# class BigDecimal

`BigDecimal` provides arbitrary-precision floating point decimal arithmetic.

## 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
10_000.times do
sum = sum + 0.0001
end
print sum #=> 0.9999999999999062
```

and contrast with the output from:

```require 'bigdecimal'

sum = BigDecimal("0")
10_000.times do
sum = sum + BigDecimal("0.0001")
end
print sum #=> 0.1E1
```

Similarly:

```(BigDecimal("1.2") - BigDecimal("1.0")) == BigDecimal("0.2") #=> true

(1.2 - 1.0) == 0.2 #=> false
```

## A Note About Precision¶ ↑

For a calculation using a BigDecimal and another `value`, the precision of the result depends on the type of `value`:

• If `value` is a Float, the precision is Float::DIG + 1.

• If `value` is a Rational, the precision is larger than Float::DIG + 1.

• If `value` is a BigDecimal, the precision is `value`‘s precision in the internal representation, which is platform-dependent.

• If `value` is other object, the precision is determined by the result of +BigDecimal(value)+.

## 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("1.0") / BigDecimal("0.0")  #=> Infinity
BigDecimal("-1.0") / BigDecimal("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("0.0") / BigDecimal("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('NaN')
n == 0.0 #=> false
n == n #=> false
```

### 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.

```BigDecimal("1.0") / BigDecimal("-Infinity") #=> -0.0
```

If the value is positive, a value of positive zero is returned.

```BigDecimal("1.0") / BigDecimal("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.

## bigdecimal/util¶ ↑

When you require `bigdecimal/util`, the `to_d` method will be available on `BigDecimal` and the native `Integer`, `Float`, `Rational`, and `String` classes:

```require 'bigdecimal/util'

42.to_d         # => 0.42e2
0.5.to_d        # => 0.5e0
(2/3r).to_d(3)  # => 0.667e0
"0.5".to_d      # => 0.5e0
```

`BigDecimal` is released under the Ruby and 2-clause BSD licenses. See LICENSE.txt for details.

Maintained by mrkn <mrkn@mrkn.jp> and ruby-core members.

Documented by zzak <zachary@zacharyscott.net>, mathew <meta@pobox.com>, and many other contributors.

### Constants

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.)

EXCEPTION_ALL

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

EXCEPTION_INFINITY

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

EXCEPTION_NaN

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

EXCEPTION_OVERFLOW

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

EXCEPTION_UNDERFLOW

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

EXCEPTION_ZERODIVIDE

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

INFINITY

Special value constants

NAN
ROUND_CEILING

Round towards +Infinity. See `BigDecimal.mode`.

ROUND_DOWN

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

ROUND_FLOOR

Round towards -Infinity. See `BigDecimal.mode`.

ROUND_HALF_DOWN

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

ROUND_HALF_EVEN

Round towards the even neighbor. See `BigDecimal.mode`.

ROUND_HALF_UP

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

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`.

ROUND_UP

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

SIGN_NEGATIVE_FINITE

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

SIGN_NEGATIVE_INFINITE

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

SIGN_NEGATIVE_ZERO

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

SIGN_NaN

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

SIGN_POSITIVE_FINITE

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

SIGN_POSITIVE_INFINITE

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

SIGN_POSITIVE_ZERO

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

VERSION

The version of bigdecimal library

### Public Class Methods

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

```static VALUE
{
ENTER(2);
Real *pv;
unsigned char *pch;
unsigned char ch;
unsigned long m=0;

pch = (unsigned char *)StringValueCStr(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");
}
m = m*10 + (unsigned long)(ch-'0');
}
if (m > VpBaseFig()) m -= VpBaseFig();
GUARD_OBJ(pv, VpNewRbClass(m, (char *)pch, self, true, true));
m /= VpBaseFig();
if (m && pv->MaxPrec > m) {
pv->MaxPrec = m+1;
}
return VpCheckGetValue(pv);
}```
double_fig() click to toggle source
```inline VALUE
BigDecimal_double_fig(VALUE self)
{
return INT2FIX(VpDblFig());
}```
interpret_loosely(p1) click to toggle source
```static VALUE
BigDecimal_s_interpret_loosely(VALUE klass, VALUE str)
{
char const *c_str = StringValueCStr(str);
Real *vp = VpNewRbClass(0, c_str, klass, false, true);
if (!vp)
return Qnil;
else
return VpCheckGetValue(vp);
}```
json_create(object) click to toggle source

Import a `JSON` Marshalled object.

method used for `JSON` marshalling support.

```# File ext/json/lib/json/add/bigdecimal.rb, line 14
def self.json_create(object)
end```
limit(digits) click to toggle source

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.

```static VALUE
BigDecimal_limit(int argc, VALUE *argv, VALUE self)
{
VALUE  nFig;
VALUE  nCur = SIZET2NUM(VpGetPrecLimit());

if (rb_scan_args(argc, argv, "01", &nFig) == 1) {
int nf;
if (NIL_P(nFig)) return nCur;
nf = NUM2INT(nFig);
if (nf < 0) {
rb_raise(rb_eArgError, "argument must be positive");
}
VpSetPrecLimit(nf);
}
return nCur;
}```
mode(mode, setting = nil) → integer click to toggle source

Returns an integer representing the mode settings for exception handling and rounding.

These modes control exception handling:

• BigDecimal::EXCEPTION_NaN.

• BigDecimal::EXCEPTION_INFINITY.

• BigDecimal::EXCEPTION_UNDERFLOW.

• BigDecimal::EXCEPTION_OVERFLOW.

• BigDecimal::EXCEPTION_ZERODIVIDE.

• BigDecimal::EXCEPTION_ALL.

Values for `setting` for exception handling:

• `true`: sets the given `mode` to `true`.

• `false`: sets the given `mode` to `false`.

• `nil`: does not modify the mode settings.

You can use method `BigDecimal.save_exception_mode` to temporarily change, and then automatically restore, exception modes.

For clarity, some examples below begin by setting all exception modes to `false`.

This mode controls the way rounding is to be performed:

• BigDecimal::ROUND_MODE

You can use method `BigDecimal.save_rounding_mode` to temporarily change, and then automatically restore, the rounding mode.

NaNs

Mode BigDecimal::EXCEPTION_NaN controls behavior when a BigDecimal NaN is created.

Settings:

Examples:

```BigDecimal.mode(BigDecimal::EXCEPTION_ALL, false) # => 0
BigDecimal('NaN')                                 # => NaN
BigDecimal.mode(BigDecimal::EXCEPTION_NaN, true)  # => 2
BigDecimal('NaN') # Raises FloatDomainError
```

Infinities

Mode BigDecimal::EXCEPTION_INFINITY controls behavior when a BigDecimal Infinity or -Infinity is created. Settings:

• `false` (default): Returns `BigDecimal('Infinity')` or `BigDecimal('-Infinity')`.

• `true`: Raises `FloatDomainError`.

