Extended maintenance of Ruby versions 1.8.7 and 1.9.2 ended on July 31, 2014. Read more

### In Files

• bigdecimal/bigdecimal.c
• bigdecimal/lib/bigdecimal/util.rb

Quicksearch

# 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.

::new(“1.0”) / ::new(“0.0”) -> infinity

::new(“-1.0”) / ::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:

::new(“0.0”) / ::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 = ::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.

::new(“1.0”) / ::new(“-Infinity”) -> -0.0

::new(“1.0”) / ::new(“Infinity”) -> 0.0

(See ::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.

### 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 ::mode.

EXCEPTION_INFINITY

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

EXCEPTION_NaN

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

EXCEPTION_OVERFLOW

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

EXCEPTION_UNDERFLOW

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

EXCEPTION_ZERODIVIDE

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

ROUND_CEILING

Round towards +infinity. See ::mode.

ROUND_DOWN

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

ROUND_FLOOR

Round towards -infinity. See ::mode.

ROUND_HALF_DOWN

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

ROUND_HALF_EVEN

Round towards the even neighbor. See ::mode.

ROUND_HALF_UP

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

ROUND_MODE

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

ROUND_UP

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

SIGN_NEGATIVE_FINITE

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

SIGN_NEGATIVE_INFINITE

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

SIGN_NEGATIVE_ZERO

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

SIGN_NaN

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

SIGN_POSITIVE_FINITE

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

SIGN_POSITIVE_INFINITE

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

SIGN_POSITIVE_ZERO

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

### 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;

SafeStringValue(str);
pch = (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");
}
m = m*10 + (unsigned long)(ch-'0');
}
if(m>VpBaseFig()) m -= VpBaseFig();
GUARD_OBJ(pv,VpNewRbClass(m,(char *)pch,self));
m /= VpBaseFig();
if(m && pv->MaxPrec>m) pv->MaxPrec = m+1;
}
```
double_fig click to toggle source

The ::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.

```
static VALUE
BigDecimal_double_fig(VALUE self)
{
return INT2FIX(VpDblFig());
}
```
induced_from(p1) click to toggle source
```
static VALUE
BigDecimal_induced_from(VALUE self, VALUE x)
{
Real *p = GetVpValue(x,1);
return p->obj;
}
```
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 ::mode.

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

The limit specified by this method takes 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 = 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");
}
VpSetPrecLimit(nf);
}
return nCur;
}
```
mode(mode, value) click to toggle source

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:

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)

```
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 */
}
if(f&VP_EXCEPTION_INFINITY) {
VpSetException((unsigned short)((val==Qtrue)?(fo|VP_EXCEPTION_INFINITY):
(fo&(~VP_EXCEPTION_INFINITY))));
}
if(f&VP_EXCEPTION_NaN) {
VpSetException((unsigned short)((val==Qtrue)?(fo|VP_EXCEPTION_NaN):
(fo&(~VP_EXCEPTION_NaN))));
}
fo = VpGetException();
return INT2FIX(fo);
}
if(VP_ROUND_MODE==f) {
/* Rounding mode setting */
fo = VpGetRoundMode();
if(val==Qnil) return INT2FIX(fo);
Check_Type(val, T_FIXNUM);
if(!VpIsRoundMode(FIX2INT(val))) {
rb_raise(rb_eTypeError, "invalid rounding mode");
return Qnil;
}
fo = VpSetRoundMode((unsigned long)FIX2INT(val));
return INT2FIX(fo);
}
rb_raise(rb_eTypeError, "first argument for BigDecimal#mode invalid");
return Qnil;
}
```
new(initial, digits) click to toggle source

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.

```
static VALUE
BigDecimal_new(int argc, VALUE *argv, VALUE self)
{
ENTER(5);
Real *pv;
S_LONG mf;
VALUE  nFig;
VALUE  iniValue;

if(rb_scan_args(argc,argv,"11",&iniValue,&nFig)==1) {
mf = 0;
} else {
mf = GetPositiveInt(nFig);
}
SafeStringValue(iniValue);
GUARD_OBJ(pv,VpNewRbClass(mf, RSTRING_PTR(iniValue),self));
}
```
ver() click to toggle source

