BigDecimal extends the native Float class to provide the to_d method.

When you require BigDecimal in your application, this method will be available on Float objects.

Float objects represent inexact real numbers using the native architecture's double-precision floating point representation.

Floating point has a different arithmetic and is an inexact number. So you should know its esoteric system. see following:

Methods
#
A
C
D
E
F
H
I
M
N
P
Q
R
T
Z
Constants
 ROUNDS = INT2FIX(FLT_ROUNDS) Represents the rounding mode for floating point addition. Usually defaults to 1, rounding to the nearest number. Other modes include: -1 Indeterminable 0 Rounding towards zero 1 Rounding to the nearest number 2 Rounding towards positive infinity 3 Rounding towards negative infinity RADIX = INT2FIX(FLT_RADIX) The base of the floating point, or number of unique digits used to represent the number. Usually defaults to 2 on most systems, which would represent a base-10 decimal. MANT_DIG = INT2FIX(DBL_MANT_DIG) The number of base digits for the `double` data type. Usually defaults to 53. DIG = INT2FIX(DBL_DIG) The minimum number of significant decimal digits in a double-precision floating point. Usually defaults to 15. MIN_EXP = INT2FIX(DBL_MIN_EXP) The smallest posable exponent value in a double-precision floating point. Usually defaults to -1021. MAX_EXP = INT2FIX(DBL_MAX_EXP) The largest possible exponent value in a double-precision floating point. Usually defaults to 1024. MIN_10_EXP = INT2FIX(DBL_MIN_10_EXP) The smallest negative exponent in a double-precision floating point where 10 raised to this power minus 1. Usually defaults to -307. MAX_10_EXP = INT2FIX(DBL_MAX_10_EXP) The largest positive exponent in a double-precision floating point where 10 raised to this power minus 1. Usually defaults to 308. MIN = DBL2NUM(DBL_MIN) The smallest positive normalized number in a double-precision floating point. Usually defaults to 2.2250738585072014e-308. If the platform supports denormalized numbers, there are numbers between zero and Float::MIN. 0.0.next_float returns the smallest positive floating point number including denormalized numbers. MAX = DBL2NUM(DBL_MAX) The largest possible integer in a double-precision floating point number. Usually defaults to 1.7976931348623157e+308. EPSILON = DBL2NUM(DBL_EPSILON) The difference between 1 and the smallest double-precision floating point number greater than 1. Usually defaults to 2.2204460492503131e-16. INFINITY = DBL2NUM(INFINITY) An expression representing positive infinity. NAN = DBL2NUM(NAN) An expression representing a value which is “not a number”.
Instance Public methods
float % other → float

Return the modulo after division of `float` by `other`.

``````6543.21.modulo(137)      #=> 104.21
6543.21.modulo(137.24)   #=> 92.9299999999996
``````
```static VALUE
flo_mod(VALUE x, VALUE y)
{
double fy;

if (RB_TYPE_P(y, T_FIXNUM)) {
fy = (double)FIX2LONG(y);
}
else if (RB_TYPE_P(y, T_BIGNUM)) {
fy = rb_big2dbl(y);
}
else if (RB_TYPE_P(y, T_FLOAT)) {
fy = RFLOAT_VALUE(y);
}
else {
return rb_num_coerce_bin(x, y, '%');
}
return DBL2NUM(ruby_float_mod(RFLOAT_VALUE(x), fy));
}```
float * other → float

Returns a new float which is the product of `float` and `other`.

```static VALUE
flo_mul(VALUE x, VALUE y)
{
if (RB_TYPE_P(y, T_FIXNUM)) {
return DBL2NUM(RFLOAT_VALUE(x) * (double)FIX2LONG(y));
}
else if (RB_TYPE_P(y, T_BIGNUM)) {
return DBL2NUM(RFLOAT_VALUE(x) * rb_big2dbl(y));
}
else if (RB_TYPE_P(y, T_FLOAT)) {
return DBL2NUM(RFLOAT_VALUE(x) * RFLOAT_VALUE(y));
}
else {
return rb_num_coerce_bin(x, y, '*');
}
}```
float ** other → float

Raises `float` to the power of `other`.

``````2.0**3      #=> 8.0
``````
```static VALUE
flo_pow(VALUE x, VALUE y)
{
double dx, dy;
if (RB_TYPE_P(y, T_FIXNUM)) {
dx = RFLOAT_VALUE(x);
dy = (double)FIX2LONG(y);
}
else if (RB_TYPE_P(y, T_BIGNUM)) {
dx = RFLOAT_VALUE(x);
dy = rb_big2dbl(y);
}
else if (RB_TYPE_P(y, T_FLOAT)) {
dx = RFLOAT_VALUE(x);
dy = RFLOAT_VALUE(y);
if (dx < 0 && dy != round(dy))
return rb_funcall(rb_complex_raw1(x), idPow, 1, y);
}
else {
return rb_num_coerce_bin(x, y, idPow);
}
return DBL2NUM(pow(dx, dy));
}```
float + other → float

Returns a new float which is the sum of `float` and `other`.