Examples:

```BigDecimal.mode(BigDecimal::EXCEPTION_ALL, false)     # => 0
BigDecimal('Infinity')                                # => Infinity
BigDecimal('-Infinity')                               # => -Infinity
BigDecimal.mode(BigDecimal::EXCEPTION_INFINITY, true) # => 1
BigDecimal('Infinity')  # Raises FloatDomainError
BigDecimal('-Infinity') # Raises FloatDomainError
```

Underflow

Mode BigDecimal::EXCEPTION_UNDERFLOW controls behavior when a BigDecimal underflow occurs. Settings:

• `false` (default): Returns `BigDecimal('0')` or `BigDecimal('-Infinity')`.

• `true`: Raises `FloatDomainError`.

Examples:

```BigDecimal.mode(BigDecimal::EXCEPTION_ALL, false)      # => 0
def flow_under
x = BigDecimal('0.1')
100.times { x *= x }
end
flow_under                                             # => 100
BigDecimal.mode(BigDecimal::EXCEPTION_UNDERFLOW, true) # => 4
flow_under # Raises FloatDomainError
```

Overflow

Mode BigDecimal::EXCEPTION_OVERFLOW controls behavior when a BigDecimal overflow occurs. Settings:

• `false` (default): Returns `BigDecimal('Infinity')` or `BigDecimal('-Infinity')`.

• `true`: Raises `FloatDomainError`.

Examples:

```BigDecimal.mode(BigDecimal::EXCEPTION_ALL, false)     # => 0
def flow_over
x = BigDecimal('10')
100.times { x *= x }
end
flow_over                                             # => 100
BigDecimal.mode(BigDecimal::EXCEPTION_OVERFLOW, true) # => 1
flow_over # Raises FloatDomainError
```

Zero Division

Mode BigDecimal::EXCEPTION_ZERODIVIDE controls behavior when a zero-division occurs. Settings:

• `false` (default): Returns `BigDecimal('Infinity')` or `BigDecimal('-Infinity')`.

• `true`: Raises `FloatDomainError`.

Examples:

```BigDecimal.mode(BigDecimal::EXCEPTION_ALL, false)       # => 0
one = BigDecimal('1')
zero = BigDecimal('0')
one / zero                                              # => Infinity
BigDecimal.mode(BigDecimal::EXCEPTION_ZERODIVIDE, true) # => 16
one / zero # Raises FloatDomainError
```

All Exceptions

Mode BigDecimal::EXCEPTION_ALL controls all of the above:

```BigDecimal.mode(BigDecimal::EXCEPTION_ALL, false) # => 0
BigDecimal.mode(BigDecimal::EXCEPTION_ALL, true)  # => 23
```

Rounding

Mode BigDecimal::ROUND_MODE controls the way rounding is to be performed; its `setting` values are:

• `ROUND_UP`: Round away from zero. Aliased as `:up`.

• `ROUND_DOWN`: Round toward zero. Aliased as `:down` and `:truncate`.

• `ROUND_HALF_UP`: Round toward the nearest neighbor; if the neighbors are equidistant, round away from zero. Aliased as `:half_up` and `:default`.

• `ROUND_HALF_DOWN`: Round toward the nearest neighbor; if the neighbors are equidistant, round toward zero. Aliased as `:half_down`.

• `ROUND_HALF_EVEN` (Banker’s rounding): Round toward the nearest neighbor; if the neighbors are equidistant, round toward the even neighbor. Aliased as `:half_even` and `:banker`.

• `ROUND_CEILING`: Round toward positive infinity. Aliased as `:ceiling` and `:ceil`.

• `ROUND_FLOOR`: Round toward negative infinity. Aliased as `:floor:`.

```static VALUE
BigDecimal_mode(int argc, VALUE *argv, VALUE self)
{
VALUE which;
VALUE val;
unsigned long f,fo;

rb_scan_args(argc, argv, "11", &which, &val);
f = (unsigned long)NUM2INT(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_eArgError, "second argument must be true or false");
return Qnil; /* Not reached */
}
if (f & VP_EXCEPTION_INFINITY) {
VpSetException((unsigned short)((val == Qtrue) ? (fo | VP_EXCEPTION_INFINITY) :
(fo & (~VP_EXCEPTION_INFINITY))));
}
fo = VpGetException();
if (f & VP_EXCEPTION_NaN) {
VpSetException((unsigned short)((val == Qtrue) ? (fo | VP_EXCEPTION_NaN) :
(fo & (~VP_EXCEPTION_NaN))));
}
fo = VpGetException();
if (f & VP_EXCEPTION_UNDERFLOW) {
VpSetException((unsigned short)((val == Qtrue) ? (fo | VP_EXCEPTION_UNDERFLOW) :
(fo & (~VP_EXCEPTION_UNDERFLOW))));
}
fo = VpGetException();
if(f & VP_EXCEPTION_ZERODIVIDE) {
VpSetException((unsigned short)((val == Qtrue) ? (fo | VP_EXCEPTION_ZERODIVIDE) :
(fo & (~VP_EXCEPTION_ZERODIVIDE))));
}
fo = VpGetException();
return INT2FIX(fo);
}
if (VP_ROUND_MODE == f) {
/* Rounding mode setting */
unsigned short sw;
fo = VpGetRoundMode();
if (NIL_P(val)) return INT2FIX(fo);
sw = check_rounding_mode(val);
fo = VpSetRoundMode(sw);
return INT2FIX(fo);
}
rb_raise(rb_eTypeError, "first argument for BigDecimal.mode invalid");
return Qnil;
}```
save_exception_mode { ... } click to toggle source

Execute the provided block, but preserve the exception mode

```BigDecimal.save_exception_mode do
BigDecimal.mode(BigDecimal::EXCEPTION_OVERFLOW, false)
BigDecimal.mode(BigDecimal::EXCEPTION_NaN, false)

BigDecimal(BigDecimal('Infinity'))
BigDecimal(BigDecimal('-Infinity'))
BigDecimal(BigDecimal('NaN'))
end
```

For use with the BigDecimal::EXCEPTION_*

```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;
}```
save_limit { ... } click to toggle source

Execute the provided block, but preserve the precision limit

```BigDecimal.limit(100)
puts BigDecimal.limit
BigDecimal.save_limit do
BigDecimal.limit(200)
puts BigDecimal.limit
end
puts BigDecimal.limit
```
```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 ret;
}```
save_rounding_mode { ... } click to toggle source

Execute the provided block, but preserve the rounding mode

```BigDecimal.save_rounding_mode do
BigDecimal.mode(BigDecimal::ROUND_MODE, :up)
puts BigDecimal.mode(BigDecimal::ROUND_MODE)
end
```

For use with the BigDecimal::ROUND_*

```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 ret;
}```

### Public Instance Methods

a % b click to toggle source

Returns the modulus from dividing by b.

```static VALUE
BigDecimal_mod(VALUE self, VALUE r) ```
Also aliased as: modulo
*(p1) click to toggle source
```static VALUE
BigDecimal_mult(VALUE self, VALUE r)
{
ENTER(5);
Real *c, *a, *b;
size_t mx;

