# Class: BigDecimal

Inherits:
Numeric
show all
Defined in:
ext/bigdecimal/bigdecimal.c

## Overview

Document-class: BigDecimal BigDecimal provides arbitrary-precision floating point decimal arithmetic.

Copyright (C) 2002 by Shigeo Kobayashi <shigeo@tinyforest.gr.jp>. You may distribute under the terms of either the GNU General Public License or the Artistic License, as specified in the README file of the BigDecimal distribution.

Documented by mathew <meta@pobox.com>.

# Introduction

Ruby provides built-in support for arbitrary precision integer arithmetic. For example:

42**13 -> 1265437718438866624512

BigDecimal provides similar support for very large or very accurate floating point numbers.

Decimal arithmetic is also useful for general calculation, because it provides the correct answers people expect--whereas normal binary floating point arithmetic often introduces subtle errors because of the conversion between base 10 and base 2. For example, try:

``````sum = 0
for i in (1..10000)
sum = sum + 0.0001
end
print sum``````

and contrast with the output from:

``````require 'bigdecimal'

sum = BigDecimal.new("0")
for i in (1..10000)
sum = sum + BigDecimal.new("0.0001")
end
print sum``````

Similarly:

(BigDecimal.new("1.2") - BigDecimal("1.0")) == BigDecimal("0.2") -> true

(1.2 - 1.0) == 0.2 -> false

# Special features of accurate decimal arithmetic

Because BigDecimal is more accurate than normal binary floating point arithmetic, it requires some special values.

## Infinity

BigDecimal sometimes needs to return infinity, for example if you divide a value by zero.

BigDecimal.new("1.0") / BigDecimal.new("0.0") -> infinity

BigDecimal.new("-1.0") / BigDecimal.new("0.0") -> -infinity

You can represent infinite numbers to BigDecimal using the strings 'Infinity', '+Infinity' and '-Infinity' (case-sensitive)

## Not a Number

When a computation results in an undefined value, the special value NaN (for 'not a number') is returned.

Example:

BigDecimal.new("0.0") / BigDecimal.new("0.0") -> NaN

You can also create undefined values. NaN is never considered to be the same as any other value, even NaN itself:

n = BigDecimal.new('NaN')

n == 0.0 -> nil

n == n -> nil

## Positive and negative zero

If a computation results in a value which is too small to be represented as a BigDecimal within the currently specified limits of precision, zero must be returned.

If the value which is too small to be represented is negative, a BigDecimal value of negative zero is returned. If the value is positive, a value of positive zero is returned.

BigDecimal.new("1.0") / BigDecimal.new("-Infinity") -> -0.0

BigDecimal.new("1.0") / BigDecimal.new("Infinity") -> 0.0

(See BigDecimal.mode for how to specify limits of precision.)

Note that -0.0 and 0.0 are considered to be the same for the purposes of comparison.

Note also that in mathematics, there is no particular concept of negative or positive zero; true mathematical zero has no sign.

## Constant Summary

BASE =

Base value used in internal calculations. On a 32 bit system, BASE is 10000, indicating that calculation is done in groups of 4 digits. (If it were larger, BASE**2 wouldn't fit in 32 bits, so you couldn't guarantee that two groups could always be multiplied together without overflow.)

`INT2FIX((SIGNED_VALUE)VpBaseVal())`
EXCEPTION_ALL =

Determines whether overflow, underflow or zero divide result in an exception being thrown. See BigDecimal.mode.

`INT2FIX(VP_EXCEPTION_ALL)`
EXCEPTION_NaN =

Determines what happens when the result of a computation is not a number (NaN). See BigDecimal.mode.

`INT2FIX(VP_EXCEPTION_NaN)`
EXCEPTION_INFINITY =

Determines what happens when the result of a computation is infinity. See BigDecimal.mode.

`INT2FIX(VP_EXCEPTION_INFINITY)`
EXCEPTION_UNDERFLOW =

Determines what happens when the result of a computation is an underflow (a result too small to be represented). See BigDecimal.mode.

`INT2FIX(VP_EXCEPTION_UNDERFLOW)`
EXCEPTION_OVERFLOW =

Determines what happens when the result of a computation is an overflow (a result too large to be represented). See BigDecimal.mode.

`INT2FIX(VP_EXCEPTION_OVERFLOW)`
EXCEPTION_ZERODIVIDE =

Determines what happens when a division by zero is performed. See BigDecimal.mode.

`INT2FIX(VP_EXCEPTION_ZERODIVIDE)`
ROUND_MODE =

Determines what happens when a result must be rounded in order to fit in the appropriate number of significant digits. See BigDecimal.mode.

`INT2FIX(VP_ROUND_MODE)`
ROUND_UP =

Indicates that values should be rounded away from zero. See BigDecimal.mode.

`INT2FIX(VP_ROUND_UP)`
ROUND_DOWN =

Indicates that values should be rounded towards zero. See BigDecimal.mode.

`INT2FIX(VP_ROUND_DOWN)`
ROUND_HALF_UP =

Indicates that digits >= 5 should be rounded up, others rounded down. See BigDecimal.mode.

`INT2FIX(VP_ROUND_HALF_UP)`
ROUND_HALF_DOWN =

Indicates that digits >= 6 should be rounded up, others rounded down. See BigDecimal.mode.

`INT2FIX(VP_ROUND_HALF_DOWN)`
ROUND_CEILING =

Round towards +infinity. See BigDecimal.mode.

`INT2FIX(VP_ROUND_CEIL)`
ROUND_FLOOR =

Round towards -infinity. See BigDecimal.mode.

`INT2FIX(VP_ROUND_FLOOR)`
ROUND_HALF_EVEN =

Round towards the even neighbor. See BigDecimal.mode.