```static VALUE
flo_plus(VALUE x, VALUE y)
{
if (RB_TYPE_P(y, T_FIXNUM)) {
return DBL2NUM(RFLOAT_VALUE(x) + (double)FIX2LONG(y));
}
else if (RB_TYPE_P(y, T_BIGNUM)) {
return DBL2NUM(RFLOAT_VALUE(x) + rb_big2dbl(y));
}
else if (RB_TYPE_P(y, T_FLOAT)) {
return DBL2NUM(RFLOAT_VALUE(x) + RFLOAT_VALUE(y));
}
else {
return rb_num_coerce_bin(x, y, '+');
}
}```
float - other → float

Returns a new float which is the difference of `float` and `other`.

```static VALUE
flo_minus(VALUE x, VALUE y)
{
if (RB_TYPE_P(y, T_FIXNUM)) {
return DBL2NUM(RFLOAT_VALUE(x) - (double)FIX2LONG(y));
}
else if (RB_TYPE_P(y, T_BIGNUM)) {
return DBL2NUM(RFLOAT_VALUE(x) - rb_big2dbl(y));
}
else if (RB_TYPE_P(y, T_FLOAT)) {
return DBL2NUM(RFLOAT_VALUE(x) - RFLOAT_VALUE(y));
}
else {
return rb_num_coerce_bin(x, y, '-');
}
}```
-float → float

Returns float, negated.

```static VALUE
flo_uminus(VALUE flt)
{
return DBL2NUM(-RFLOAT_VALUE(flt));
}```
float / other → float

Returns a new float which is the result of dividing `float` by `other`.

```static VALUE
flo_div(VALUE x, VALUE y)
{
long f_y;
double d;

if (RB_TYPE_P(y, T_FIXNUM)) {
f_y = FIX2LONG(y);
return DBL2NUM(RFLOAT_VALUE(x) / (double)f_y);
}
else if (RB_TYPE_P(y, T_BIGNUM)) {
d = rb_big2dbl(y);
return DBL2NUM(RFLOAT_VALUE(x) / d);
}
else if (RB_TYPE_P(y, T_FLOAT)) {
return DBL2NUM(RFLOAT_VALUE(x) / RFLOAT_VALUE(y));
}
else {
return rb_num_coerce_bin(x, y, '/');
}
}```
float < real → true or false

Returns `true` if `float` is less than `real`.

The result of `NaN < NaN` is undefined, so the implementation-dependent value is returned.

```static VALUE
flo_lt(VALUE x, VALUE y)
{
double a, b;

a = RFLOAT_VALUE(x);
if (RB_TYPE_P(y, T_FIXNUM) || RB_TYPE_P(y, T_BIGNUM)) {
VALUE rel = rb_integer_float_cmp(y, x);
if (FIXNUM_P(rel))
return -FIX2INT(rel) < 0 ? Qtrue : Qfalse;
return Qfalse;
}
else if (RB_TYPE_P(y, T_FLOAT)) {
b = RFLOAT_VALUE(y);
#if defined(_MSC_VER) && _MSC_VER < 1300
if (isnan(b)) return Qfalse;
#endif
}
else {
return rb_num_coerce_relop(x, y, '<');
}
#if defined(_MSC_VER) && _MSC_VER < 1300
if (isnan(a)) return Qfalse;
#endif
return (a < b)?Qtrue:Qfalse;
}```
float <= real → true or false

Returns `true` if `float` is less than or equal to `real`.

The result of `NaN <= NaN` is undefined, so the implementation-dependent value is returned.

```static VALUE
flo_le(VALUE x, VALUE y)
{
double a, b;

a = RFLOAT_VALUE(x);
if (RB_TYPE_P(y, T_FIXNUM) || RB_TYPE_P(y, T_BIGNUM)) {
VALUE rel = rb_integer_float_cmp(y, x);
if (FIXNUM_P(rel))
return -FIX2INT(rel) <= 0 ? Qtrue : Qfalse;
return Qfalse;
}
else if (RB_TYPE_P(y, T_FLOAT)) {
b = RFLOAT_VALUE(y);
#if defined(_MSC_VER) && _MSC_VER < 1300
if (isnan(b)) return Qfalse;
#endif
}
else {
return rb_num_coerce_relop(x, y, idLE);
}
#if defined(_MSC_VER) && _MSC_VER < 1300
if (isnan(a)) return Qfalse;
#endif
return (a <= b)?Qtrue:Qfalse;
}```
float <=> real → -1, 0, +1 or nil

Returns -1, 0, +1 or nil depending on whether `float` is less than, equal to, or greater than `real`. This is the basis for the tests in Comparable.

The result of `NaN <=> NaN` is undefined, so the implementation-dependent value is returned.

`nil` is returned if the two values are incomparable.

