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U:RDoc::NormalClass[iI"BigDecimal:ET@I"Numeric;Fo:RDoc::Markup::Document:@parts[o;;[Lo:RDoc::Markup::Paragraph;[I"OBigDecimal provides arbitrary-precision floating point decimal arithmetic.;To:RDoc::Markup::BlankLine o; ;[ I"FCopyright (C) 2002 by Shigeo Kobayashi <shigeo@tinyforest.gr.jp>.;TI"HYou may distribute under the terms of either the GNU General Public;TI"ELicense or the Artistic License, as specified in the README file;TI"$of the BigDecimal distribution.;T@o; ;[I"+Documented by mathew <meta@pobox.com>.;T@S:RDoc::Markup::Heading: leveli: textI"Introduction;T@o; ;[I"ORuby provides built-in support for arbitrary precision integer arithmetic.;TI"For example:;T@o; ;[I")42**13 -> 1265437718438866624512;T@o; ;[I"QBigDecimal provides similar support for very large or very accurate floating;TI"point numbers.;T@o; ;[ I"JDecimal arithmetic is also useful for general calculation, because it;TI"Oprovides the correct answers people expect--whereas normal binary floating;TI"Npoint arithmetic often introduces subtle errors because of the conversion;TI"2between base 10 and base 2. For example, try:;T@o:RDoc::Markup::Verbatim;[ I" sum = 0 ;FI"for i in (1..10000) ;FI" sum = sum + 0.0001 ;FI" end ;FI"print sum ;Fo; ;[I"'and contrast with the output from:;T@o;;[I"require 'bigdecimal' ;FI" ;FI"sum = BigDecimal.new("0") ;FI"for i in (1..10000) ;FI", sum = sum + BigDecimal.new("0.0001") ;FI" end ;FI"print sum ;Fo; ;[I"Similarly:;T@o; ;[I"M(BigDecimal.new("1.2") - BigDecimal("1.0")) == BigDecimal("0.2") -> true;T@o; ;[I" (1.2 - 1.0) == 0.2 -> false;T@S;;i; I"4Special features of accurate decimal arithmetic;T@o; ;[I"JBecause BigDecimal is more accurate than normal binary floating point;TI"1arithmetic, it requires some special values.;T@S;;i; I" Infinity;T@o; ;[I"MBigDecimal sometimes needs to return infinity, for example if you divide;TI"a value by zero.;T@o; ;[I"?BigDecimal.new("1.0") / BigDecimal.new("0.0") -> infinity;T@o; ;[I"ABigDecimal.new("-1.0") / BigDecimal.new("0.0") -> -infinity;T@o; ;[I"GYou can represent infinite numbers to BigDecimal using the strings;TI"='Infinity', '+Infinity' and '-Infinity' (case-sensitive);T@S;;i; I"Not a Number;T@o; ;[I"LWhen a computation results in an undefined value, the special value NaN;TI"&(for 'not a number') is returned.;T@o; ;[I" Example:;T@o; ;[I"9BigDecimal.new("0.0") / BigDecimal.new("0.0") -> NaN;T@o; ;[I"MYou can also create undefined values. NaN is never considered to be the;TI".same as any other value, even NaN itself:;T@o; ;[I"n = BigDecimal.new('NaN');T@o; ;[I"n == 0.0 -> nil;T@o; ;[I"n == n -> nil;T@S;;i; I"Positive and negative zero;T@o; ;[I"PIf a computation results in a value which is too small to be represented as;TI"Oa BigDecimal within the currently specified limits of precision, zero must;TI"be returned.;T@o; ;[I"PIf the value which is too small to be represented is negative, a BigDecimal;TI"Mvalue of negative zero is returned. If the value is positive, a value of;TI"positive zero is returned.;T@o; ;[I"@BigDecimal.new("1.0") / BigDecimal.new("-Infinity") -> -0.0;T@o; ;[I">BigDecimal.new("1.0") / BigDecimal.new("Infinity") -> 0.0;T@o; ;[I"B(See BigDecimal.mode for how to specify limits of precision.);T@o; ;[I"MNote that -0.0 and 0.0 are considered to be the same for the purposes of;TI"comparison.;T@o; ;[I"NNote also that in mathematics, there is no particular concept of negative;TI":or positive zero; true mathematical zero has no sign.;T: @fileI" ext/bigdecimal/bigdecimal.c;T;0[ [[I" BASE;To;;[o; ;[ I"HBase value used in internal calculations. On a 32 bit system, BASE;TI"Iis 10000, indicating that