Ruby Forum Ruby-dev > ComplexFloat

村田です．

C99 の double _Complex をラップした ComplexFloat を実装しました．
Rev 15910 に対する patch を添付します．
# サイズがデカいと fml に怒られたので gzip しました．

「C99 の double _Complex をラップした」と書きましたが，
Ruby は C99 を要求していないはずなので，configure --with-c99-complex することで
double _Complex を使うようにしています．--with-c99-complex が指定されていない場合は，
double _Complex と同一レイアウトの構造体を使用します．

ComplexFloat::Math モジュールには，C99 で追加された複素数用関数のラッパを定義しています．
この複素数用関数も，--with-c99-complex が指定されなければ互換性がある(はず)の独自実装を使います．

Complex 組み込みのスレッドでは僕の意図がきちんと伝わらず，
話が変な方に行ってしまい残念な思いをしたので，実装で意図を示す事にしました．
complex.rb で提供れていた Complex が組み込みで提供されるなら，
こういう実装の複素数が組み込みで提供されていても良いと思いますがどうでしょう？

私の希望としては，ふなばさんの Complex と僕の ComplexFloat を両方組み込みで提供してもらいたいです．
ふなばさんの Complex は多倍長固定小数点数などを使用する場合に必要になります．
私の ComplexFloat は拡張モジュールで計算ルーチンを書く場合に使い易い実装になってるはずです．
そして，できれば Complex <-> ComplexFloat 間の変換を Rational,Integer <-> Float 間の変換と
同じようなルールにすべきかなと考えています (まだなってない)．

$BB<ED$G$9!%(B

2008/4/6 Kenta Murata <muraken@gmail.com>:
>  C99 $B$N(B double _Complex $B$r%i%C%W$7$?(B ComplexFloat $B$r<BAu$7$^$7$?!%(B
>  Rev 15910 $B$KBP$9$k(B patch $B$rE:IU$7$^$9!%(B
>  # $B%5%$%:$,%G%+$$$H(B fml $B$KE\$i$l$?$N$G(B gzip $B$7$^$7$?!%(B

$B$*K;$7$$$+$H;W$$$^$9$,!$(Bpatch 
$B$KBP$9$k%3%a%s%H$rD:$1$^$;$s$+!)(B
$B:NMQ$G$-$J$$$H$$$&$3$H$J$i!$$G$-$l$P$=$NM}M3$b65$($F$$$?$@$-$?$$$G$9!%(B
$B?7$7$/F3F~$7$?4X?t$NL>A0$,0-$$$J$I!$=$@5$,2DG=$JM}M3$G$7$?$i!$(B
$B=$@5$r;\$7$?(B patch $B$r:n$jD>$7$^$9!%(B

$B$h$m$7$/$*4j$$$7$^$9!%(B

$B$^$D$b$H(B $B$f$-$R$m$G$9(B

In message "Re: [ruby-dev:34280] Re: ComplexFloat"
    on Thu, 10 Apr 2008 15:34:09 +0900, "Kenta Murata" 
<muraken@gmail.com> writes:

|2008/4/6 Kenta Murata <muraken@gmail.com>:
|>  C99 $B$N(B double _Complex $B$r%i%C%W$7$?(B ComplexFloat $B$r<BAu$7$^$7$?!%(B
|>  Rev 15910 $B$KBP$9$k(B patch $B$rE:IU$7$^$9!%(B
|>  # $B%5%$%:$,%G%+$$$H(B fml $B$KE\$i$l$?$N$G(B gzip $B$7$^$7$?!%(B
|
|$B$*K;$7$$$+$H;W$$$^$9$,!$(Bpatch $B$KBP$9$k%3%a%s%H$rD:$1$^$;$s$+!)(B
|$B:NMQ$G$-$J$$$H$$$&$3$H$J$i!$$G$-$l$P$=$NM}M3$b65$($F$$$?$@$-$?$$$G$9!%(B

$B;d<+?H$OJ#AG?t$r;H$&5!2q$,$J$$$N$G!"$G$-$,NI$$$H$+0-$$$H$+H=(B
$BJL$9$k$3$H$O$G$-$J$$$N$G$9$,!"(BComplexFloat$B$H(BComplex$B$NN>J}$rDs(B
$B6!$9$k$N$O!"(BRuby$BE*$K$I$&$J$N$+5?Ld$r46$8$F$$$k$H$$$&$,@5D>$J(B
$B$H$3$m$G$9!#(B

$B4JC1$K=$@5$G$-$J$$$H$3$m$G0z$C$+$+$C$F$7$^$C$F$$$k$N$,?=$7Lu(B
$B$J$$$H$3$m$G$9$,!#(B

$B$`$i$?$G$9!%(B

$B%3%a%s%H$"$j$,$H$&$4$6$$$^$9!%(B

2008/4/10 Yukihiro Matsumoto <matz@ruby-lang.org>:
>  $B;d<+?H$OJ#AG?t$r;H$&5!2q$,$J$$$N$G!"$G$-$,NI$$$H$+0-$$$H$+H=(B
>  $BJL$9$k$3$H$O$G$-$J$$$N$G$9$,!"(BComplexFloat$B$H(BComplex$B$NN>J}$rDs(B
>  $B6!$9$k$N$O!"(BRuby$BE*$K$I$&$J$N$+5?Ld$r46$8$F$$$k$H$$$&$,@5D>$J(B
>  $B$H$3$m$G$9!#(B

Ruby $B$O:#8e$b(B C99 $B$N(B complex.h 
$B$rAH$_9~$_%/%i%9(B/$B%b%8%e!<%k$G$O(B
$B%5%]!<%H$7$J$$$H2r<a$7$FNI$$$G$9$+!)(B

Math $B%b%8%e!<%k$,(B math.h $B$N(B wrapper 
$B$G$"$k$H6D$C$F$*$j$^$7$?$,!$(B
complex.h $B$K4^$^$l$kJ#AG4X?t$b(B C99 
$B$HF1$8;EMM$N$b$N$,Ds6!$5$l$k(B
$B$3$H$OJ]>Z$5$l$J$$$H2r<a$7$FNI$$$G$9$+!)(B

$B$^$D$b$H(B $B$f$-$R$m$G$9(B

In message "Re: [ruby-dev:34283] Re: ComplexFloat"
    on Thu, 10 Apr 2008 16:31:27 +0900, "Kenta Murata" 
<muraken@gmail.com> writes:

|2008/4/10 Yukihiro Matsumoto <matz@ruby-lang.org>:
|>  $B;d<+?H$OJ#AG?t$r;H$&5!2q$,$J$$$N$G!"$G$-$,NI$$$H$+0-$$$H$+H=(B
|>  $BJL$9$k$3$H$O$G$-$J$$$N$G$9$,!"(BComplexFloat$B$H(BComplex$B$NN>J}$rDs(B
|>  $B6!$9$k$N$O!"(BRuby$BE*$K$I$&$J$N$+5?Ld$r46$8$F$$$k$H$$$&$,@5D>$J(B
|>  $B$H$3$m$G$9!#(B
|
|Ruby $B$O:#8e$b(B C99 $B$N(B complex.h $B$rAH$_9~$_%/%i%9(B/$B%b%8%e!<%k$G$O(B
|$B%5%]!<%H$7$J$$$H2r<a$7$FNI$$$G$9$+!)(B

$B$=$&7h$a$F$$$k$N$G$"$l$P!"!V5?Ld$r46$8$F$$$k!W$H$$$&$h$&$J[#(B
$BKf$J8@$$J}$G$J$/!"$b$&$A$g$C$H$O$C$-$j$7$?I=8=$r;H$$$^$9!#MW(B
$B$9$k$K!VL>A0$HMQES$,;w$F$$$k$,0c$&$U$?$D$N%/%i%9$,$"$k>l9g!"(B
$B$-$A$s$H=;$_J,$1$k$?$a$KG[N8$,I,MW!#(BComplexFloat$B$H$$$&L>A0$,(B
$B=;$_J,$1$N$?$a:GA1$+$I$&$+(B($B$^$@(B)$B<+?.$,$J$$!W$H$$$&%l%Y%k$G$9!#(B

|Math $B%b%8%e!<%k$,(B math.h $B$N(B wrapper $B$G$"$k$H6D$C$F$*$j$^$7$?$,!$(B
|complex.h $B$K4^$^$l$kJ#AG4X?t$b(B C99 $B$HF1$8;EMM$N$b$N$,Ds6!$5$l$k(B
|$B$3$H$OJ]>Z$5$l$J$$$H2r<a$7$FNI$$$G$9$+!)(B

$B>e5-$HF1MM$K!":#$9$0$=$N$^$^F3F~$5$l$k$3$H$O$J$$$H;W$$$^$9$,!"(B
$B>-Mh$KEO$C$FF3F~$7$J$$$H7h$a$F$$$k$o$1$G$O$J$$$G$9!#(BRuby$B$N4p(B
$BK\;EMM$,$+$J$j(BC$B$K0z$-$:$i$l$F$$$k(B($B?t3XA4HL$G$O$J$/(Blibm$B$N$?$a(B
$B$K(BMath$B$H$$$&L>A0$r;H$C$?$j(B)$B$3$H$r9M$($k$H!"F3F~$,$^$C$?$/$"(B
$B$j$($J$$OC$H$$$&$o$1$G$O$J$$$H;W$$$^$9!#(B

                                $B$^$D$b$H(B $B$f$-$R$m(B /:|)

$B$J$+$@$G$9!#(B

At Thu, 10 Apr 2008 15:34:09 +0900,
Kenta Murata wrote in [ruby-dev:34280]:
> >  C99 $B$N(B double _Complex $B$r%i%C%W$7$?(B ComplexFloat $B$r<BAu$7$^$7$?!%(B
> >  Rev 15910 $B$KBP$9$k(B patch $B$rE:IU$7$^$9!%(B
> >  # $B%5%$%:$,%G%+$$$H(B fml $B$KE\$i$l$?$N$G(B gzip $B$7$^$7$?!%(B
> 
> $B$*K;$7$$$+$H;W$$$^$9$,!$(Bpatch $B$KBP$9$k%3%a%s%H$rD:$1$^$;$s$+!)(B
> $B:NMQ$G$-$J$$$H$$$&$3$H$J$i!$$G$-$l$P$=$NM}M3$b65$($F$$$?$@$-$?$$$G$9!%(B

$BAH9~$_$G$"$kI,A3@-$,$h$/$o$+$j$^$;$s$G$7$?!#(B

$B$^$?!"(Blong=32bit,double=64bit$B$N4D6-$G$O!"A4(BVALUE$B$,(B1word$BBg$-$/$J(B
$B$j$^$9!#$*$=$i$/$[$H$s$I$N?M4V$,;H$&$3$H$,$J$$$G$"$m$&5!G=$KJ'$&(B
$BBe=~$H$7$F$O!"$$$5$5$+Bg$-$9$.$k$h$&$J!#(B

$B$`$i$?$G$9!%(B

2008/4/10 Nobuyoshi Nakada <nobu@ruby-lang.org>:
>  $B$^$?!"(Blong=32bit,double=64bit$B$N4D6-$G$O!"A4(BVALUE$B$,(B1word$BBg$-$/$J(B
>  $B$j$^$9!#$*$=$i$/$[$H$s$I$N?M4V$,;H$&$3$H$,$J$$$G$"$m$&5!G=$KJ'$&(B
>  $BBe=~$H$7$F$O!"$$$5$5$+Bg$-$9$.$k$h$&$J!#(B

VALUE $B$N%5%$%:$,A}2C$9$k$3$H$K$O5$IU$$$F$$$^$;$s$G$7$?!%(B
$B$4;XE&$"$j$,$H$&$4$6$$$^$9!%3N$+$K!$(BComplexFloat 
$B$N<{MW$r9M$($k$H!$(B
$B$3$l$OBg$-$JBe=~$K$J$j$^$9$M!%(B
$B$7$+$7!$$3$NBe=~$O(B rb_double_complex $B$r(B VALUE 
$B$KKd$a9~$^$:$K(B
$B%]%$%s%?$G;}$D$h$&$K$9$l$P2r7h$G$-$^$9$h$M!)(B

$B$=$l$+$i!$AH$_9~$_$K$9$kI,MW@-$r46$8$J$$$H$N$3$H$G$9$,!&!&!&(B
Complex $B$O!$<BIt$H5uIt$,N>J}(B Float 
$B$K$J$k$H!$$=$NCM$H$N1i;;$G@8@.$5$l$k(B
$B$9$Y$F$N(B Complex $B%*%V%8%'%/%H$N<BIt$H5uIt$O(B Float 
$B$G$9!%(B
$B<BIt$H5uIt$,N>J}6&(B Float $B$G$"$k>l9g!$$=$l$i$r(B VALUE 
$B$G;}$D$h$j$b(B
($B$b$7;H$($k$J$i(B) double _Complex $B$GI=8=$7$F(B C99 
$B$NJ#AG4X?t$d(B
$BJ#AG?t7W;;$r;H$&$Y$-$G$O$J$$$+$H;W$$$^$;$s$+!)(B

$B$3$s$K$A$O!"$J$+$`$i(B($B$&(B)$B$G$9!#(B

In message "[ruby-dev:34288] Re: ComplexFloat"
    on Apr.10,2008 17:09:20, <muraken@gmail.com> wrote:
> $B$=$l$+$i!$AH$_9~$_$K$9$kI,MW@-$r46$8$J$$$H$N$3$H$G$9$,!&!&!&(B
> Complex $B$O!$<BIt$H5uIt$,N>J}(B Float $B$K$J$k$H!$$=$NCM$H$N1i;;$G@8@.$5$l$k(B
> $B$9$Y$F$N(B Complex $B%*%V%8%'%/%H$N<BIt$H5uIt$O(B Float $B$G$9!%(B
> $B<BIt$H5uIt$,N>J}6&(B Float $B$G$"$k>l9g!$$=$l$i$r(B VALUE $B$G;}$D$h$j$b(B
> ($B$b$7;H$($k$J$i(B) double _Complex $B$GI=8=$7$F(B C99 $B$NJ#AG4X?t$d(B
> $BJ#AG?t7W;;$r;H$&$Y$-$G$O$J$$$+$H;W$$$^$;$s$+!)(B