```static VALUE
flo_cmp(VALUE x, VALUE y)
{
double a, b;
VALUE i;

a = RFLOAT_VALUE(x);
if (isnan(a)) return Qnil;
if (RB_TYPE_P(y, T_FIXNUM) || RB_TYPE_P(y, T_BIGNUM)) {
VALUE rel = rb_integer_float_cmp(y, x);
if (FIXNUM_P(rel))
return INT2FIX(-FIX2INT(rel));
return rel;
}
else if (RB_TYPE_P(y, T_FLOAT)) {
b = RFLOAT_VALUE(y);
}
else {
if (isinf(a) && (i = rb_check_funcall(y, rb_intern("infinite?"), 0, 0)) != Qundef) {
if (RTEST(i)) {
int j = rb_cmpint(i, x, y);
j = (a > 0.0) ? (j > 0 ? 0 : +1) : (j < 0 ? 0 : -1);
return INT2FIX(j);
}
if (a > 0.0) return INT2FIX(1);
return INT2FIX(-1);
}
return rb_num_coerce_cmp(x, y, id_cmp);
}
return rb_dbl_cmp(a, b);
}```
float == obj → true or false

Returns `true` only if `obj` has the same value as `float`. Contrast this with #eql?, which requires obj to be a Float.

The result of `NaN == NaN` is undefined, so the implementation-dependent value is returned.

``````1.0 == 1   #=> true
``````
```static VALUE
flo_eq(VALUE x, VALUE y)
{
volatile double a, b;

if (RB_TYPE_P(y, T_FIXNUM) || RB_TYPE_P(y, T_BIGNUM)) {
return rb_integer_float_eq(y, x);
}
else if (RB_TYPE_P(y, T_FLOAT)) {
b = RFLOAT_VALUE(y);
#if defined(_MSC_VER) && _MSC_VER < 1300
if (isnan(b)) return Qfalse;
#endif
}
else {
return num_equal(x, y);
}
a = RFLOAT_VALUE(x);
#if defined(_MSC_VER) && _MSC_VER < 1300
if (isnan(a)) return Qfalse;
#endif
return (a == b)?Qtrue:Qfalse;
}```
float == obj → true or false

Returns `true` only if `obj` has the same value as `float`. Contrast this with #eql?, which requires obj to be a Float.

The result of `NaN == NaN` is undefined, so the implementation-dependent value is returned.

``````1.0 == 1   #=> true
``````
```static VALUE
flo_eq(VALUE x, VALUE y)
{
volatile double a, b;

if (RB_TYPE_P(y, T_FIXNUM) || RB_TYPE_P(y, T_BIGNUM)) {
return rb_integer_float_eq(y, x);
}
else if (RB_TYPE_P(y, T_FLOAT)) {
b = RFLOAT_VALUE(y);
#if defined(_MSC_VER) && _MSC_VER < 1300
if (isnan(b)) return Qfalse;
#endif
}
else {
return num_equal(x, y);
}
a = RFLOAT_VALUE(x);
#if defined(_MSC_VER) && _MSC_VER < 1300
if (isnan(a)) return Qfalse;
#endif
return (a == b)?Qtrue:Qfalse;
}```
float > real → true or false

Returns `true` if `float` is greater than `real`.

The result of `NaN > NaN` is undefined, so the implementation-dependent value is returned.

```static VALUE
flo_gt(VALUE x, VALUE y)
{
double a, b;

a = RFLOAT_VALUE(x);
if (RB_TYPE_P(y, T_FIXNUM) || RB_TYPE_P(y, T_BIGNUM)) {
VALUE rel = rb_integer_float_cmp(y, x);
if (FIXNUM_P(rel))
return -FIX2INT(rel) > 0 ? Qtrue : Qfalse;
return Qfalse;
}
else if (RB_TYPE_P(y, T_FLOAT)) {
b = RFLOAT_VALUE(y);
#if defined(_MSC_VER) && _MSC_VER < 1300
if (isnan(b)) return Qfalse;
#endif
}
else {
return rb_num_coerce_relop(x, y, '>');
}
#if defined(_MSC_VER) && _MSC_VER < 1300
if (isnan(a)) return Qfalse;
#endif
return (a > b)?Qtrue:Qfalse;
}```
float >= real → true or false

Returns `true` if `float` is greater than or equal to `real`.

The result of `NaN >= NaN` is undefined, so the implementation-dependent value is returned.

