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<TITLE>BigDecimal:An extension library for Ruby</TITLE>
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<H1>BigDecimal(ϒ_ZpgCu)</H1>
<DIV align="right"><A HREF="./bigdecimal_en.html">English</A></DIV><BR>
BigDecimal ̓IuWFNgw̋͂ȃXNvgł Ruby ɉϒ_
vZ@\ǉ邽߂̊gCułB
Ruby ɂĂ̏ڂe͈ȉURLQƂĂB
<UL>
<LI><A HREF="http://www.ruby-lang.org/ja/">http://www.ruby-lang.org/ja/</A>FRubyy[W</LI>
<LI><A HREF="http://kahori.com/ruby/ring/">http://kahori.com/ruby/ring/</A>FRubyɊւy[WH܂</LI>
</UL>
<hr>
<H2>ڎ</H2>
<UL>
<LI><A HREF="#INTRO">͂߂</LI>
<LI><A HREF="#SPEC">gp@ƃ\bḧꗗ</A></LI>
<LI><A HREF="#UNDEF">A񐔁A[̈</A></LI>
<LI><A HREF="#STRUCT">\</A></LI>
<LI><A HREF="#BASE">2i10i</A></LI>
<LI><A HREF="#PREC">vZxɂ</A></LI>
</UL>

<HR>
<A NAME="#INTRO">
<H2>͂߂</H2>
Ruby ɂ Bignum ƂNXAS̐łvZ邱Ƃł܂B
ACӌ̕_ZpNX悤łBŁA
Cӌ̕_ZpgCu BigDecimal 쐬܂B
s⏕EĂꍇǂǂA
<A HREF="mailto:shigeo@tinyforest.gr.jp">shigeo@tinyforest.gr.jp</A>
܂łm点Bs𒼂C͑傢ɂ܂BAԂȂǂ̊֌WŖ
͂ł܂B܂AʂɂĂۏ؂ł̂ł͂܂B
\߁AB
<BR><BR>
̃vÓARɔzzEςč\܂BA쌠͕Ă܂B
zzEϓ̌ Ruby ̂ɏ܂Bڂ README ǂłB

<hr>
<H2>CXg[ɂ</H2>
BigDecimal ܂ Ruby ̍ŐVł<A HREF="http://www.ruby-lang.org/ja/">Rubyy[W</A>_E[hł܂B
_E[hŐVł𓀂Aʏ̃CXg[菇sĉB
Ruby CXg[΁A BigDecimal pł悤ɂȂ͂łB
\[Xt@C
bigdecimal.c,bigdecimal.h
̂Q݂̂łB<BR>

<hr>
<A NAME="#SPEC">
<H2>gp@ƃ\bḧꗗ</H2>
uRuby͊ɏvƂOŁA
<CODE><PRE>
require 'bigdecimal'
a=BigDecimal::new("0.123456789123456789")
b=BigDecimal("123456.78912345678",40)
c=a+b
</PRE></CODE>
<br>
Ƃ悤ȊŎgp܂B

<H3>\bhꗗ</H3>
ȉ̃\bhp\łB
uLvƂ BigDecimal xۏ؂錅łB
҂ł͂܂A኱̗]TČvZ܂B
܂AႦ΂RQrbg̃VXeł͂POiłSɌvZ܂B]āAł́A
́uLv͂S̔{ƂȂĂ܂B
<P>
ȉ̃\bhȊOɂA(C ł͂Ȃ) Ruby \[X̌`
񋟂Ă̂܂BႦ΁A
<CODE><PRE>
require "bigdecimal/math.rb"
</PRE></CODE>
Ƃ邱ƂŁAsin  cos Ƃ֐gpł悤ɂȂ܂B
gp@ȂǁAڍׂ math.rb ̓eQƂĉB

̑AFloat Ƃ̑ݕϊȂǂ̃\bh util.rb ŃT|[gĂ܂B
pɂ
<CODE><PRE>
require "bigdecimal/util.rb"
</PRE></CODE>
̂悤ɂ܂Bڍׂ util.rb ̓eQƂĉB

<H4><U>NX\bh</U></H4>
<UL>
<LI><B>new</B></LI><BLOCKQUOTE>
V BigDecimal IuWFNg𐶐܂B<BR>
a=BigDecimal::new(s[,n]) ܂<BR>
a=BigDecimal(s[,n])<BR>
s ͐\鏉l𕶎Ŏw肵܂B
Xy[X͖܂B܂AfłȂo_
͏ÎƂ݂Ȃ܂B
n ͕KvȗLia ̍őLj𐮐Ŏw肵܂B
n  0 ܂͏ȗꂽƂ́An ̒l s ̗LƂ݂Ȃ܂B
s ̗L n Ƃ n=0 ̂ƂƓłB
a ̍őL n ኱傢l̗p܂B
őL͈ȉ̂悤ȊZsƂɈӖ܂B
<CODE><PRE>
BigDecimal("1")    / BigDecimal("3")    # => 0.3333333333 33E0
BigDecimal("1",10) / BigDecimal("3",10) # => 0.3333333333 3333333333 33333333E0
</PRE></CODE>
AX̉ZɂőL n ̎舵͏̃o[W
኱ύX\܂B
</BLOCKQUOTE>