`INT2FIX(VP_ROUND_HALF_EVEN)`
SIGN_NaN =

Indicates that a value is not a number. See BigDecimal.sign.

`INT2FIX(VP_SIGN_NaN)`
SIGN_POSITIVE_ZERO =

Indicates that a value is +0. See BigDecimal.sign.

`INT2FIX(VP_SIGN_POSITIVE_ZERO)`
SIGN_NEGATIVE_ZERO =

Indicates that a value is -0. See BigDecimal.sign.

`INT2FIX(VP_SIGN_NEGATIVE_ZERO)`
SIGN_POSITIVE_FINITE =

Indicates that a value is positive and finite. See BigDecimal.sign.

`INT2FIX(VP_SIGN_POSITIVE_FINITE)`
SIGN_NEGATIVE_FINITE =

Indicates that a value is negative and finite. See BigDecimal.sign.

`INT2FIX(VP_SIGN_NEGATIVE_FINITE)`
SIGN_POSITIVE_INFINITE =

Indicates that a value is positive and infinite. See BigDecimal.sign.

`INT2FIX(VP_SIGN_POSITIVE_INFINITE)`
SIGN_NEGATIVE_INFINITE =

Indicates that a value is negative and infinite. See BigDecimal.sign.

`INT2FIX(VP_SIGN_NEGATIVE_INFINITE)`
INFINITY =
`BigDecimal_global_new(1, &arg, rb_cBigDecimal)`
NAN =
`BigDecimal_global_new(1, &arg, rb_cBigDecimal)`

## Class Method Summary (collapse)

• Internal method used to provide marshalling support.

• BigDecimal.double_fig.

• BigDecimal.limit(digits).

• BigDecimal.mode(mode, value).

• new(initial, digits).

• BigDecimal.save_exception_mode { ... }.

• BigDecimal.save_limit { ... }.

• BigDecimal.save_rounding_mode { ... }.

• Returns the BigDecimal version number.

## Instance Method Summary (collapse)

• a % b a.modulo(b).

• mult(value, digits).

• power(n).

• sub(value, digits).

• div(value, digits) quo(value).

• a < b.

• a <= b.

• The comparison operator.

• Tests for value equality; returns true if the values are equal.

• Tests for value equality; returns true if the values are equal.

• a > b.

• a >= b.

• Returns the absolute value.

• ceil(n).

• The coerce method provides support for Ruby type coercion.

• Divides by the specified value, and returns the quotient and modulus as BigDecimal numbers.

• Tests for value equality; returns true if the values are equal.

• Returns the exponent of the BigDecimal number, as an Integer.

• Returns True if the value is finite (not NaN or infinite).

• Return the integer part of the number.

• floor(n).

• Return the fractional part of the number.

• Returns nil, -1, or +1 depending on whether the value is finite, -infinity, or +infinity.

• Returns debugging information about the value as a string of comma-separated values in angle brackets with a leading #:.

• a % b a.modulo(b).

• Returns True if the value is Not a Number.

• Returns self if the value is non-zero, nil otherwise.

• power(n).

• precs.

• div(value, digits) quo(value).

• Returns the remainder from dividing by the value.

• round(n,mode).

• Returns the sign of the value.

• Splits a BigDecimal number into four parts, returned as an array of values.

• sqrt(n).

• Returns a new Float object having approximately the same value as the BigDecimal number.

• Returns the value as an integer (Fixnum or Bignum).

• Returns the value as an integer (Fixnum or Bignum).

• Converts a BigDecimal to a Rational.

• to_s(s).

• truncate(n).

• Returns True if the value is zero.

#im

## Class Method Details

### + (Object) _load

Internal method used to provide marshalling support. See the Marshal module.

 ``` ``` ```# File 'ext/bigdecimal/bigdecimal.c' static VALUE BigDecimal_load(VALUE self, VALUE str) { ENTER(2); Real *pv; const unsigned char *pch; unsigned char ch; unsigned long m=0; SafeStringValue(str); pch = (const unsigned char *)RSTRING_PTR(str); /* First get max prec */ while((*pch)!=(unsigned char)'\0' && (ch=*pch++)!=(unsigned char)':') { if(!ISDIGIT(ch)) { rb_raise(rb_eTypeError, "load failed: invalid character in the marshaled string"); }```

### + (Object) double_fig

BigDecimal.double_fig

The BigDecimal.double_fig class method returns the number of digits a Float number is allowed to have. The result depends upon the CPU and OS in use.

 ``` ``` ```# File 'ext/bigdecimal/bigdecimal.c' static VALUE BigDecimal_double_fig(VALUE self) { return INT2FIX(VpDblFig()); }```

### + (Object) limit

BigDecimal.limit(digits)

Limit the number of significant digits in newly created BigDecimal numbers to the specified value. Rounding is performed as necessary, as specified by BigDecimal.mode.

A limit of 0, the default, means no upper limit.