```static VALUE
flo_ge(VALUE x, VALUE y)
{
double a, b;

a = RFLOAT_VALUE(x);
if (RB_TYPE_P(y, T_FIXNUM) || RB_TYPE_P(y, T_BIGNUM)) {
VALUE rel = rb_integer_float_cmp(y, x);
if (FIXNUM_P(rel))
return -FIX2INT(rel) >= 0 ? Qtrue : Qfalse;
return Qfalse;
}
else if (RB_TYPE_P(y, T_FLOAT)) {
b = RFLOAT_VALUE(y);
#if defined(_MSC_VER) && _MSC_VER < 1300
if (isnan(b)) return Qfalse;
#endif
}
else {
return rb_num_coerce_relop(x, y, idGE);
}
#if defined(_MSC_VER) && _MSC_VER < 1300
if (isnan(a)) return Qfalse;
#endif
return (a >= b)?Qtrue:Qfalse;
}```
float.abs → float

Returns the absolute value of `float`.

``````(-34.56).abs   #=> 34.56
-34.56.abs     #=> 34.56
``````
```static VALUE
flo_abs(VALUE flt)
{
double val = fabs(RFLOAT_VALUE(flt));
return DBL2NUM(val);
}```
flo.angle → 0 or float

Returns 0 if the value is positive, pi otherwise.

```static VALUE
float_arg(VALUE self)
{
if (isnan(RFLOAT_VALUE(self)))
return self;
if (f_tpositive_p(self))
return INT2FIX(0);
return rb_const_get(rb_mMath, id_PI);
}```
flo.arg → 0 or float

Returns 0 if the value is positive, pi otherwise.

```static VALUE
float_arg(VALUE self)
{
if (isnan(RFLOAT_VALUE(self)))
return self;
if (f_tpositive_p(self))
return INT2FIX(0);
return rb_const_get(rb_mMath, id_PI);
}```
float.ceil → integer

Returns the smallest Integer greater than or equal to `float`.

``````1.2.ceil      #=> 2
2.0.ceil      #=> 2
(-1.2).ceil   #=> -1
(-2.0).ceil   #=> -2
``````
```static VALUE
flo_ceil(VALUE num)
{
double f = ceil(RFLOAT_VALUE(num));
long val;

if (!FIXABLE(f)) {
return rb_dbl2big(f);
}
val = (long)f;
return LONG2FIX(val);
}```
float.coerce(numeric) → array

Returns an array with both a `numeric` and a `float` represented as Float objects.

This is achieved by converting a `numeric` to a Float.

``````1.2.coerce(3)       #=> [3.0, 1.2]
2.5.coerce(1.1)     #=> [1.1, 2.5]
``````
```static VALUE
flo_coerce(VALUE x, VALUE y)
{
return rb_assoc_new(rb_Float(y), x);
}```
dclone()

provides a unified `clone` operation, for REXML::XPathParser to use across multiple Object types

```# File lib/rexml/xpath_parser.rb, line 28
def dclone ; self ; end```
flo.denominator → integer

Returns the denominator (always positive). The result is machine dependent.

See numerator.

```static VALUE
float_denominator(VALUE self)
{
double d = RFLOAT_VALUE(self);
if (isinf(d) || isnan(d))
return INT2FIX(1);
return rb_call_super(0, 0);
}```
float.divmod(numeric) → array

See Numeric#divmod.

``````42.0.divmod 6 #=> [7, 0.0]
42.0.divmod 5 #=> [8, 2.0]
``````
```static VALUE
flo_divmod(VALUE x, VALUE y)
{
double fy, div, mod;
volatile VALUE a, b;

if (RB_TYPE_P(y, T_FIXNUM)) {
fy = (double)FIX2LONG(y);
}
else if (RB_TYPE_P(y, T_BIGNUM)) {
fy = rb_big2dbl(y);
}
else if (RB_TYPE_P(y, T_FLOAT)) {
fy = RFLOAT_VALUE(y);
}
else {
return rb_num_coerce_bin(x, y, id_divmod);
}
flodivmod(RFLOAT_VALUE(x), fy, &div, &mod);
a = dbl2ival(div);
b = DBL2NUM(mod);
return rb_assoc_new(a, b);
}```
float.eql?(obj) → true or false

Returns `true` only if `obj` is a Float with the same value as `float`. Contrast this with Float#==, which performs type conversions.

The result of `NaN.eql?(NaN)` is undefined, so the implementation-dependent value is returned.

``````1.0.eql?(1)   #=> false
``````
```static VALUE
flo_eql(VALUE x, VALUE y)
{
if (RB_TYPE_P(y, T_FLOAT)) {
double a = RFLOAT_VALUE(x);
double b = RFLOAT_VALUE(y);
#if defined(_MSC_VER) && _MSC_VER < 1300
if (isnan(a) || isnan(b)) return Qfalse;
#endif
if (a == b)
return Qtrue;
}
return Qfalse;
}```
float.fdiv(numeric) → float

Returns `float / numeric`, same as Float#/.

```static VALUE
flo_quo(VALUE x, VALUE y)
{
return rb_funcall(x, '/', 1, y);
}```
float.finite? → true or false

Returns `true` if `float` is a valid IEEE floating point number (it is not infinite, and #nan? is `false`).

```static VALUE
flo_is_finite_p(VALUE num)
{
double value = RFLOAT_VALUE(num);

#ifdef HAVE_ISFINITE
if (!isfinite(value))
return Qfalse;
#else
if (isinf(value) || isnan(value))
return Qfalse;
#endif

return Qtrue;
}```
float.floor → integer

Returns the largest integer less than or equal to `float`.

