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U:RDoc::NormalClass[iI"BigDecimal:ET@I"Numeric;To:RDoc::Markup::Document:@parts[o;;[Po:RDoc::Markup::Paragraph;[I"OBigDecimal provides arbitrary-precision floating point decimal arithmetic.;To:RDoc::Markup::BlankLine�S:RDoc::Markup::Heading:
leveli:	textI"Introduction;T@o;	;[I"ORuby provides built-in support for arbitrary precision integer arithmetic.;T@o;	;[I"For example:;T@o:RDoc::Markup::Verbatim;[I"*42**13  #=>   1265437718438866624512
;T:@format0o;	;[I"RBigDecimal provides similar support for very large or very accurate floating ;TI"point numbers.;T@o;	;[	I"KDecimal arithmetic is also useful for general calculation, because it ;TI"Pprovides the correct answers people expect--whereas normal binary floating ;TI"Opoint arithmetic often introduces subtle errors because of the conversion ;TI" between base 10 and base 2.;T@o;	;[I"For example, try:;T@o;;[
I"
sum = 0
;TI"10_000.times do
;TI"  sum = sum + 0.0001
;TI"	end
;TI"&print sum #=> 0.9999999999999062
;T;0o;	;[I"'and contrast with the output from:;T@o;;[I"require 'bigdecimal'
;TI"
;TI"sum = BigDecimal("0")
;TI"10_000.times do
;TI"(  sum = sum + BigDecimal("0.0001")
;TI"	end
;TI"print sum #=> 0.1E1
;T;0o;	;[I"Similarly:;T@o;;[I"K(BigDecimal("1.2") - BigDecimal("1.0")) == BigDecimal("0.2") #=> true
;TI"
;TI""(1.2 - 1.0) == 0.2 #=> false
;T;0S;;i;
I"4Special features of accurate decimal arithmetic;T@o;	;[I"KBecause BigDecimal is more accurate than normal binary floating point ;TI"1arithmetic, it requires some special values.;T@S;;i;
I"
Infinity;T@o;	;[I"NBigDecimal sometimes needs to return infinity, for example if you divide ;TI"a value by zero.;T@o;;[I"9BigDecimal("1.0") / BigDecimal("0.0")  #=> Infinity
;TI";BigDecimal("-1.0") / BigDecimal("0.0")  #=> -Infinity
;T;0o;	;[I"HYou can represent infinite numbers to BigDecimal using the strings ;TI";<code>'Infinity'</code>, <code>'+Infinity'</code> and ;TI".<code>'-Infinity'</code> (case-sensitive);T@S;;i;
I"Not a Number;T@o;	;[I"OWhen 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"3BigDecimal("0.0") / BigDecimal("0.0") #=> NaN
;T;0o;	;[I"*You can also create undefined values.;T@o;	;[I"PNaN is never considered to be the same as any other value, even NaN itself:;T@o;;[I"n = BigDecimal('NaN')
;TI"n == 0.0 #=> false
;TI"n == n #=> false
;T;0S;;i;
I"Positive and negative zero;T@o;	;[I"QIf a computation results in a value which is too small to be represented as ;TI"Pa BigDecimal within the currently specified limits of precision, zero must ;TI"be returned.;T@o;	;[I"QIf the value which is too small to be represented is negative, a BigDecimal ;TI"(value of negative zero is returned.;T@o;;[I":BigDecimal("1.0") / BigDecimal("-Infinity") #=> -0.0
;T;0o;	;[I"DIf the value is positive, a value of positive zero is returned.;T@o;;[I"8BigDecimal("1.0") / BigDecimal("Infinity") #=> 0.0