The limit specified by this method takes less priority over any limit specified to instance methods such as ceil, floor, truncate, or round.

 ``` ``` ```# File 'ext/bigdecimal/bigdecimal.c' static VALUE BigDecimal_limit(int argc, VALUE *argv, VALUE self) { VALUE nFig; VALUE nCur = INT2NUM(VpGetPrecLimit()); if(rb_scan_args(argc,argv,"01",&nFig)==1) { int nf; if(nFig==Qnil) return nCur; Check_Type(nFig, T_FIXNUM); nf = FIX2INT(nFig); if(nf<0) { rb_raise(rb_eArgError, "argument must be positive"); }```

### + (Object) mode

BigDecimal.mode(mode, value)

Controls handling of arithmetic exceptions and rounding. If no value is supplied, the current value is returned.

Six values of the mode parameter control the handling of arithmetic exceptions:

BigDecimal::EXCEPTION_NaN BigDecimal::EXCEPTION_INFINITY BigDecimal::EXCEPTION_UNDERFLOW BigDecimal::EXCEPTION_OVERFLOW BigDecimal::EXCEPTION_ZERODIVIDE BigDecimal::EXCEPTION_ALL

For each mode parameter above, if the value set is false, computation continues after an arithmetic exception of the appropriate type. When computation continues, results are as follows:

 EXCEPTION_NaN NaN EXCEPTION_INFINITY +infinity or -infinity EXCEPTION_UNDERFLOW 0 EXCEPTION_OVERFLOW +infinity or -infinity EXCEPTION_ZERODIVIDE +infinity or -infinity

One value of the mode parameter controls the rounding of numeric values: BigDecimal::ROUND_MODE. The values it can take are:

 ROUND_UP round away from zero ROUND_DOWN round towards zero (truncate) ROUND_HALF_UP round up if the appropriate digit >= 5, otherwise truncate (default) ROUND_HALF_DOWN round up if the appropriate digit >= 6, otherwise truncate ROUND_HALF_EVEN round towards the even neighbor (Banker's rounding) ROUND_CEILING round towards positive infinity (ceil) ROUND_FLOOR round towards negative infinity (floor)
 ``` ``` ```# File 'ext/bigdecimal/bigdecimal.c' static VALUE BigDecimal_mode(int argc, VALUE *argv, VALUE self) { VALUE which; VALUE val; unsigned long f,fo; if(rb_scan_args(argc,argv,"11",&which,&val)==1) val = Qnil; Check_Type(which, T_FIXNUM); f = (unsigned long)FIX2INT(which); if(f&VP_EXCEPTION_ALL) { /* Exception mode setting */ fo = VpGetException(); if(val==Qnil) return INT2FIX(fo); if(val!=Qfalse && val!=Qtrue) { rb_raise(rb_eTypeError, "second argument must be true or false"); return Qnil; /* Not reached */ }```

### + (Object) new

new(initial, digits)

Create a new BigDecimal object.

 initial The initial value, as a String. Spaces are ignored, unrecognized characters terminate the value. digits The number of significant digits, as a Fixnum. If omitted or 0, the number of significant digits is determined from the initial value.

The actual number of significant digits used in computation is usually larger than the specified number.

 ``` ``` ```# File 'ext/bigdecimal/bigdecimal.c' static VALUE BigDecimal_new(int argc, VALUE *argv, VALUE self) { ENTER(5); Real *pv; size_t mf; VALUE nFig; VALUE iniValue; if(rb_scan_args(argc,argv,"11",&iniValue,&nFig)==1) { mf = 0; }```

### + (Object) save_exception_mode

BigDecimal.save_exception_mode { ... }

 ``` ``` ```# File 'ext/bigdecimal/bigdecimal.c' static VALUE BigDecimal_save_exception_mode(VALUE self) { unsigned short const exception_mode = VpGetException(); int state; VALUE ret = rb_protect(rb_yield, Qnil, &state); VpSetException(exception_mode); if (state) rb_jump_tag(state); return ret; }```

### + (Object) save_limit

BigDecimal.save_limit { ... }

 ``` ``` ```# File 'ext/bigdecimal/bigdecimal.c' static VALUE BigDecimal_save_limit(VALUE self) { size_t const limit = VpGetPrecLimit(); int state; /*VALUE ret =*/ rb_protect(rb_yield, Qnil, &state); VpSetPrecLimit(limit); if (state) rb_jump_tag(state); return Qnil; }```

### + (Object) save_rounding_mode

BigDecimal.save_rounding_mode { ... }

 ``` ``` ```# File 'ext/bigdecimal/bigdecimal.c' static VALUE BigDecimal_save_rounding_mode(VALUE self) { unsigned short const round_mode = VpGetRoundMode(); int state; /*VALUE ret =*/ rb_protect(rb_yield, Qnil, &state); VpSetRoundMode(round_mode); if (state) rb_jump_tag(state); return Qnil; }```

### + (Object) ver

Returns the BigDecimal version number.

Ruby 1.8.0 returns 1.0.0. Ruby 1.8.1 thru 1.8.3 return 1.0.1.

 ``` ``` ```# File 'ext/bigdecimal/bigdecimal.c' static VALUE BigDecimal_version(VALUE self) { /* * 1.0.0: Ruby 1.8.0 * 1.0.1: Ruby 1.8.1 */ return rb_str_new2("1.0.1"); }```

## Instance Method Details

### - (Object) %

a % b a.modulo(b)

Returns the modulus from dividing by b. See divmod.

 ``` ``` ```# File 'ext/bigdecimal/bigdecimal.c' static VALUE BigDecimal_mod(VALUE self, VALUE r) ```

### - (Object) *

mult(value, digits)

Multiply by the specified value.

e.g.

``````c = a.mult(b,n)
c = a * b``````
 digits If specified and less than the number of significant digits of the result, the result is rounded to that number of digits, according to BigDecimal.mode.
 ``` ``` ```# File 'ext/bigdecimal/bigdecimal.c' static VALUE BigDecimal_mult(VALUE self, VALUE r) { ENTER(5); Real *c, *a, *b; size_t mx; GUARD_OBJ(a,GetVpValue(self,1)); b = GetVpValue(r,0); if(!b) return DoSomeOne(self,r,'*'); SAVE(b); mx = a->Prec + b->Prec; GUARD_OBJ(c,VpCreateRbObject(mx *(VpBaseFig() + 1), "0")); VpMult(c, a, b); return ToValue(c); }```

### - (Object) **

power(n)

Returns the value raised to the power of n. Note that n must be an Integer.