$BC1$K(BRData$B$r;H$C$F3HD%%i%$%V%i%j$G$$$$$N$G$O!"$H$$$&$N$,$J$+$@(B
$B$5$s$N;XE&$@$H;W$$$^$9!#(B
$B$=$&$9$k$@$1$G!"(BVALUE$B$N%5%$%:$NLdBj$H!"<BBN$r(Bdouble _Complex
$B$GI=8=$9$k$3$H$HN>J}$,<B8=$G$-$k$H;W$&$N$G$9$,!"$=$&$;$:$KK\(B
$BBN$X$NAH$_9~$_$K$7$J$$$H$$$1$J$$M}M3$O$J$s$G$7$g$&$+(B?
# $BJL$KH?BP$7$F$k$o$1$8$c$J$$$s$G$9$1$I$M(B


$B$=$l$G$O!#(B

$B$^$D$b$H(B $B$f$-$R$m$G$9(B

In message "Re: [ruby-dev:34288] Re: ComplexFloat"
    on Thu, 10 Apr 2008 17:09:20 +0900, "Kenta Murata" 
<muraken@gmail.com> writes:

|VALUE $B$N%5%$%:$,A}2C$9$k$3$H$K$O5$IU$$$F$$$^$;$s$G$7$?!%(B
|$B$4;XE&$"$j$,$H$&$4$6$$$^$9!%3N$+$K!$(BComplexFloat $B$N<{MW$r9M$($k$H!$(B
|$B$3$l$OBg$-$JBe=~$K$J$j$^$9$M!%(B
|$B$7$+$7!$$3$NBe=~$O(B rb_double_complex $B$r(B VALUE $B$KKd$a9~$^$:$K(B
|$B%]%$%s%?$G;}$D$h$&$K$9$l$P2r7h$G$-$^$9$h$M!)(B

$B$=$NLdBj$O2r7h$7$^$9$M!#(B

|$B$=$l$+$i!$AH$_9~$_$K$9$kI,MW@-$r46$8$J$$$H$N$3$H$G$9$,!&!&!&(B
|Complex $B$O!$<BIt$H5uIt$,N>J}(B Float $B$K$J$k$H!$$=$NCM$H$N1i;;$G@8@.$5$l$k(B
|$B$9$Y$F$N(B Complex $B%*%V%8%'%/%H$N<BIt$H5uIt$O(B Float $B$G$9!%(B
|$B<BIt$H5uIt$,N>J}6&(B Float $B$G$"$k>l9g!$$=$l$i$r(B VALUE $B$G;}$D$h$j$b(B
|($B$b$7;H$($k$J$i(B) double _Complex $B$GI=8=$7$F(B C99 $B$NJ#AG4X?t$d(B
|$BJ#AG?t7W;;$r;H$&$Y$-$G$O$J$$$+$H;W$$$^$;$s$+!)(B

$B$=$l$O<BAu$NLdBj$@$HG'<1$7$F$$$^$9!#N>J}$H$b(BFloat$B$@$C$?(B
$B$iFbItE*$K(Bcomplex$B$r:n$C$F(BC99$B$N4X?t$r8F$Y$P$h$$$H$$$&$N$b$R$H(B
$B$D$N9M$(J}$G$9$+$i!#(B

                                $B$^$D$b$H(B $B$f$-$R$m(B /:|)

$B$`$i$?$G$9!%(B

2008/4/10 U.Nakamura <usa@garbagecollect.jp>:
>  $BC1$K(BRData$B$r;H$C$F3HD%%i%$%V%i%j$G$$$$$N$G$O!"$H$$$&$N$,$J$+$@(B
>  $B$5$s$N;XE&$@$H;W$$$^$9!#(B

$B$=$l$O==J,>5CN$7$F$$$^$9!%3HD%%i%$%V%i%j$O8D?ME*$K;H$C$F$$$k$b$N$G(B
$B4{$K;}$C$F$$$k$N$G!$$=$l$GNI$$$J$i(B ruby-dev 
$B$K%a!<%k$OAw$j$^$;$s!%(B

>  $B$=$&$9$k$@$1$G!"(BVALUE$B$N%5%$%:$NLdBj$H!"<BBN$r(Bdouble _Complex
>  $B$GI=8=$9$k$3$H$HN>J}$,<B8=$G$-$k$H;W$&$N$G$9$,!"$=$&$;$:$KK\(B
>  $BBN$X$NAH$_9~$_$K$7$J$$$H$$$1$J$$M}M3$O$J$s$G$7$g$&$+(B?

Ruby $B$K(B C99 $B$N(B complex.h 
$B$rAH$_9~$_$G%5%]!<%H$5$;$?$$$H$$$&A[$$$H!$(B
$B8=>u$N(B Complex $B$X$N<c43$NITK~$G$9$+$M$'!%(B

ComplexFloat ($B2>>N(B) $B$,AH9~$_$G%5%]!<%H$5$l$k$H!$(B

(1) TYPE(obj) == T_COMPLEX_FLOAT $B$G7?$rD4$Y$k$3$H$,$G$-$k(B
(2) T_COMPLEX_FLOAT $B$G$"$kJ#AG?t$O<BIt$b5uIt$b3N<B$K(B
double $B$G$"$k$3$H$,J]>Z$5$l$k(B

$B$H$$$&(B2$B$D$N4r$7$$;v$,$"$j$^$9!%$3$N;EMM$,<B8=$9$k$H$H$F$b2wE,$G$9!%(B
$B$=$7$F$3$l$i$N$&$A(B T_COMPLEX_FLOAT $B$G7?$rD4$Y$k$3$H$O(B
$B3HD%%b%8%e!<%k$G$O<B8=$G$-$J$$$G$9$7!$8=>u$N(B Complex 
$B$O<BIt$H5uIt$N(B
$B7?$rKh2s5$$K$7$J$1$l$P$J$j$^$;$s!%$=$N$&$(!$JL$N%a!<%k$K=q$$$?$h$&$K!$(B
$BJ#AG?t$N@.J,$,0lEY(B Float 
$B$K$J$k$H!$$=$l$H$N1i;;$G@8@.$5$l$kJ#AG?t(B
$B$N@.J,$b(B Float $B$G$9!%(B

$B$3$s$K$A$O!"$J$+$`$i(B($B$&(B)$B$G$9!#(B

In message "[ruby-dev:34293] Re: ComplexFloat"
    on Apr.10,2008 17:40:29, <muraken@gmail.com> wrote:
> (1) TYPE(obj) == T_COMPLEX_FLOAT $B$G7?$rD4$Y$k$3$H$,$G$-$k(B
> (2) T_COMPLEX_FLOAT $B$G$"$kJ#AG?t$O<BIt$b5uIt$b3N<B$K(B
> double $B$G$"$k$3$H$,J]>Z$5$l$k(B
> 
> $B$H$$$&(B2$B$D$N4r$7$$;v$,$"$j$^$9!%$3$N;EMM$,<B8=$9$k$H$H$F$b2wE,$G$9!%(B
> $B$=$7$F$3$l$i$N$&$A(B T_COMPLEX_FLOAT $B$G7?$rD4$Y$k$3$H$O(B
> $B3HD%%b%8%e!<%k$G$O<B8=$G$-$J$$$G$9$7!$8=>u$N(B Complex $B$O<BIt$H5uIt$N(B
> $B7?$rKh2s5$$K$7$J$1$l$P$J$j$^$;$s!%$=$N$&$(!$JL$N%a!<%k$K=q$$$?$h$&$K!$(B
> $BJ#AG?t$N@.J,$,0lEY(B Float $B$K$J$k$H!$$=$l$H$N1i;;$G@8@.$5$l$kJ#AG?t(B
> $B$N@.J,$b(B Float $B$G$9!%(B

(2)$B$O(BComplexFloat$B$N$&$l$7$5$G$"$C$F!"$=$l$O7?$rF1Dj$G$-$F$5$((B
$B$$$l$P!"AH$_9~$_$@$m$&$,$J$s$@$m$&$,4X78$J$$$G$9$h$M!#(B
$B$H$J$k$H!"AH$_9~$_$K$7$?$$$H$$$&OC$N>GE@$O(B(1)$B$K=8Ls$5$l$F$$$k!"(B
$B$H$$$&$3$H$G$$$$$s$G$7$g$&$+(B?
$B8@$$49$($k$H!"$b$74JC1$K7?$rF1Dj$G$-$kJL$NJ}K!$,$"$C$?$H$7$?(B
$B$i!"AH$_9~$_$G$J$/$F$b$$$$$s$G$7$g$&$+(B?


$B$=$l$G$O!#(B

$BKNIt$GC1=c$J5?Ld$J$N$G$9$,!"(B

Kenta Murata $B$5$s$O=q$-$^$7$?(B:
> (1) TYPE(obj) == T_COMPLEX_FLOAT $B$G7?$rD4$Y$k$3$H$,$G$-$k(B
>   
$B%5%V%/%i%9:n$C$?;~$N5sF0$H$+$O$"$s$^$j9M$($J$$$C$F$3$H$G$7$g$&$+(B?

$B$`$i$?$G$9!%(B

2008/4/10 U.Nakamura <usa@garbagecollect.jp>:
>  $B8@$$49$($k$H!"$b$74JC1$K7?$rF1Dj$G$-$kJL$NJ}K!$,$"$C$?$H$7$?(B
>  $B$i!"AH$_9~$_$G$J$/$F$b$$$$$s$G$7$g$&$+(B?

$B$4$a$s$J$5$$!%AH$_9~$_$K$9$kMxE@$O$b$&0l$D$"$j$^$9!%(B
$B8=>u$N(B Complex $B$r$$$8$C$F!$<BIt$H5uIt$,N>J}(B Float 
$B$K$J$k$H$-$K(B
ComplexFloat $B$rJV$9$h$&$J;EMM$K$G$-$^$9!%$3$&$9$k$H(B
Ruby $B%9%/%j%W%H>e$G$O(B Complex $B$H(B ComplexFloat 
$B$r6hJL$;$:$K;H$(!$(B
C $B>e$G$O(B TYPE(obj) $B%^%/%m$r;H$&$@$1$G(B Complex $B$H(B 
ComplexFloat $B$r(B
$B6hJL$7$F07$&$3$H$,2DG=$K$J$j$^$9!%(B

$B$`$i$?$G$9!%(B

2008/4/10 Urabe Shyouhei <shyouhei@ruby-lang.org>:
> $BKNIt$GC1=c$J5?Ld$J$N$G$9$,!"(B
>
>  Kenta Murata $B$5$s$O=q$-$^$7$?(B:
>
> > (1) TYPE(obj) == T_COMPLEX_FLOAT $B$G7?$rD4$Y$k$3$H$,$G$-$k(B
>  >
>  $B%5%V%/%i%9:n$C$?;~$N5sF0$H$+$O$"$s$^$j9M$($J$$$C$F$3$H$G$7$g$&$+(B?

$B$O$$!$$=$&$J$j$^$9!%AH$_9~$_$N(B Float 
$B$N<BAu$b$=$&$J$C$F$$$^$9$h$M!%(B
$BDs0F$7$?(B patch $B$N(B ComplexFloat ($B2>>N(B) $B$O(B Float 
$B$NJ#AG?tHG$N$h$&$J(B
$B0LCVIU$1$rA[Dj$7$F<BAu$7$^$7$?!%(B

In article 
<761216ce0804100221x67f10f12iab12b0e35b6f50e4@mail.gmail.com>,
  "Kenta Murata" <muraken@gmail.com> writes:

> $B$4$a$s$J$5$$!%AH$_9~$_$K$9$kMxE@$O$b$&0l$D$"$j$^$9!%(B
> $B8=>u$N(B Complex $B$r$$$8$C$F!$<BIt$H5uIt$,N>J}(B Float $B$K$J$k$H$-$K(B
> ComplexFloat $B$rJV$9$h$&$J;EMM$K$G$-$^$9!%$3$&$9$k$H(B
> Ruby $B%9%/%j%W%H>e$G$O(B Complex $B$H(B ComplexFloat $B$r6hJL$;$:$K;H$(!$(B
> C $B>e$G$O(B TYPE(obj) $B%^%/%m$r;H$&$@$1$G(B Complex $B$H(B ComplexFloat $B$r(B
> $B6hJL$7$F07$&$3$H$,2DG=$K$J$j$^$9!%(B

$B6hJL$7$J$$$J$i!"(BComplex $B$NFbIt$K%U%i%0$r@_$1$F!"<B?t$H5u?t$H(B
$BN>J}$,(B Float $B$J$iFbIt$N<BAu$r(B double _Complex $B$J$$$7(B 
double
$B$U$?$D$r$D$+$&$h$&$K$9$k$H$$$&$N$OFq$7$$$G$7$g$&$+!#(B