GUARD_OBJ(a, GetVpValue(self, 1));
if (RB_TYPE_P(r, T_FLOAT)) {
b = GetVpValueWithPrec(r, 0, 1);
}
else if (RB_TYPE_P(r, T_RATIONAL)) {
b = GetVpValueWithPrec(r, a->Prec*VpBaseFig(), 1);
}
else {
b = GetVpValue(r,0);
}

if (!b) return DoSomeOne(self, r, '*');
SAVE(b);

mx = a->Prec + b->Prec;
GUARD_OBJ(c, NewZeroWrapLimited(1, mx * (VpBaseFig() + 1)));
VpMult(c, a, b);
return VpCheckGetValue(c);
}```
self ** other → bigdecimal click to toggle source

Returns the BigDecimal value of `self` raised to power `other`:

```b = BigDecimal('3.14')
b ** 2              # => 0.98596e1
b ** 2.0            # => 0.98596e1
b ** Rational(2, 1) # => 0.98596e1
```

Related: `BigDecimal#power`.

```static VALUE
BigDecimal_power_op(VALUE self, VALUE exp)
{
return BigDecimal_power(1, &exp, self);
}```
self + value → bigdecimal click to toggle source

Returns the BigDecimal sum of `self` and `value`:

```b = BigDecimal('111111.111') # => 0.111111111e6
b + 2                        # => 0.111113111e6
b + 2.0                      # => 0.111113111e6
b + Rational(2, 1)           # => 0.111113111e6
b + Complex(2, 0)            # => (0.111113111e6+0i)
```

```static VALUE
{
ENTER(5);
Real *c, *a, *b;
size_t mx;

GUARD_OBJ(a, GetVpValue(self, 1));
if (RB_TYPE_P(r, T_FLOAT)) {
b = GetVpValueWithPrec(r, 0, 1);
}
else if (RB_TYPE_P(r, T_RATIONAL)) {
b = GetVpValueWithPrec(r, a->Prec*VpBaseFig(), 1);
}
else {
b = GetVpValue(r, 0);
}

if (!b) return DoSomeOne(self,r,'+');
SAVE(b);

if (VpIsNaN(b)) return b->obj;
if (VpIsNaN(a)) return a->obj;

if (mx == (size_t)-1L) {
GUARD_OBJ(c, NewZeroWrapLimited(1, VpBaseFig() + 1));
}
else {
GUARD_OBJ(c, NewZeroWrapLimited(1, mx * (VpBaseFig() + 1)));
if (!mx) {
VpSetInf(c, VpGetSign(a));
}
else {
}
}
return VpCheckGetValue(c);
}```
+big_decimal → self click to toggle source

Returns `self`:

```+BigDecimal(5)  # => 0.5e1
+BigDecimal(-5) # => -0.5e1
```
```static VALUE
BigDecimal_uplus(VALUE self)
{
return self;
}```
self - value → bigdecimal click to toggle source

Returns the BigDecimal difference of `self` and `value`:

```b = BigDecimal('333333.333') # => 0.333333333e6
b - 2                        # => 0.333331333e6
b - 2.0                      # => 0.333331333e6
b - Rational(2, 1)           # => 0.333331333e6
b - Complex(2, 0)            # => (0.333331333e6+0i)
```

```static VALUE
BigDecimal_sub(VALUE self, VALUE r)
{
ENTER(5);
Real *c, *a, *b;
size_t mx;

GUARD_OBJ(a, GetVpValue(self,1));
if (RB_TYPE_P(r, T_FLOAT)) {
b = GetVpValueWithPrec(r, 0, 1);
}
else if (RB_TYPE_P(r, T_RATIONAL)) {
b = GetVpValueWithPrec(r, a->Prec*VpBaseFig(), 1);
}
else {
b = GetVpValue(r,0);
}

if (!b) return DoSomeOne(self,r,'-');
SAVE(b);

if (VpIsNaN(b)) return b->obj;
if (VpIsNaN(a)) return a->obj;

if (mx == (size_t)-1L) {
GUARD_OBJ(c, NewZeroWrapLimited(1, VpBaseFig() + 1));
}
else {
GUARD_OBJ(c, NewZeroWrapLimited(1, mx *(VpBaseFig() + 1)));
if (!mx) {
VpSetInf(c,VpGetSign(a));
}
else {
}
}
return VpCheckGetValue(c);
}```
-self → bigdecimal click to toggle source

Returns the BigDecimal negation of self:

```b0 = BigDecimal('1.5')
b1 = -b0 # => -0.15e1
b2 = -b1 # => 0.15e1
```
```static VALUE
BigDecimal_neg(VALUE self)
{
ENTER(5);
Real *c, *a;
GUARD_OBJ(a, GetVpValue(self, 1));
GUARD_OBJ(c, NewZeroWrapLimited(1, a->Prec *(VpBaseFig() + 1)));
VpAsgn(c, a, -1);
return VpCheckGetValue(c);
}```
a / b → bigdecimal click to toggle source

Divide by the specified value.

The result precision will be the precision of the larger operand, but its minimum is 2*Float::DIG.

```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(self, r, &c, &res, &div);
if (!NIL_P(r)) 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], (DECDIG)(VpBaseVal() * (DECDIG_DBL)res->frac[0] / div->frac[0]));
}
return VpCheckGetValue(c);
}```
self < other → true or false click to toggle source

Returns `true` if `self` is less than `other`, `false` otherwise:

```b = BigDecimal('1.5') # => 0.15e1
b < 2                 # => true
b < 2.0               # => true
b < Rational(2, 1)    # => true
b < 1.5               # => false
```

Raises an exception if the comparison cannot be made.

```static VALUE
BigDecimal_lt(VALUE self, VALUE r)
{
return BigDecimalCmp(self, r, '<');
}```
self <= other → true or false click to toggle source

Returns `true` if `self` is less or equal to than `other`, `false` otherwise:

```b = BigDecimal('1.5') # => 0.15e1
b <= 2                # => true
b <= 2.0              # => true
b <= Rational(2, 1)   # => true
b <= 1.5              # => true
b < 1                 # => false
```

Raises an exception if the comparison cannot be made.

```static VALUE
BigDecimal_le(VALUE self, VALUE r)
{
return BigDecimalCmp(self, r, 'L');
}```
<=>(p1) click to toggle source

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

```static VALUE
BigDecimal_comp(VALUE self, VALUE r)
{
return BigDecimalCmp(self, r, '*');
}```
==(p1) click to toggle source

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('1.0') == 1.0  #=> true
```
```static VALUE
BigDecimal_eq(VALUE self, VALUE r)
{
return BigDecimalCmp(self, r, '=');
}```
Also aliased as: ===, eql?
===(p1)

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('1.0') == 1.0  #=> true
```
Alias for: ==
self > other → true or false click to toggle source

Returns `true` if `self` is greater than `other`, `false` otherwise:

```b = BigDecimal('1.5')
b > 1              # => true
b > 1.0            # => true
b > Rational(1, 1) # => true
b > 2              # => false
```

Raises an exception if the comparison cannot be made.

```static VALUE
BigDecimal_gt(VALUE self, VALUE r)
{
return BigDecimalCmp(self, r, '>');
}```
self >= other → true or false click to toggle source

Returns `true` if `self` is greater than or equal to `other`, `false` otherwise:

```b = BigDecimal('1.5')
b >= 1              # => true
b >= 1.0            # => true
b >= Rational(1, 1) # => true
b >= 1.5            # => true
b > 2               # => false
```

Raises an exception if the comparison cannot be made.