Also available as the operator **

 ``` ``` ```# File 'ext/bigdecimal/bigdecimal.c' static VALUE BigDecimal_power(VALUE self, VALUE p) { ENTER(5); Real *x, *y; ssize_t mp, ma; SIGNED_VALUE n; Check_Type(p, T_FIXNUM); n = FIX2INT(p); ma = n; if (ma < 0) ma = -ma; if (ma == 0) ma = 1; GUARD_OBJ(x, GetVpValue(self, 1)); if (VpIsDef(x)) { mp = x->Prec * (VpBaseFig() + 1); GUARD_OBJ(y, VpCreateRbObject(mp * (ma + 1), "0")); }```

### - (Object) +

Add the specified value.

e.g.

``````c = a.add(b,n)
c = a + b``````
 digits If specified and less than the number of significant digits of the result, the result is rounded to that number of digits, according to BigDecimal.mode.
 ``` ``` ```# File 'ext/bigdecimal/bigdecimal.c' static VALUE BigDecimal_add(VALUE self, VALUE r) { ENTER(5); Real *c, *a, *b; size_t mx; GUARD_OBJ(a,GetVpValue(self,1)); b = GetVpValue(r,0); if(!b) return DoSomeOne(self,r,'+'); SAVE(b); if(VpIsNaN(b)) return b->obj; if(VpIsNaN(a)) return a->obj; mx = GetAddSubPrec(a,b); if (mx == (size_t)-1L) { GUARD_OBJ(c,VpCreateRbObject(VpBaseFig() + 1, "0")); VpAddSub(c, a, b, 1); }```

### - (Object) -

sub(value, digits)

Subtract the specified value.

e.g.

``````c = a.sub(b,n)
c = a - b``````
 digits If specified and less than the number of significant digits of the result, the result is rounded to that number of digits, according to BigDecimal.mode.
 ``` ``` ```# File 'ext/bigdecimal/bigdecimal.c' static VALUE BigDecimal_sub(VALUE self, VALUE r) { ENTER(5); Real *c, *a, *b; size_t mx; GUARD_OBJ(a,GetVpValue(self,1)); b = GetVpValue(r,0); if(!b) return DoSomeOne(self,r,'-'); SAVE(b); if(VpIsNaN(b)) return b->obj; if(VpIsNaN(a)) return a->obj; mx = GetAddSubPrec(a,b); if (mx == (size_t)-1L) { GUARD_OBJ(c,VpCreateRbObject(VpBaseFig() + 1, "0")); VpAddSub(c, a, b, -1); }```

### - (Object) /

div(value, digits) quo(value)

Divide by the specified value.

e.g.

``c = a.div(b,n)``
 digits If specified and less than the number of significant digits of the result, the result is rounded to that number of digits, according to BigDecimal.mode.

If digits is 0, the result is the same as the / operator. If not, the result is an integer BigDecimal, by analogy with Float#div.

The alias quo is provided since div(value, 0) is the same as computing the quotient; see divmod.

 ``` ``` ```# File 'ext/bigdecimal/bigdecimal.c' static VALUE BigDecimal_div(VALUE self, VALUE r) /* For c = self/r: with round operation */ { ENTER(5); Real *c=NULL, *res=NULL, *div = NULL; r = BigDecimal_divide(&c, &res, &div, self, r); if(r!=(VALUE)0) return r; /* coerced by other */ SAVE(c);SAVE(res);SAVE(div); /* a/b = c + r/b */ /* c xxxxx r 00000yyyyy ==> (y/b)*BASE >= HALF_BASE */ /* Round */ if(VpHasVal(div)) { /* frac[0] must be zero for NaN,INF,Zero */ VpInternalRound(c, 0, c->frac[c->Prec-1], (BDIGIT)(VpBaseVal()*(BDIGIT_DBL)res->frac[0]/div->frac[0])); }```

### - (Object) <

a < b

Returns true if a is less than b. Values may be coerced to perform the comparison (see ==, coerce).

 ``` ``` ```# File 'ext/bigdecimal/bigdecimal.c' static VALUE BigDecimal_lt(VALUE self, VALUE r) { return BigDecimalCmp(self, r, '<'); }```

### - (Object) <=

a <= b

Returns true if a is less than or equal to b. Values may be coerced to perform the comparison (see ==, coerce).

 ``` ``` ```# File 'ext/bigdecimal/bigdecimal.c' static VALUE BigDecimal_le(VALUE self, VALUE r) { return BigDecimalCmp(self, r, 'L'); }```

### - (Object) <=>

The comparison operator. a <=> b is 0 if a == b, 1 if a > b, -1 if a < b.

 ``` ``` ```# File 'ext/bigdecimal/bigdecimal.c' static VALUE BigDecimal_comp(VALUE self, VALUE r) { return BigDecimalCmp(self, r, '*'); }```

### - (Object) ==

Tests for value equality; returns true if the values are equal.

The == and === operators and the eql? method have the same implementation for BigDecimal.

Values may be coerced to perform the comparison:

BigDecimal.new('1.0') == 1.0 -> true

 ``` ``` ```# File 'ext/bigdecimal/bigdecimal.c' static VALUE BigDecimal_eq(VALUE self, VALUE r) { return BigDecimalCmp(self, r, '='); }```

### - (Object) ===

Tests for value equality; returns true if the values are equal.

The == and === operators and the eql? method have the same implementation for BigDecimal.

Values may be coerced to perform the comparison:

BigDecimal.new('1.0') == 1.0 -> true

 ``` ``` ```# File 'ext/bigdecimal/bigdecimal.c' static VALUE BigDecimal_eq(VALUE self, VALUE r) { return BigDecimalCmp(self, r, '='); }```

### - (Object) >

a > b

Returns true if a is greater than b. Values may be coerced to perform the comparison (see ==, coerce).