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.

```
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");
}
```

### Public Instance Methods

a % b click to toggle source

Returns the modulus from dividing by b. See divmod.

```
static VALUE
BigDecimal_mod(VALUE self, VALUE r)
```
mult(value, digits) click to toggle source

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 ::mode.

```
static VALUE
BigDecimal_mult(VALUE self, VALUE r)
{
ENTER(5);
Real *c, *a, *b;
U_LONG 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);
}
```
power(n) click to toggle source

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(VALUE self, VALUE p)
{
ENTER(5);
Real *x, *y;
S_LONG mp, ma, 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"));
} else {
GUARD_OBJ(y,VpCreateRbObject(1, "0"));
}
VpPower(y, x, n);
}
```
add(value, digits) click to toggle source

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 ::mode.

```
static VALUE
{
ENTER(5);
Real *c, *a, *b;
U_LONG 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;
if(mx==(-1L)) {
GUARD_OBJ(c,VpCreateRbObject(VpBaseFig() + 1, "0"));
} else {
GUARD_OBJ(c,VpCreateRbObject(mx *(VpBaseFig() + 1), "0"));
if(!mx) {
VpSetInf(c,VpGetSign(a));
} else {
}
}
}
```
+@() click to toggle source
```
static VALUE
BigDecimal_uplus(VALUE self)
{
return self;
}
```
sub(value, digits) click to toggle source

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 ::mode.

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

if(mx==(-1L)) {
GUARD_OBJ(c,VpCreateRbObject(VpBaseFig() + 1, "0"));
} else {
GUARD_OBJ(c,VpCreateRbObject(mx *(VpBaseFig() + 1), "0"));
if(!mx) {
VpSetInf(c,VpGetSign(a));
} else {
}
}
}
```
-@() click to toggle source
```
static VALUE
BigDecimal_neg(VALUE self)
{
ENTER(5);
Real *c, *a;
GUARD_OBJ(a,GetVpValue(self,1));
GUARD_OBJ(c,VpCreateRbObject(a->Prec *(VpBaseFig() + 1), "0"));
VpAsgn(c, a, -1);
}
```
div(value, digits) click to toggle source
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 ::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.

```
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],(VpBaseVal()*res->frac[0])/div->frac[0]);
}
}
```
a < b click to toggle source

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

```
static VALUE
BigDecimal_lt(VALUE self, VALUE r)
{
return BigDecimalCmp(self, r, '<');
}
```
a <= b click to toggle source

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

```
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:

::new('1.0') == 1.0 -> true

```
static VALUE
BigDecimal_eq(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:

::new('1.0') == 1.0 -> true

```
static VALUE
BigDecimal_eq(VALUE self, VALUE r)
{
return BigDecimalCmp(self, r, '=');
}
```
a > b click to toggle source

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

```
static VALUE
BigDecimal_gt(VALUE self, VALUE r)
{
return BigDecimalCmp(self, r, '>');
}
```
a >= b click to toggle source

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

```
static VALUE
BigDecimal_ge(VALUE self, VALUE r)
{
return BigDecimalCmp(self, r, 'G');
}
```
_dump(p1 = v1) click to toggle source
```
static VALUE
BigDecimal_dump(int argc, VALUE *argv, VALUE self)
{
ENTER(5);
Real *vp;
char *psz;
VALUE dummy;
volatile VALUE dump;

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);
sprintf(psz,"%lu:",VpMaxPrec(vp)*VpBaseFig());
VpToString(vp, psz+strlen(psz), 0, 0);
rb_str_resize(dump, strlen(psz));
return dump;
}
```
abs() click to toggle source

Returns the absolute value.