``````1.2.floor      #=> 1
2.0.floor      #=> 2
(-1.2).floor   #=> -2
(-2.0).floor   #=> -2
``````
```static VALUE
flo_floor(VALUE num)
{
double f = floor(RFLOAT_VALUE(num));
long val;

if (!FIXABLE(f)) {
return rb_dbl2big(f);
}
val = (long)f;
return LONG2FIX(val);
}```
float.hash → integer

Returns a hash code for this float.

See also Object#hash.

```static VALUE
flo_hash(VALUE num)
{
return rb_dbl_hash(RFLOAT_VALUE(num));
}```
float.infinite? → nil, -1, +1

Return values corresponding to the value of `float`:

finite

`nil`

-Infinity

`-1`

+`Infinity`

`1`

For example:

``````(0.0).infinite?        #=> nil
(-1.0/0.0).infinite?   #=> -1
(+1.0/0.0).infinite?   #=> 1
``````
```static VALUE
flo_is_infinite_p(VALUE num)
{
double value = RFLOAT_VALUE(num);

if (isinf(value)) {
return INT2FIX( value < 0 ? -1 : 1 );
}

return Qnil;
}```
inspect()
Alias for: to_s
float.magnitude → float

Returns the absolute value of `float`.

``````(-34.56).abs   #=> 34.56
-34.56.abs     #=> 34.56
``````
```static VALUE
flo_abs(VALUE flt)
{
double val = fabs(RFLOAT_VALUE(flt));
return DBL2NUM(val);
}```
float.modulo(other) → float

Return the modulo after division of `float` by `other`.

``````6543.21.modulo(137)      #=> 104.21
6543.21.modulo(137.24)   #=> 92.9299999999996
``````
```static VALUE
flo_mod(VALUE x, VALUE y)
{
double fy;

if (RB_TYPE_P(y, T_FIXNUM)) {
fy = (double)FIX2LONG(y);
}
else if (RB_TYPE_P(y, T_BIGNUM)) {
fy = rb_big2dbl(y);
}
else if (RB_TYPE_P(y, T_FLOAT)) {
fy = RFLOAT_VALUE(y);
}
else {
return rb_num_coerce_bin(x, y, '%');
}
return DBL2NUM(ruby_float_mod(RFLOAT_VALUE(x), fy));
}```
float.nan? → true or false

Returns `true` if `float` is an invalid IEEE floating point number.

``````a = -1.0      #=> -1.0
a.nan?        #=> false
a = 0.0/0.0   #=> NaN
a.nan?        #=> true
``````
```static VALUE
flo_is_nan_p(VALUE num)
{
double value = RFLOAT_VALUE(num);

return isnan(value) ? Qtrue : Qfalse;
}```
float.negative? → true or false

Returns `true` if `float` is less than 0.

```static VALUE
flo_negative_p(VALUE num)
{
double f = RFLOAT_VALUE(num);
return f < 0.0 ? Qtrue : Qfalse;
}```
float.next_float → float

Returns the next representable floating-point number.

Float::MAX.next_float and Float::INFINITY.next_float is Float::INFINITY.

Float::NAN.next_float is Float::NAN.

For example:

``````p 0.01.next_float  #=> 0.010000000000000002
p 1.0.next_float   #=> 1.0000000000000002
p 100.0.next_float #=> 100.00000000000001

p 0.01.next_float - 0.01   #=> 1.734723475976807e-18
p 1.0.next_float - 1.0     #=> 2.220446049250313e-16
p 100.0.next_float - 100.0 #=> 1.4210854715202004e-14

f = 0.01; 20.times { printf "%-20a %s\n", f, f.to_s; f = f.next_float }
#=> 0x1.47ae147ae147bp-7 0.01
#   0x1.47ae147ae147cp-7 0.010000000000000002
#   0x1.47ae147ae147dp-7 0.010000000000000004
#   0x1.47ae147ae147ep-7 0.010000000000000005
#   0x1.47ae147ae147fp-7 0.010000000000000007
#   0x1.47ae147ae148p-7  0.010000000000000009
#   0x1.47ae147ae1481p-7 0.01000000000000001
#   0x1.47ae147ae1482p-7 0.010000000000000012
#   0x1.47ae147ae1483p-7 0.010000000000000014
#   0x1.47ae147ae1484p-7 0.010000000000000016
#   0x1.47ae147ae1485p-7 0.010000000000000018
#   0x1.47ae147ae1486p-7 0.01000000000000002
#   0x1.47ae147ae1487p-7 0.010000000000000021
#   0x1.47ae147ae1488p-7 0.010000000000000023
#   0x1.47ae147ae1489p-7 0.010000000000000024
#   0x1.47ae147ae148ap-7 0.010000000000000026
#   0x1.47ae147ae148bp-7 0.010000000000000028
#   0x1.47ae147ae148cp-7 0.01000000000000003
#   0x1.47ae147ae148dp-7 0.010000000000000031
#   0x1.47ae147ae148ep-7 0.010000000000000033

f = 0.0
100.times { f += 0.1 }
p f                            #=> 9.99999999999998       # should be 10.0 in the ideal world.
p 10-f                         #=> 1.9539925233402755e-14 # the floating-point error.
p(10.0.next_float-10)          #=> 1.7763568394002505e-15 # 1 ulp (units in the last place).
p((10-f)/(10.0.next_float-10)) #=> 11.0                   # the error is 11 ulp.
p((10-f)/(10*Float::EPSILON))  #=> 8.8                    # approximation of the above.
p "%a" % f                     #=> "0x1.3fffffffffff5p+3" # the last hex digit is 5.  16 - 5 = 11 ulp.
``````
```static VALUE
flo_next_float(VALUE vx)
{
double x, y;
x = NUM2DBL(vx);
y = nextafter(x, INFINITY);
return DBL2NUM(y);
}```
flo.numerator → integer

Returns the numerator. The result is machine dependent.