```static VALUE
BigDecimal_ge(VALUE self, VALUE r)
{
return BigDecimalCmp(self, r, 'G');
}```
_dump → string click to toggle source

Returns a string representing the marshalling of `self`. See module `Marshal`.

```inf = BigDecimal('Infinity') # => Infinity
dumped = inf._dump           # => "9:Infinity"
```
```static VALUE
BigDecimal_dump(int argc, VALUE *argv, VALUE self)
{
ENTER(5);
Real *vp;
char *psz;
VALUE dummy;
volatile VALUE dump;
size_t len;

rb_scan_args(argc, argv, "01", &dummy);
GUARD_OBJ(vp,GetVpValue(self, 1));
dump = rb_str_new(0, VpNumOfChars(vp, "E")+50);
psz = RSTRING_PTR(dump);
snprintf(psz, RSTRING_LEN(dump), "%"PRIuSIZE":", VpMaxPrec(vp)*VpBaseFig());
len = strlen(psz);
VpToString(vp, psz+len, RSTRING_LEN(dump)-len, 0, 0);
rb_str_resize(dump, strlen(psz));
return dump;
}```
abs → bigdecimal click to toggle source

Returns the BigDecimal absolute value of `self`:

```BigDecimal('5').abs  # => 0.5e1
BigDecimal('-3').abs # => 0.3e1
```
```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, NewZeroWrapLimited(1, mx));
VpAsgn(c, a, 1);
VpChangeSign(c, 1);
return VpCheckGetValue(c);
}```
add(value, ndigits) → new_bigdecimal click to toggle source

Returns the BigDecimal sum of `self` and `value` with a precision of `ndigits` decimal digits.

When `ndigits` is less than the number of significant digits in the sum, the sum is rounded to that number of digits, according to the current rounding mode; see `BigDecimal.mode`.

Examples:

```# Set the rounding mode.
BigDecimal.mode(BigDecimal::ROUND_MODE, :half_up)
b = BigDecimal('111111.111')
b.add(Rational(1, 1), 15) # => 0.111112111e6
```
```static VALUE
BigDecimal_add2(VALUE self, VALUE b, VALUE n)
{
ENTER(2);
Real *cv;
SIGNED_VALUE mx = check_int_precision(n);
if (mx == 0) return BigDecimal_add(self, b);
else {
size_t pl = VpSetPrecLimit(0);
VpSetPrecLimit(pl);
GUARD_OBJ(cv, GetVpValue(c, 1));
VpLeftRound(cv, VpGetRoundMode(), mx);
return VpCheckGetValue(cv);
}
}```
as_json(*) click to toggle source

`Marshal` the object to `JSON`.

method used for `JSON` marshalling support.

```# File ext/json/lib/json/add/bigdecimal.rb, line 21
def as_json(*)
{
JSON.create_id => self.class.name,
'b'            => _dump,
}
end```
ceil(n) click to toggle source

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
```
```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;
} else {
iLoc = NUM2INT(vLoc);
}

GUARD_OBJ(a, GetVpValue(self, 1));
mx = a->Prec * (VpBaseFig() + 1);
GUARD_OBJ(c, NewZeroWrapLimited(1, mx));
VpSetPrecLimit(pl);
VpActiveRound(c, a, VP_ROUND_CEIL, iLoc);
if (argc == 0) {
return BigDecimal_to_i(VpCheckGetValue(c));
}
return VpCheckGetValue(c);
}```
clone() click to toggle source
```static VALUE
BigDecimal_clone(VALUE self)
{
return self;
}```
Also aliased as: dup
coerce(p1) click to toggle source

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("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.

```static VALUE
BigDecimal_coerce(VALUE self, VALUE other)
{
ENTER(2);
VALUE obj;
Real *b;

if (RB_TYPE_P(other, T_FLOAT)) {
GUARD_OBJ(b, GetVpValueWithPrec(other, 0, 1));
obj = rb_assoc_new(VpCheckGetValue(b), self);
}
else {
if (RB_TYPE_P(other, T_RATIONAL)) {
Real* pv = DATA_PTR(self);
GUARD_OBJ(b, GetVpValueWithPrec(other, pv->Prec*VpBaseFig(), 1));
}
else {
GUARD_OBJ(b, GetVpValue(other, 1));
}
obj = rb_assoc_new(b->obj, self);
}

return obj;
}```
div(value) → integer click to toggle source
div(value, digits) → bigdecimal or integer

Divide by the specified value.

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 for the / operator or `quo`.

If digits is not specified, the result is an integer, by analogy with `Float#div`; see also `BigDecimal#divmod`.

Examples:

```a = BigDecimal("4")
b = BigDecimal("3")

a.div(b, 3)  # => 0.133e1

a.div(b, 0)  # => 0.1333333333333333333e1
a / b        # => 0.1333333333333333333e1
a.quo(b)     # => 0.1333333333333333333e1

a.div(b)     # => 1
```
```static VALUE
BigDecimal_div3(int argc, VALUE *argv, VALUE self)
{
VALUE b,n;

rb_scan_args(argc, argv, "11", &b, &n);

return BigDecimal_div2(self, b, n);
}```
divmod(value) click to toggle source

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("42")
b = BigDecimal("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.

```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(VpCheckGetValue(div), VpCheckGetValue(mod));
}
return DoSomeOne(self,r,rb_intern("divmod"));
}```
dup()
Alias for: clone
eql?(p1)

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('1.0') == 1.0  #=> true
```
Alias for: ==
exponent() click to toggle source

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.

```static VALUE
BigDecimal_exponent(VALUE self)
{
ssize_t e = VpExponent10(GetVpValue(self, 1));
return SSIZET2NUM(e);
}```
finite?() click to toggle source

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

```static VALUE
BigDecimal_IsFinite(VALUE self)
{
Real *p = GetVpValue(self, 1);
if (VpIsNaN(p)) return Qfalse;
if (VpIsInf(p)) return Qfalse;
return Qtrue;
}```
fix() click to toggle source

Return the integer part of the number, as a `BigDecimal`.