BigDecimal('5').abs -> 5

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

```
static VALUE
BigDecimal_abs(VALUE self)
{
ENTER(5);
Real *c, *a;
U_LONG mx;

GUARD_OBJ(a,GetVpValue(self,1));
mx = a->Prec *(VpBaseFig() + 1);
GUARD_OBJ(c,VpCreateRbObject(mx, "0"));
VpAsgn(c, a, 1);
VpChangeSign(c,(S_INT)1);
}
```
add(p1, p2) click to toggle source
```
static VALUE
BigDecimal_add2(VALUE self, VALUE b, VALUE n)
{
ENTER(2);
Real   *cv;
U_LONG mx = (U_LONG)GetPositiveInt(n);
else {
U_LONG pl = VpSetPrecLimit(0);
VpSetPrecLimit(pl);
GUARD_OBJ(cv,GetVpValue(c,1));
VpLeftRound(cv,VpGetRoundMode(),mx);
}
}
```
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;
U_LONG mx;
int iLoc;
VALUE vLoc;
U_LONG pl = VpSetPrecLimit(0);

if(rb_scan_args(argc,argv,"01",&vLoc)==0) {
iLoc = 0;
} else {
Check_Type(vLoc, T_FIXNUM);
iLoc = FIX2INT(vLoc);
}

GUARD_OBJ(a,GetVpValue(self,1));
mx = a->Prec *(VpBaseFig() + 1);
GUARD_OBJ(c,VpCreateRbObject(mx, "0"));
VpSetPrecLimit(pl);
VpActiveRound(c,a,VP_ROUND_CEIL,iLoc);
}
```
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 = ::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.

```
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));
} else {
GUARD_OBJ(b,GetVpValue(other,1));
obj = rb_assoc_new(b->obj, self);
}
return obj;
}
```
div(p1, p2 = v2) click to toggle source
```
static VALUE
BigDecimal_div2(int argc, VALUE *argv, VALUE self)
{
ENTER(5);
VALUE b,n;
int na = rb_scan_args(argc,argv,"11",&b,&n);
if(na==1) { /* div in Float sense */
VALUE obj;
Real *div=NULL;
Real *mod;
obj = BigDecimal_DoDivmod(self,b,&div,&mod);
if(obj!=(VALUE)0) return obj;
} else {    /* div in BigDecimal sense */
U_LONG ix = (U_LONG)GetPositiveInt(n);
if(ix==0) return BigDecimal_div(self,b);
else {
Real *res=NULL;
Real *av=NULL, *bv=NULL, *cv=NULL;
U_LONG mx = (ix+VpBaseFig()*2);
U_LONG pl = VpSetPrecLimit(0);

GUARD_OBJ(cv,VpCreateRbObject(mx,"0"));
GUARD_OBJ(av,GetVpValue(self,1));
GUARD_OBJ(bv,GetVpValue(b,1));
mx = av->Prec + bv->Prec + 2;
if(mx <= cv->MaxPrec) mx = cv->MaxPrec+1;
GUARD_OBJ(res,VpCreateRbObject((mx * 2  + 2)*VpBaseFig(), "#0"));
VpDivd(cv,res,av,bv);
VpSetPrecLimit(pl);
VpLeftRound(cv,VpGetRoundMode(),ix);
}
}
}
```
divmod(p1) 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 = ::new(“42”) b = ::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.

```
static VALUE
BigDecimal_divmod(VALUE self, VALUE r)
{
ENTER(5);
VALUE obj;
Real *div=NULL, *mod=NULL;

obj = BigDecimal_DoDivmod(self,r,&div,&mod);
if(obj!=(VALUE)0) return obj;
SAVE(div);SAVE(mod);
obj = rb_assoc_new(ToValue(div), ToValue(mod));
return obj;
}
```
eql?(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:

::new('1.0') == 1.0 -> true

```
static VALUE
BigDecimal_eq(VALUE self, VALUE r)
{
return BigDecimalCmp(self, r, '=');
}
```
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)
{
S_LONG e = VpExponent10(GetVpValue(self,1));
return INT2NUM(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.