;T;0o;	;[I"B(See BigDecimal.mode for how to specify limits of precision.);T@o;	;[I"RNote that +-0.0+ and +0.0+ are considered to be the same for the purposes of ;TI"comparison.;T@o;	;[I"ONote also that in mathematics, there is no particular concept of negative ;TI":or positive zero; true mathematical zero has no sign.;T@S;;i;
I"bigdecimal/util;T@o;	;[I"BWhen you require +bigdecimal/util+, the #to_d method will be ;TI"Favailable on BigDecimal and the native Integer, Float, Rational, ;TI"and String classes:;T@o;;[I"require 'bigdecimal/util'
;TI"
;TI"!42.to_d         # => 0.42e2
;TI" 0.5.to_d        # => 0.5e0
;TI""(2/3r).to_d(3)  # => 0.667e0
;TI" "0.5".to_d      # => 0.5e0
;T;0S;;i;
I"License;T@o;	;[I"FCopyright (C) 2002 by Shigeo Kobayashi <shigeo@tinyforest.gr.jp>.;T@o;	;[I"FBigDecimal is released under the Ruby and 2-clause BSD licenses. ;TI"!See LICENSE.txt for details.;T@o;	;[I"=Maintained by mrkn <mrkn@mrkn.jp> and ruby-core members.;T@o;	;[I"QDocumented by zzak <zachary@zacharyscott.net>, mathew <meta@pobox.com>, and ;TI"many other contributors.;T:
@fileI" ext/bigdecimal/bigdecimal.c;T:0@omit_headings_from_table_of_contents_below0o;;[�;I"*ext/bigdecimal/lib/bigdecimal/util.rb;T;0o;;[�;I"(ext/json/lib/json/add/bigdecimal.rb;T;0;0;0[�[U:RDoc::Constant[i�I"VERSION;TI"BigDecimal::VERSION;T:public0o;;[o;	;[I"&The version of bigdecimal library;T;@�;0@�@cRDoc::NormalClass0U;[i�I"	BASE;TI"BigDecimal::BASE;T;0o;;[o;	;[
I"IBase value used in internal calculations.  On a 32 bit system, BASE ;TI"Jis 10000, indicating that calculation is done in groups of 4 digits. ;TI"J(If it were larger, BASE**2 wouldn't fit in 32 bits, so you couldn't ;TI"Kguarantee that two groups could always be multiplied together without ;TI"overflow.);T;@�;0@�@@�0U;[i�I"EXCEPTION_ALL;TI"BigDecimal::EXCEPTION_ALL;T;0o;;[o;	;[I"EDetermines whether overflow, underflow or zero divide result in ;TI"4an exception being thrown. See BigDecimal.mode.;T;@�;0@�@@�0U;[i�I"EXCEPTION_NaN;TI"BigDecimal::EXCEPTION_NaN;T;0o;;[o;	;[I"GDetermines what happens when the result of a computation is not a ;TI"'number (NaN). See BigDecimal.mode.;T;@�;0@�@@�0U;[i�I"EXCEPTION_INFINITY;TI"#BigDecimal::EXCEPTION_INFINITY;T;0o;;[o;	;[I"ADetermines what happens when the result of a computation is ;TI"$infinity.  See BigDecimal.mode.;T;@�;0@�@@�0U;[i�I"EXCEPTION_UNDERFLOW;TI"$BigDecimal::EXCEPTION_UNDERFLOW;T;0o;;[o;	;[I"DDetermines what happens when the result of a computation is an ;TI"Kunderflow (a result too small to be represented). See BigDecimal.mode.;T;@�;0@�@@�0U;[i�I"EXCEPTION_OVERFLOW;TI"#BigDecimal::EXCEPTION_OVERFLOW;T;0o;;[o;	;[I"DDetermines what happens when the result of a computation is an ;TI"Joverflow (a result too large to be represented). See BigDecimal.mode.;T;@�;0@�@@�0U;[i�I"EXCEPTION_ZERODIVIDE;TI"%BigDecimal::EXCEPTION_ZERODIVIDE;T;0o;;[o;	;[I"CDetermines what happens when a division by zero is performed. ;TI"See BigDecimal.mode.;T;@�;0@�@@�0U;[i�I"ROUND_MODE;TI"BigDecimal::ROUND_MODE;T;0o;;[o;	;[I"GDetermines 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@�@@�0U;[i�I"