```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, NewZeroWrapLimited(1, mx));
VpActiveRound(c, a, VP_ROUND_DOWN, 0); /* 0: round off */
return VpCheckGetValue(c);
}```
floor(n) click to toggle source

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
```
```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;
}
else {
iLoc = NUM2INT(vLoc);
}

GUARD_OBJ(a, GetVpValue(self, 1));
mx = a->Prec * (VpBaseFig() + 1);
GUARD_OBJ(c, NewZeroWrapLimited(1, mx));
VpSetPrecLimit(pl);
VpActiveRound(c, a, VP_ROUND_FLOOR, iLoc);
#ifdef BIGDECIMAL_DEBUG
VPrint(stderr, "floor: c=%\n", c);
#endif
if (argc == 0) {
return BigDecimal_to_i(VpCheckGetValue(c));
}
return VpCheckGetValue(c);
}```
frac() click to toggle source

Return the fractional part of the number, as a `BigDecimal`.

```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, NewZeroWrapLimited(1, mx));
VpFrac(c, a);
return VpCheckGetValue(c);
}```
hash → integer click to toggle source

Returns the integer hash value for `self`.

Two instances of BigDecimal have the same hash value if and only if they have equal:

• Sign.

• Fractional part.

• Exponent.

```static VALUE
BigDecimal_hash(VALUE self)
{
ENTER(1);
Real *p;
st_index_t hash;

GUARD_OBJ(p, GetVpValue(self, 1));
hash = (st_index_t)p->sign;
/* hash!=2: the case for 0(1),NaN(0) or +-Infinity(3) is sign itself */
if(hash == 2 || hash == (st_index_t)-2) {
hash ^= rb_memhash(p->frac, sizeof(DECDIG)*p->Prec);
hash += p->exponent;
}
return ST2FIX(hash);
}```
infinite?() click to toggle source

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

```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;
}```
inspect() click to toggle source

Returns a string representation of self.

```BigDecimal("1234.5678").inspect
#=> "0.12345678e4"
```
```static VALUE
BigDecimal_inspect(VALUE self)
{
ENTER(5);
Real *vp;
volatile VALUE str;
size_t nc;

GUARD_OBJ(vp, GetVpValue(self, 1));
nc = VpNumOfChars(vp, "E");

str = rb_str_new(0, nc);
VpToString(vp, RSTRING_PTR(str), RSTRING_LEN(str), 0, 0);
rb_str_resize(str, strlen(RSTRING_PTR(str)));
return str;
}```
modulo(b)

Returns the modulus from dividing by b.

Alias for: %
mult(other, ndigits) → bigdecimal click to toggle source

Returns the BigDecimal product of `self` and `value` with a precision of `ndigits` decimal digits.

When `ndigits` is less than the number of significant digits in the sum, the sum is rounded to that number of digits, according to the current rounding mode; see `BigDecimal.mode`.

Examples:

```# Set the rounding mode.
BigDecimal.mode(BigDecimal::ROUND_MODE, :half_up)
b = BigDecimal('555555.555')
b.mult(3, 0)              # => 0.1666666665e7
b.mult(3, 3)              # => 0.167e7
b.mult(3, 6)              # => 0.166667e7
b.mult(3, 15)             # => 0.1666666665e7
b.mult(3.0, 0)            # => 0.1666666665e7
b.mult(Rational(3, 1), 0) # => 0.1666666665e7
b.mult(Complex(3, 0), 0)  # => (0.1666666665e7+0.0i)
```
```static VALUE
BigDecimal_mult2(VALUE self, VALUE b, VALUE n)
{
ENTER(2);
Real *cv;
SIGNED_VALUE mx = check_int_precision(n);
if (mx == 0) return BigDecimal_mult(self, b);
else {
size_t pl = VpSetPrecLimit(0);
VALUE   c = BigDecimal_mult(self, b);
VpSetPrecLimit(pl);
GUARD_OBJ(cv, GetVpValue(c, 1));
VpLeftRound(cv, VpGetRoundMode(), mx);
return VpCheckGetValue(cv);
}
}```
n_significant_digits → integer click to toggle source

Returns the number of decimal significant digits in `self`.

```BigDecimal("0").n_significant_digits         # => 0
BigDecimal("1").n_significant_digits         # => 1
BigDecimal("1.1").n_significant_digits       # => 2
BigDecimal("3.1415").n_significant_digits    # => 5
BigDecimal("-1e20").n_significant_digits     # => 1
BigDecimal("1e-20").n_significant_digits     # => 1
BigDecimal("Infinity").n_significant_digits  # => 0
BigDecimal("-Infinity").n_significant_digits # => 0
BigDecimal("NaN").n_significant_digits       # => 0
```
```static VALUE
BigDecimal_n_significant_digits(VALUE self)
{
ENTER(1);

Real *p;
GUARD_OBJ(p, GetVpValue(self, 1));
if (VpIsZero(p) || !VpIsDef(p)) {
return INT2FIX(0);
}

ssize_t n = p->Prec;  /* The length of frac without trailing zeros. */
for (n = p->Prec; n > 0 && p->frac[n-1] == 0; --n);
if (n == 0) return INT2FIX(0);

DECDIG x;
int nlz = BASE_FIG;
for (x = p->frac[0]; x > 0; x /= 10) --nlz;

int ntz = 0;
for (x = p->frac[n-1]; x > 0 && x % 10 == 0; x /= 10) ++ntz;

ssize_t n_significant_digits = BASE_FIG*n - nlz - ntz;
return SSIZET2NUM(n_significant_digits);
}```
nan?() click to toggle source

Returns True if the value is Not a Number.

```static VALUE
BigDecimal_IsNaN(VALUE self)
{
Real *p = GetVpValue(self, 1);
if (VpIsNaN(p))  return Qtrue;
return Qfalse;
}```
nonzero?() click to toggle source

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

```static VALUE
BigDecimal_nonzero(VALUE self)
{
Real *a = GetVpValue(self, 1);
return VpIsZero(a) ? Qnil : self;
}```
power(n) click to toggle source
power(n, prec)

Returns the value raised to the power of n.

Note that n must be an `Integer`.