```
static VALUE
BigDecimal_fix(VALUE self)
{
ENTER(5);
Real *c, *a;
U_LONG 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 */
}
```
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;
U_LONG mx;
int iLoc;
VALUE vLoc;
U_LONG pl = VpSetPrecLimit(0);

if(rb_scan_args(argc,argv,"01",&vLoc)==0) {
iLoc = 0;
} else {
Check_Type(vLoc, T_FIXNUM);
iLoc = FIX2INT(vLoc);
}

GUARD_OBJ(a,GetVpValue(self,1));
mx = a->Prec *(VpBaseFig() + 1);
GUARD_OBJ(c,VpCreateRbObject(mx, "0"));
VpSetPrecLimit(pl);
VpActiveRound(c,a,VP_ROUND_FLOOR,iLoc);
}
```
frac() click to toggle source

Return the fractional part of the number.

```
static VALUE
BigDecimal_frac(VALUE self)
{
ENTER(5);
Real *c, *a;
U_LONG mx;

GUARD_OBJ(a,GetVpValue(self,1));
mx = a->Prec *(VpBaseFig() + 1);
GUARD_OBJ(c,VpCreateRbObject(mx, "0"));
VpFrac(c, a);
}
```
hash() click to toggle source
```
static VALUE
BigDecimal_hash(VALUE self)
{
ENTER(1);
Real *p;
U_LONG hash,i;

GUARD_OBJ(p,GetVpValue(self,1));
hash = (U_LONG)p->sign;
/* hash!=2: the case for 0(1),NaN(0) or +-Infinity(3) is sign itself */
if(hash==2) {
for(i = 0; i < p->Prec;i++) {
hash = 31 * hash + p->frac[i];
hash ^= p->frac[i];
}
hash += p->exponent;
}
return INT2FIX(hash);
}
```
infinite?() click to toggle source

Returns True if the value is infinite

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

::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.

```
static VALUE
BigDecimal_inspect(VALUE self)
{
ENTER(5);
Real *vp;
volatile VALUE obj;
unsigned int nc;
char *psz, *tmp;

GUARD_OBJ(vp,GetVpValue(self,1));
nc = VpNumOfChars(vp,"E");
nc +=(nc + 9) / 10;

obj = rb_str_new(0, nc+256);
psz = RSTRING_PTR(obj);
sprintf(psz,"#<BigDecimal:%lx,'",self);
tmp = psz + strlen(psz);
VpToString(vp, tmp, 10, 0);
tmp += strlen(tmp);
sprintf(tmp,"',%lu(%lu)>",VpPrec(vp)*VpBaseFig(),VpMaxPrec(vp)*VpBaseFig());
rb_str_resize(obj, strlen(psz));
return obj;
}
```
modulo(b) click to toggle source

Returns the modulus from dividing by b. See divmod.

```
static VALUE
BigDecimal_mod(VALUE self, VALUE r)
```
mult(p1, p2) click to toggle source
```
static VALUE
BigDecimal_mult2(VALUE self, VALUE b, VALUE n)
{
ENTER(2);
Real *cv;
U_LONG mx = (U_LONG)GetPositiveInt(n);
if(mx==0) return BigDecimal_mult(self,b);
else {
U_LONG pl = VpSetPrecLimit(0);
VALUE   c = BigDecimal_mult(self,b);
VpSetPrecLimit(pl);
GUARD_OBJ(cv,GetVpValue(c,1));
VpLeftRound(cv,VpGetRoundMode(),mx);
}
}
```
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 True if the value is non-zero.

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

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(VALUE self, VALUE p)
{
ENTER(5);
Real *x, *y;
S_LONG mp, ma, 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"));
} else {
GUARD_OBJ(y,VpCreateRbObject(1, "0"));
}
VpPower(y, x, n);
}
```
precs click to toggle source

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.

```
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;
}
```
quo(value) click to toggle source

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 ::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.