<LI><B>mode</B></LI><BLOCKQUOTE>
f = BigDecimal.mode(s[,v])<BR>
BigDecimal̎sʂ𐧌䂵܂BQȗA܂ nil w肷
̐ݒl߂܂B<BR>
ȉ̎gp@`Ă܂B
<P>
<B>[O]</B><P>
vZʂ(NaN)[ɂ鏜ZɂȂƂ̏`邱Ƃł܂B
<BLOCKQUOTE>
f = BigDecimal::mode(BigDecimal::EXCEPTION_NaN,flag)<BR>
f = BigDecimal::mode(BigDecimal::EXCEPTION_INFINITY,flag)<BR>
f = BigDecimal::mode(BigDecimal::EXCEPTION_UNDERFLOW,flag)<BR>
f = BigDecimal::mode(BigDecimal::EXCEPTION_OVERFLOW,flag)<BR>
f = BigDecimal::mode(BigDecimal::EXCEPTION_ZERODIVIDE,flag)<BR>
f = BigDecimal::mode(BigDecimal::EXCEPTION_ALL,flag)<BR>
</BLOCKQUOTE>

EXCEPTION_NaN ͌ʂ NaN ɂȂƂ̎włB<BR>
EXCEPTION_INFINITY ͌ʂ(}Infinity)ɂȂƂ̎włB<BR>
EXCEPTION_UNDERFLOW ͎wA_[t[Ƃ̎włB<BR>
EXCEPTION_OVERFLOW ͎wI[o[t[Ƃ̎włB<BR>
EXCEPTION_ZERODIVIDE ̓[ɂ銄ZsƂ̎włB<BR>
EXCEPTION_ALL ́A\ȑSĂɑ΂ĈꊇĐݒ肷ƂɎgp܂B<BR><BR>

flag  true ̂Ƃ́Aw肵ԂɂȂƂɗO𔭍s悤ɂȂ܂B<BR>
flag  falseiftHgjȂAO͔s܂BvZʂ͈ȉ̂悤ɂȂ܂B<BR>
<BLOCKQUOTE>
EXCEPTION_NaN ̂ƂA(NaN)<BR>
EXCEPTION_INFINITY ̂ƂA(+ or -Infinity)<BR>
EXCEPTION_UNDERFLOW ̂ƂA[<BR>
EXCEPTION_OVERFLOW ̂ƂA+Infinity  -Infinity<BR>
EXCEPTION_ZERODIVIDE ̂ƂA+Infinity  -Infinity<BR>
</BLOCKQUOTE>
EXCEPTION_INFINITYAEXCEPTION_OVERFLOWAEXCEPTION_ZERODIVIDE
͍̂Ƃ듯łB<BR>
߂ĺAݒ̒lłBulv̈Ӗ́AႦ
BigDecimal::EXCEPTION_NaNƁulv &  [ȊOȂ
EXCEPTION_NaNݒ肳ĂƂӖłB

<P>
<B>[ۂߏw]</B><P>
vZr̊ۂߑ̎w肪ł܂B
<BLOCKQUOTE>
f = BigDecimal::mode(BigDecimal::ROUND_MODE,flag)
</BLOCKQUOTE>
̌`Ŏw肵܂B<BR>
ŁAflag ͈ȉ(ʓ͑ΉCX^X\bh)̈w肵܂B
<TABLE>
<TR><TD>ROUND_UP</TD><TD>SĐ؂グ܂B</TD></TR>
<TR><TD>ROUND_DOWN</TD><TD>SĐ؂̂Ă܂(truncate)B</TD></TR>
<TR><TD>ROUND_HALF_UP</TD><TD>ľܓ܂(ftHg)B</TD></TR>
<TR><TD>ROUND_HALF_DOWN</TD><TD>܎̘Z܂B</TD></TR>
<TR><TD>ROUND_HALF_EVEN</TD><TD>l̘Z܂BT̎͏ʂP̎̂݌Jグ܂(Banker's rounding)B</TD></TR>
<TR><TD>ROUND_CEILING</TD><TD>l̑傫ɌJグ܂(ceil)B</TD></TR>
<TR><TD>ROUND_FLOOR</TD><TD>l̏ɌJ艺܂(floor)B</TD></TR>