Also available as the operator **.

```static VALUE
BigDecimal_power(int argc, VALUE*argv, VALUE self)
{
ENTER(5);
VALUE vexp, prec;
Real* exp = NULL;
Real *x, *y;
ssize_t mp, ma, n;
SIGNED_VALUE int_exp;
double d;

rb_scan_args(argc, argv, "11", &vexp, &prec);

GUARD_OBJ(x, GetVpValue(self, 1));
n = NIL_P(prec) ? (ssize_t)(x->Prec*VpBaseFig()) : NUM2SSIZET(prec);

if (VpIsNaN(x)) {
y = NewZeroWrapLimited(1, n);
VpSetNaN(y);
RB_GC_GUARD(y->obj);
return VpCheckGetValue(y);
}

retry:
switch (TYPE(vexp)) {
case T_FIXNUM:
break;

case T_BIGNUM:
break;

case T_FLOAT:
d = RFLOAT_VALUE(vexp);
if (d == round(d)) {
if (FIXABLE(d)) {
vexp = LONG2FIX((long)d);
}
else {
vexp = rb_dbl2big(d);
}
goto retry;
}
if (NIL_P(prec)) {
n += BIGDECIMAL_DOUBLE_FIGURES;
}
exp = GetVpValueWithPrec(vexp, 0, 1);
break;

case T_RATIONAL:
if (is_zero(rb_rational_num(vexp))) {
if (is_positive(vexp)) {
vexp = INT2FIX(0);
goto retry;
}
}
else if (is_one(rb_rational_den(vexp))) {
vexp = rb_rational_num(vexp);
goto retry;
}
exp = GetVpValueWithPrec(vexp, n, 1);
if (NIL_P(prec)) {
n += n;
}
break;

case T_DATA:
if (is_kind_of_BigDecimal(vexp)) {
VALUE zero = INT2FIX(0);
VALUE rounded = BigDecimal_round(1, &zero, vexp);
if (RTEST(BigDecimal_eq(vexp, rounded))) {
vexp = BigDecimal_to_i(vexp);
goto retry;
}
if (NIL_P(prec)) {
GUARD_OBJ(y, GetVpValue(vexp, 1));
n += y->Prec*VpBaseFig();
}
exp = DATA_PTR(vexp);
break;
}
/* fall through */
default:
rb_raise(rb_eTypeError,
"wrong argument type %"PRIsVALUE" (expected scalar Numeric)",
RB_OBJ_CLASSNAME(vexp));
}

if (VpIsZero(x)) {
if (is_negative(vexp)) {
y = NewZeroWrapNolimit(1, n);
if (BIGDECIMAL_NEGATIVE_P(x)) {
if (is_integer(vexp)) {
if (is_even(vexp)) {
/* (-0) ** (-even_integer)  -> Infinity */
VpSetPosInf(y);
}
else {
/* (-0) ** (-odd_integer)  -> -Infinity */
VpSetNegInf(y);
}
}
else {
/* (-0) ** (-non_integer)  -> Infinity */
VpSetPosInf(y);
}
}
else {
/* (+0) ** (-num)  -> Infinity */
VpSetPosInf(y);
}
RB_GC_GUARD(y->obj);
return VpCheckGetValue(y);
}
else if (is_zero(vexp)) {
return VpCheckGetValue(NewOneWrapLimited(1, n));
}
else {
return VpCheckGetValue(NewZeroWrapLimited(1, n));
}
}

if (is_zero(vexp)) {
return VpCheckGetValue(NewOneWrapLimited(1, n));
}
else if (is_one(vexp)) {
return self;
}

if (VpIsInf(x)) {
if (is_negative(vexp)) {
if (BIGDECIMAL_NEGATIVE_P(x)) {
if (is_integer(vexp)) {
if (is_even(vexp)) {
/* (-Infinity) ** (-even_integer) -> +0 */
return VpCheckGetValue(NewZeroWrapLimited(1, n));
}
else {
/* (-Infinity) ** (-odd_integer) -> -0 */
return VpCheckGetValue(NewZeroWrapLimited(-1, n));
}
}
else {
/* (-Infinity) ** (-non_integer) -> -0 */
return VpCheckGetValue(NewZeroWrapLimited(-1, n));
}
}
else {
return VpCheckGetValue(NewZeroWrapLimited(1, n));
}
}
else {
y = NewZeroWrapLimited(1, n);
if (BIGDECIMAL_NEGATIVE_P(x)) {
if (is_integer(vexp)) {
if (is_even(vexp)) {
VpSetPosInf(y);
}
else {
VpSetNegInf(y);
}
}
else {
/* TODO: support complex */
rb_raise(rb_eMathDomainError,
"a non-integral exponent for a negative base");
}
}
else {
VpSetPosInf(y);
}
return VpCheckGetValue(y);
}
}

if (exp != NULL) {
return bigdecimal_power_by_bigdecimal(x, exp, n);
}
else if (RB_TYPE_P(vexp, T_BIGNUM)) {
VALUE abs_value = BigDecimal_abs(self);
if (is_one(abs_value)) {
return VpCheckGetValue(NewOneWrapLimited(1, n));
}
else if (RTEST(rb_funcall(abs_value, '<', 1, INT2FIX(1)))) {
if (is_negative(vexp)) {
y = NewZeroWrapLimited(1, n);
VpSetInf(y, (is_even(vexp) ? 1 : -1) * VpGetSign(x));
return VpCheckGetValue(y);
}
else if (BIGDECIMAL_NEGATIVE_P(x) && is_even(vexp)) {
return VpCheckGetValue(NewZeroWrapLimited(-1, n));
}
else {
return VpCheckGetValue(NewZeroWrapLimited(1, n));
}
}
else {
if (is_positive(vexp)) {
y = NewZeroWrapLimited(1, n);
VpSetInf(y, (is_even(vexp) ? 1 : -1) * VpGetSign(x));
return VpCheckGetValue(y);
}
else if (BIGDECIMAL_NEGATIVE_P(x) && is_even(vexp)) {
return VpCheckGetValue(NewZeroWrapLimited(-1, n));
}
else {
return VpCheckGetValue(NewZeroWrapLimited(1, n));
}
}
}

int_exp = FIX2LONG(vexp);
ma = int_exp;
if (ma <  0) ma = -ma;
if (ma == 0) ma = 1;

if (VpIsDef(x)) {
mp = x->Prec * (VpBaseFig() + 1);
GUARD_OBJ(y, NewZeroWrapLimited(1, mp * (ma + 1)));
}
else {
GUARD_OBJ(y, NewZeroWrapLimited(1, 1));
}
VpPowerByInt(y, x, int_exp);
if (!NIL_P(prec) && VpIsDef(y)) {
VpMidRound(y, VpGetRoundMode(), n);
}
return VpCheckGetValue(y);
}```
precision → integer click to toggle source

Returns the number of decimal digits in `self`:

```BigDecimal("0").precision         # => 0
BigDecimal("1").precision         # => 1
BigDecimal("1.1").precision       # => 2
BigDecimal("3.1415").precision    # => 5
BigDecimal("-1e20").precision     # => 21
BigDecimal("1e-20").precision     # => 20
BigDecimal("Infinity").precision  # => 0
BigDecimal("-Infinity").precision # => 0
BigDecimal("NaN").precision       # => 0
```
```static VALUE
BigDecimal_precision(VALUE self)
{
ssize_t precision;
BigDecimal_count_precision_and_scale(self, &precision, NULL);
return SSIZET2NUM(precision);
}```
precision_scale → [integer, integer] click to toggle source

Returns a 2-length array; the first item is the result of `BigDecimal#precision` and the second one is of `BigDecimal#scale`.

```static VALUE
BigDecimal_precision_scale(VALUE self)
{
ssize_t precision, scale;
BigDecimal_count_precision_and_scale(self, &precision, &scale);
return rb_assoc_new(SSIZET2NUM(precision), SSIZET2NUM(scale));
}```
precs → array click to toggle source

Returns an `Array` of two `Integer` values that represent platform-dependent internal storage properties.

This method is deprecated and will be removed in the future. Instead, use `BigDecimal#n_significant_digits` for obtaining the number of significant digits in scientific notation, and `BigDecimal#precision` for obtaining the number of digits in decimal notation.