$B$`$i$?$G$9!%(B

2008/4/10 Tanaka Akira <akr@fsij.org>:
>  $B$U$?$D$r$D$+$&$h$&$K$9$k$H$$$&$N$OFq$7$$$G$7$g$&$+!#(B
$BNc$($P(B FL_COMPLEX_FLOAT 
$B$N$h$&$J%U%i%0$r;H$&$H$$$&$3$H$G$7$g$&$+!)(B
$B$=$l$O2DG=$G$9$7!$$=$N$h$&$KJQ99$9$k$@$1$J$iFq$7$/$J$$$h$&$J5$$,$7$^$9!%(B
$B$5$i$K!$$=$N$h$&$KJQ99$7$F$b(B TYPE(obj) 
$B$r;H$&>l9g$H$[$H$s$IF1$8%3%9%H$G(B
$B>uBV$r6hJL$G$-$^$9$M!%(B
$B$?$@$7!$JQ998e$N(B complex.c 
$B$N%a%s%F%J%s%9$OBgJQ$+$b$7$l$^$;$s!&!&!&(B

$B$`$i$?$G$9!%(B

2008/4/10 Kenta Murata <muraken@gmail.com>:
>  >  $B6hJL$7$J$$$J$i!"(BComplex $B$NFbIt$K%U%i%0$r@_$1$F!"<B?t$H5u?t$H(B
>  >  $BN>J}$,(B Float $B$J$iFbIt$N<BAu$r(B double _Complex $B$J$$$7(B double
>  >  $B$U$?$D$r$D$+$&$h$&$K$9$k$H$$$&$N$OFq$7$$$G$7$g$&$+!#(B
>
>
> $BNc$($P(B FL_COMPLEX_FLOAT $B$N$h$&$J%U%i%0$r;H$&$H$$$&$3$H$G$7$g$&$+!)(B
>  $B$=$l$O2DG=$G$9$7!$$=$N$h$&$KJQ99$9$k$@$1$J$iFq$7$/$J$$$h$&$J5$$,$7$^$9!%(B
>  $B$5$i$K!$$=$N$h$&$KJQ99$7$F$b(B TYPE(obj) $B$r;H$&>l9g$H$[$H$s$IF1$8%3%9%H$G(B
>  $B>uBV$r6hJL$G$-$^$9$M!%(B
>  $B$?$@$7!$JQ998e$N(B complex.c $B$N%a%s%F%J%s%9$OBgJQ$+$b$7$l$^$;$s!&!&!&(B

$B<B:]$K$=$N$h$&$KJQ99$7$F$$$?$@$1$k$N$G$7$?$i!$;d$O%a%s%F%J%s%9$r(B
$B$*<jEA$$$G$-$^$9!%(B

$B$^$D$b$H(B $B$f$-$R$m$G$9(B

In message "Re: [ruby-dev:34301] Re: ComplexFloat"
    on Thu, 10 Apr 2008 18:36:13 +0900, "Kenta Murata" 
<muraken@gmail.com> writes:

|>  $B6hJL$7$J$$$J$i!"(BComplex $B$NFbIt$K%U%i%0$r@_$1$F!"<B?t$H5u?t$H(B
|>  $BN>J}$,(B Float $B$J$iFbIt$N<BAu$r(B double _Complex $B$J$$$7(B double
|>  $B$U$?$D$r$D$+$&$h$&$K$9$k$H$$$&$N$OFq$7$$$G$7$g$&$+!#(B
|
|$BNc$($P(B FL_COMPLEX_FLOAT $B$N$h$&$J%U%i%0$r;H$&$H$$$&$3$H$G$7$g$&$+!)(B
|$B$=$l$O2DG=$G$9$7!$$=$N$h$&$KJQ99$9$k$@$1$J$iFq$7$/$J$$$h$&$J5$$,$7$^$9!%(B
|$B$5$i$K!$$=$N$h$&$KJQ99$7$F$b(B TYPE(obj) $B$r;H$&>l9g$H$[$H$s$IF1$8%3%9%H$G(B
|$B>uBV$r6hJL$G$-$^$9$M!%(B

$B$U$`!#Mn$H$7=j$,8+$($F$-$?$h$&$G$9$M!#(B

|$B$?$@$7!$JQ998e$N(B complex.c $B$N%a%s%F%J%s%9$OBgJQ$+$b$7$l$^$;$s!&!&!&(B

$B$U$J$P$5$s$N0U8+$b$*J9$-$7$?$$$H$3$m$G$9!#(B

$B$3$s$K$A$O!"$J$+$`$i(B($B$&(B)$B$G$9!#(B

In message "[ruby-dev:34298] Re: ComplexFloat"
    on Apr.10,2008 18:21:45, <muraken@gmail.com> wrote:
> $B$4$a$s$J$5$$!%AH$_9~$_$K$9$kMxE@$O$b$&0l$D$"$j$^$9!%(B
> $B8=>u$N(B Complex $B$r$$$8$C$F!$<BIt$H5uIt$,N>J}(B Float $B$K$J$k$H$-$K(B
> ComplexFloat $B$rJV$9$h$&$J;EMM$K$G$-$^$9!%$3$&$9$k$H(B
> Ruby $B%9%/%j%W%H>e$G$O(B Complex $B$H(B ComplexFloat $B$r6hJL$;$:$K;H$(!$(B
> C $B>e$G$O(B TYPE(obj) $B%^%/%m$r;H$&$@$1$G(B Complex $B$H(B ComplexFloat $B$r(B
> $B6hJL$7$F07$&$3$H$,2DG=$K$J$j$^$9!%(B

$B$3$NOC$G!"!V(BComplex$B$rAH$_9~$_$K$9$k$J$i(BComplexFloat$B$b!W$H$$$&(B
$B%9%H!<%j!<$KG<F@$7$^$7$?!#$J$k$[$I!#(B


$B$=$l$G$O!#(B

In article 
<761216ce0804100236i49f909ccn9b54b186678b22b6@mail.gmail.com>,
  "Kenta Murata" <muraken@gmail.com> writes:

> $BNc$($P(B FL_COMPLEX_FLOAT $B$N$h$&$J%U%i%0$r;H$&$H$$$&$3$H$G$7$g$&$+!)(B
> $B$=$l$O2DG=$G$9$7!$$=$N$h$&$KJQ99$9$k$@$1$J$iFq$7$/$J$$$h$&$J5$$,$7$^$9!%(B
> $B$5$i$K!$$=$N$h$&$KJQ99$7$F$b(B TYPE(obj) $B$r;H$&>l9g$H$[$H$s$IF1$8%3%9%H$G(B
> $B>uBV$r6hJL$G$-$^$9$M!%(B
> $B$?$@$7!$JQ998e$N(B complex.c $B$N%a%s%F%J%s%9$OBgJQ$+$b$7$l$^$;$s!&!&!&(B

$B$J$k$[$I!#$`$i$?$5$s$N4uK>$K$OJL$N%/%i%9$r:n$k$H$$$&$3$H$OF~$C(B
$B$F$$$J$$$o$1$G$9$M!#(B

$B$G$O!"$$$^$N$^$^$N(B Complex $B$G!"(BC $B%l%Y%k$G(B
Complex $B$J(B VALUE $B$+$i(B double _Complex 
$B$r<h$j=P$94X?t5Z$S(B
double _Complex $B$+$i(B Complex $B$J(B VALUE 
$B$r@8@.$9$k4X?t$r?7@_$9(B
$B$k$H$$$&$N$J$i$I$&$G$7$g$&$+(B?

$B$`$i$?$G$9!%(B

2008/4/10 Tanaka Akira <akr@fsij.org>:
> In article <761216ce0804100236i49f909ccn9b54b186678b22b6@mail.gmail.com>,
> > $BNc$($P(B FL_COMPLEX_FLOAT $B$N$h$&$J%U%i%0$r;H$&$H$$$&$3$H$G$7$g$&$+!)(B
>  > $B$=$l$O2DG=$G$9$7!$$=$N$h$&$KJQ99$9$k$@$1$J$iFq$7$/$J$$$h$&$J5$$,$7$^$9!%(B
>  > $B$5$i$K!$$=$N$h$&$KJQ99$7$F$b(B TYPE(obj) $B$r;H$&>l9g$H$[$H$s$IF1$8%3%9%H$G(B
>  > $B>uBV$r6hJL$G$-$^$9$M!%(B
>  > $B$?$@$7!$JQ998e$N(B complex.c $B$N%a%s%F%J%s%9$OBgJQ$+$b$7$l$^$;$s!&!&!&(B
>
>  $B$J$k$[$I!#$`$i$?$5$s$N4uK>$K$OJL$N%/%i%9$r:n$k$H$$$&$3$H$OF~$C(B
>  $B$F$$$J$$$o$1$G$9$M!#(B

$B$=$&$G$9$M!%(BRuby 
$B%l%Y%k$G6hJL$9$kI,MW$,$J$$$N$G!$?7$7$$%/%i%9$N:n$i$J(B
$B$1$l$P$J$i$J$$!$$H$$$&$o$1$G$O$"$j$^$;$s!%(B

$B%/%i%9$r?7@_$9$k$+!$(BComplex $B$N<BAu$NCf$G$d$j$/$j$9$k$+!$(B
$B$3$l$i$N$I$C$A$,$d$j$d$9$$$+$H$$$&LdBj$@$H;W$C$F$$$^$9!%(B
$BA0<T$NJ}$,4JC1$@$C$?$N$G!$$^$@(B Complex -> ComplexFloat 
$B$NJQ49$J$I(B
$B<BAu$7$F$$$J$$;EMM$O$"$j$^$9$,!$Nc$N(B patch $B$G$O(B ComplexFloat 
$B$H$$$&(B
$B%/%i%9$r?7@_$7$^$7$?!%(B

>  $B$G$O!"$$$^$N$^$^$N(B Complex $B$G!"(BC $B%l%Y%k$G(B
>  Complex $B$J(B VALUE $B$+$i(B double _Complex $B$r<h$j=P$94X?t5Z$S(B
>  double _Complex $B$+$i(B Complex $B$J(B VALUE $B$r@8@.$9$k4X?t$r?7@_$9(B
>  $B$k$H$$$&$N$J$i$I$&$G$7$g$&$+(B?

$B$=$N4X?t$NCf$G$OKh2s<BIt$H5uIt$N7?$rFHN)$K%A%'%C%/$7I,MW$J$iJQ49$9$k(B
$B=hM}$,9T$J$o$l$^$9!%$3$l$O!$(BFL_COMPLEX_FLOAT $B$d(B TYPE 
$B%^%/%m(B
$B$G6hJL$9$k>l9g$HHf3S$7$FL5BL$,B?$$$N$GHr$1$?$$$G$9!%(B

$B$=$N$h$&$J4X?t(B*$B$b(B*$BDs6!$9$k$H$$$&$3$H$G$7$?$i!$>l9g$K$h$C$F$OJXMx$G(B
$B$7$g$&$+$i;?@.$G$9!%(B

$BMxE@$H$7$F$O!"3HD%%i%$%V%i%j$,=q$-$d$9$$!"$H$$$&$3$H!#@5Ev2=$NM}M3$H$7(B
$B$F$O!"(BNumeric $B$K$*$1$k(B Float 
$B$N$h$&$J$b$N$@$+$i!"$H$$$&$3$H$,$"$k$N$@(B
$B$H;W$$$^$9!#(B

$B$?$H$($P!":#8=:_$N$d$j$+$?$G$O!"(BRational 
$B$NB.EY$O!"(BFixnum$B!"(BBignum$B!"(BVM
$B$NB.EY$N8B3&$r1[$($i$l$^$;$s!#(BBignum 
$B$O!"$b$C$HB.$/$J$k2DG=@-$,$"$k$H(B
$B;W$$$^$9$,!"$=$l$r$;$:$K!"(BRational $B$,<+A0$G!"(BBignum 
$B$r;}$D$H$$$&$3$H$b(B
$B2DG=$@$H;W$$$^$9!#(B

$B$3$&$$$&9M$($r40A4$KH]Dj$O$7$^$;$s$,!"$d$O$j$$$S$D$J?J2=$H$$$&46$8$,$7(B
$B$^$9!#(B

Complex $B$d(B Rational 
$B$,4{B8$N?tCM%/%i%9$K0MB8$7$F$$$k$3$H$O!"Bg$-$JMxE@(B
$B$G$9!#(BComplexFloat 
$B$@$18+$l$P!"B<ED$5$s$N$h$&$J?M$K$H$C$FET9g$,$$$$$N(B
$B$O!"H=$k$h$&$J5$$,$9$k$N$G$9$,!"A4BN$+$i8+$k$H!"J#;($G!"MxE@$b>/$J$$$H(B
$B;W$$$^$9!#(B

$B3HD%%i%$%V%i%j$r=q$/?M$K$H$C$F$b!"(BComplexFloat 
$B$@$1$D$+$&$H7h$a$F$7$^(B
$B$($P4JC1$+$b$7$l$^$;$s$,!"$h$j0lHLE*$J$b$N$rDs6!$9$k$J$i$P!"5U$KJ#;($K(B
$B$J$C$F$7$^$$$^$9!#(B

Complex $BFb$G!"(BC $B$N(B Complex 
$B$r$D$+$&$3$H$O$"$jF@$k!"$H;W$$$^$9$,!"$=$l(B
$B$@$1$N$3$H$r$9$k2ACM$,$"$k$N$+!":#$N$H$3$m$o$+$j$^$;$s!#(B

$B$`$i$?$G$9!%(B

2008/4/10 Tadayoshi Funaba <tadf@dotrb.org>:
>  $B$?$H$($P!":#8=:_$N$d$j$+$?$G$O!"(BRational $B$NB.EY$O!"(BFixnum$B!"(BBignum$B!"(BVM
>  $B$NB.EY$N8B3&$r1[$($i$l$^$;$s!#(BBignum $B$O!"$b$C$HB.$/$J$k2DG=@-$,$"$k$H(B
>  $B;W$$$^$9$,!"$=$l$r$;$:$K!"(BRational $B$,<+A0$G!"(BBignum $B$r;}$D$H$$$&$3$H$b(B
>  $B2DG=$@$H;W$$$^$9!#(B
>
>  $B$3$&$$$&9M$($r40A4$KH]Dj$O$7$^$;$s$,!"$d$O$j$$$S$D$J?J2=$H$$$&46$8$,$7(B
>  $B$^$9!#(B