</TABLE>
߂l͎w flag ̒lłB
Q nil w肷ƁA̐ݒlԂ܂B
mode \bhł͊ۂߑ̈ʒu[Uw肷邱Ƃ͂ł܂B
ۂߑƈʒuŐ䂵ꍇ BigDecimal::limit  truncate/round/ceil/floorA
add/sub/mult/div ƂCX^X\bhgpĉB
</BLOCKQUOTE>
<LI><B>limit([n])</B></LI><BLOCKQUOTE>
BigDecimalIuWFNg̍ő包nɐ܂B
߂l͐ݒ肷O̒lłBݒl̃ftHgl͂OŁAƂӖłB
n w肵ȂA܂ n  nil ̏ꍇ́A̍ő包Ԃ܂B<BR>
vZ𑱍sԂɁǍɑĂ܂悤ȏꍇ
 limit ŗ\ߌ𐧌ł܂B̏ꍇ BigDecimal.mode Ŏw肳ꂽ
ۂߏs܂B
ACX^X\bh (truncate/round/ceil/floor/add/sub/mult/div) 
 limit D悳܂B<BR>
mf = BigDecimal::limit(n)<BR>
</BLOCKQUOTE>

<LI><B>double_fig</B></LI><BLOCKQUOTE>
Ruby  Float NXێłL̐Ԃ܂B
<CODE><PRE>
  p BigDecimal::double_fig  # ==> 20 (depends on the CPU etc.)
</PRE></CODE>
double_fig͈ȉ C vǑʂƓłB
<CODE><PRE>
 double v          = 1.0;
 int    double_fig = 0;
 while(v + 1.0 > 1.0) {
    ++double_fig;
    v /= 10;
 }
</PRE></CODE>
</BLOCKQUOTE>

<LI><B>BASE</B></LI><BLOCKQUOTE>
Ŏgp̒lłB 32 rbg̏nł10000łB<BR>
b = BigDecimal::BASE<BR>
</BLOCKQUOTE>
</UL>

<H4><U>CX^X\bh</U></H4>
<UL>
<LI><B>+</B></LI><BLOCKQUOTE>
Zic = a + bj<BR>
c ̐xɂẮu<A HREF="#PREC">vZxɂ</A>vQƂĂB
</BLOCKQUOTE>

<LI><B>-</B></LI><BLOCKQUOTE>
Zic = a - bjA܂͕]ic = -aj<BR>
c ̐xɂẮu<A HREF="#PREC">vZxɂ</A>vQƂĂB

</BLOCKQUOTE>
<LI><B>*</B></LI><BLOCKQUOTE>
Z(c = a * b)<BR>
c̐x(a̐x)+(b̐x)xłB<br>
ڂ́u<A HREF="#PREC">vZxɂ</A>vQƂĂB

</BLOCKQUOTE>
<LI><B>/</B></LI><BLOCKQUOTE>
Z(c = a / b)<BR>
c ̐xɂẮu<A HREF="#PREC">vZxɂ</A>vQƂĂB

</BLOCKQUOTE>

<LI><B>add(b,n)</B></LI><BLOCKQUOTE>
ȉ̂悤Ɏgp܂B<BR>
c = a.add(b,n)<BR>
c = a + b ő n ܂ŌvZ܂B<BR>
a + b ̐x n 傫Ƃ BigDecimal.mode Ŏw肳ꂽ@Ŋۂ߂܂B<BR>
n [Ȃ + ƓłB
</BLOCKQUOTE>
<LI><B>sub(b,n)</B></LI><BLOCKQUOTE>
ȉ̂悤Ɏgp܂B<BR>
c = a.sub(b,n)<BR>
c = a - b ő n ܂ŌvZ܂B<BR>
a - b ̐x n 傫Ƃ BigDecimal.mode Ŏw肳ꂽ@Ŋۂ߂܂B<BR>
n [Ȃ - ƓłB

</BLOCKQUOTE>
<LI><B>mult(b,n)</B></LI><BLOCKQUOTE>
ȉ̂悤Ɏgp܂B<BR>
c = a.mult(b,n)<BR>
c = a * b ő n ܂ŌvZ܂B<BR>
a * b ̐x n 傫Ƃ BigDecimal.mode Ŏw肳ꂽ@Ŋۂ߂܂B<BR>
n [Ȃ * ƓłB

</BLOCKQUOTE>
<LI><B>div(b[,n])</B></LI><BLOCKQUOTE>
ȉ̂悤Ɏgp܂B<BR>
c = a.div(b,n)<BR>
c = a / b ő n ܂ŌvZ܂B
a / b ̐x n 傫Ƃ BigDecimal.mode Ŏw肳ꂽ@Ŋۂ߂܂B<BR>
n [Ȃ / ƓłB<BR>
n ȗꂽƂ Float#div ƓlɌʂ(BigDecimal)ɂȂ܂B
</BLOCKQUOTE>

<LI><B>fix</B></LI><BLOCKQUOTE>
a ̏_ȉ̐؂̂āB<BR>
c = a.fix
</BLOCKQUOTE>
<LI><B>frac</B></LI><BLOCKQUOTE>
a ̐̐؂̂āB<BR>
c = a.frac
</BLOCKQUOTE>