```static VALUE
BigDecimal_prec(VALUE self)
{
ENTER(1);
Real *p;
VALUE obj;

rb_category_warn(RB_WARN_CATEGORY_DEPRECATED,
"BigDecimal#precs is deprecated and will be removed in the future; "

GUARD_OBJ(p, GetVpValue(self, 1));
obj = rb_assoc_new(SIZET2NUM(p->Prec*VpBaseFig()),
SIZET2NUM(p->MaxPrec*VpBaseFig()));
return obj;
}```
quo(value) → bigdecimal click to toggle source
quo(value, digits) → bigdecimal

Divide by the specified value.

digits

If specified and less than the number of significant digits of the result, the result is rounded to the given number of digits, according to the rounding mode indicated by `BigDecimal.mode`.

If digits is 0 or omitted, the result is the same as for the / operator.

```static VALUE
BigDecimal_quo(int argc, VALUE *argv, VALUE self)
{
VALUE value, digits, result;
SIGNED_VALUE n = -1;

argc = rb_scan_args(argc, argv, "11", &value, &digits);
if (argc > 1) {
n = check_int_precision(digits);
}

if (n > 0) {
result = BigDecimal_div2(self, value, digits);
}
else {
result = BigDecimal_div(self, value);
}

return result;
}```
remainder(value) click to toggle source

Returns the remainder from dividing by the value.

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

```static VALUE
BigDecimal_remainder(VALUE self, VALUE r) /* remainder */
{
VALUE  f;
Real  *d, *rv = 0;
f = BigDecimal_divremain(self, r, &d, &rv);
if (!NIL_P(f)) return f;
return VpCheckGetValue(rv);
}```
round(n, mode) click to toggle source

Round to the nearest integer (by default), returning the result as a `BigDecimal` if n is specified, or as an `Integer` if it isn’t.

```BigDecimal('3.14159').round #=> 3
BigDecimal('8.7').round #=> 9
BigDecimal('-9.9').round #=> -10

BigDecimal('3.14159').round(2).class.name #=> "BigDecimal"
BigDecimal('3.14159').round.class.name #=> "Integer"
```

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, and return value will be an `Integer`.

```BigDecimal('3.14159').round(3) #=> 3.142
BigDecimal('13345.234').round(-2) #=> 13300
```

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

```static VALUE
BigDecimal_round(int argc, VALUE *argv, VALUE self)
{
ENTER(5);
Real   *c, *a;
int    iLoc = 0;
VALUE  vLoc;
VALUE  vRound;
int    round_to_int = 0;
size_t mx, pl;

unsigned short sw = VpGetRoundMode();

switch (rb_scan_args(argc, argv, "02", &vLoc, &vRound)) {
case 0:
iLoc = 0;
round_to_int = 1;
break;
case 1:
if (RB_TYPE_P(vLoc, T_HASH)) {
sw = check_rounding_mode_option(vLoc);
}
else {
iLoc = NUM2INT(vLoc);
if (iLoc < 1) round_to_int = 1;
}
break;
case 2:
iLoc = NUM2INT(vLoc);
if (RB_TYPE_P(vRound, T_HASH)) {
sw = check_rounding_mode_option(vRound);
}
else {
sw = check_rounding_mode(vRound);
}
break;
default:
break;
}

pl = VpSetPrecLimit(0);
GUARD_OBJ(a, GetVpValue(self, 1));
mx = a->Prec * (VpBaseFig() + 1);
GUARD_OBJ(c, NewZeroWrapLimited(1, mx));
VpSetPrecLimit(pl);
VpActiveRound(c, a, sw, iLoc);
if (round_to_int) {
return BigDecimal_to_i(VpCheckGetValue(c));
}
return VpCheckGetValue(c);
}```
scale → integer click to toggle source

Returns the number of decimal digits following the decimal digits in `self`.

```BigDecimal("0").scale         # => 0
BigDecimal("1").scale         # => 1
BigDecimal("1.1").scale       # => 1
BigDecimal("3.1415").scale    # => 4
BigDecimal("-1e20").precision # => 0
BigDecimal("1e-20").precision # => 20
BigDecimal("Infinity").scale  # => 0
BigDecimal("-Infinity").scale # => 0
BigDecimal("NaN").scale       # => 0
```
```static VALUE
BigDecimal_scale(VALUE self)
{
ssize_t scale;
BigDecimal_count_precision_and_scale(self, NULL, &scale);
return SSIZET2NUM(scale);
}```
sign() click to toggle source

Returns the sign of the value.

Returns a positive value if > 0, a negative value if < 0. It behaves the same with zeros - it returns a positive value for a positive zero (BigDecimal(‘0’)) and a negative value for a negative zero (BigDecimal(‘-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

```static VALUE
BigDecimal_sign(VALUE self)
{ /* sign */
int s = GetVpValue(self, 1)->sign;
return INT2FIX(s);
}```
split() click to toggle source

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`.)

```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_str_new(0, VpNumOfChars(vp, "E"));
psz1 = RSTRING_PTR(str);
VpSzMantissa(vp, psz1, RSTRING_LEN(str));
s = 1;
if(psz1[0] == '-') {
size_t len = strlen(psz1 + 1);

memmove(psz1, psz1 + 1, len);
psz1[len] = '\0';
s = -1;
}
if (psz1[0] == 'N') s = 0; /* NaN */
e = VpExponent10(vp);
obj = rb_ary_new2(4);
rb_ary_push(obj, INT2FIX(s));
rb_ary_push(obj, str);
rb_str_resize(str, strlen(psz1));
rb_ary_push(obj, INT2FIX(10));
rb_ary_push(obj, SSIZET2NUM(e));
return obj;
}```
sqrt(n) click to toggle source

Returns the square root of the value.

Result has at least n significant digits.

```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 = check_int_precision(nFig);
n += VpDblFig() + VpBaseFig();
if (mx <= n) mx = n;
GUARD_OBJ(c, NewZeroWrapLimited(1, mx));
VpSqrt(c, a);
return VpCheckGetValue(c);
}```
sub(value, digits) → bigdecimal click to toggle source

Subtract the specified value.

e.g.

```c = a.sub(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`.

```static VALUE
BigDecimal_sub2(VALUE self, VALUE b, VALUE n)
{
ENTER(2);
Real *cv;
SIGNED_VALUE mx = check_int_precision(n);
if (mx == 0) return BigDecimal_sub(self, b);
else {
size_t pl = VpSetPrecLimit(0);
VALUE   c = BigDecimal_sub(self, b);
VpSetPrecLimit(pl);
GUARD_OBJ(cv, GetVpValue(c, 1));
VpLeftRound(cv, VpGetRoundMode(), mx);
return VpCheckGetValue(cv);
}
}```
to_d → bigdecimal click to toggle source

Returns self.

```require 'bigdecimal/util'

d = BigDecimal("3.14")
d.to_d                       # => 0.314e1
```
```# File ext/bigdecimal/lib/bigdecimal/util.rb, line 110
def to_d
self
end```
to_digits → string click to toggle source

Converts a `BigDecimal` to a `String` of the form “nnnnnn.mmm”. This method is deprecated; use `BigDecimal#to_s`(“F”) instead.

```require 'bigdecimal/util'

d = BigDecimal("3.14")
d.to_digits                  # => "3.14"
```
```# File ext/bigdecimal/lib/bigdecimal/util.rb, line 90
def to_digits
if self.nan? || self.infinite? || self.zero?
self.to_s
else
i       = self.to_i.to_s
_,f,_,z = self.frac.split
i + "." + ("0"*(-z)) + f
end
end```
to_f() click to toggle source

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.