$B;d$K$O$$$S$D$J?J2=$H$$$&46$8$O$7$^$;$s!%$`$7$m!$$;$C$+$/(B C 
$B$G<BAu$G$-$k$N$K(B
$B$J$<:GE,2=$G$-$k$3$H$r:GE,2=$7$J$$$N$+IT;W5D$J$/$i$$$G$9!%(B

$B$U$J$P$5$s$O!$(BRational $B$O(B Bignum $B$d(B Fixnum 
$B0J30$N@0?t%/%i%9$bJ];}$G$-$k(B
$BI,MW$,$"$k$H$*9M$($J$N$G$7$g$&$+!)$b$7$=$&$@$H$9$k$H!$8=>u$N(B 
Rational
$B$NJ}$,$$$S$D$J46$8$,$7$^$9!%(B

$BNc$($P(B GMP $B$NB?G\D9@0?t$r%i%C%W$7$?%/%i%9$H$7$F(B GMPInt 
$B$N$h$&$J$b$N$,(B
$B$"$C$?$H$7$F!$$3$l$r;H$C$?(B Rational 
$B$r:n$k$3$H$r9M$($^$7$g$&!%(B
1/2 $B$N$h$&$K4JC1$K5-=R2DG=$J?t$G$b7W;;2aDx$K$h$C$F$O!$(BGMPInt 
$B$G9=@.$5$l$k(B
Rational $B$rL@<(E*$K!$(BRational(GMPInt(1), GMPInt(2)) 
$B$N$h$&$K$7$F(B
$B@8@.$7$J$1$l$P$J$i$J$$$o$1$G$9!%(B

$B$b$A$m$s!$(BGMPInt $B$G9=@.$5$l$?(B Rational $B$H(B Fixnum 
$B$G9=@.$5$l$?(B Rational $BF1;N(B
$B$N1i;;$O(B coerce 
$B$G$-$A$s$H=hM}$5$l$k$O$:$G$9!%$=$l$G$b!$>/$J$/$H$b0l$D$O(B
Rational(GMPInt(1), GMPInt(2)) $B$N$h$&$K@8@.$9$kI,MW$,$"$j$^$9!%(B

$B$=$l$J$i$`$7$m!$(BRational[GMPInt] 
$B$N$h$&$JJ}K!$G!$MWAG%/%i%9$,;XDj$5$l$?(B
Rational 
$B%/%i%9$r@8@.$7!$$3$l$rMQ$$$FM-M}?t$rI=8=$G$-$k$h$&$K$9$kJ}$,!$(B
$B;d$O$-$l$$$K46$8$^$9!%$=$&$G$J$$$J$i!$AH$_9~$_$N(B Rational $B$O(B 
Fixnum
$B$b$7$/$O(B Bignum $B$G9=@.$5$l$k$b$N$G$"$k$H7hDj$7$F$7$^$&$[$&$,(B
$BNI$$$H;W$$$^$9$,G!2?$G$7$g$&!)(B

$B$b$7$3$N0U8+$KH?BP$5$l$k$J$i!$Nc$($P!$J,;R$,(B GMPInt $B$GJ,Jl$,(B 
Bignum
$B$G$"$k$h$&$J(B Rational 
$B$,:n$l$kI,MW@-$,$"$k$+$I$&$+9M$($F$_$F$/$@$5$$!%(B
($BJ,;R$,(B GMPInt$B!$J,Jl$,(B Fixnum 
$B$H$$$&AH9g$;$OM-$jF@$k$H;W$$$^$9(B)

>  $B3HD%%i%$%V%i%j$r=q$/?M$K$H$C$F$b!"(BComplexFloat $B$@$1$D$+$&$H7h$a$F$7$^(B
>  $B$($P4JC1$+$b$7$l$^$;$s$,!"$h$j0lHLE*$J$b$N$rDs6!$9$k$J$i$P!"5U$KJ#;($K(B
>  $B$J$C$F$7$^$$$^$9!#(B

$B$=$N$h$&$JJ#;(@-$O(B API 
$B$r9)IW$9$k$3$H$G$"$kDxEYKI$0$3$H$O2DG=$G$7$g$&!%(B

>  Complex $BFb$G!"(BC $B$N(B Complex $B$r$D$+$&$3$H$O$"$jF@$k!"$H;W$$$^$9$,!"$=$l(B
>  $B$@$1$N$3$H$r$9$k2ACM$,$"$k$N$+!":#$N$H$3$m$o$+$j$^$;$s!#(B

C $B$N(B _Complex $B7?$HJ#AG4X?t72$O(B C99 
$B$G9q:]I8=`5,3J$K$J$C$F$$$^$9!%(B

> $B;d$K$O$$$S$D$J?J2=$H$$$&46$8$O$7$^$;$s!%$`$7$m!$$;$C$+$/(B C $B$G<BAu$G$-$k$N$K(B
> $B$J$<:GE,2=$G$-$k$3$H$r:GE,2=$7$J$$$N$+IT;W5D$J$/$i$$$G$9!%(B

$B$7$J$$!"$H$b8@$C$F$$$^$;$s!#(B

> $B$U$J$P$5$s$O!$(BRational $B$O(B Bignum $B$d(B Fixnum $B0J30$N@0?t%/%i%9$bJ];}$G$-$k(B
> $BI,MW$,$"$k$H$*9M$($J$N$G$7$g$&$+!)$b$7$=$&$@$H$9$k$H!$8=>u$N(B Rational
> $B$NJ}$,$$$S$D$J46$8$,$7$^$9!%(B

$BI,MW$J$$$H;W$$$^$9!#(B

> $B$=$N$h$&$JJ#;(@-$O(B API $B$r9)IW$9$k$3$H$G$"$kDxEYKI$0$3$H$O2DG=$G$7$g$&!%(B

$B$=$&$G$9!#$D$^$j!"(BComplexFloat 
$B$,$"$k$H3HD%%i%$%V%i%j$,=q$-$d$9$$!"$H(B
$B$$$&$N$b$"$^$j@bF@NO$,$J$$$N$G$9!#(B

> C $B$N(B _Complex $B7?$HJ#AG4X?t72$O(B C99 $B$G9q:]I8=`5,3J$K$J$C$F$$$^$9!%(B

$B4X78$,$J$$$H;W$$$^$9!#(B

$B$`$i$?$G$9!%(B

2008/4/11 Tadayoshi Funaba <tadf@dotrb.org>:
> > $B;d$K$O$$$S$D$J?J2=$H$$$&46$8$O$7$^$;$s!%$`$7$m!$$;$C$+$/(B C $B$G<BAu$G$-$k$N$K(B
>  > $B$J$<:GE,2=$G$-$k$3$H$r:GE,2=$7$J$$$N$+IT;W5D$J$/$i$$$G$9!%(B
>
>  $B$7$J$$!"$H$b8@$C$F$$$^$;$s!#(B
>
>  > $B$U$J$P$5$s$O!$(BRational $B$O(B Bignum $B$d(B Fixnum $B0J30$N@0?t%/%i%9$bJ];}$G$-$k(B
>  > $BI,MW$,$"$k$H$*9M$($J$N$G$7$g$&$+!)$b$7$=$&$@$H$9$k$H!$8=>u$N(B Rational
>  > $B$NJ}$,$$$S$D$J46$8$,$7$^$9!%(B
>
>  $BI,MW$J$$$H;W$$$^$9!#(B

$B$@$H$9$k$H!$$U$J$P$5$s$O;d$NDs0F$N2?$KBP$7$F!V$$$S$D!W$G$"$k$H(B
$B$*46$8$K$J$C$F$$$k$N$G$7$g$&$+!)$=$3$,$^$@M}2r$G$-$F$$$J$$$N$G(B
$B65$($F$/$@$5$$!%(B

>  > $B$=$N$h$&$JJ#;(@-$O(B API $B$r9)IW$9$k$3$H$G$"$kDxEYKI$0$3$H$O2DG=$G$7$g$&!%(B
>
>  $B$=$&$G$9!#$D$^$j!"(BComplexFloat $B$,$"$k$H3HD%%i%$%V%i%j$,=q$-$d$9$$!"$H(B
>  $B$$$&$N$b$"$^$j@bF@NO$,$J$$$N$G$9!#(B

$BFbItI=8=$,(B double 
$B$G$"$k$h$&$JJ#AG?t$r07$&%k!<%A%s$,=q$-$d$9$/$J$j$^$9!%(B
$B$=$&$G$J$$>l9g$N=q$-0W$5$OJQ2=$7$J$$$O$:$G$9!%(B
$B$J$<$J$i(B TYPE(obj) == T_COMPLEX_FLOAT $B$G$"$l$P(B
($B$b$7$/$O(B FL_COMPLEX_FLOAT $B%U%i%0$,N)$C$F$$$l$P(B) 
$BFbItI=8=$O(B
double $B$G$"$j!$$=$&$G$J$1$l$PFbItI=8=$O(B Float $B$G$O$J$$(B 
VALUE$B!$(B
$B$H$$$&FsBr$K$J$j$^$9!%(B

ComplexFloat $B$N$h$&$JFC<lHG$,L5$1$l$P!$<BIt$H5uIt$KJ,$1$F(B Float 
$B$+H]$+(B
$B$rH=Dj$9$kI,MW$,$"$j$^$9!%(B

$BA0<T$NJ}$,3Z$@$H;W$$$^$9!%(B

>  > C $B$N(B _Complex $B7?$HJ#AG4X?t72$O(B C99 $B$G9q:]I8=`5,3J$K$J$C$F$$$^$9!%(B
>
>  $B4X78$,$J$$$H;W$$$^$9!#(B

$B>/$J$/$H$b(B C99 $B$NJ#AG4X?t72$r%5%]!<%H$9$k$+H]$+$O(B Ruby 
$B$N?tCM7O$N(B
$BJ}8~@-$KBg$-$/1F6A$9$k$O$:$G$9!%$=$7$F!$J#AG4X?t72$r%5%]!<%H$9$k>l9g$N(B
$B<BAuJ}K!$H$7$F(B _Complex 
$B$r;}$D$+$I$&$+$H$$$&OC$K$J$k$o$1$G$9$,!$(B
$B$=$l$O:#Kx$N5DO@$G==J,OC$79g$o$l$F$$$k$H;W$$$^$9!%$9$J$o$A!$(B
Float $B$r(B VALUE $B$G;}$DI,MW@-$OL5$$$H$$$&$3$H$G$9!%(B

In article <761216ce0804100433k93c7069k5330bda47e925fe6@mail.gmail.com>,
  "Kenta Murata" <muraken@gmail.com> writes:

> $B$=$N4X?t$NCf$G$OKh2s<BIt$H5uIt$N7?$rFHN)$K%A%'%C%/$7I,MW$J$iJQ49$9$k(B
> $B=hM}$,9T$J$o$l$^$9!%$3$l$O!$(BFL_COMPLEX_FLOAT $B$d(B TYPE $B%^%/%m(B
> $B$G6hJL$9$k>l9g$HHf3S$7$FL5BL$,B?$$$N$GHr$1$?$$$G$9!%(B

$B$=$&$$$&%A%'%C%/$N<B9T;~4V$C$F!"$I$N$/$i$$=EMW$J$s$G$7$g$&$+(B?

Ruby $B$+$i8F$S=P$9$N$G$"$l$P!"%a%=%C%I8F$S=P$7<+BN$N%*!<%P!<(B
$B%X%C%I$N$[$&$,$:$C$HBg$-$$$h$&$J5$$,$7$^$9!#(B

In article 
<761216ce0804101030u21a86e48id34981031b077ccf@mail.gmail.com>,
  "Kenta Murata" <muraken@gmail.com> writes:

> $BFbItI=8=$,(B double $B$G$"$k$h$&$JJ#AG?t$r07$&%k!<%A%s$,=q$-$d$9$/$J$j$^$9!%(B
> $B$=$&$G$J$$>l9g$N=q$-0W$5$OJQ2=$7$J$$$O$:$G$9!%(B
> $B$J$<$J$i(B TYPE(obj) == T_COMPLEX_FLOAT $B$G$"$l$P(B
> ($B$b$7$/$O(B FL_COMPLEX_FLOAT $B%U%i%0$,N)$C$F$$$l$P(B) $BFbItI=8=$O(B
> double $B$G$"$j!$$=$&$G$J$1$l$PFbItI=8=$O(B Float $B$G$O$J$$(B VALUE$B!$(B
> $B$H$$$&FsBr$K$J$j$^$9!%(B

[ruby-dev:34300] $B$G=R$Y$?$h$&$J4X?t$r:n$l$P!"%U%i%0$K$h$kJ,(B
$B4t$bITMW$K$J$j$^$9$+$i!"$=$l$,$$$A$P$s=q$-$d$9$$$s$8$c$J$$$G(B
$B$7$g$&$+!#(B

$B=q$-$d$9$5$HFbItI=8=$OFHN)$7$?OC$G$O$J$$$+$H;W$$$^$9!#(B

In article <87hce9iefi.fsf@fsij.org>,
  Tanaka Akira <akr@fsij.org> writes:

> [ruby-dev:34300] $B$G=R$Y$?$h$&$J4X?t$r:n$l$P!"%U%i%0$K$h$kJ,(B

$B$&!"(B[ruby-dev:34308] $B$N4V0c$$$G$9!#(BVALUE $B$H(B double 
_Complex
$B$NJQ494X?t!#(B