<LI><B>floor[(n)]</B></LI><BLOCKQUOTE>
c = a.floor<BR>
a ȉ̍ő吮iBigDecimal ljԂ܂B
<CODE><PRE>
c = BigDecimal("1.23456").floor  #  ==> 1
c = BigDecimal("-1.23456").floor #  ==> -2
</PRE></CODE>
ȉ̂悤Ɉ n ^邱Ƃł܂B<BR>
n>=0 ȂA_ȉ n+1 ʂ̐𑀍삵܂(_ȉAő n ɂ܂)B<BR>
n ̂Ƃ͏_ȏ n ڂ𑀍삵܂(_ʒu獶ɏȂƂ n  0 т܂)B<BR>
<CODE><PRE>
 c = BigDecimal("1.23456").floor(4)   #  ==> 1.2345
 c = BigDecimal("15.23456").floor(-1) #  ==> 10.0
</PRE></CODE>

</BLOCKQUOTE>
<LI><B>ceil[(n)]</B></LI><BLOCKQUOTE>
c = a.ceil<BR>
a ȏ̐̂AłvZA̒liBigDecimal ljԂ܂B
<CODE><PRE>
c = BigDecimal("1.23456").ceil  #  ==> 2
c = BigDecimal("-1.23456").ceil #  ==> -1
</PRE></CODE>

ȉ̂悤Ɉ^āA_ȉ n+1 ʂ̐𑀍삷邱Ƃł܂B<BR>
n>=0 ȂA_ȉ n+1 ʂ̐𑀍삵܂(_ȉAő n ɂ܂)B<BR>
 n ̂Ƃ͏_ȏ n ڂ𑀍삵܂(_ʒu獶ɏȂƂ n  0 т܂)B<BR>
<CODE><PRE>
 c = BigDecimal("1.23456").ceil(4)   # ==> 1.2346
 c = BigDecimal("15.23456").ceil(-1) # ==> 20.0
</PRE></CODE>

</BLOCKQUOTE>
<LI><B>round[(n[,b])]</B></LI><BLOCKQUOTE>
c = a.round<BR>

NX\bh BigDecimal::mode(BigDecimal::ROUND_MODE,flag) Ŏw肵
ROUND_MODE ɏ]Ċۂߑs܂B
BigDecimal::mode(BigDecimal::ROUND_MODE,flag) ŉw肹AA
w肵Ȃꍇ́u_ȉʂ̐ľܓĐiBigDecimal ljvɂ܂B<BR>
<CODE><PRE>
 c = BigDecimal("1.23456").round  #  ==> 1
 c = BigDecimal("-1.23456").round #  ==> -1
</PRE></CODE>

ȉ̂悤Ɉ^āA_ȉ n+1 ʂ̐𑀍삷邱Ƃł܂B<BR>
n ̎́A_ȉ n+1 ʂ̐ۂ߂܂(_ȉAő n ɂ܂)B<BR>
n ̂Ƃ͏_ȏ n ڂۂ߂܂(_ʒu獶ɏȂƂ n  0 т܂)B
<CODE><PRE>
c = BigDecimal("1.23456").round(4)   #  ==> 1.2346
c = BigDecimal("15.23456").round(-1) #  ==> 20.0
</PRE></CODE>
QԖڂ̈w肷ƁABigDecimal#mode ̎w𖳎āAw肳ꂽ@
ۂߑs܂B
<CODE><PRE>
c = BigDecimal("1.23456").round(3,BigDecimal::ROUND_HALF_EVEN)   #  ==> 1.234
c = BigDecimal("1.23356").round(3,BigDecimal::ROUND_HALF_EVEN)   #  ==> 1.234
</PRE></CODE>

</BLOCKQUOTE>
<LI><B>truncate</B></LI><BLOCKQUOTE>
c = a.truncate<BR>
_ȉ̐؂̂ĂĐiBigDecimal ljɂ܂B<BR>
ȉ̂悤Ɉ^āA_ȉ n+1 ʂ̐𑀍삷邱Ƃł܂B<BR>
n ̎́A_ȉ n+1 ʂ̐؂̂Ă܂(_ȉAő n ɂ܂)B
n ̂Ƃ͏_ȏ n ڂ𑀍삵܂(_ʒu獶ɏȂƂ n  0 т܂)B<BR>
<CODE><PRE>
c = BigDecimal("1.23456").truncate(4)   #  ==> 1.2345
c = BigDecimal("15.23456").truncate(-1) #  ==> 10.0
</PRE></CODE>
</BLOCKQUOTE>

