32 int32ton:: |
* ntoint32 int32ton:: |
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* setround:: |
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* inttorat:: |
| @end menu |
@end menu |
| |
|
| \JP @node idiv irem,,, $B?t$N1i;;(B |
\JP @node idiv irem,,, $B?t$N1i;;(B |
| Line 756 These functions works also for polynomials with comple |
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| Line 758 These functions works also for polynomials with comple |
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| @code{eval} $B$K$*$$$F$O(B, |
@code{eval} $B$K$*$$$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}.) |
(@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 799 done by the C math library. |
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| Line 801 done by the C math library. |
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| 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. |
| |
|
| Line 846 Napier's number (@t{exp}(1)) |
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| Line 848 Napier's number (@t{exp}(1)) |
|
| @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{setbprec}. |
@fref{ctrl}, @fref{setbprec setprec}. |
| @end table |
@end table |
| |
|
| \JP @node pari,,, $B?t$N1i;;(B |
\JP @node pari,,, $B?t$N1i;;(B |
| Line 1080 For details of individual functions, refer to the @b{P |
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| Line 1082 For details of individual functions, refer to the @b{P |
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| @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 setbprec setprec,,, $B?t$N1i;;(B |
\JP @node setbprec setprec,,, $B?t$N1i;;(B |
| Line 1342 integer. These functions are used in such a case. |
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| Line 1344 integer. These functions are used in such a case. |
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| \EG @item References |
\EG @item References |
| \JP @fref{$BJ,;67W;;(B}, @fref{$B?t$N7?(B}. |
\JP @fref{$BJ,;67W;;(B}, @fref{$B?t$N7?(B}. |
| \EG @fref{Distributed computation}, @fref{Types of numbers}. |
\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}. |
| @end table |
@end table |
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