calculation is done in groups of 4 digits.;TI"I(If it were larger, BASE**2 wouldn't fit in 32 bits, so you couldn't;TI"Jguarantee that two groups could always be multiplied together without;TI"overflow.);T;0@�[I"EXCEPTION_ALL;To;;[o; ;[I"DDetermines whether overflow, underflow or zero divide result in;TI"4an exception being thrown. See BigDecimal.mode.;T;0@�[I"EXCEPTION_NaN;To;;[o; ;[I"FDetermines what happens when the result of a computation is not a;TI"'number (NaN). See BigDecimal.mode.;T;0@�[I"EXCEPTION_INFINITY;To;;[o; ;[I"@Determines what happens when the result of a computation is;TI"$infinity. See BigDecimal.mode.;T;0@�[I"EXCEPTION_UNDERFLOW;To;;[o; ;[I"CDetermines what happens when the result of a computation is an;TI"Kunderflow (a result too small to be represented). See BigDecimal.mode.;T;0@�[I"EXCEPTION_OVERFLOW;To;;[o; ;[I"CDetermines what happens when the result of a computation is an;TI"Joverflow (a result too large to be represented). See BigDecimal.mode.;T;0@�[I"EXCEPTION_ZERODIVIDE;To;;[o; ;[I"BDetermines what happens when a division by zero is performed.;TI"See BigDecimal.mode.;T;0@�[I"ROUND_MODE;To;;[o; ;[I"FDetermines what happens when a result must be rounded in order to;TI"=fit in the appropriate number of significant digits. See;TI"BigDecimal.mode.;T;0@�[I" ROUND_UP;To;;[o; ;[I"@Indicates that values should be rounded away from zero. See;TI"BigDecimal.mode.;T;0@�[I"ROUND_DOWN;To;;[o; ;[I">Indicates that values should be rounded towards zero. See;TI"BigDecimal.mode.;T;0@�[I"ROUND_HALF_UP;To;;[o; ;[I"JIndicates that digits >= 5 should be rounded up, others rounded down.;TI"See BigDecimal.mode. ;T;0@�[I"ROUND_HALF_DOWN;To;;[o; ;[I"JIndicates that digits >= 6 should be rounded up, others rounded down.;TI"See BigDecimal.mode.;T;0@�[I"ROUND_CEILING;To;;[o; ;[I"5Round towards +infinity. See BigDecimal.mode. ;T;0@�[I"ROUND_FLOOR;To;;[o; ;[I"5Round towards -infinity. See BigDecimal.mode. ;T;0@�[I"ROUND_HALF_EVEN;To;;[o; ;[I"=Round towards the even neighbor. See BigDecimal.mode. ;T;0@�[I" SIGN_NaN;To;;[o; ;[I"DIndicates that a value is not a number. See BigDecimal.sign. ;T;0@�[I"SIGN_POSITIVE_ZERO;To;;[o; ;[I":Indicates that a value is +0. See BigDecimal.sign. ;T;0@�[I"SIGN_NEGATIVE_ZERO;To;;[o; ;[I":Indicates that a value is -0. See BigDecimal.sign. ;T;0@�[I"SIGN_POSITIVE_FINITE;To;;[o; ;[I"KIndicates that a value is positive and finite. See BigDecimal.sign. ;T;0@�[I"SIGN_NEGATIVE_FINITE;To;;[o; ;[I"KIndicates that a value is negative and finite. See BigDecimal.sign. ;T;0@�[I"SIGN_POSITIVE_INFINITE;To;;[o; ;[I"MIndicates that a value is positive and infinite. See BigDecimal.sign. ;T;0@�[I"SIGN_NEGATIVE_INFINITE;To;;[o; ;[I"MIndicates that a value is negative and infinite. See BigDecimal.sign. ;T;0@�[I" INFINITY;To;;[ ;0@�[I"NAN;To;;[ ;0@�[ [[I" class;F[[:public[[I" _load;T@�[I"double_fig;T@�[I" limit;T@�[I" mode;T@�[I"new;T@�[I"save_exception_mode;T@�[I"save_limit;T@�[I"save_rounding_mode;T@�[I"ver;T@�[:protected[ [:private[ [I" instance;F[[;[:[I"%;T@�[I"*;T@�[I"**;T@�[I"+;T@�[I"+@;T@�[I"-;T@�[I"-@;T@�[I"/;T@�[I"<;T@�[I"<=;T@�[I"<=>;T@�[I"==;T@�[I"===;T@�[I">;T@�[I">=;T@�[I" _dump;T@�[I"abs;T@�[I"add;T@�[I" ceil;T@�[I"coerce;T@�[I"div;T@�[I"divmod;T@�[I" eql?;T@�[I" exponent;T@�[I"finite?;T@�[I"fix;T@�[I" floor;T@�[I" frac;T@�[I" hash;T@�[I"infinite?;T@�[I"inspect;T@�[I"modulo;T@�[I" mult;T@�[I" nan?;T@�[I" nonzero?;T@�[I" power;T@�[I" precs;T@�[I"quo;T@�[I"remainder;T@�[I" round;T@�[I" sign;T@�[I" split;T@�[I" sqrt;T@�[I"sub;T@�[I" to_d;FI"*ext/bigdecimal/lib/bigdecimal/util.rb;T[I"to_digits;F@�[I" to_f;T@�[I" to_i;T@�[I"to_int;T@�[I" to_r;T@�[I" to_s;T@�[I" truncate;T@�[I" zero?;T@�[;[ [;[