``````n = 0.3.numerator    #=> 5404319552844595
d = 0.3.denominator  #=> 18014398509481984
n.fdiv(d)            #=> 0.3
``````
```static VALUE
float_numerator(VALUE self)
{
double d = RFLOAT_VALUE(self);
if (isinf(d) || isnan(d))
return self;
return rb_call_super(0, 0);
}```
flo.phase → 0 or float

Returns 0 if the value is positive, pi otherwise.

```static VALUE
float_arg(VALUE self)
{
if (isnan(RFLOAT_VALUE(self)))
return self;
if (f_tpositive_p(self))
return INT2FIX(0);
return rb_const_get(rb_mMath, id_PI);
}```
float.positive? → true or false

Returns `true` if `float` is greater than 0.

```static VALUE
flo_positive_p(VALUE num)
{
double f = RFLOAT_VALUE(num);
return f > 0.0 ? Qtrue : Qfalse;
}```
float.prev_float → float

Returns the previous representable floating-point number.

(-Float::MAX).prev_float and (-Float::INFINITY).prev_float is -Float::INFINITY.

Float::NAN.prev_float is Float::NAN.

For example:

``````p 0.01.prev_float  #=> 0.009999999999999998
p 1.0.prev_float   #=> 0.9999999999999999
p 100.0.prev_float #=> 99.99999999999999

p 0.01 - 0.01.prev_float   #=> 1.734723475976807e-18
p 1.0 - 1.0.prev_float     #=> 1.1102230246251565e-16
p 100.0 - 100.0.prev_float #=> 1.4210854715202004e-14

f = 0.01; 20.times { printf "%-20a %s\n", f, f.to_s; f = f.prev_float }
#=> 0x1.47ae147ae147bp-7 0.01
#   0x1.47ae147ae147ap-7 0.009999999999999998
#   0x1.47ae147ae1479p-7 0.009999999999999997
#   0x1.47ae147ae1478p-7 0.009999999999999995
#   0x1.47ae147ae1477p-7 0.009999999999999993
#   0x1.47ae147ae1476p-7 0.009999999999999992
#   0x1.47ae147ae1475p-7 0.00999999999999999
#   0x1.47ae147ae1474p-7 0.009999999999999988
#   0x1.47ae147ae1473p-7 0.009999999999999986
#   0x1.47ae147ae1472p-7 0.009999999999999985
#   0x1.47ae147ae1471p-7 0.009999999999999983
#   0x1.47ae147ae147p-7  0.009999999999999981
#   0x1.47ae147ae146fp-7 0.00999999999999998
#   0x1.47ae147ae146ep-7 0.009999999999999978
#   0x1.47ae147ae146dp-7 0.009999999999999976
#   0x1.47ae147ae146cp-7 0.009999999999999974
#   0x1.47ae147ae146bp-7 0.009999999999999972
#   0x1.47ae147ae146ap-7 0.00999999999999997
#   0x1.47ae147ae1469p-7 0.009999999999999969
#   0x1.47ae147ae1468p-7 0.009999999999999967
``````
```static VALUE
flo_prev_float(VALUE vx)
{
double x, y;
x = NUM2DBL(vx);
y = nextafter(x, -INFINITY);
return DBL2NUM(y);
}```
float.quo(numeric) → float

Returns `float / numeric`, same as Float#/.