</BLOCKQUOTE>
<LI><B>abs</B></LI><BLOCKQUOTE>
̐Βl<BR>
c = a.abs<BR>

</BLOCKQUOTE>
<LI><B>to_i</B></LI><BLOCKQUOTE>
_ȉ؂̂ĂĐɕϊ܂B<BR>
i = a.to_i<BR>
i ͒lɉ Fixnum  Bignum ɂȂ܂B
a  Infinity  NaN ̂ƂAi  nil ɂȂ܂B
</BLOCKQUOTE>
<LI><B>to_f</B></LI><BLOCKQUOTE>
Float IuWFNgɕϊ܂B
肫ߍׂlKvȂ split \bh𗘗p
B
</BLOCKQUOTE>
<LI><B>to_s[(n)]</B></LI><BLOCKQUOTE>
ɕϊ܂(ftHg "0.xxxxxEn" ̌`ɂȂ܂jB
<CODE><PRE>
BigDecimal("1.23456").to_s  #  ==> "0.123456E1"
</PRE></CODE>
 n ɐ̐w肳ꂽƂ́A_ŕ鍶EAꂼ n 
ɋ󔒂ŋ؂܂B
<CODE><PRE>
BigDecimal("0.1234567890123456789").to_s(10)   #  ==> "0.1234567890 123456789E0"
</PRE></CODE>
 n ɐ̐\w肷邱Ƃł܂B
<CODE><PRE>
BigDecimal("0.1234567890123456789").to_s("10") #  ==> "0.1234567890 123456789E0"
</PRE></CODE>
̍ŏ '+'i܂ ' 'jtƁAl̏ꍇA擪 '+'i܂ ' 'jt܂
ȉꍇ́A '-' t܂BjB
<CODE><PRE>
BigDecimal("0.1234567890123456789").to_s(" 10") #  ==> " 0.1234567890 123456789E0"
BigDecimal("0.1234567890123456789").to_s("+10") #  ==> "+0.1234567890 123456789E0"
BigDecimal("-0.1234567890123456789").to_s("10") #  ==> "-0.1234567890 123456789E0"
</PRE></CODE>

ɕ̍Ō E(܂ e)  F(܂ f) w肷邱ƂŁAȉ̂悤
\`ύX邱Ƃł܂B
<CODE><PRE>
BigDecimal("1234567890.123456789").to_s("E")  #  ==> "0.1234567890123456789E10"
BigDecimal("1234567890.123456789").to_s("F")  #  ==> "1234567890.123456789"
BigDecimal("1234567890.123456789").to_s("5E") #  ==> "0.12345 67890 12345 6789E10"
BigDecimal("1234567890.123456789").to_s("5F") #  ==> "12345 67890.12345 6789"
</PRE></CODE>

</BLOCKQUOTE>
<LI><B>exponent</B></LI><BLOCKQUOTE>
w𐮐lŕԂ܂B
n = a.exponent <BR>
 a ̒l 0.xxxxxxx*10**n Ӗ܂B
</BLOCKQUOTE>

<LI><B>precs</B></LI><BLOCKQUOTE>
n,m  = a.precs<BR>
a ̗L (n) ƍőL (m) ̔zԂ܂B

</BLOCKQUOTE>

<LI><B>sign</B></LI><BLOCKQUOTE>
l(sign &gt; 0)A(sign &lt; 0)Ȃ(sigh==0)ł邩̏Ԃ܂B
n = a.sign <BR>
ƂƂ n ̒l a ȉ̂ƂӖ܂B<BR>
() ̒̐́Aۂ̒lł(<A HREF="#STRUCT">u\v</A>Q)B<BR>
n = BigDecimal::SIGN_NaN(0) : a  NaN<BR>
n = BigDecimal::SIGN_POSITIVE_ZERO(1) : a  +0<BR>
n = BigDecimal::SIGN_NEGATIVE_ZERO(-1) : a  -0<BR>
n = BigDecimal::SIGN_POSITIVE_FINITE(2) : a ͐̒l<BR>
n = BigDecimal::SIGN_NEGATIVE_FINITE(-2) : a ͕̒l<BR>
n = BigDecimal::SIGN_POSITIVE_INFINITE(3) : a +Infinity<BR>
n = BigDecimal::SIGN_NEGATIVE_INFINITE(-3) : a -Infinity<BR>

</BLOCKQUOTE>
<LI><B>nan?</B></LI><BLOCKQUOTE>
a.nan?  a NaN̂Ƃ^Ԃ܂B
</BLOCKQUOTE>
<LI><B>infinite?</B></LI><BLOCKQUOTE>
a.infinite?  a +̂Ƃ 1 A-̂Ƃ -1AȊÔƂ nil Ԃ܂B
</BLOCKQUOTE>
<LI><B>finite?</B></LI><BLOCKQUOTE>
a.finite?  a ܂ NaN łȂƂ^Ԃ܂B
</BLOCKQUOTE>

<LI><B>zero?</B></LI><BLOCKQUOTE>
a  0 Ȃ true ɂȂ܂B<BR>
c = a.zero?
</BLOCKQUOTE>
<LI><B>nonzero?</B></LI><BLOCKQUOTE>
a  0 Ȃ nilA0 ȊOȂ a ̂̂Ԃ܂B<BR>
c = a.nonzero?