 ``` ``` ```# File 'ext/bigdecimal/bigdecimal.c' static VALUE BigDecimal_gt(VALUE self, VALUE r) { return BigDecimalCmp(self, r, '>'); }```

### - (Object) >=

a >= b

Returns true if a is greater than or equal to b. Values may be coerced to perform the comparison (see ==, coerce)

 ``` ``` ```# File 'ext/bigdecimal/bigdecimal.c' static VALUE BigDecimal_ge(VALUE self, VALUE r) { return BigDecimalCmp(self, r, 'G'); }```

### - (Object) abs

Returns the absolute value.

BigDecimal('5').abs -> 5

BigDecimal('-3').abs -> 3

 ``` ``` ```# File 'ext/bigdecimal/bigdecimal.c' static VALUE BigDecimal_abs(VALUE self) { ENTER(5); Real *c, *a; size_t mx; GUARD_OBJ(a,GetVpValue(self,1)); mx = a->Prec *(VpBaseFig() + 1); GUARD_OBJ(c,VpCreateRbObject(mx, "0")); VpAsgn(c, a, 1); VpChangeSign(c, 1); return ToValue(c); }```

### - (Object) ceil

ceil(n)

Return the smallest integer greater than or equal to the value, as a BigDecimal.

BigDecimal('3.14159').ceil -> 4

BigDecimal('-9.1').ceil -> -9

If n is specified and positive, the fractional part of the result has no more than that many digits.

If n is specified and negative, at least that many digits to the left of the decimal point will be 0 in the result.

BigDecimal('3.14159').ceil(3) -> 3.142

BigDecimal('13345.234').ceil(-2) -> 13400.0

 ``` ``` ```# File 'ext/bigdecimal/bigdecimal.c' static VALUE BigDecimal_ceil(int argc, VALUE *argv, VALUE self) { ENTER(5); Real *c, *a; int iLoc; VALUE vLoc; size_t mx, pl = VpSetPrecLimit(0); if(rb_scan_args(argc,argv,"01",&vLoc)==0) { iLoc = 0; }```

### - (Object) coerce

The coerce method provides support for Ruby type coercion. It is not enabled by default.

This means that binary operations like + * / or - can often be performed on a BigDecimal and an object of another type, if the other object can be coerced into a BigDecimal value.

e.g. a = BigDecimal.new("1.0") b = a / 2.0 -> 0.5

Note that coercing a String to a BigDecimal is not supported by default; it requires a special compile-time option when building Ruby.

 ``` ``` ```# File 'ext/bigdecimal/bigdecimal.c' static VALUE BigDecimal_coerce(VALUE self, VALUE other) { ENTER(2); VALUE obj; Real *b; if (TYPE(other) == T_FLOAT) { obj = rb_assoc_new(other, BigDecimal_to_f(self)); }```

### - (Object) divmod

Divides by the specified value, and returns the quotient and modulus as BigDecimal numbers. The quotient is rounded towards negative infinity.

For example:

require 'bigdecimal'

a = BigDecimal.new("42") b = BigDecimal.new("9")

q,m = a.divmod(b)

c = q * b + m

a == c -> true

The quotient q is (a/b).floor, and the modulus is the amount that must be added to q * b to get a.

 ``` ``` ```# File 'ext/bigdecimal/bigdecimal.c' static VALUE BigDecimal_divmod(VALUE self, VALUE r) { ENTER(5); Real *div=NULL, *mod=NULL; if(BigDecimal_DoDivmod(self,r,&div,&mod)) { SAVE(div); SAVE(mod); return rb_assoc_new(ToValue(div), ToValue(mod)); }```

### - (Object) eql?

Tests for value equality; returns true if the values are equal.

The == and === operators and the eql? method have the same implementation for BigDecimal.

Values may be coerced to perform the comparison:

BigDecimal.new('1.0') == 1.0 -> true

 ``` ``` ```# File 'ext/bigdecimal/bigdecimal.c' static VALUE BigDecimal_eq(VALUE self, VALUE r) { return BigDecimalCmp(self, r, '='); }```

### - (Object) exponent

Returns the exponent of the BigDecimal number, as an Integer.

If the number can be represented as 0.xxxxxx*10**n where xxxxxx is a string of digits with no leading zeros, then n is the exponent.

 ``` ``` ```# File 'ext/bigdecimal/bigdecimal.c' static VALUE BigDecimal_exponent(VALUE self) { ssize_t e = VpExponent10(GetVpValue(self, 1)); return INT2NUM(e); }```

### - (Object) finite?

Returns True if the value is finite (not NaN or infinite)

 ``` ``` ```# File 'ext/bigdecimal/bigdecimal.c' static VALUE BigDecimal_IsFinite(VALUE self) { Real *p = GetVpValue(self,1); if(VpIsNaN(p)) return Qfalse; if(VpIsInf(p)) return Qfalse; return Qtrue; }```

### - (Object) fix

Return the integer part of the number.

 ``` ``` ```# File 'ext/bigdecimal/bigdecimal.c' static VALUE BigDecimal_fix(VALUE self) { ENTER(5); Real *c, *a; size_t mx; GUARD_OBJ(a,GetVpValue(self,1)); mx = a->Prec *(VpBaseFig() + 1); GUARD_OBJ(c,VpCreateRbObject(mx, "0")); VpActiveRound(c,a,VP_ROUND_DOWN,0); /* 0: round off */ return ToValue(c); }```

### - (Object) floor

floor(n)

Return the largest integer less than or equal to the value, as a BigDecimal.

BigDecimal('3.14159').floor -> 3

BigDecimal('-9.1').floor -> -10

If n is specified and positive, the fractional part of the result has no more than that many digits.

If n is specified and negative, at least that many digits to the left of the decimal point will be 0 in the result.

BigDecimal('3.14159').floor(3) -> 3.141

BigDecimal('13345.234').floor(-2) -> 13300.0