$B$^$D$b$H(B $B$f$-$R$m$G$9(B

In message "Re: [ruby-dev:34318] Re: ComplexFloat"
    on Fri, 11 Apr 2008 02:30:58 +0900, "Kenta Murata" 
<muraken@gmail.com> writes:

|$B$@$H$9$k$H!$$U$J$P$5$s$O;d$NDs0F$N2?$KBP$7$F!V$$$S$D!W$G$"$k$H(B
|$B$*46$8$K$J$C$F$$$k$N$G$7$g$&$+!)$=$3$,$^$@M}2r$G$-$F$$$J$$$N$G(B
|$B65$($F$/$@$5$$!%(B

$B!VAa$9$.$k:GE,2=!W$r7|G0$7$F$*$i$l$k5$$,$7$^$9!#;d$H$7$F$OB<(B
$BED$5$s$N<g4c$,FI$_@Z$l$F$J$$$N$GJ]N1$7$^$9!#(B

  * $B5!G=%;%C%H(B(C99 complex$B4X?tAjEv$rDs6!$9$k(B)
  * $BFbIt<BAu(B(C99 complex$B$r%*%V%8%'%/%H$KKd$a9~$`(B)
  * $B8zN((B($B%a%b%j8zN(!"7W;;8zN((B)
  * $B3HD%%i%$%V%i%j$N=q$-$d$9$5(B

$B$NOC$,F1;~$K=P$F$/$k$N$GH=CG$7$,$?$$$G$9!#(B

$B$?$H$($P!"(B

|$B>/$J$/$H$b(B C99 $B$NJ#AG4X?t72$r%5%]!<%H$9$k$+H]$+$O(B Ruby $B$N?tCM7O$N(B
|$BJ}8~@-$KBg$-$/1F6A$9$k$O$:$G$9!%$=$7$F!$J#AG4X?t72$r%5%]!<%H$9$k>l9g$N(B
|$B<BAuJ}K!$H$7$F(B _Complex $B$r;}$D$+$I$&$+$H$$$&OC$K$J$k$o$1$G$9$,!$(B
|$B$=$l$O:#Kx$N5DO@$G==J,OC$79g$o$l$F$$$k$H;W$$$^$9!%$9$J$o$A!$(B
|Float $B$r(B VALUE $B$G;}$DI,MW@-$OL5$$$H$$$&$3$H$G$9!%(B

$B$G8+$k$H!"!V1F6A$9$k$O$:$G$9!W$^$G$O5!G=%;%C%H$NOC!"(B
$B!V(BComplex$B$r;}$D$+$I$&$+$H$$$&OC!W$OFbIt<BAu$NOC$G$9!#$^$?!"(B
ComplexFloat$B$rF3F~$9$k$N$G$"$l$P!"$=$3$G!V(BFloat$B$r(BVALUE$B$G;}$D(B
$BI,MW@-$OL5$$!W$N$O$=$NDL$j$G$9$,!"(BComplex$B%/%i%9$7$+F3F~$7$J(B
$B$$$H$$$&A0Ds$G$O5U$K!V(BFloat$B$rFCJL07$$$7$F(BVALUE$B$G;}$?$J$$I,MW(B
$B@-!W$O$^$@7kO@$,=P$F$$$J$$(B($B8D?ME*$K$O>C6KE*(B)$B$G$9!#(B

$B$5$F!"8DJL$NO@E@$K$D$$$F@0M}$7$^$7$g$&!#(B

$B$^$:!"5!G=%;%C%H$K$D$$$F$OH?BP$7$^$;$s!#$^$?!"$=$N<BAu$H$7$F(B
($B$"$l$P(B)C99 complex$B$r7PM3$9$k$N$b$h$$$H;W$$$^$9!#$?$@$7!"(BC99
$B$rI,?\$K$9$k$N$OEvLLHr$1$?$$$N$G!"MxMQ$9$k$K$7$F$b7k6I8_49AX(B
$B$rMQ0U$9$kI,MW$,$"$k$H;W$$$^$9!#(B

$BFbIt<BAu$K$D$$$F$G$9$,!"0JA0$$$?$@$$$?%Q%C%A$N$h$&$KD>@\%*%V(B
$B%8%'%/%H$KKd$a9~$`$N$OA4BN$N%a%b%j8zN($rDc2<$5$;$k$N$G:NMQ$7(B
$B$,$?$$$G$9!#FHN)$7$?(BComplexFloat($B$"$k$$$O(BFloatComplex?)$B%/%i(B
$B%9$r:NMQ$9$k$H7h$a$k$^$G$O$3$l$OJ]N1$9$k$N$,$h$$$N$G$O$J$$$+(B
$B$H;W$$$^$9!#8D?ME*$K$O$"$^$jFHN)$7$?%/%i%9$rF3F~$7$?$/$J$$$G(B
$B$9$,!#(B

$B8zN($K$D$$$F$G$9$,!"%a%b%j$O$G$-$k$@$1>CHq$7$J$$!"B.EY$OB.$$(B
$B$K1[$7$?$3$H$O$J$$$G$9$,!"B(CM$G$J$$0J>e!"8B3&$,$"$k$H;W$$$^(B
$B$9!#$^$?!"(BRuby$B$+$i8F$S=P$90J>e!"%a%=%C%I8F$S=P$7$N%3%9%H$,Bg(B
$B$-$$$N$G!";vA0$NM=B,$O:$Fq$G$9$+$i$"$^$j5^$$$G:GE,2=$K$D$$$F(B
$B9M$($kI,MW$O$J$5$=$&$K;W$$$^$9!#(B

$B:G8e$K3HD%%i%$%V%i%j$N=q$-$d$9$5$G$9$,!"(BC99$B$rI,?\$K$G$-$J$$(B
$BE@$J$I$+$i$"$kDxEY:$Fq$r$H$b$J$$$^$9$,!"7k6I$O(BC$B$N(Bcomplex$B$rI=(B
$B8=$9$k%G!<%?$H(BRuby$B$N%*%V%8%'%/%H$rAj8_JQ49$9$k(BAPI$B$,$"$k$+$I(B
$B$&$+$K5"7k$9$k$h$&$K;W$$$^$9!#$3$l$OFbIt<BAu$r$I$N$h$&$K$9$k(B
$B$+$H$OFHN)$NOC$G$9!#(B

                                $B$^$D$b$H(B $B$f$-$R$m(B /:|)

> $B$@$H$9$k$H!$$U$J$P$5$s$O;d$NDs0F$N2?$KBP$7$F!V$$$S$D!W$G$"$k$H(B
> $B$*46$8$K$J$C$F$$$k$N$G$7$g$&$+!)$=$3$,$^$@M}2r$G$-$F$$$J$$$N$G(B
> $B65$($F$/$@$5$$!%(B

Rational $B$G!"<+A0$N(B Bignum $B$rMQ0U$7$??M$O!"(BRational 
$B$N;v$@$19M$($F$?$s(B
$B$8$c$J$$$G$7$g$&$+!#$=$N$"$?$j$,$$$S$D$N860x$@$H;W$$$^$9!#(B

> $B>/$J$/$H$b(B C99 $B$NJ#AG4X?t72$r%5%]!<%H$9$k$+H]$+$O(B Ruby $B$N?tCM7O$N(B
> $BJ}8~@-$KBg$-$/1F6A$9$k$O$:$G$9!%$=$7$F!$J#AG4X?t72$r%5%]!<%H$9$k>l9g$N(B

$B$J$/$O$J$$$+$b$7$l$^$;$s!#0l1~!"(BC99 
$B$O$D$+$o$J$$$3$H$K$9$k!"$H$+!#(B

$BB<ED$5$s$O!"(BC $B$N(B Complex 
$B7?$r$D$+$($PB.$/$J$k!"$H$$$&$h$&$J$3$H$OD>@\(B
$BE*$K$$$o$J$$$h$&$K$7$F$$$k$h$&$G$9$M!#$?$V$s!"$=$&$7$F$b(B Complex 
$B$,7`(B
$BE*$KB.$/$J$/$o$1$G$b!"(Bruby 
$B$N?tCM1i;;G=NO$,HtLvE*$K8~>e$9$k$o$1$G$b$J(B
$B$$$3$H$rCN$C$F$$$k$+$i$8$c$J$$$+$J!"$H;W$C$F$$$^$9!#(B

$B<j85$G>/$7%F%9%H$7$?$H$3$m$G$O!"$^$C$?$/B.EY2~A1$N$?$a$NG[N8$,$J$$AGKQ(B
$B$J(B Complex $B$H(B RVALUE $B$r3HBg$9$k$J$IM-Mx$J>r7o$,$"$k(B 
ComplexFloat $B$rHf(B
$B$Y$F$b6C$/$[$I$N0c$$$O$J$$$h$&$G$9!#$^$?!"<BAu$H(B API 
$B$OJL!"$H$$$&$3$H(B
$B$OB<ED$5$s<+?H$,G'$a$i$l$?$H;W$$$^$9!#(B

$B2?$,L\E*$G!"2?$,<jCJ$J$N$+$h$/$o$+$i$J$/$J$C$F$$$k5$$,$7$^$9!#(BC 
$B$N(B
Complex 
$B7?$r$D$+$$$5$($9$l$PK~B-!"$H$$$&$3$H$+$b$7$l$J$$$1$I!"KM$+$i$9(B
$B$k$H!"8=;~E@$G$=$l$,I,$:$7$b:GA1$H$b;W$($^$;$s!#(B

$B$3$N7o$O!":G=i$K$$$C$?$h$&$K!"<BAu$NLdBj$G$7$+$J$$$H;W$$$^$9!#(BC 
$B$N(B
Complex 
$B7?$r$D$+$&2DG=@-$OH]Dj$7$^$;$s$,!"8=;~E@$G!"$D$+$(!"$D$+$o$J$$(B
$B$N$O$*$+$7$$!"$H$o$l$k6Z$O$J$$!"$H8D?ME*$K$OH=CG$7$^$7$?!#(B

$B$3$NA0!":XF#$5$s$,>R2p$7$F$/$l$?$h$&$J$3$H$b$"$j$^$9$7!":#$9$02?$+$7$J(B
$B$1$l$P$J$i$J$$$3$H$G$b$"$j$^$;$s!#$$$:$l!"B.EY2~A1$J$I$,I,MW$@$HH=CG$7(B
$B$?>l9g!"$=$N;~NI$$$H;W$($P!"(BC $B$N(B Complex 
$B7?$r$D$+$&$3$H$b$"$k$N$+$b$7(B
$B$l$^$;$s!#:#$O$^$@!"(BComplex 
$B$NAH$_9~$_<+BN$,@5<0$K7h$^$k$+$I$&$+$o$+$i(B
$B$J$$;~4|$G$9!#(B

$B$3$N7o$O!"(BComplex $B<+BN$b4^$a$F!"$^$D$b$H$5$s$KMB$1$^$9!#(B

$B$^$D$b$H(B $B$f$-$R$m$G$9(B

In message "Re: [ruby-dev:34324] Re: ComplexFloat"
    on Fri, 11 Apr 2008 08:19:16 +0900, Tadayoshi Funaba 
<tadf@dotrb.org> writes:

|$B$3$N7o$O!"(BComplex $B<+BN$b4^$a$F!"$^$D$b$H$5$s$KMB$1$^$9!#(B

$B$"$j$,$H$&$4$6$$$^$9!#;d$H$7$F$O(B[ruby-dev:34322]$B$N$h$&$K9M$((B
$B$F$$$^$9!#0J8e!"B<ED$5$s$H$NBPOC$O<g$K;d$,0z$-<u$1$^$9!#(B

$B$,!";d$N?t3XE*CN<1(B($B$*$h$SAGM\(B)$B$NL5$5$,>c32$K$J$C$?;~$K$O!"$_(B
$B$J$5$s$K=u$1$F$$$?$@$-$?$$$H;W$$$^$9!#(B

$B$`$i$?$G$9!%(B

2008/4/11 Yukihiro Matsumoto <matz@ruby-lang.org>:
>   * $B3HD%%i%$%V%i%j$N=q$-$d$9$5(B
>
>  $B$NOC$,F1;~$K=P$F$/$k$N$GH=CG$7$,$?$$$G$9!#(B

$B;d$N<g4c$O!$>e5-$N(B4$B$DA4$F!$$*$h$S!$$U$J$P$5$s$N(B Complex
($B%3%s%F%J$H$7$F$N(B Complex) 
$B$H$N6&B8$r$G$-$k8B$j<B8=$9$k$3$H$G$9!%(B

>  $B$$$H$$$&A0Ds$G$O5U$K!V(BFloat$B$rFCJL07$$$7$F(BVALUE$B$G;}$?$J$$I,MW(B
>  $B@-!W$O$^$@7kO@$,=P$F$$$J$$(B($B8D?ME*$K$O>C6KE*(B)$B$G$9!#(B

$B>e5-(B4$B9`L\$K$D$$$FF~$jMp$l$F$$$?$3$H$GJ,$+$j$K$/$/$J$C$F$$$k$H$7$?$i(B
$B?=$7J,$1$"$j$^$;$s$G$7$?!%(B

>  $B$5$F!"8DJL$NO@E@$K$D$$$F@0M}$7$^$7$g$&!#(B
>
>  $B$^$:!"5!G=%;%C%H$K$D$$$F$OH?BP$7$^$;$s!#$^$?!"$=$N<BAu$H$7$F(B
>  ($B$"$l$P(B)C99 complex$B$r7PM3$9$k$N$b$h$$$H;W$$$^$9!#$?$@$7!"(BC99
>  $B$rI,?\$K$9$k$N$OEvLLHr$1$?$$$N$G!"MxMQ$9$k$K$7$F$b7k6I8_49AX(B
>  $B$rMQ0U$9$kI,MW$,$"$k$H;W$$$^$9!#(B