</BLOCKQUOTE>
<LI><B>split</B></LI><BLOCKQUOTE>
BigDecimal l 0.xxxxxxx*10**n ƕ\ƂɁAiNaN̂Ƃ
0AȊO+1-1ɂȂ܂jA
̕i"xxxxxxx"jƁAi10jAXɎw n z
Ԃ܂B<BR>
a=BigDecimal::new("3.14159265")<BR>
f,x,y,z = a.split<BR>
ƂƁAf=+1Ax="314159265"Ay=10Az=1ɂȂ܂B<BR>
]āA<BR>
s = "0."+x<BR>
b = f*(s.to_f)*(y**z)<BR>
 Float ɕϊ邱Ƃł܂B
</BLOCKQUOTE>
<LI><B>inspect</B></LI><BLOCKQUOTE>
fobOo͂Ɏgp܂B<BR>
p a=BigDecimal::new("3.14",10)<BR>
ƂƁA[0x112344:'0.314E1',4(12)]̂悤ɏo͂܂B
ŏ16i̓IuWFNg̃AhXA '0.314E1' ͒lA
4݂̗͌L(\኱傫Ƃ܂)A
Ō̓IuWFNg蓾ő包ɂȂ܂B
</BLOCKQUOTE>
<LI><B>**</B></LI><BLOCKQUOTE>
a  n vZ܂B͐B<BR>
c = a ** n<BR>
ʂƂ c ̗L a  n {ȏɂȂ̂ŒӁB
</BLOCKQUOTE>
<LI><B>power</B></LI><BLOCKQUOTE>
** ƓŁAa  n vZ܂B͐B<BR>
c = a.power(n)<BR>
ʂƂ c ̗L a  n {ȏɂȂ̂ŒӁB
</BLOCKQUOTE>
<LI><B>sqrt</B></LI><BLOCKQUOTE>
a̗L n ̕in ̕ł͂܂j
j[g@ŌvZ܂B<BR>
c = a.sqrt(n)<BR>
</BLOCKQUOTE>

<LI><B>divmod,quo,modulo,%,remainder</B></LI><BLOCKQUOTE>
ڍׂ͑Ή Float ̊e\bhQƂĉB
</BLOCKQUOTE>

<LI><B>&lt=&gt</B></LI><BLOCKQUOTE>
a==b Ȃ 0Aa &gt b Ȃ 1Aa &lt b Ȃ -1 ɂȂ܂B<BR>
c = a &lt=&gt b
</BLOCKQUOTE>
</UL>
́AǂŎ̔@łB<BR>
<UL>
<LI><B>==</B></LI>
<LI><B>===</B></LI>
u==vƓł case Ŏgp܂B
<LI><B>!=</B></LI>
<LI><B>&lt</B></LI>
<LI><B>&lt=</B></LI>
<LI><B>&gt</B></LI>
<LI><B>&gt=</B></LI>
</UL>

<H3>coerceɂ</H3>
BigDecimal IuWFNgZpZq̍ɂƂ́ABigDecimal IuWFNg
EɂIuWFNg(KvȂ) BigDecimal ɕϊĂvZ܂B
]āABigDecimal IuWFNgȊOłlӖ̂ȂEɒu
Z͉\łB<BR>
ÁiʏjlɎϊ邱Ƃ͂ł܂B
𐔒lɎϊꍇ bigfloat.c 
u/* #define ENABLE_NUMERIC_STRING */ṽRgOĂA
ăRpCAăCXg[Kv܂B
Ől^ꍇ͒ӂKvłBlɕϊłȂƁA
Pɕϊ~߂邾ŃG[ɂ͂Ȃ܂B"10XX"ȂPOA"XXXX"͂O
ƈ܂B<BR>
<CODE><PRE>
   a = BigDecimal.E(20)
   c = a * "0.123456789123456789123456789" #  BigDecimal ɕϊĂvZ
</PRE></CODE>
񐔂\ƂāA"Infinity"A"+Infinity"A"-Infinity"A"NaN"
gpł܂(啶Eʂ܂)BAmode \bh false 
w肵ꍇ͗O܂B
<BR>
܂ABigDecimalNX coerceiRuby{QƁjT|[gĂ܂B
]āABigDecimal IuWFNgEɂꍇ͑vłB
A݂ Ruby C^v^̎dlA񂪍ɂƌvZł܂B<BR>
<CODE><PRE>
  a = BigDecimal.E(20)
  c = "0.123456789123456789123456789" * a # G[
</PRE></CODE>
KvƂ͎v܂񂪁AǂĂƌl
 String IuWFNgpVȃNX쐬ĂA
̃NX coerce T|[gĂB

<hr>
<A NAME="#UNDEF">
<H2>A񐔁A[̈</H2>
uvƂ͕\łȂ炢傫ȐłBʂɈ߂
 +Infinityi̖j -Infinityi̖jƂ
悤ɕ\L܂B
 1.0/0.0 ̂悤Ƀ[Ŋ悤ȌvZƂɐ܂B
<BR><BR>
u񐔁v 0.0/0.0  Infinity-Infinity ̌ʂ`łȂ
vZƂɐ܂B񐔂 NaNiNot a Numberjƕ\L܂B
NaN ܂ތvZ͑S NaN ɂȂ܂B܂ NaN ͎܂߂āAǂȐ
Ƃv܂B
<BR><BR>
[ +0.0  -0.0 ݂܂BA+0.0==-0.0  true łB
<BR><BR>
InfinityANaNA +0.0  -0.0 ܂񂾌vZʂ͑gݍ킹
蕡GłB̂ĺAȉ̃vOsČʂ
mFĂiʂɂāA^ԈႢ𔭌ꂽ
m点肢܂jB