 ``` ``` ```# File 'ext/bigdecimal/bigdecimal.c' static VALUE BigDecimal_floor(int argc, VALUE *argv, VALUE self) { ENTER(5); Real *c, *a; int iLoc; VALUE vLoc; size_t mx, pl = VpSetPrecLimit(0); if(rb_scan_args(argc,argv,"01",&vLoc)==0) { iLoc = 0; }```

### - (Object) frac

Return the fractional part of the number.

 ``` ``` ```# File 'ext/bigdecimal/bigdecimal.c' static VALUE BigDecimal_frac(VALUE self) { ENTER(5); Real *c, *a; size_t mx; GUARD_OBJ(a,GetVpValue(self,1)); mx = a->Prec *(VpBaseFig() + 1); GUARD_OBJ(c,VpCreateRbObject(mx, "0")); VpFrac(c, a); return ToValue(c); }```

### - (Object) infinite?

Returns nil, -1, or +1 depending on whether the value is finite, -infinity, or +infinity.

 ``` ``` ```# File 'ext/bigdecimal/bigdecimal.c' static VALUE BigDecimal_IsInfinite(VALUE self) { Real *p = GetVpValue(self,1); if(VpIsPosInf(p)) return INT2FIX(1); if(VpIsNegInf(p)) return INT2FIX(-1); return Qnil; }```

### - (Object) inspect

Returns debugging information about the value as a string of comma-separated values in angle brackets with a leading #:

BigDecimal.new("1234.5678").inspect -> "#<BigDecimal:b7ea1130,'0.12345678E4',8(12)>"

The first part is the address, the second is the value as a string, and the final part ss(mm) is the current number of significant digits and the maximum number of significant digits, respectively.

 ``` ``` ```# File 'ext/bigdecimal/bigdecimal.c' static VALUE BigDecimal_inspect(VALUE self) { ENTER(5); Real *vp; volatile VALUE obj; size_t nc; char *psz, *tmp; GUARD_OBJ(vp,GetVpValue(self,1)); nc = VpNumOfChars(vp,"E"); nc +=(nc + 9) / 10; obj = rb_bstr_new_with_data(0, nc+256); psz = (char *)rb_bstr_bytes(obj); snprintf(psz,nc+256,"#", VpPrec(vp)*VpBaseFig(), VpMaxPrec(vp)*VpBaseFig()); rb_bstr_resize(obj, strlen(psz)); return obj; }```

### - (Object) modulo

a % b a.modulo(b)

Returns the modulus from dividing by b. See divmod.

 ``` ``` ```# File 'ext/bigdecimal/bigdecimal.c' static VALUE BigDecimal_mod(VALUE self, VALUE r) ```

### - (Object) nan?

Returns True if the value is Not a Number

 ``` ``` ```# File 'ext/bigdecimal/bigdecimal.c' static VALUE BigDecimal_IsNaN(VALUE self) { Real *p = GetVpValue(self,1); if(VpIsNaN(p)) return Qtrue; return Qfalse; }```

### - (Object) nonzero?

Returns self if the value is non-zero, nil otherwise.

 ``` ``` ```# File 'ext/bigdecimal/bigdecimal.c' static VALUE BigDecimal_nonzero(VALUE self) { Real *a = GetVpValue(self,1); return VpIsZero(a) ? Qnil : self; }```

### - (Object) power

power(n)

Returns the value raised to the power of n. Note that n must be an Integer.

Also available as the operator **

 ``` ``` ```# File 'ext/bigdecimal/bigdecimal.c' static VALUE BigDecimal_power(VALUE self, VALUE p) { ENTER(5); Real *x, *y; ssize_t mp, ma; SIGNED_VALUE n; Check_Type(p, T_FIXNUM); n = FIX2INT(p); ma = n; if (ma < 0) ma = -ma; if (ma == 0) ma = 1; GUARD_OBJ(x, GetVpValue(self, 1)); if (VpIsDef(x)) { mp = x->Prec * (VpBaseFig() + 1); GUARD_OBJ(y, VpCreateRbObject(mp * (ma + 1), "0")); }```

### - (Object) precs

precs

Returns an Array of two Integer values.

The first value is the current number of significant digits in the BigDecimal. The second value is the maximum number of significant digits for the BigDecimal.

 ``` ``` ```# File 'ext/bigdecimal/bigdecimal.c' static VALUE BigDecimal_prec(VALUE self) { ENTER(1); Real *p; VALUE obj; GUARD_OBJ(p,GetVpValue(self,1)); obj = rb_assoc_new(INT2NUM(p->Prec*VpBaseFig()), INT2NUM(p->MaxPrec*VpBaseFig())); return obj; }```

### - (Object) quo

div(value, digits) quo(value)

Divide by the specified value.

e.g.

``c = a.div(b,n)``
 digits If specified and less than the number of significant digits of the result, the result is rounded to that number of digits, according to BigDecimal.mode.

If digits is 0, the result is the same as the / operator. If not, the result is an integer BigDecimal, by analogy with Float#div.