```
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],(VpBaseVal()*res->frac[0])/div->frac[0]);
}
}
```
remainder(p1) click to toggle source

Returns the remainder from dividing by the value.

If the values divided are of the same sign, the remainder is the same as the modulus (see divmod).

Otherwise, the remainder is the modulus minus the value divided by.

```
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;
}
```
round(n,mode) click to toggle source

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 ::mode.

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

int    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   = FIX2INT(vRound);
if(!VpIsRoundMode(sw)) {
rb_raise(rb_eTypeError, "invalid rounding mode");
return Qnil;
}
break;
}

pl = VpSetPrecLimit(0);
GUARD_OBJ(a,GetVpValue(self,1));
mx = a->Prec *(VpBaseFig() + 1);
GUARD_OBJ(c,VpCreateRbObject(mx, "0"));
VpSetPrecLimit(pl);
VpActiveRound(c,a,sw,iLoc);
}
```
sign() click to toggle source

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

```
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;
S_LONG e;
S_LONG s;
char *psz1;

GUARD_OBJ(vp,GetVpValue(self,1));
str = rb_str_new(0, VpNumOfChars(vp,"E"));
psz1 = RSTRING_PTR(str);
VpSzMantissa(vp,psz1);
s = 1;
if(psz1[0]=='-') {
int 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, INT2NUM(e));
return obj;
}
```
sqrt(n) click to toggle source

Returns the square root of the value.

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

```
static VALUE
BigDecimal_sqrt(VALUE self, VALUE nFig)
{
ENTER(5);
Real *c, *a;
S_INT 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);
}
```
sub(p1, p2) click to toggle source
```
static VALUE
BigDecimal_sub2(VALUE self, VALUE b, VALUE n)
{
ENTER(2);
Real *cv;
U_LONG mx = (U_LONG)GetPositiveInt(n);
if(mx==0) return BigDecimal_sub(self,b);
else {
U_LONG pl = VpSetPrecLimit(0);
VALUE   c = BigDecimal_sub(self,b);
VpSetPrecLimit(pl);
GUARD_OBJ(cv,GetVpValue(c,1));
VpLeftRound(cv,VpGetRoundMode(),mx);
}
}
```
to_digits() click to toggle source

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

```
# File bigdecimal/lib/bigdecimal/util.rb, line 33
def to_digits
if self.nan? || self.infinite? || self.zero?
self.to_s
else
i       = self.to_i.to_s
s,f,y,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;
S_LONG 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 > DBL_MAX_10_EXP) goto erange;
str = rb_str_new(0, VpNumOfChars(p,"E"));
buf = RSTRING_PTR(str);
VpToString(p, buf, 0, 0);
errno = 0;
d = strtod(buf, 0);
if(errno == ERANGE) {
erange:
VpException(VP_EXCEPTION_OVERFLOW,"BigDecimal to Float conversion",0);
if(d>0.0) d = VpGetDoublePosInf();
else      d = VpGetDoubleNegInf();
}
return rb_float_new(d);
}
```
to_i() click to toggle source

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

If the BigNumber is infinity or NaN, returns nil.

```
static VALUE
BigDecimal_to_i(VALUE self)
{
ENTER(5);
int e,n,i,nf;
U_LONG v,b,j;
volatile VALUE str;
char *psz,*pch;
Real *p;

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

/* Infinity or NaN not converted. */
if(VpIsNaN(p)) {
VpException(VP_EXCEPTION_NaN,"Computation results to 'NaN'(Not a Number)",0);
return Qnil;
} else if(VpIsPosInf(p)) {
VpException(VP_EXCEPTION_INFINITY,"Computation results to 'Infinity'",0);
return Qnil;
} else if(VpIsNegInf(p)) {
VpException(VP_EXCEPTION_INFINITY,"Computation results to '-Infinity'",0);
return Qnil;
}

e = VpExponent10(p);
if(e<=0) return INT2FIX(0);
nf = VpBaseFig();
if(e<=nf) {
e = VpGetSign(p)*p->frac[0];
return INT2FIX(e);
}
str = rb_str_new(0, e+nf+2);
psz = RSTRING_PTR(str);

n = (e+nf-1)/nf;
pch = psz;
if(VpGetSign(p)<0) *pch++ = '-';
for(i=0;i<n;++i) {
b = VpBaseVal()/10;
if(i>=(int)p->Prec) {
while(b) {
*pch++ = '0';
b /= 10;
}
continue;
}
v = p->frac[i];
while(b) {
j = v/b;
*pch++ = (char)(j + '0');
v -= j*b;
b /= 10;
}
}
*pch++ = 0;
return rb_cstr2inum(psz,10);
}
```
to_int() click to toggle source