<PRE>
<CODE>
require "bigdecimal"

aa  = %w(1 -1 +0.0 -0.0 +Infinity -Infinity NaN)
ba  = %w(1 -1 +0.0 -0.0 +Infinity -Infinity NaN)
opa = %w(+ - * / <=> > >=  < == != <=)

for a in aa
  for b in ba
    for op in opa
      x = BigDecimal::new(a)
      y = BigDecimal::new(b)
      eval("ans= x #{op} y;print a,' ',op,' ',b,' ==> ',ans.to_s,\"\n\"")
    end
  end
end
</CODE>
</PRE>

<hr>
<A NAME="#STRUCT">
<H2>\</H2>
BigDecimalŕ_͍\(Real)ŕ\܂B
̂ unsigned long ̔z(ȉ̍\̗vffrac)ŊǗ܂B
TOIɂ́Aȉ̂悤ɂȂ܂B<BR><BR>
 <_> = 0.xxxxxxxxx*BASE**n<BR><BR>
ŁAx͉\ABASE͊iPOiȂPOjAn͎w\
lłBBASE傫قǁA傫Ȑl\ł܂B܂Az̃TCY
Ȃł܂BBASE͑傫قǓs悢킯łAfobÔ₷Ȃǂ
lāA10000ɂȂĂ܂iBASEVpInit()֐ŎIɌvZ܂jB
́A32rbg̏ꍇłB64rbg̏ꍇ͂Ƒ傫ȒlɂȂ܂B
cOȂA64rbgł̃eXg͂܂Ă܂iAꂽ
ʂĂ΂肪łjB
BASE10000̂Ƃ́Aȉ̉̔z(frac)̊evfɂ͍őłS
i[܂B<BR><BR>
_\(Real)͈ȉ̂悤ɂȂĂ܂B
<BR>
<CODE><PRE>
  typedef struct {
     unsigned long MaxPrec; // ő吸x(frac[]̔zTCY)
     unsigned long Prec;    // x(frac[]̎gpTCY)
     short    sign;         // ȉ̂悤ɕ̏Ԃ`܂B
                            //  ==0 : NaN
                            //    1 : +0
                            //   -1 : -0
                            //    2 : ̒l
                            //   -2 : ̒l
                            //    3 : +Infinity
                            //   -3 : -Infinity
     unsigned short flag;   // e̐tbO
     int      exponent;     // w̒l(*BASE**exponent)
     unsigned long frac[1]; // ̔z()
  } Real;
</CODE></PRE>
Ⴆ 1234.56784321 Ƃ(BASE=10000Ȃ)<BR>
<PRE>
    0.1234 5678 4321*(10000)**1
</PRE>
ł frac[0]=1234Afrac[1]=5678Afrac[2]=4321A
Prec=3Asign=2Aexponent=1 ƂȂ܂BMaxPrec
Prec 傫΂ł܂܂Bflag 
gp@͎ɈˑēŎgp܂B

<hr>
<A NAME="#BASE">
<H2>2i10i</H2>
BigDecimal  <_> = 0.xxxxxxxxx*10**n Ƃ10i`Őlێ܂B
AvZ@̕_̓\́A܂łȂ <_> = 0.bbbbbbbb*2**n Ƃ
2i`ʂł(x  0  9 ܂ŁAb  0  1 ̐)B
BigDecimal Ȃ10i̓\`̗p̂ȉɐ܂B
<H4>10ĩbg</H4>
<DL>
<DT>fobÔ₷
<DD>܂AvO쐬yłBfrac[0]=1234Afrac[1]=5678Afrac[2]=4321A
exponent=1Asign=2 Ȃ琔l 1234.56784321 ł̂͌Βɕ܂B

<DT>10i\LꂽlȂmɓ\ɕϊł
<DD>Ⴆ΁Aȉ̂悤ȃvO͑S덷
vZ邱Ƃł܂Bȉ̗́AsɈ̐l
Ăt@C file ̍vl߂̂łB
<CODE><PRE>
   file = File::open(....,"r")
   s = BigDecimal::new("0")
   while line = file.gets
      s = s + line
   end
</PRE></CODE>
̗2iłƌ덷荞މ\܂B
Ⴆ 0.1 2iŕ\ 0.1 = b1*2**(-1)+b1*2**(-2)+b3*2**(-3)+b4*2**(-4)....
ƖɑĂ܂܂(b1=0,b2=0,b3=0,b4=1...)B bn(n=1,2,3,...) 
2i\ 0  1 ̐łB]āAǂőł؂Kv܂B
ŕϊ덷܂BAēx10i\LɂĈ悤
ꍇ͓K؂ȊۂߑiľܓjɂčĂ "0.1" ƕ\܂BA
ł͐m 0.1 ł͂܂B