ROUND_UP;TI"BigDecimal::ROUND_UP;T;0o;;[o;	;[I"AIndicates that values should be rounded away from zero. See ;TI"BigDecimal.mode.;T;@�;0@�@@�0U;[i�I"ROUND_DOWN;TI"BigDecimal::ROUND_DOWN;T;0o;;[o;	;[I"?Indicates that values should be rounded towards zero. See ;TI"BigDecimal.mode.;T;@�;0@�@@�0U;[i�I"ROUND_HALF_UP;TI"BigDecimal::ROUND_HALF_UP;T;0o;;[o;	;[I"KIndicates that digits >= 5 should be rounded up, others rounded down. ;TI"See BigDecimal.mode.;T@;@�;0@�@@�0U;[i�I"ROUND_HALF_DOWN;TI" BigDecimal::ROUND_HALF_DOWN;T;0o;;[o;	;[I"KIndicates that digits >= 6 should be rounded up, others rounded down. ;TI"See BigDecimal.mode.;T;@�;0@�@@�0U;[i�I"ROUND_CEILING;TI"BigDecimal::ROUND_CEILING;T;0o;;[o;	;[I"2Round towards +Infinity. See BigDecimal.mode.;T@;@�;0@�@@�0U;[i�I"ROUND_FLOOR;TI"BigDecimal::ROUND_FLOOR;T;0o;;[o;	;[I"2Round towards -Infinity. See BigDecimal.mode.;T@;@�;0@�@@�0U;[i�I"ROUND_HALF_EVEN;TI" BigDecimal::ROUND_HALF_EVEN;T;0o;;[o;	;[I":Round towards the even neighbor. See BigDecimal.mode.;T@;@�;0@�@@�0U;[i�I"
SIGN_NaN;TI"BigDecimal::SIGN_NaN;T;0o;;[o;	;[I"AIndicates that a value is not a number. See BigDecimal.sign.;T@;@�;0@�@@�0U;[i�I"SIGN_POSITIVE_ZERO;TI"#BigDecimal::SIGN_POSITIVE_ZERO;T;0o;;[o;	;[I"7Indicates that a value is +0. See BigDecimal.sign.;T@;@�;0@�@@�0U;[i�I"SIGN_NEGATIVE_ZERO;TI"#BigDecimal::SIGN_NEGATIVE_ZERO;T;0o;;[o;	;[I"7Indicates that a value is -0. See BigDecimal.sign.;T@;@�;0@�@@�0U;[i�I"SIGN_POSITIVE_FINITE;TI"%BigDecimal::SIGN_POSITIVE_FINITE;T;0o;;[o;	;[I"HIndicates that a value is positive and finite. See BigDecimal.sign.;T@;@�;0@�@@�0U;[i�I"SIGN_NEGATIVE_FINITE;TI"%BigDecimal::SIGN_NEGATIVE_FINITE;T;0o;;[o;	;[I"HIndicates that a value is negative and finite. See BigDecimal.sign.;T@;@�;0@�@@�0U;[i�I"SIGN_POSITIVE_INFINITE;TI"'BigDecimal::SIGN_POSITIVE_INFINITE;T;0o;;[o;	;[I"JIndicates that a value is positive and infinite. See BigDecimal.sign.;T@;@�;0@�@@�0U;[i�I"SIGN_NEGATIVE_INFINITE;TI"'BigDecimal::SIGN_NEGATIVE_INFINITE;T;0o;;[o;	;[I"JIndicates that a value is negative and infinite. See BigDecimal.sign.;T@;@�;0@�@@�0U;[i�I"
INFINITY;TI"BigDecimal::INFINITY;T;0o;;[o;	;[I"Positive infinity value.;T@;@�;0@�@@�0U;[i�I"NAN;TI"BigDecimal::NAN;T;0o;;[o;	;[I"'Not a Number' value.;T@;@�;0@�@@�0[�[[I"
class;T[[;[[I"
_load;TI" ext/bigdecimal/bigdecimal.c;T[I"double_fig;T@�[I"interpret_loosely;T@�[I"json_create;TI"(ext/json/lib/json/add/bigdecimal.rb;T[I"
limit;T@�[I"	mode;T@�[I"save_exception_mode;T@�[I"save_limit;T@�[I"save_rounding_mode;T@�[:protected[�[:private[�[I"
instance;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">=;T@�[I"
_dump;T@�[I"abs;T@�[I"add;T@�[I"as_json;T@�[I"	ceil;T@�[I"
clone;T@�[I"coerce;T@�[I"div;T@�[I"divmod;T@�[I"dup;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"n_significant_digits;T@�[I"	nan?;T@�[I"
nonzero?;T@�[I"
power;T@�[I"precision;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;TI"*ext/bigdecimal/lib/bigdecimal/util.rb;T[I"to_digits;T@,[I"	to_f;T@�[I"	to_i;T@�[I"to_int;T@�[I"to_json;T@�[I"	to_r;T@�[I"	to_s;T@�[I"
truncate;T@�[I"
zero?;T@�[;[�[;[�[�[U:RDoc::Context::Section[i�0o;;[�;0;0[@�@�@�@�cRDoc::TopLevel