The alias quo is provided since div(value, 0) is the same as computing the quotient; see divmod.

 ``` ``` ```# File 'ext/bigdecimal/bigdecimal.c' static VALUE BigDecimal_div(VALUE self, VALUE r) /* For c = self/r: with round operation */ { ENTER(5); Real *c=NULL, *res=NULL, *div = NULL; r = BigDecimal_divide(&c, &res, &div, self, r); if(r!=(VALUE)0) return r; /* coerced by other */ SAVE(c);SAVE(res);SAVE(div); /* a/b = c + r/b */ /* c xxxxx r 00000yyyyy ==> (y/b)*BASE >= HALF_BASE */ /* Round */ if(VpHasVal(div)) { /* frac[0] must be zero for NaN,INF,Zero */ VpInternalRound(c, 0, c->frac[c->Prec-1], (BDIGIT)(VpBaseVal()*(BDIGIT_DBL)res->frac[0]/div->frac[0])); }```

### - (Object) remainder

Returns the remainder from dividing by the value.

x.remainder(y) means x-y*(x/y).truncate

 ``` ``` ```# File 'ext/bigdecimal/bigdecimal.c' static VALUE BigDecimal_remainder(VALUE self, VALUE r) /* remainder */ { VALUE f; Real *d,*rv=0; f = BigDecimal_divremain(self,r,&d,&rv); if(f!=(VALUE)0) return f; return ToValue(rv); }```

### - (Object) round

round(n,mode)

Round to the nearest 1 (by default), returning the result as a BigDecimal.

BigDecimal('3.14159').round -> 3

BigDecimal('8.7').round -> 9

If n is specified and positive, the fractional part of the result has no more than that many digits.

If n is specified and negative, at least that many digits to the left of the decimal point will be 0 in the result.

BigDecimal('3.14159').round(3) -> 3.142

BigDecimal('13345.234').round(-2) -> 13300.0

The value of the optional mode argument can be used to determine how rounding is performed; see BigDecimal.mode.

 ``` ``` ```# File 'ext/bigdecimal/bigdecimal.c' static VALUE BigDecimal_round(int argc, VALUE *argv, VALUE self) { ENTER(5); Real *c, *a; int iLoc = 0; VALUE vLoc; VALUE vRound; size_t mx, pl; unsigned short sw = VpGetRoundMode(); int na = rb_scan_args(argc,argv,"02",&vLoc,&vRound); switch(na) { case 0: iLoc = 0; break; case 1: Check_Type(vLoc, T_FIXNUM); iLoc = FIX2INT(vLoc); break; case 2: Check_Type(vLoc, T_FIXNUM); iLoc = FIX2INT(vLoc); Check_Type(vRound, T_FIXNUM); sw = (unsigned short)FIX2INT(vRound); if(!VpIsRoundMode(sw)) { rb_raise(rb_eTypeError, "invalid rounding mode"); return Qnil; }```

### - (Object) sign

Returns the sign of the value.

Returns a positive value if > 0, a negative value if < 0, and a zero if == 0.

The specific value returned indicates the type and sign of the BigDecimal, as follows:

 BigDecimal::SIGN_NaN value is Not a Number BigDecimal::SIGN_POSITIVE_ZERO value is +0 BigDecimal::SIGN_NEGATIVE_ZERO value is -0 BigDecimal::SIGN_POSITIVE_INFINITE value is +infinity BigDecimal::SIGN_NEGATIVE_INFINITE value is -infinity BigDecimal::SIGN_POSITIVE_FINITE value is positive BigDecimal::SIGN_NEGATIVE_FINITE value is negative
 ``` ``` ```# File 'ext/bigdecimal/bigdecimal.c' static VALUE BigDecimal_sign(VALUE self) { /* sign */ int s = GetVpValue(self,1)->sign; return INT2FIX(s); }```

### - (Object) split

Splits a BigDecimal number into four parts, returned as an array of values.

The first value represents the sign of the BigDecimal, and is -1 or 1, or 0 if the BigDecimal is Not a Number.

The second value is a string representing the significant digits of the BigDecimal, with no leading zeros.

The third value is the base used for arithmetic (currently always 10) as an Integer.

The fourth value is an Integer exponent.

If the BigDecimal can be represented as 0.xxxxxx*10**n, then xxxxxx is the string of significant digits with no leading zeros, and n is the exponent.

From these values, you can translate a BigDecimal to a float as follows:

``````sign, significant_digits, base, exponent = a.split
f = sign * "0.#{significant_digits}".to_f * (base ** exponent)``````

(Note that the to_f method is provided as a more convenient way to translate a BigDecimal to a Float.)

 ``` ``` ```# File 'ext/bigdecimal/bigdecimal.c' static VALUE BigDecimal_split(VALUE self) { ENTER(5); Real *vp; VALUE obj,str; ssize_t e, s; char *psz1; GUARD_OBJ(vp,GetVpValue(self,1)); str = rb_bstr_new_with_data(0, VpNumOfChars(vp,"E")); psz1 = (char *)rb_bstr_bytes(str); VpSzMantissa(vp,psz1); s = 1; if(psz1[0]=='-') { size_t len = strlen(psz1+1); memmove(psz1, psz1+1, len); psz1[len] = '\0'; s = -1; }```

### - (Object) sqrt

sqrt(n)

Returns the square root of the value.

If n is specified, returns at least that many significant digits.

 ``` ``` ```# File 'ext/bigdecimal/bigdecimal.c' static VALUE BigDecimal_sqrt(VALUE self, VALUE nFig) { ENTER(5); Real *c, *a; size_t mx, n; GUARD_OBJ(a,GetVpValue(self,1)); mx = a->Prec *(VpBaseFig() + 1); n = GetPositiveInt(nFig) + VpDblFig() + 1; if(mx <= n) mx = n; GUARD_OBJ(c,VpCreateRbObject(mx, "0")); VpSqrt(c, a); return ToValue(c); }```

### - (Object) to_f

Returns a new Float object having approximately the same value as the BigDecimal number. Normal accuracy limits and built-in errors of binary Float arithmetic apply.