```static VALUE
flo_quo(VALUE x, VALUE y)
{
return rb_funcall(x, '/', 1, y);
}```
flt.rationalize([eps]) → rational

Returns a simpler approximation of the value (flt-|eps| <= result <= flt+|eps|). if the optional eps is not given, it will be chosen automatically.

``````0.3.rationalize          #=> (3/10)
1.333.rationalize        #=> (1333/1000)
1.333.rationalize(0.01)  #=> (4/3)
``````

See to_r.

```static VALUE
float_rationalize(int argc, VALUE *argv, VALUE self)
{
VALUE e;

if (f_negative_p(self))
return f_negate(float_rationalize(argc, argv, f_abs(self)));

rb_scan_args(argc, argv, "01", &e);

if (argc != 0) {
return rb_flt_rationalize_with_prec(self, e);
}
else {
return rb_flt_rationalize(self);
}
}```
float.round([ndigits]) → integer or float

Rounds `float` to a given precision in decimal digits (default 0 digits).

Precision may be negative. Returns a floating point number when `ndigits` is more than zero.

``````1.4.round      #=> 1
1.5.round      #=> 2
1.6.round      #=> 2
(-1.5).round   #=> -2

1.234567.round(2)  #=> 1.23
1.234567.round(3)  #=> 1.235
1.234567.round(4)  #=> 1.2346
1.234567.round(5)  #=> 1.23457

34567.89.round(-5) #=> 0
34567.89.round(-4) #=> 30000
34567.89.round(-3) #=> 35000
34567.89.round(-2) #=> 34600
34567.89.round(-1) #=> 34570
34567.89.round(0)  #=> 34568
34567.89.round(1)  #=> 34567.9
34567.89.round(2)  #=> 34567.89
34567.89.round(3)  #=> 34567.89
``````
```static VALUE
flo_round(int argc, VALUE *argv, VALUE num)
{
VALUE nd;
double number, f, x;
int ndigits = 0;
int binexp;
enum {float_dig = DBL_DIG+2};

if (argc > 0 && rb_scan_args(argc, argv, "01", &nd) == 1) {
ndigits = NUM2INT(nd);
}
if (ndigits < 0) {
return int_round_0(flo_truncate(num), ndigits);
}
number  = RFLOAT_VALUE(num);
if (ndigits == 0) {
return dbl2ival(number);
}
frexp(number, &binexp);

/* Let `exp` be such that `number` is written as:"0.#{digits}e#{exp}",
i.e. such that  10 ** (exp - 1) <= |number| < 10 ** exp
Recall that up to float_dig digits can be needed to represent a double,
so if ndigits + exp >= float_dig, the intermediate value (number * 10 ** ndigits)
will be an integer and thus the result is the original number.
If ndigits + exp <= 0, the result is 0 or "1e#{exp}", so
if ndigits + exp < 0, the result is 0.
We have:
2 ** (binexp-1) <= |number| < 2 ** binexp
10 ** ((binexp-1)/log_2(10)) <= |number| < 10 ** (binexp/log_2(10))
If binexp >= 0, and since log_2(10) = 3.322259:
10 ** (binexp/4 - 1) < |number| < 10 ** (binexp/3)
floor(binexp/4) <= exp <= ceil(binexp/3)
If binexp <= 0, swap the /4 and the /3
So if ndigits + floor(binexp/(4 or 3)) >= float_dig, the result is number
If ndigits + ceil(binexp/(3 or 4)) < 0 the result is 0
*/
if (isinf(number) || isnan(number) ||
(ndigits >= float_dig - (binexp > 0 ? binexp / 4 : binexp / 3 - 1))) {
return num;
}
if (ndigits < - (binexp > 0 ? binexp / 3 + 1 : binexp / 4)) {
return DBL2NUM(0);
}
f = pow(10, ndigits);
x = round(number * f);
if (x > 0) {
if ((double)((x + 0.5) / f) <= number) x += 1;
}
else {
if ((double)((x - 0.5) / f) >= number) x -= 1;
}
return DBL2NUM(x / f);}

/*
*  call-seq:
*     float.to_i      ->  integer
*     float.to_int    ->  integer
*     float.truncate  ->  integer
*
*  Returns the +float+ truncated to an Integer.
*
*  Synonyms are #to_i, #to_int, and #truncate.
*/

static VALUE
flo_truncate(VALUE num)
{
double f = RFLOAT_VALUE(num);
long val;

if (f > 0.0) f = floor(f);
if (f < 0.0) f = ceil(f);

if (!FIXABLE(f)) {
return rb_dbl2big(f);
}
val = (long)f;
return LONG2FIX(val);
}```
flt.to_d → bigdecimal

Convert `flt` to a BigDecimal and return it.

``````require 'bigdecimal'
require 'bigdecimal/util'

0.5.to_d
# => #<BigDecimal:1dc69e0,'0.5E0',9(18)>
``````
```# File ext/bigdecimal/lib/bigdecimal/util.rb, line 39
def to_d(precision=nil)
BigDecimal(self, precision || Float::DIG)
end```
float.to_f → self

Since `float` is already a float, returns `self`.

```static VALUE
flo_to_f(VALUE num)
{
return num;
}```
float.to_i → integer
float.to_int → integer

Returns the `float` truncated to an Integer.