```static VALUE
BigDecimal_to_f(VALUE self)
{
ENTER(1);
Real *p;
double d;
SIGNED_VALUE e;
char *buf;
volatile VALUE str;

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;

str = rb_str_new(0, VpNumOfChars(p, "E"));
buf = RSTRING_PTR(str);
VpToString(p, buf, RSTRING_LEN(str), 0, 0);
errno = 0;
d = strtod(buf, 0);
if (errno == ERANGE) {
if (d == 0.0) goto underflow;
if (fabs(d) >= HUGE_VAL) goto overflow;
}
return rb_float_new(d);

overflow:
VpException(VP_EXCEPTION_OVERFLOW, "BigDecimal to Float conversion", 0);
if (BIGDECIMAL_NEGATIVE_P(p))
return rb_float_new(VpGetDoubleNegInf());
else
return rb_float_new(VpGetDoublePosInf());

underflow:
VpException(VP_EXCEPTION_UNDERFLOW, "BigDecimal to Float conversion", 0);
if (BIGDECIMAL_NEGATIVE_P(p))
return rb_float_new(-0.0);
else
return rb_float_new(0.0);
}```
to_i() click to toggle source

Returns the value as an `Integer`.

If the `BigDecimal` is infinity or NaN, raises `FloatDomainError`.

```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) * (DECDIG_DBL_SIGNED)p->frac[0]));
}
else {
VALUE a = BigDecimal_split(self);
VALUE digits = RARRAY_AREF(a, 1);
VALUE numerator = rb_funcall(digits, rb_intern("to_i"), 0);
VALUE ret;
ssize_t dpower = e - (ssize_t)RSTRING_LEN(digits);

if (BIGDECIMAL_NEGATIVE_P(p)) {
numerator = rb_funcall(numerator, '*', 1, INT2FIX(-1));
}
if (dpower < 0) {
ret = rb_funcall(numerator, rb_intern("div"), 1,
rb_funcall(INT2FIX(10), rb_intern("**"), 1,
INT2FIX(-dpower)));
}
else {
ret = rb_funcall(numerator, '*', 1,
rb_funcall(INT2FIX(10), rb_intern("**"), 1,
INT2FIX(dpower)));
}
if (RB_TYPE_P(ret, T_FLOAT)) {
rb_raise(rb_eFloatDomainError, "Infinity");
}
return ret;
}
}```
Also aliased as: to_int
to_int()

Returns the value as an `Integer`.

If the `BigDecimal` is infinity or NaN, raises `FloatDomainError`.

Alias for: to_i
to_json(*args) click to toggle source

return the `JSON` value

```# File ext/json/lib/json/add/bigdecimal.rb, line 29
def to_json(*args)
as_json.to_json(*args)
end```
to_r() click to toggle source

Converts a `BigDecimal` to a `Rational`.

```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_AREF(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));
}
if (denomi_power < 0) {
return rb_Rational(numerator,
rb_funcall(INT2FIX(10), rb_intern("**"), 1,
INT2FIX(-denomi_power)));
}
else {
return rb_Rational1(rb_funcall(numerator, '*', 1,
rb_funcall(INT2FIX(10), rb_intern("**"), 1,
INT2FIX(denomi_power))));
}
}```
to_s(s) click to toggle source

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 digits, starting from ‘.’ and counting outwards.

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('-1234567890123.45678901234567890').to_s('5F')
#=> '-123 45678 90123.45678 90123 45678 9'

BigDecimal('1234567890123.45678901234567890').to_s('+8F')
#=> '+12345 67890123.45678901 23456789'

BigDecimal('1234567890123.45678901234567890').to_s(' F')
#=> ' 1234567890123.4567890123456789'
```
```static VALUE
BigDecimal_to_s(int argc, VALUE *argv, VALUE self)
{
ENTER(5);
int   fmt = 0;   /* 0: E format, 1: F format */
int   fPlus = 0; /* 0: default, 1: set ' ' before digits, 2: set '+' before digits. */
Real  *vp;
volatile VALUE str;
char  *psz;
char   ch;
size_t nc, mc = 0;
SIGNED_VALUE m;
VALUE  f;

GUARD_OBJ(vp, GetVpValue(self, 1));

if (rb_scan_args(argc, argv, "01", &f) == 1) {
if (RB_TYPE_P(f, T_STRING)) {
psz = StringValueCStr(f);
if (*psz == ' ') {
fPlus = 1;
psz++;
}
else if (*psz == '+') {
fPlus = 2;
psz++;
}
while ((ch = *psz++) != 0) {
if (ISSPACE(ch)) {
continue;
}
if (!ISDIGIT(ch)) {
if (ch == 'F' || ch == 'f') {
fmt = 1; /* F format */
}
break;
}
mc = mc*10 + ch - '0';
}
}
else {
m = NUM2INT(f);
if (m <= 0) {
rb_raise(rb_eArgError, "argument must be positive");
}
mc = (size_t)m;
}
}
if (fmt) {
nc = VpNumOfChars(vp, "F");
}
else {
nc = VpNumOfChars(vp, "E");
}
if (mc > 0) {
nc += (nc + mc - 1) / mc + 1;
}

str = rb_usascii_str_new(0, nc);
psz = RSTRING_PTR(str);

if (fmt) {
VpToFString(vp, psz, RSTRING_LEN(str), mc, fPlus);
}
else {
VpToString (vp, psz, RSTRING_LEN(str), mc, fPlus);
}
rb_str_resize(str, strlen(psz));
return str;
}```
truncate(n) click to toggle source

Truncate to the nearest integer (by default), returning the result as a `BigDecimal`.

```BigDecimal('3.14159').truncate #=> 3
BigDecimal('8.7').truncate #=> 8
BigDecimal('-9.9').truncate #=> -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').truncate(3) #=> 3.141
BigDecimal('13345.234').truncate(-2) #=> 13300.0
```
```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;
}
else {
iLoc = NUM2INT(vLoc);
}

GUARD_OBJ(a, GetVpValue(self, 1));
mx = a->Prec * (VpBaseFig() + 1);
GUARD_OBJ(c, NewZeroWrapLimited(1, mx));
VpSetPrecLimit(pl);
VpActiveRound(c, a, VP_ROUND_DOWN, iLoc); /* 0: truncate */
if (argc == 0) {
return BigDecimal_to_i(VpCheckGetValue(c));
}
return VpCheckGetValue(c);
}```
zero?() click to toggle source

Returns True if the value is zero.

```static VALUE
BigDecimal_zero(VALUE self)
{
Real *a = GetVpValue(self, 1);
return VpIsZero(a) ? Qtrue : Qfalse;
}```