<DT>L͗Lłi܂莩łj
<DD>0.1 \邽߂̗̈͂̔zvfi frac[0]=1 jōς݂܂B
zvf̐10il玩IɌł܂B́Aϒ_Zł
厖ȂƂłBt 0.1 2i\Ƃɂ2i̗Lɂ̂ 0.1 
ł͌ł܂B
</DL>

<H3>10ĩfbg</H3>
͍܂ł̃bǵÂ܂܃fbgɂȂ܂B
A10i2iɕϊ悤ȑ͕ϊ덷
𔺂ꍇ邱Ƃ͂ł܂B
T̃Rs[^10i̓\ĂȂ̂ŁA
BigDecimal 𗘗pČ덷̌vZꍇ́AvZx
𖳎ĂŌ܂ BigDecimal gpKv܂B

<H3>ŏ͉H</H3>
ŌvZƂɂ킴킴2igl͋ɂ߂Ă܂łB
vZ@Ƀf[^͂ƂقƂǂ̏ꍇA
10iœ͂܂B̌ʁAdouble ̌vZ@
\͍ŏ덷Ăꍇ܂B
BigDecimal ̓[U͂덷Ŏ荞ނƂł܂B
fobO₷̂ƁAf[^ǂ݂ݎɌ덷Ȃ
Ƃ̂ۂ̃bgłB

<hr>
<A NAME="#PREC">
<H2>vZxɂ</H2>
c = a op b ƂvZ(op  + - * /)Ƃ̓
ȉ̂悤ɂȂ܂B<BR><BR>
PDZ(a ̗L)+(b ̗L)A
Z(a ̍őL)+(b ̍őL)̍ő包iۂ́A]TāA
傫Ȃ܂jϐ c Vɐ܂B
Z̏ꍇ́A덷oȂ̐x c 𐶐܂BႦ
 c = 0.1+0.1*10**(-100) ̂悤ȏꍇAc ̐x͂POOȏ̐x
悤ɂȂ܂B
<BR><BR>
QD c = a op b ̌vZs܂B<BR><BR>
̂悤ɁAZƏZł c ͕Ku덷oȂv̐x
Đ܂(BigDecimal.limit w肵Ȃꍇ)B
Z(a ̍őL)+(b ̍őL)̍ő包
 c ܂Ac = 1.0/3.0 ̂悤ȌvZŖ炩Ȃ悤ɁA
 c ̍ő吸x𒴂ƂŌvZł؂ꍇ܂B<BR><BR>
ɂAc ̍ő吸x a  b 傫Ȃ܂̂ c KvƂ
[̈͑傫Ȃ邱ƂɒӂĉB
<BR><BR>
ӁFu+,-,*,/vł͌ʂ̐xiLjŎwł܂B
xRg[ꍇ́Aȉ̃CX^X\bhgp܂B<BR>
<UL>
<LI>add,sub,mult,div</LI><BLOCKQUOTE>
̃\bh͐擪(ō)̐̌wł܂B
<CODE><PRE>
 BigDecimal("2").div(3,12) # 2.0/3.0 => 0.6666666666 67E0
</PRE></CODE>
</BLOCKQUOTE>
<LI>truncate,round,ceil,floor</LI><BLOCKQUOTE>
̃\bh͏_̑Έʒuw肵Č肵܂B
<CODE><PRE>
 BigDecimal("6.66666666666666").round(12) # => 0.6666666666 667E1
</PRE></CODE>
</BLOCKQUOTE>
</UL>
<H3>ŐxRg[ꍇ</H3>
Őx(L)Rg[ꍇ addAsubAmultAdiv ̃\bh
gpł܂B
ȉ̉~vZvÔ悤ɁA
߂錅͎Ŏw肷邱Ƃł܂B
<BR><BR>
<CODE><PRE>
#!/usr/local/bin/ruby

require "bigdecimal"
#
# Calculates 3.1415.... (the number of times that a circle's diameter
# will fit around the circle) using J. Machin's formula.
#
def big_pi(sig) # sig: Number of significant figures
  exp    = -sig
  pi     = BigDecimal::new("0")
  two    = BigDecimal::new("2")
  m25    = BigDecimal::new("-0.04")
  m57121 = BigDecimal::new("-57121")

  u = BigDecimal::new("1")
  k = BigDecimal::new("1")
  w = BigDecimal::new("1")
  t = BigDecimal::new("-80")
  while (u.nonzero? && u.exponent >= exp)
    t   = t*m25
    u   = t.div(k,sig)
    pi  = pi + u
    k   = k+two
  end

  u = BigDecimal::new("1")
  k = BigDecimal::new("1")
  w = BigDecimal::new("1")
  t = BigDecimal::new("956")
  while (u.nonzero? && u.exponent >= exp )
    t   = t.div(m57121,sig)
    u   = t.div(k,sig)
    pi  = pi + u
    k   = k+two
  end
  pi
end

if $0 == __FILE__
  if ARGV.size == 1
    print "PI("+ARGV[0]+"):\n"
    p big_pi(ARGV[0].to_i)
  else
    print "TRY: ruby pi.rb 1000 \n"
  end
end

</PRE></CODE>
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