$B8_49AX$O@hF|$N(B patch 
$B$K4^$s$G$"$k$N$G!$$"$l$rMxMQ$G$-$k$O$:$G$9!%(B

>  $BFbIt<BAu$K$D$$$F$G$9$,!"0JA0$$$?$@$$$?%Q%C%A$N$h$&$KD>@\%*%V(B
>  $B%8%'%/%H$KKd$a9~$`$N$OA4BN$N%a%b%j8zN($rDc2<$5$;$k$N$G:NMQ$7(B
>  $B$,$?$$$G$9!#(B

$B3N$+$K$=$N$H$*$j$@$H;W$$$^$9!%;d$b(B RVALUE $B$X(B double _Complex 
$B$r(B
$BKd$a9~$`<BAu$O<h$j2<$2$^$9!%$=$NBe$o$j$H$7$F!$(Bdouble _Complex*
$B$r;}$?$;$k<BAu$rDs0F$7$?$$$G$9!%<B$O$=$&$9$k;v$G!$J#AG?tCM$N(B
$B%a%b%j%"%i%$%a%s%H$rD4@0$G$-$k2DG=@-$,$G$F$-$^$7$?!%$9$k$H!$(B
$B%"!<%-%F%/%A%c$K$h$C$F$OCM$N%l%8%9%?$X$NE>Aw$,9bB.2=$7$^$9!%(B
($B$H$$$C$F$b$3$l$OK\Ev$K:3:Y$J0c$$$G$7$+$"$j$^$;$s$M(B)

>  $BFHN)$7$?(BComplexFloat($B$"$k$$$O(BFloatComplex?)$B%/%i(B
>  $B%9$r:NMQ$9$k$H7h$a$k$^$G$O$3$l$OJ]N1$9$k$N$,$h$$$N$G$O$J$$$+(B
>  $B$H;W$$$^$9!#8D?ME*$K$O$"$^$jFHN)$7$?%/%i%9$rF3F~$7$?$/$J$$$G(B
>  $B$9$,!#(B

$B$U$J$P$5$s$N(B Complex $B$O!$@.J,%/%i%9(B (Fixnum, Bignum, 
Rational, Float)
$B$G%a%=%C%I$,:FDj5A$5$l$?$H$-$K$=$N1F6A$rHo$j$^$9!%$3$l$O!$(BComplex 
$B$,(B
$B%3%s%F%J$H$7$F<BAu$5$l$F$$$k$+$i$G$9!%(B

$B$=$l$KBP$7$F!$(BComplexFloat ($B$"$k$$$O(B FloatComplex) 
$B$rB>$N%/%i%9$N(B
$B%a%=%C%I:FDj5A$K1F6A$5$l$J$$7O$H$7$FF3F~$G$-$^$;$s$+!)(B
$B$D$^$j!$%3%s%F%J$G$O$J$$J#AG?t$H$7$FB8:_$7$F$b$i$$$?$$$N$G$9!%(B
$BF1$8M}M3$G%3%s%F%J$G$O$J$$(B Rational 
$B$,$"$C$F$bNI$$$H;W$$$^$9!%(B
$B<+J,$N%/%i%9$@$1$GJD$8$F$$$l$P(B YARV $B$G$N:GE,2=$,2DG=$G$9!%(B

>  $B8zN($K$D$$$F$G$9$,!"%a%b%j$O$G$-$k$@$1>CHq$7$J$$!"B.EY$OB.$$(B
>  $B$K1[$7$?$3$H$O$J$$$G$9$,!"B(CM$G$J$$0J>e!"8B3&$,$"$k$H;W$$$^(B
>  $B$9!#(B

C99 $B$N(B double _Complex 
$B$r;H$&>l9g!$CM$N%m!<%I!&%9%H%"$*$h$S1i;;$b4^$a$F(B
$B%3%s%Q%$%i$K$h$k:GE,2=$r4|BT$G$-$^$9!%(BC99 $B$r;H$o$:$K(B double 
2$B8D$NG[Ns$r(B
$B;H$&>l9g$G$b!$%"!<%-%F%/%A%c$K$h$C$F$O(B SIMD 
$BL?Na$r;H$C$?:GE,2=$,2DG=$G$9!%(B

# $B$^$!!$$3$l$b:3:Y$J$3$H$@$H8@$o$l$l$P$=$l$^$G$G$9$,!%(B

>  $B$^$?!"(BRuby$B$+$i8F$S=P$90J>e!"%a%=%C%I8F$S=P$7$N%3%9%H$,Bg(B
>  $B$-$$$N$G!";vA0$NM=B,$O:$Fq$G$9$+$i$"$^$j5^$$$G:GE,2=$K$D$$$F(B
>  $B9M$($kI,MW$O$J$5$=$&$K;W$$$^$9!#(B

$B$3$l$O>e=R$7$?$h$&$K!$(BComplexFloat ($B$"$k$$$O(B FloatComplex) 
$B$rJD$8$?(B
$B1i;;7O$r;}$D%3%s%F%J$G$O$J$$J#AG?t$H$7$F<BAu$9$l$P!$(B
YARV $B$K$h$k:GE,2=$r<B8=$G$-!$(BComplex $B$N<BAu$N$h$&$K!$(B
rb_funcall $B$r<!!9$H8F$S=P$9I,MW$OL5$$$N$G9bB.2=$,K>$a$^$9!%(B

$B$^$?!$(BComplexFloat 
$BF1;N$N1i;;$r$^$H$a$F:GE,2=$9$k$3$H$b2DG=$G$9$h$M!%(B
$B$3$l$b!$$d$k$H$7$?$i(B YARV $B$G<B8=$9$k$3$H$K$J$j$^$9!%(B

$B$3$&$$$C$?>-MhE*$J:GE,2=$N2DG=@-$OMxE@$H9M$($F$h$$$H;W$&$N$G$9$,(B
$BG!2?$G$7$g$&$+!%(B

>  $B:G8e$K3HD%%i%$%V%i%j$N=q$-$d$9$5$G$9$,!"(BC99$B$rI,?\$K$G$-$J$$(B
>  $BE@$J$I$+$i$"$kDxEY:$Fq$r$H$b$J$$$^$9$,!"7k6I$O(BC$B$N(Bcomplex$B$rI=(B
>  $B8=$9$k%G!<%?$H(BRuby$B$N%*%V%8%'%/%H$rAj8_JQ49$9$k(BAPI$B$,$"$k$+$I(B
>  $B$&$+$K5"7k$9$k$h$&$K;W$$$^$9!#$3$l$OFbIt<BAu$r$I$N$h$&$K$9$k(B
>  $B$+$H$OFHN)$NOC$G$9!#(B

$B3N$+$K(B API 
$B$rMQ0U$9$k$3$H$G3HD%%b%8%e!<%k$,:n$j0W$/$J$k$H$$$&<gD%$O(B
$B0UL#$r;}$?$J$/$J$j$^$9$M!%$?$@$7!$$3$l$OFH<+%/%i%9$r:n$i$J$$$H$$$&(B
$BA0Ds$G$NOC$7$G$9!%(B

$BEDCf$5$s$N%"%I%P%$%9$G!$FH<+%/%i%9$r:n$i$J$/$F$bNI$$$+$J$H;W$$=i$a!$(B
$B$=$l$KBP$7$F$^$D$b$H$5$s$b!VMn$H$7=j$,8+$D$+$C$?!W$H6D$C$F$$$^$7$?!%(B
$B$7$+$7$J$,$i!$;d$,M_$7$+$C$?(B ComplexFloat 
$B$O%3%s%F%J$G$O$J$$J#AG?t!$(B
$B$D$^$j1i;;7O$,JD$8$F$$$kJ#AG?t$J$N$G!$%U%i%0$GFbIt<BAu$r@Z$jBX$($k(B
Complex $B$NFbIt<BAu$r%U%i%0$G@Z$jBX$($k7A$G$O%@%a$G$7$?!%(B


$B$H$3$m$G!$(Bcomplex.rb 
$B$,AH9~$_$K$J$k$3$H$GF@$i$l$kMxE@$O2?$G$9$+!)(B
$B8=:_$N(B complex.c $B$N;EMM$J$i(B Ruby 
$B$G$b<BAu$G$-$k$7!$$`$7$m$=$NJ}$,(B
$B%a%s%F%J%s%9$7$d$9$$$H;W$&$N$G$9!%(B

$B;d$,M_$7$$%3%s%F%J$G$O$J$$J#AG?t$H$7$F$N(B ComplexFloat 
$B$,5Q2<$5$l$k(B
$B:GBg$NM}M3$O!$4{$K$U$J$P$5$s$N(B Complex $B$,AH9~$^$l$F$$$F!$(B
$B$=$l$H$N:.Mp$,M=A[$5$l$k$+$i$G$9$h$M!)(B

$BAH9~$_$K$9$k$3$H$G1i;;Ey$N:GE,2=$,K>$a$k(B ComplexFloat 
$B$G$O$J$/!$(B
complex.rb $B$N(B Complex $B$r(B C 
$B$KD>Lu$7$FAH9~$_$K$9$kM}M3$,CN$j$?$$$G$9!%(B

$BF1MM$NM}M3$G!$(BRational $B$K$D$$$F$b!$(BFixnum $B$H(B Bignum 
$B0J30$r;}$D;v$O(B
$BA[Dj$7$F$$$J$$(B [ruby-dev:34317] 
$B$N$K!$$J$<1i;;7O$,<+J,$N%/%i%9$G(B
$BJD$8$F$J$$$N$+5$$K$J$j$^$9!%$=$NM}M3$r65$($F$$$?$@$1$^$;$s$+!)(B

# $B$3$l$i$O!$$U$J$P$5$s$K<ALd$9$Y$-$G$7$g$&$+!)(B

$B$h$m$7$/$*4j$$$7$^$9!%(B

$B$`$i$?$G$9!%(B

2008/4/11 Tadayoshi Funaba <tadf@dotrb.org>:
> > $B$@$H$9$k$H!$$U$J$P$5$s$O;d$NDs0F$N2?$KBP$7$F!V$$$S$D!W$G$"$k$H(B
>  > $B$*46$8$K$J$C$F$$$k$N$G$7$g$&$+!)$=$3$,$^$@M}2r$G$-$F$$$J$$$N$G(B
>  > $B65$($F$/$@$5$$!%(B
>
>  Rational $B$G!"<+A0$N(B Bignum $B$rMQ0U$7$??M$O!"(BRational $B$N;v$@$19M$($F$?$s(B
>  $B$8$c$J$$$G$7$g$&$+!#$=$N$"$?$j$,$$$S$D$N860x$@$H;W$$$^$9!#(B

$B;DG0$J$,$i!$$=$l$,$$$S$D$G$"$k$H$O46$8$i$l$J$$$s$G$9$h$M!%(B
Rational $B0J30$H$NAj8_:nMQ$O(B coerce $B$rE,@Z$KDj5A$9$k$3$H$G(B
$B$I$&$H$G$b$G$-$^$9$h$M!%(BFixnum/Bignum $B0J30$O;}$?$J$$;v$r(B
$BA[Dj$7$F$$$k$N$G$7$?$i!$(BRational $B$r%3%s%F%J$H$7<BAu$9$k(B
$BI,MW@-$bL5$$!$$H$$$&$N$,;d$N9M$(J}$G$9!%(B

>  > $B>/$J$/$H$b(B C99 $B$NJ#AG4X?t72$r%5%]!<%H$9$k$+H]$+$O(B Ruby $B$N?tCM7O$N(B
>  > $BJ}8~@-$KBg$-$/1F6A$9$k$O$:$G$9!%$=$7$F!$J#AG4X?t72$r%5%]!<%H$9$k>l9g$N(B
>
>  $B$J$/$O$J$$$+$b$7$l$^$;$s!#0l1~!"(BC99 $B$O$D$+$o$J$$$3$H$K$9$k!"$H$+!#(B

C99 $B$C$F$=$s$J$K7y$o$l$F$k$s$G$9$+$M$'(B >_<

>  $BB<ED$5$s$O!"(BC $B$N(B Complex $B7?$r$D$+$($PB.$/$J$k!"$H$$$&$h$&$J$3$H$OD>@\(B
>  $BE*$K$$$o$J$$$h$&$K$7$F$$$k$h$&$G$9$M!#$?$V$s!"$=$&$7$F$b(B Complex $B$,7`(B
>  $BE*$KB.$/$J$/$o$1$G$b!"(Bruby $B$N?tCM1i;;G=NO$,HtLvE*$K8~>e$9$k$o$1$G$b$J(B
>  $B$$$3$H$rCN$C$F$$$k$+$i$8$c$J$$$+$J!"$H;W$C$F$$$^$9!#(B

$B:#$^$G$OD>@\E*$JI=8=$OHr$1$^$7$?$,!$@hDx$^$D$b$H$5$s$N%a!<%k$X$NJV?.$G(B
$B$=$N$3$H$bL@5-$7$^$7$?!%(BC99 $B$N(B _Complex 
$B$GB.$/$J$k$+$I$&$+$O%3%s%Q%$%i(B
$B$H%i%$%V%i%j$K0MB8$7$^$9!%(B

ruby $B$N?tCM1i;;G=NO$N8~>e$O!$(BC99 $B$N(B _Complex 
$B$r;H$&;v$H$OJLLdBj$G$9!%(B
$B$R$H$DA0$N%a!<%k$K$b=q$$$?$h$&$K!$%3%s%F%J$G$O$J$$J#AG?t$,$"$l$P!$(B
YARV $B$G1i;;$N:GE,2=$r$9$k$3$H$,$G$-$^$9!%(B