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

If the BigNumber is infinity or NaN, returns nil.

```
static VALUE
BigDecimal_to_i(VALUE self)
{
ENTER(5);
int e,n,i,nf;
U_LONG v,b,j;
volatile VALUE str;
char *psz,*pch;
Real *p;

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

/* Infinity or NaN not converted. */
if(VpIsNaN(p)) {
VpException(VP_EXCEPTION_NaN,"Computation results to 'NaN'(Not a Number)",0);
return Qnil;
} else if(VpIsPosInf(p)) {
VpException(VP_EXCEPTION_INFINITY,"Computation results to 'Infinity'",0);
return Qnil;
} else if(VpIsNegInf(p)) {
VpException(VP_EXCEPTION_INFINITY,"Computation results to '-Infinity'",0);
return Qnil;
}

e = VpExponent10(p);
if(e<=0) return INT2FIX(0);
nf = VpBaseFig();
if(e<=nf) {
e = VpGetSign(p)*p->frac[0];
return INT2FIX(e);
}
str = rb_str_new(0, e+nf+2);
psz = RSTRING_PTR(str);

n = (e+nf-1)/nf;
pch = psz;
if(VpGetSign(p)<0) *pch++ = '-';
for(i=0;i<n;++i) {
b = VpBaseVal()/10;
if(i>=(int)p->Prec) {
while(b) {
*pch++ = '0';
b /= 10;
}
continue;
}
v = p->frac[i];
while(b) {
j = v/b;
*pch++ = (char)(j + '0');
v -= j*b;
b /= 10;
}
}
*pch++ = 0;
return rb_cstr2inum(psz,10);
}
```
to_r() click to toggle source

Converts a BigDecimal to a Rational.

```
# File bigdecimal/lib/bigdecimal/util.rb, line 44
def to_r
sign,digits,base,power = self.split
numerator = sign*digits.to_i
denomi_power = power - digits.size # base is always 10
if denomi_power < 0
Rational(numerator,base ** (-denomi_power))
else
Rational(numerator * (base ** denomi_power),1)
end
end
```
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 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:

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

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

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

```
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;
char  *psz;
char   ch;
U_LONG nc;
S_INT  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++;
} 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 {
mc  = GetPositiveInt(f);
}
}
if(fmt) {
nc = VpNumOfChars(vp,"F");
} else {
nc = VpNumOfChars(vp,"E");
}
if(mc>0) nc += (nc + mc - 1) / mc + 1;

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

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

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

```
static VALUE
BigDecimal_truncate(int argc, VALUE *argv, VALUE self)
{
ENTER(5);
Real *c, *a;
int iLoc;
U_LONG mx;
VALUE vLoc;
U_LONG pl = VpSetPrecLimit(0);

if(rb_scan_args(argc,argv,"01",&vLoc)==0) {
iLoc = 0;
} else {
Check_Type(vLoc, T_FIXNUM);
iLoc = FIX2INT(vLoc);
}

GUARD_OBJ(a,GetVpValue(self,1));
mx = a->Prec *(VpBaseFig() + 1);
GUARD_OBJ(c,VpCreateRbObject(mx, "0"));
VpSetPrecLimit(pl);
VpActiveRound(c,a,VP_ROUND_DOWN,iLoc); /* 0: truncate */
}
```
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;
}
```