class Float

`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:

Constants

DIG

The minimum number of significant decimal digits in a double-precision floating point.

Usually defaults to 15.

EPSILON

The difference between 1 and the smallest double-precision floating point number greater than 1.

Usually defaults to 2.2204460492503131e-16.

INFINITY

An expression representing positive infinity.

MANT_DIG

The number of base digits for the `double` data type.

Usually defaults to 53.

MAX

The largest possible integer in a double-precision floating point number.

Usually defaults to 1.7976931348623157e+308.

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.

MAX_EXP

The largest possible exponent value in a double-precision floating point.

Usually defaults to 1024.

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.

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.

MIN_EXP

The smallest possible exponent value in a double-precision floating point.

Usually defaults to -1021.

NAN

An expression representing a value which is “not a number”.

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.

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

Public Instance Methods

float % other → float click to toggle source

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

```6543.21.modulo(137)      #=> 104.21000000000004
6543.21.modulo(137.24)   #=> 92.92999999999961
```
```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 click to toggle source

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

```VALUE
rb_float_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 click to toggle source

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

```2.0**3   #=> 8.0
```
```VALUE
rb_float_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_dbl_complex_new_polar_pi(pow(-dx, dy), dy);
}
else {
return rb_num_coerce_bin(x, y, idPow);
}
return DBL2NUM(pow(dx, dy));
}```
float + other → float click to toggle source

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

```VALUE
rb_float_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 click to toggle source

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 click to toggle source

Returns `float`, negated.

```VALUE
rb_float_uminus(VALUE flt)
{
return DBL2NUM(-RFLOAT_VALUE(flt));
}```
float / other → float click to toggle source

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

```static VALUE
flo_div(VALUE x, VALUE y)
{
double num = RFLOAT_VALUE(x);
double den;
double ret;

if (RB_TYPE_P(y, T_FIXNUM)) {
den = FIX2LONG(y);
}
else if (RB_TYPE_P(y, T_BIGNUM)) {
den = rb_big2dbl(y);
}
else if (RB_TYPE_P(y, T_FLOAT)) {
den = RFLOAT_VALUE(y);
}
else {
return rb_num_coerce_bin(x, y, '/');
}

ret = double_div_double(num, den);
return DBL2NUM(ret);
}```
float < real → true or false click to toggle source

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

The result of `NaN < NaN` is undefined, so an 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 click to toggle source

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

The result of `NaN <= NaN` is undefined, so an 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 click to toggle source

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

The result of `NaN <=> NaN` is undefined, so an 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 click to toggle source

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

```1.0 == 1   #=> true
```

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

```MJIT_FUNC_EXPORTED VALUE
rb_float_equal(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 click to toggle source

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

```1.0 == 1   #=> true
```

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

```MJIT_FUNC_EXPORTED VALUE
rb_float_equal(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 click to toggle source

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

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

```VALUE
rb_float_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 click to toggle source

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

The result of `NaN >= NaN` is undefined, so an 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;
}```
abs → float click to toggle source

Returns the absolute value of `float`.

```(-34.56).abs   #=> 34.56
-34.56.abs     #=> 34.56
34.56.abs      #=> 34.56
```

`Float#magnitude` is an alias for `Float#abs`.

```VALUE
rb_float_abs(VALUE flt)
{
double val = fabs(RFLOAT_VALUE(flt));
return DBL2NUM(val);
}```
angle → 0 or float click to toggle source

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);
}```
arg → 0 or float click to toggle source

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);
}```
ceil([ndigits]) → integer or float click to toggle source

Returns the smallest number greater than or equal to `float` with a precision of `ndigits` decimal digits (default: 0).

When the precision is negative, the returned value is an integer with at least `ndigits.abs` trailing zeros.

Returns a floating point number when `ndigits` is positive, otherwise returns an integer.

```1.2.ceil      #=> 2
2.0.ceil      #=> 2
(-1.2).ceil   #=> -1
(-2.0).ceil   #=> -2

1.234567.ceil(2)   #=> 1.24
1.234567.ceil(3)   #=> 1.235
1.234567.ceil(4)   #=> 1.2346
1.234567.ceil(5)   #=> 1.23457

34567.89.ceil(-5)  #=> 100000
34567.89.ceil(-4)  #=> 40000
34567.89.ceil(-3)  #=> 35000
34567.89.ceil(-2)  #=> 34600
34567.89.ceil(-1)  #=> 34570
34567.89.ceil(0)   #=> 34568
34567.89.ceil(1)   #=> 34567.9
34567.89.ceil(2)   #=> 34567.89
34567.89.ceil(3)   #=> 34567.89
```