Synonyms are to_i, to_int, and truncate.

```static VALUE
flo_truncate(VALUE num)
{
double f = RFLOAT_VALUE(num);
long val;

if (f > 0.0) f = floor(f);
if (f < 0.0) f = ceil(f);

if (!FIXABLE(f)) {
return rb_dbl2big(f);
}
val = (long)f;
return LONG2FIX(val);
}```
float.to_int → integer

Returns the `float` truncated to an Integer.

Synonyms are to_i, to_int, and truncate.

```static VALUE
flo_truncate(VALUE num)
{
double f = RFLOAT_VALUE(num);
long val;

if (f > 0.0) f = floor(f);
if (f < 0.0) f = ceil(f);

if (!FIXABLE(f)) {
return rb_dbl2big(f);
}
val = (long)f;
return LONG2FIX(val);
}```
flt.to_r → rational

Returns the value as a rational.

NOTE: 0.3.to_r isn't the same as '0.3'.to_r. The latter is equivalent to '3/10'.to_r, but the former isn't so.

``````2.0.to_r    #=> (2/1)
2.5.to_r    #=> (5/2)
-0.75.to_r  #=> (-3/4)
0.0.to_r    #=> (0/1)
``````

See rationalize.

```static VALUE
float_to_r(VALUE self)
{
VALUE f, n;

float_decode_internal(self, &f, &n);
#if FLT_RADIX == 2
{
long ln = FIX2LONG(n);

if (ln == 0)
return f_to_r(f);
if (ln > 0)
return f_to_r(f_lshift(f, n));
ln = -ln;
return rb_rational_new2(f, f_lshift(ONE, INT2FIX(ln)));
}
#else
return f_to_r(f_mul(f, f_expt(INT2FIX(FLT_RADIX), n)));
#endif
}```
float.to_s → string

Returns a string containing a representation of self. As well as a fixed or exponential form of the `float`, the call may return `NaN`, `Infinity`, and `-Infinity`.

Also aliased as: inspect
```static VALUE
flo_to_s(VALUE flt)
{
enum {decimal_mant = DBL_MANT_DIG-DBL_DIG};
enum {float_dig = DBL_DIG+1};
char buf[float_dig + (decimal_mant + CHAR_BIT - 1) / CHAR_BIT + 10];
double value = RFLOAT_VALUE(flt);
VALUE s;
char *p, *e;
int sign, decpt, digs;

if (isinf(value))
return rb_usascii_str_new2(value < 0 ? "-Infinity" : "Infinity");
else if (isnan(value))
return rb_usascii_str_new2("NaN");

p = ruby_dtoa(value, 0, 0, &decpt, &sign, &e);
s = sign ? rb_usascii_str_new_cstr("-") : rb_usascii_str_new(0, 0);
if ((digs = (int)(e - p)) >= (int)sizeof(buf)) digs = (int)sizeof(buf) - 1;
memcpy(buf, p, digs);
xfree(p);
if (decpt > 0) {
if (decpt < digs) {
memmove(buf + decpt + 1, buf + decpt, digs - decpt);
buf[decpt] = '.';
rb_str_cat(s, buf, digs + 1);
}
else if (decpt <= DBL_DIG) {
long len;
char *ptr;
rb_str_cat(s, buf, digs);
rb_str_resize(s, (len = RSTRING_LEN(s)) + decpt - digs + 2);
ptr = RSTRING_PTR(s) + len;
if (decpt > digs) {
memset(ptr, '0', decpt - digs);
ptr += decpt - digs;
}
memcpy(ptr, ".0", 2);
}
else {
goto exp;
}
}
else if (decpt > -4) {
long len;
char *ptr;
rb_str_cat(s, "0.", 2);
rb_str_resize(s, (len = RSTRING_LEN(s)) - decpt + digs);
ptr = RSTRING_PTR(s);
memset(ptr += len, '0', -decpt);
memcpy(ptr -= decpt, buf, digs);
}
else {
exp:
if (digs > 1) {
memmove(buf + 2, buf + 1, digs - 1);
}
else {
buf[2] = '0';
digs++;
}
buf[1] = '.';
rb_str_cat(s, buf, digs + 1);
rb_str_catf(s, "e%+03d", decpt - 1);
}
return s;
}```
float.truncate → integer

Returns the `float` truncated to an Integer.

Synonyms are to_i, to_int, and truncate.

```static VALUE
flo_truncate(VALUE num)
{
double f = RFLOAT_VALUE(num);
long val;

if (f > 0.0) f = floor(f);
if (f < 0.0) f = ceil(f);

if (!FIXABLE(f)) {
return rb_dbl2big(f);
}
val = (long)f;
return LONG2FIX(val);
}```
float.zero? → true or false

Returns `true` if `float` is 0.0.

```static VALUE
flo_zero_p(VALUE num)
{
if (RFLOAT_VALUE(num) == 0.0) {
return Qtrue;
}
return Qfalse;
}```