>  $B<j85$G>/$7%F%9%H$7$?$H$3$m$G$O!"$^$C$?$/B.EY2~A1$N$?$a$NG[N8$,$J$$AGKQ(B
>  $B$J(B Complex $B$H(B RVALUE $B$r3HBg$9$k$J$IM-Mx$J>r7o$,$"$k(B ComplexFloat $B$rHf(B
>  $B$Y$F$b6C$/$[$I$N0c$$$O$J$$$h$&$G$9!#$^$?!"<BAu$H(B API $B$OJL!"$H$$$&$3$H(B
>  $B$OB<ED$5$s<+?H$,G'$a$i$l$?$H;W$$$^$9!#(B

$B;d$N(B patch 
$B$O<BAu0F$r<($9$?$a$K5^$$$G:n$C$?$b$N$G!$$R$H$D$b:GE,2=$5$l$F(B
$B$$$^$;$s!%$7$+$7!$$"$N<BAu$+$i$N:GE,2=$O2DG=$G$9$h$M!%(B

# $B$A$J$_$K!$(BRVALUE $B$N3HBg$OITMx$J>r7o$G$9(B >_<

>  $B2?$,L\E*$G!"2?$,<jCJ$J$N$+$h$/$o$+$i$J$/$J$C$F$$$k5$$,$7$^$9!#(BC $B$N(B
>  Complex $B7?$r$D$+$$$5$($9$l$PK~B-!"$H$$$&$3$H$+$b$7$l$J$$$1$I!"KM$+$i$9(B
>  $B$k$H!"8=;~E@$G$=$l$,I,$:$7$b:GA1$H$b;W$($^$;$s!#(B

$BJ#AG?t$NI=8=$r(B C 
$B$G;}$D;v$NMxE@$O!$J#AG?t%/%i%9$N1i;;$,B>$N%/%i%9$K(B
$B0MB8$;$:$K7hDj$G$-$k;v$G$9!%$=$l$G!$A0$K$b=R$Y$^$7$?$,!$%3%s%F%J$H$7$F(B
$B$NJ#AG?t$bI,MW$J$N$G!$K\Ev$O$I$C$A$bAH9~$^$l$F$$$k$Y$-$@$H;W$&$s$G$9!%(B
$B;d$K$H$C$F$N:GA1$O!$$U$J$P$5$s$N(B Complex $B$HKM$N(B ComplexFloat 
$B$,6&B8(B
$B$9$k$3$H$G$9!%$=$7$F!$$=$l$,(B Ruby 
$B$K$H$C$F$b:GA1$G$"$k$H?.$8$F$$$^$9!%(B

>  $B$3$N7o$O!":G=i$K$$$C$?$h$&$K!"<BAu$NLdBj$G$7$+$J$$$H;W$$$^$9!#(BC $B$N(B
>  Complex $B7?$r$D$+$&2DG=@-$OH]Dj$7$^$;$s$,!"8=;~E@$G!"$D$+$(!"$D$+$o$J$$(B
>  $B$N$O$*$+$7$$!"$H$o$l$k6Z$O$J$$!"$H8D?ME*$K$OH=CG$7$^$7$?!#(B

$BAH9~$_%/%i%9$K$J$k2DG=@-$,$"$C$?$N$G!$6/$/H]Dj$7$^$7$?!%(B
$B$b$7!$!VI8=`E:IU%i%$%V%i%j$N$^$^<BAu$,(B C 
$B$K$J$j$^$7$?!W$H$$$&(B
$B$@$1$@$C$?$i2?$b8@$o$J$+$C$?$H;W$$$^$9!%AH9~$_$K$J$k$H$$$&$3$H$O!$(B
ruby $B$r5/F0$7$?$@$1$G$=$3$K(B Complex 
$B$,B8:_$9$k$3$H$K$J$j$^$9!%(B
require "complex" $B$7$J$1$l$PB8:_$7$J$$(B Complex 
$B$H!$2?$b$7$J$/$F$b(B
$BB8:_$9$k(B Complex 
$B$G$O0UL#$,0c$$$^$9$h$M!)AH9~$_2=$C$F$=$N$/$i$$(B
$BBg$-$J1F6A$,$"$k$H;W$&$s$G$9$h!%(B

>  $B$3$NA0!":XF#$5$s$,>R2p$7$F$/$l$?$h$&$J$3$H$b$"$j$^$9$7!":#$9$02?$+$7$J(B
>  $B$1$l$P$J$i$J$$$3$H$G$b$"$j$^$;$s!#$$$:$l!"B.EY2~A1$J$I$,I,MW$@$HH=CG$7(B
>  $B$?>l9g!"$=$N;~NI$$$H;W$($P!"(BC $B$N(B Complex $B7?$r$D$+$&$3$H$b$"$k$N$+$b$7(B
>  $B$l$^$;$s!#:#$O$^$@!"(BComplex $B$NAH$_9~$_<+BN$,@5<0$K7h$^$k$+$I$&$+$o$+$i(B
>  $B$J$$;~4|$G$9!#(B

$B;d$OFI$_0c$($F$$$?$+$b$7$l$^$;$s!%(BComplex 
$B$NAH9~$_2=$O$[$H$s$I7hDj(B
$B$5$l$F$$$k$b$N$@$H$P$+$j;W$C$F$$$^$7$?!%$b$7$+$7$?$iAH$_9~$_%/%i%9(B
$B$G$O$J$/$J$k2DG=@-$b$"$k$s$G$9$+!)(B

$B$^$D$b$H(B $B$f$-$R$m$G$9(B

In message "Re: [ruby-dev:34328] Re: ComplexFloat"
    on Fri, 11 Apr 2008 15:49:53 +0900, "Kenta Murata" 
<muraken@gmail.com> writes:

|$B$U$J$P$5$s$N(B Complex $B$O!$@.J,%/%i%9(B (Fixnum, Bignum, Rational, Float)
|$B$G%a%=%C%I$,:FDj5A$5$l$?$H$-$K$=$N1F6A$rHo$j$^$9!%$3$l$O!$(BComplex $B$,(B
|$B%3%s%F%J$H$7$F<BAu$5$l$F$$$k$+$i$G$9!%(B

$B8=:_$N<BAu$G$O3N$+$K$=$&$J$C$F$$$^$9$,!"$3$l$O;EMM$N0lIt$G$"(B
$B$k$H$OG'<1$7$F$$$^$;$s!#$N$G!"$=$l$r7x;}$9$k$?$a$KJL$NJD$8$?(B
$B7O$H$7$F$N(BComplexFloat$B$rF3F~$9$kI,A3@-$b46$8$F$$$^$;$s!#(B

|$BF1MM$NM}M3$G!$(BRational $B$K$D$$$F$b!$(BFixnum $B$H(B Bignum $B0J30$r;}$D;v$O(B
|$BA[Dj$7$F$$$J$$(B [ruby-dev:34317] $B$N$K!$$J$<1i;;7O$,<+J,$N%/%i%9$G(B
|$BJD$8$F$J$$$N$+5$$K$J$j$^$9!%$=$NM}M3$r65$($F$$$?$@$1$^$;$s$+!)(B

$B$3$l$b8=:_$N<BAu>e$NM}M3$@$H;W$$$^$9!#(B

$BKNIt$GC1=c$J5?Ld$J$N$G$9$,!"(B

Kenta Murata $B$5$s$O=q$-$^$7$?(B:
>>  $B$^$?!"(BRuby$B$+$i8F$S=P$90J>e!"%a%=%C%I8F$S=P$7$N%3%9%H$,Bg(B
>>  $B$-$$$N$G!";vA0$NM=B,$O:$Fq$G$9$+$i$"$^$j5^$$$G:GE,2=$K$D$$$F(B
>>  $B9M$($kI,MW$O$J$5$=$&$K;W$$$^$9!#(B
>>     
>
> $B$3$l$O>e=R$7$?$h$&$K!$(BComplexFloat ($B$"$k$$$O(B FloatComplex) $B$rJD$8$?(B
> $B1i;;7O$r;}$D%3%s%F%J$G$O$J$$J#AG?t$H$7$F<BAu$9$l$P!$(B
> YARV $B$K$h$k:GE,2=$r<B8=$G$-!$(BComplex $B$N<BAu$N$h$&$K!$(B
> rb_funcall $B$r<!!9$H8F$S=P$9I,MW$OL5$$$N$G9bB.2=$,K>$a$^$9!%(B
>   

YARV$B$C$F$=$s$J5!G=$,$"$k$s$G$9$+(B?$B$"$k$$$ODs6!M=Dj$G$9$+(B?$B$"$k$$$O86M}E*$K(B
$B2DG=$G$9$+(B?

$B$`$i$?$G$9!%(B

2008/4/11 Urabe Shyouhei <shyouhei@ruby-lang.org>:
>  > $B$3$l$O>e=R$7$?$h$&$K!$(BComplexFloat ($B$"$k$$$O(B FloatComplex) $B$rJD$8$?(B
>  > $B1i;;7O$r;}$D%3%s%F%J$G$O$J$$J#AG?t$H$7$F<BAu$9$l$P!$(B
>  > YARV $B$K$h$k:GE,2=$r<B8=$G$-!$(BComplex $B$N<BAu$N$h$&$K!$(B
>  > rb_funcall $B$r<!!9$H8F$S=P$9I,MW$OL5$$$N$G9bB.2=$,K>$a$^$9!%(B
>  >
>
>  YARV$B$C$F$=$s$J5!G=$,$"$k$s$G$9$+(B?$B$"$k$$$ODs6!M=Dj$G$9$+(B?$B$"$k$$$O86M}E*$K(B
>  $B2DG=$G$9$+(B?

Fixnum $B$KBP$7$F;w$?$h$&$J:GE,2=$,9T$J$o$l$F$$$^$9$h$M!%$G$9$+$i!$(B
$BJD$8$?1i;;7O$r;}$D%/%i%9$K$D$$$F$O86M}E*$KF1MM$N:GE,2=$,2DG=$J$s$8$c(B
$B$J$$$+$H;W$C$F$$$k$s$G$9$,!$4V0c$C$F$$$^$9$+!)(B

# $B5^$KIT0B$K$J$C$F$-$?!&!&!&(B

$B!!$5$5$@$G$9!%(B

Kenta Murata wrote:
> Fixnum $B$KBP$7$F;w$?$h$&$J:GE,2=$,9T$J$o$l$F$$$^$9$h$M!%$G$9$+$i!$(B
> $BJD$8$?1i;;7O$r;}$D%/%i%9$K$D$$$F$O86M}E*$KF1MM$N:GE,2=$,2DG=$J$s$8$c(B
> $B$J$$$+$H;W$C$F$$$k$s$G$9$,!$4V0c$C$F$$$^$9$+!)(B

$B!!2?$r$I$3$^$G!$$H$$$&$N$rGD0.$7$F$$$J$$$N$G$9$,!$6I=jE*$J:GE,2=$O2D(B
$BG=$+$H;W$$$^$9!%(B

$B$`$i$?$G$9!%(B

2008/4/11 Yukihiro Matsumoto <matz@ruby-lang.org>:
>  |$B$U$J$P$5$s$N(B Complex $B$O!$@.J,%/%i%9(B (Fixnum, Bignum, Rational, Float)
>  |$B$G%a%=%C%I$,:FDj5A$5$l$?$H$-$K$=$N1F6A$rHo$j$^$9!%$3$l$O!$(BComplex $B$,(B
>  |$B%3%s%F%J$H$7$F<BAu$5$l$F$$$k$+$i$G$9!%(B
>
>  $B8=:_$N<BAu$G$O3N$+$K$=$&$J$C$F$$$^$9$,!"$3$l$O;EMM$N0lIt$G$"(B
>  $B$k$H$OG'<1$7$F$$$^$;$s!#$N$G!"$=$l$r7x;}$9$k$?$a$KJL$NJD$8$?(B
>  $B7O$H$7$F$N(BComplexFloat$B$rF3F~$9$kI,A3@-$b46$8$F$$$^$;$s!#(B

$BJ#AG?t$K$D$$$F$O!$$I$A$i$bI,MW$G$9!%8=:_(B Ruby 
$B$KG$0U@)EY$N>.?t$r(B
$BI=8=$G$-$k%/%i%9$,AH9~$_$GDs6!$5$l$F$$$J$$$N$G!$(BBigDecimal 
$B$N$h$&$J(B
$B%/%i%9$r;H$C$FJ#AG?t$r<B8=$9$k$H$-$O%3%s%F%J7?$NJ#AG?t$,I,MW$K$J$j$^$9!%(B
$B$G$9$+$i!$$U$J$P$5$s$N(B Complex 
$B$,%3%s%F%JE*$G$"$k;v$O<BAu>e$NET9g(B
$B$G$O$J$/$F!$K\Mh$N;EMM$N0lIt$K$9$Y$-$G$9!%(B

$B$=$N>e$G!$$d$O$jJD$8$?J#AG?t$b$"$k$Y$-$@$H;W$$$^$9!%$=$7$F!$:GE,2=Ey$N(B
$B2DG=@-$r9M$($l$P!$JD$8$?J#AG?t$,AH9~$_$GDs6!$5$l$F$$$kJ}$,<+A3$G$"$k(B
$B$H;W$$$^$9!%(B

$B$^$D$b$H(B $B$f$-$R$m$G$9(B

In message "Re: [ruby-dev:34340] Re: ComplexFloat"
    on Fri, 11 Apr 2008 18:36:41 +0900, "Kenta Murata" 
<muraken@gmail.com> writes:

|$BJ#AG?t$K$D$$$F$O!$$I$A$i$bI,MW$G$9!%8=:_(B Ruby $B$KG$0U@)EY$N>.?t$r(B
|$BI=8=$G$-$k%/%i%9$,AH9~$_$GDs6!$5$l$F$$$J$$$N$G!$(BBigDecimal $B$N$h$&$J(B
|$B%/%i%9$r;H$C$FJ#AG?t$r<B8=$9$k$H$-$O%3%s%F%J7?$NJ#AG?t$,I,MW$K$J$j$^$9!%(B
|$B$G$9$+$i!$$U$J$P$5$s$N(B Complex $B$,%3%s%F%JE*$G$"$k;v$O<BAu>e$NET9g(B
|$B$G$O$J$/$F!$K\Mh$N;EMM$N0lIt$K$9$Y$-$G$9!%(B