 ``` ``` ```# File 'ext/bigdecimal/bigdecimal.c' static VALUE BigDecimal_to_f(VALUE self) { ENTER(1); Real *p; double d; SIGNED_VALUE e; char *buf; GUARD_OBJ(p, GetVpValue(self, 1)); if (VpVtoD(&d, &e, p) != 1) return rb_float_new(d); if (e > (SIGNED_VALUE)(DBL_MAX_10_EXP+BASE_FIG)) goto overflow; if (e < (SIGNED_VALUE)(DBL_MIN_10_EXP-BASE_FIG)) goto underflow; buf = xmalloc(VpNumOfChars(p,"E")); VpToString(p, buf, 0, 0); errno = 0; d = strtod(buf, 0); if (errno == ERANGE) goto overflow; return rb_float_new(d); overflow: VpException(VP_EXCEPTION_OVERFLOW, "BigDecimal to Float conversion", 0); if (d > 0.0) return rb_float_new(VpGetDoublePosInf()); else return rb_float_new(VpGetDoubleNegInf()); underflow: VpException(VP_EXCEPTION_UNDERFLOW, "BigDecimal to Float conversion", 0); if (d > 0.0) return rb_float_new(0.0); else return rb_float_new(-0.0); }```

### - (Object) to_i

Returns the value as an integer (Fixnum or Bignum).

If the BigNumber is infinity or NaN, raises FloatDomainError.

 ``` ``` ```# File 'ext/bigdecimal/bigdecimal.c' static VALUE BigDecimal_to_i(VALUE self) { ENTER(5); ssize_t e, nf; Real *p; GUARD_OBJ(p,GetVpValue(self,1)); BigDecimal_check_num(p); e = VpExponent10(p); if(e<=0) return INT2FIX(0); nf = VpBaseFig(); if(e<=nf) { return LONG2NUM((long)(VpGetSign(p)*(BDIGIT_DBL_SIGNED)p->frac[0])); }```

### - (Object) to_int

Returns the value as an integer (Fixnum or Bignum).

If the BigNumber is infinity or NaN, raises FloatDomainError.

 ``` ``` ```# File 'ext/bigdecimal/bigdecimal.c' static VALUE BigDecimal_to_i(VALUE self) { ENTER(5); ssize_t e, nf; Real *p; GUARD_OBJ(p,GetVpValue(self,1)); BigDecimal_check_num(p); e = VpExponent10(p); if(e<=0) return INT2FIX(0); nf = VpBaseFig(); if(e<=nf) { return LONG2NUM((long)(VpGetSign(p)*(BDIGIT_DBL_SIGNED)p->frac[0])); }```

### - (Object) to_r

Converts a BigDecimal to a Rational.

 ``` ``` ```# File 'ext/bigdecimal/bigdecimal.c' static VALUE BigDecimal_to_r(VALUE self) { Real *p; ssize_t sign, power, denomi_power; VALUE a, digits, numerator; p = GetVpValue(self,1); BigDecimal_check_num(p); sign = VpGetSign(p); power = VpExponent10(p); a = BigDecimal_split(self); digits = RARRAY_PTR(a)[1]; denomi_power = power - RSTRING_LEN(digits); numerator = rb_funcall(digits, rb_intern("to_i"), 0); if (sign < 0) { numerator = rb_funcall(numerator, '*', 1, INT2FIX(-1)); }```

### - (Object) to_s

to_s(s)

Converts the value to a string.

The default format looks like 0.xxxxEnn.

The optional parameter s consists of either an integer; or an optional '+' or ' ', followed by an optional number, followed by an optional 'E' or 'F'.

If there is a '+' at the start of s, positive values are returned with a leading '+'.

A space at the start of s returns positive values with a leading space.

If s contains a number, a space is inserted after each group of that many fractional digits.

If s ends with an 'E', engineering notation (0.xxxxEnn) is used.

If s ends with an 'F', conventional floating point notation is used.

Examples:

BigDecimal.new('-123.45678901234567890').to_s('5F') -> '-123.45678 90123 45678 9'

BigDecimal.new('123.45678901234567890').to_s('+8F') -> '+123.45678901 23456789'

BigDecimal.new('123.45678901234567890').to_s(' F') -> ' 123.4567890123456789'

 ``` ``` ```# File 'ext/bigdecimal/bigdecimal.c' static VALUE BigDecimal_to_s(int argc, VALUE *argv, VALUE self) { ENTER(5); int fmt=0; /* 0:E format */ int fPlus=0; /* =0:default,=1: set ' ' before digits ,set '+' before digits. */ Real *vp; volatile VALUE str; const char *psz; char ch; size_t nc, mc = 0; VALUE f; GUARD_OBJ(vp,GetVpValue(self,1)); if(rb_scan_args(argc,argv,"01",&f)==1) { if(TYPE(f)==T_STRING) { SafeStringValue(f); psz = RSTRING_PTR(f); if(*psz==' ') { fPlus = 1; psz++; }```

### - (Object) truncate

truncate(n)

Truncate to the nearest 1, returning the result as a BigDecimal.

BigDecimal('3.14159').truncate -> 3

BigDecimal('8.7').truncate -> 8

If n is specified and positive, the fractional part of the result has no more than that many digits.

If n is specified and negative, at least that many digits to the left of the decimal point will be 0 in the result.

BigDecimal('3.14159').truncate(3) -> 3.141

BigDecimal('13345.234').truncate(-2) -> 13300.0

 ``` ``` ```# File 'ext/bigdecimal/bigdecimal.c' static VALUE BigDecimal_truncate(int argc, VALUE *argv, VALUE self) { ENTER(5); Real *c, *a; int iLoc; VALUE vLoc; size_t mx, pl = VpSetPrecLimit(0); if(rb_scan_args(argc,argv,"01",&vLoc)==0) { iLoc = 0; }```

### - (Object) zero?

Returns True if the value is zero.

 ``` ``` ```# File 'ext/bigdecimal/bigdecimal.c' static VALUE BigDecimal_zero(VALUE self) { Real *a = GetVpValue(self,1); return VpIsZero(a) ? Qtrue : Qfalse; }```