$B$J$k$[$I!#(B

|$B$=$N>e$G!$$d$O$jJD$8$?J#AG?t$b$"$k$Y$-$@$H;W$$$^$9!%$=$7$F!$:GE,2=Ey$N(B
|$B2DG=@-$r9M$($l$P!$JD$8$?J#AG?t$,AH9~$_$GDs6!$5$l$F$$$kJ}$,<+A3$G$"$k(B
|$B$H;W$$$^$9!%(B

$BC1=c$5$dB>$N%/%i%99=@.$H$N@09g@-$r5>@7$K$7$F$^$GJD$8$?J#AG?t(B
$B%/%i%9$rJL$KMQ0U$9$Y$-M}M3$O:GE,2=$@$1$G$9$+!)(B

$B8=:_$N(BYARV$B$N:GE,2=<BAu$r9M$($k$H!"AH$_9~$_%/%i%9(B($B$?$H$($P(B
Float)$B$,JQ99$5$l$F$$$J$$;~$K$O9bB.$J%W%j%_%F%#%V$,F0$/$H$$$&(B
$BF0:n$r(BComplex($B$d(BRational)$B$KE,MQ$7$F$O$$$1$J$$(B(or 
$B$G$-$J$$(B)$BM}(B
$BM3$OL5$$$H;W$&$N$G$9$,!#(B

                                $B$^$D$b$H(B $B$f$-$R$m(B /:|)

$B$`$i$?$G$9!%(B

2008/4/11 Yukihiro Matsumoto <matz@ruby-lang.org>:
>  |$B$=$N>e$G!$$d$O$jJD$8$?J#AG?t$b$"$k$Y$-$@$H;W$$$^$9!%$=$7$F!$:GE,2=Ey$N(B
>  |$B2DG=@-$r9M$($l$P!$JD$8$?J#AG?t$,AH9~$_$GDs6!$5$l$F$$$kJ}$,<+A3$G$"$k(B
>  |$B$H;W$$$^$9!%(B
>
>  $BC1=c$5$dB>$N%/%i%99=@.$H$N@09g@-$r5>@7$K$7$F$^$GJD$8$?J#AG?t(B
>  $B%/%i%9$rJL$KMQ0U$9$Y$-M}M3$O:GE,2=$@$1$G$9$+!)(B

$B:GBg$NM}M3$O:GE,2=$G$9!%0J2<$N$h$&$JM}M3$b$"$j$^$9!%(B

$B@.J,$,IbF0>.?tE@$K$J$C$F$7$^$&$H!$$=$NCM$OB>$NI=8=$K0EL[$KJQ49$G$-$^$;$s!%(B
$B8@$$49$($k$H!$IbF0>.?tE@?t$r;}$DJ#AG?t$O!$(BRational $B$d(B 
Integer $B$r;}$DJ#AG?t$r(B
$BA4It?)$Y$F$7$^$&$s$G$9!%$=$l$@$1$G$J$/!$$?$H$($P(B 
CMath.sin$B!$(BCMath.exp $B$J$I$N(B
$B?t3X4X?t$N7k2L$OIbF0>.?tE@?t$r;}$DJ#AG?t$K$J$k$N$G!$@8@.$5$l$kJ#AG?t$NB?$/$,(B
$BIbF0>.?tE@?t$r;}$D$3$H$,M=A[$G$-$^$9!%(B

$B$[$H$s$I$N(B Complex 
$B$N@.J,$,IbF0>.?tE@?t$J$s$@$7!$IbF0>.?tE@?t$+$iB>$N7?$K$O(B
$BJQ49$5$l$J$$$s$@$+$i!$(BComplexFloat 
$B$H$7$FFC<l2=$7$F$bNI$$$@$m$&$H$b9M$($F$$$^$9!%(B

# sin($B&P(B / 6) = 1/2 $B$G$9$,!$(BMath.sin(Math::PI / 6) 
$B$N7k2L$H$7$F(B Rational(1, 2) $B$r(B
# $BJV$7$F$O$J$i$J$$$H$$$&;v$KCm0U$7$F$/$@$5$$!%(BMath::PI $B$O(B 
$B&P(B $B$G$O$J$/!$(B
# $B&P(B $B$N6a;wCM$G$9!%(B

>  $B8=:_$N(BYARV$B$N:GE,2=<BAu$r9M$($k$H!"AH$_9~$_%/%i%9(B($B$?$H$($P(B
>  Float)$B$,JQ99$5$l$F$$$J$$;~$K$O9bB.$J%W%j%_%F%#%V$,F0$/$H$$$&(B
>  $BF0:n$r(BComplex($B$d(BRational)$B$KE,MQ$7$F$O$$$1$J$$(B(or $B$G$-$J$$(B)$BM}(B
>  $BM3$OL5$$$H;W$&$N$G$9$,!#(B

$B8=:_$N(B Complex $B$O<BIt$,(B Float $B$G5uIt$,(B Rational 
$B$N$h$&$J>uBV$K$J$l$^$9!%(B
$B$G$9$+$i!$(BComplex 
$B$KBP$7$F$=$N$h$&$J:GE,2=$r9T$&$H$9$k$H!$@.J,$N7?8!::$r(B
$B<BIt!&5uIt$KJ,$1$FKh2s9T$&I,MW$,$"$j$^$9!%(BComplexFloat 
$B$rF3F~$9$k$H!$(B
$B%G!<%?%U%m!<2r@O$G3N<B$K(B ComplexFloat 
$B$K$J$k$3$H$,J,$+$C$F$$$kItJ,$O(B
$B7?8!::$J$7$G:GE,2=$G$-$^$9!%(B

# ComplexFloat $B$,Mm$`7W;;$G$O(B ComplexFloat 
$B$7$+=P$F$3$J$$;v$KCm0U$7$F$/$@$5$$!%(B
# $B$?$@$7!$1i;;$NAj<j$,(B Complex(BigDeciam, BigDeciam) 
$B$G$"$k>l9g$K$D$$$F$O!$(B
# $B$I$&$9$k$Y$-$+$^$@J,$+$j$^$;$s!%(BBigDecimal $B$H(B Float 
$B$O2>?tIt$N4p?t$NDl$,(B
# $B0[$J$C$F$*$j!$0EL[$KJQ49$9$Y$-$G$O$J$$$+$i$G$9!%(B

In article 
<761216ce0804120723n16bfbad7qdae90f142978d256@mail.gmail.com>,
  "Kenta Murata" <muraken@gmail.com> writes:

> $B8=:_$N(B Complex $B$O<BIt$,(B Float $B$G5uIt$,(B Rational $B$N$h$&$J>uBV$K$J$l$^$9!%(B
> $B$G$9$+$i!$(BComplex $B$KBP$7$F$=$N$h$&$J:GE,2=$r9T$&$H$9$k$H!$@.J,$N7?8!::$r(B
> $B<BIt!&5uIt$KJ,$1$FKh2s9T$&I,MW$,$"$j$^$9!%(BComplexFloat $B$rF3F~$9$k$H!$(B
> $B%G!<%?%U%m!<2r@O$G3N<B$K(B ComplexFloat $B$K$J$k$3$H$,J,$+$C$F$$$kItJ,$O(B
> $B7?8!::$J$7$G:GE,2=$G$-$^$9!%(B

Ruby $B%W%m%0%i%`$KBP$9$k%G!<%?%U%m!<2r@O$C$F$I$&$d$k$s$G$9$+(B?

$B$^$D$b$H(B $B$f$-$R$m$G$9(B

In message "Re: [ruby-dev:34362] Re: ComplexFloat"
    on Sat, 12 Apr 2008 23:23:20 +0900, "Kenta Murata" 
<muraken@gmail.com> writes:

|>  $BC1=c$5$dB>$N%/%i%99=@.$H$N@09g@-$r5>@7$K$7$F$^$GJD$8$?J#AG?t(B
|>  $B%/%i%9$rJL$KMQ0U$9$Y$-M}M3$O:GE,2=$@$1$G$9$+!)(B
|
|$B:GBg$NM}M3$O:GE,2=$G$9!%0J2<$N$h$&$JM}M3$b$"$j$^$9!%(B
|
|$B@.J,$,IbF0>.?tE@$K$J$C$F$7$^$&$H!$$=$NCM$OB>$NI=8=$K0EL[$KJQ49$G$-$^$;$s!%(B
|$B8@$$49$($k$H!$IbF0>.?tE@?t$r;}$DJ#AG?t$O!$(BRational $B$d(B Integer $B$r;}$DJ#AG?t$r(B
|$BA4It?)$Y$F$7$^$&$s$G$9!%$=$l$@$1$G$J$/!$$?$H$($P(B CMath.sin$B!$(BCMath.exp $B$J$I$N(B
|$B?t3X4X?t$N7k2L$OIbF0>.?tE@?t$r;}$DJ#AG?t$K$J$k$N$G!$@8@.$5$l$kJ#AG?t$NB?$/$,(B
|$BIbF0>.?tE@?t$r;}$D$3$H$,M=A[$G$-$^$9!%(B
|
|$B$[$H$s$I$N(B Complex $B$N@.J,$,IbF0>.?tE@?t$J$s$@$7!$IbF0>.?tE@?t$+$iB>$N7?$K$O(B
|$BJQ49$5$l$J$$$s$@$+$i!$(BComplexFloat $B$H$7$FFC<l2=$7$F$bNI$$$@$m$&$H$b9M$($F$$$^$9!%(B

$B$3$NJU$,H/A[$N0c$$$G!";d$N9M$($G$O!":GE,2=$H$$$&$N$O$"$/$^$G$b(B
$B<BAu$NET9g$G!"30$K8+$($k$N$O$+$C$30-$$$H;W$C$F$^$9!#$@$+$i!"(B
$B@5D>(BFixnum$B$H(BBignum$B$N6hJL$b$+$C$30-$$!#$3$l$O(BFixnum$B$,B(CM$G$"$C(B
$B$?4X78$G2sHr$G$-$^$;$s$G$7$?!#(B

|$B8=:_$N(B Complex $B$O<BIt$,(B Float $B$G5uIt$,(B Rational $B$N$h$&$J>uBV$K$J$l$^$9!%(B
|$B$G$9$+$i!$(BComplex $B$KBP$7$F$=$N$h$&$J:GE,2=$r9T$&$H$9$k$H!$@.J,$N7?8!::$r(B
|$B<BIt!&5uIt$KJ,$1$FKh2s9T$&I,MW$,$"$j$^$9!%(BComplexFloat $B$rF3F~$9$k$H!$(B
|$B%G!<%?%U%m!<2r@O$G3N<B$K(B ComplexFloat $B$K$J$k$3$H$,J,$+$C$F$$$kItJ,$O(B
|$B7?8!::$J$7$G:GE,2=$G$-$^$9!%(B

$BN>@.J,$,(BFloat$B$G$"$k(BComplex$B$r:n$k;~E@$G%U%i%0$rN)$F$l$P$h$$$3(B
$B$H$G$O$J$$$s$G$7$g$&$+!#$[$H$s$I$N>l9g$K$O(BFloat$B$J(BComplex$B$O@8(B
$B@.;~$KJ,$+$C$F$$$k$s$G$O$J$$$+$H;W$&$N$G!#%U%i%0$,N)$C$F$$$l(B
$B$P9bB.$K7W;;$G$-$k$N$G$"$l$P!"B<ED$5$s$N4uK>$9$kDxEY$N:GE,2=(B
$B$O(B($B$o$:$+$J%S%C%H1i;;$NA}2CDxEY$G(B)$B<B8=$G$-$=$&$J5$$,$7$^$9!#(B

                                $B$^$D$b$H(B $B$f$-$R$m(B /:|)

$B$`$i$?$G$9!%(B

2008/4/12 Yukihiro Matsumoto <matz@ruby-lang.org>:
>  |$B$[$H$s$I$N(B Complex $B$N@.J,$,IbF0>.?tE@?t$J$s$@$7!$IbF0>.?tE@?t$+$iB>$N7?$K$O(B
>  |$BJQ49$5$l$J$$$s$@$+$i!$(BComplexFloat $B$H$7$FFC<l2=$7$F$bNI$$$@$m$&$H$b9M$($F$$$^$9!%(B
>
>  $B$3$NJU$,H/A[$N0c$$$G!";d$N9M$($G$O!":GE,2=$H$$$&$N$O$"$/$^$G$b(B
>  $B<BAu$NET9g$G!"30$K8+$($k$N$O$+$C$30-$$$H;W$C$F$^$9!#$@$+$i!"(B
>  $B@5D>(BFixnum$B$H(BBignum$B$N6hJL$b$+$C$30-$$!#$3$l$O(BFixnum$B$,B(CM$G$"$C(B
>  $B$?4X78$G2sHr$G$-$^$;$s$G$7$?!#(B

$B$H$$$&$3$H$O$^$D$b$H$5$s$NM}A[$O!$(B Fixnum $B$b(B Bignum 
$B$bL5$/$F!$(B
Integer $B$@$1$,B8:_$9$k>uBV$J$s$G$9$M!%3N$+$K$=$NJ}$,e:No$@$H(B
$B;d$b;W$$$^$9!%(B

>  $BN>@.J,$,(BFloat$B$G$"$k(BComplex$B$r:n$k;~E@$G%U%i%0$rN)$F$l$P$h$$$3(B