Note that the limited precision of floating point arithmetic might lead to surprising results:

```(2.1 / 0.7).ceil  #=> 4 (!)
```
```static VALUE
flo_ceil(int argc, VALUE *argv, VALUE num)
{
double number, f;
int ndigits = 0;

if (rb_check_arity(argc, 0, 1)) {
ndigits = NUM2INT(argv[0]);
}
number = RFLOAT_VALUE(num);
if (number == 0.0) {
return ndigits > 0 ? DBL2NUM(number) : INT2FIX(0);
}
if (ndigits > 0) {
int binexp;
frexp(number, &binexp);
if (float_round_overflow(ndigits, binexp)) return num;
if (number < 0.0 && float_round_underflow(ndigits, binexp))
return DBL2NUM(0.0);
f = pow(10, ndigits);
f = ceil(number * f) / f;
return DBL2NUM(f);
}
else {
num = dbl2ival(ceil(number));
if (ndigits < 0) num = rb_int_ceil(num, ndigits);
return num;
}
}```
coerce(numeric) → array click to toggle source

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

This is achieved by converting `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() click to toggle source

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```
denominator → integer click to toggle source

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

See also `Float#numerator`.

```static VALUE
float_denominator(VALUE self)
{
double d = RFLOAT_VALUE(self);
VALUE r;
if (isinf(d) || isnan(d))
return INT2FIX(1);
r = float_to_r(self);
if (canonicalization && k_integer_p(r)) {
return ONE;
}
return nurat_denominator(r);
}```
divmod(numeric) → array click to toggle source
```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);
}```
eql?(obj) → true or false click to toggle source

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

```1.0.eql?(1)   #=> false
```

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

```MJIT_FUNC_EXPORTED VALUE
rb_float_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;
}```
fdiv(numeric) → float click to toggle source

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

```static VALUE
flo_quo(VALUE x, VALUE y)
{
return num_funcall1(x, '/', y);
}```
finite? → true or false click to toggle source

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

```VALUE
rb_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;
}```
floor([ndigits]) → integer or float click to toggle source

Returns the largest number less than or equal to `float` with a precision of `ndigits` decimal digits (default: 0).

When the precision is negative, the returned value is an integer with at least `ndigits.abs` trailing zeros.

Returns a floating point number when `ndigits` is positive, otherwise returns an integer.

```1.2.floor      #=> 1
2.0.floor      #=> 2
(-1.2).floor   #=> -2
(-2.0).floor   #=> -2

1.234567.floor(2)   #=> 1.23
1.234567.floor(3)   #=> 1.234
1.234567.floor(4)   #=> 1.2345
1.234567.floor(5)   #=> 1.23456

34567.89.floor(-5)  #=> 0
34567.89.floor(-4)  #=> 30000
34567.89.floor(-3)  #=> 34000
34567.89.floor(-2)  #=> 34500
34567.89.floor(-1)  #=> 34560
34567.89.floor(0)   #=> 34567
34567.89.floor(1)   #=> 34567.8
34567.89.floor(2)   #=> 34567.89
34567.89.floor(3)   #=> 34567.89
```

Note that the limited precision of floating point arithmetic might lead to surprising results:

```(0.3 / 0.1).floor  #=> 2 (!)
```
```static VALUE
flo_floor(int argc, VALUE *argv, VALUE num)
{
double number, f;
int ndigits = 0;

if (rb_check_arity(argc, 0, 1)) {
ndigits = NUM2INT(argv[0]);
}
number = RFLOAT_VALUE(num);
if (number == 0.0) {
return ndigits > 0 ? DBL2NUM(number) : INT2FIX(0);
}
if (ndigits > 0) {
int binexp;
frexp(number, &binexp);
if (float_round_overflow(ndigits, binexp)) return num;
if (number > 0.0 && float_round_underflow(ndigits, binexp))
return DBL2NUM(0.0);
f = pow(10, ndigits);
f = floor(number * f) / f;
return DBL2NUM(f);
}
else {
num = dbl2ival(floor(number));
if (ndigits < 0) num = rb_int_floor(num, ndigits);
return num;
}
}```
hash → integer click to toggle source

Returns a hash code for this float.

```static VALUE
flo_hash(VALUE num)
{
return rb_dbl_hash(RFLOAT_VALUE(num));
}```
infinite? → -1, 1, or nil click to toggle source

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

```(0.0).infinite?        #=> nil
(-1.0/0.0).infinite?   #=> -1
(+1.0/0.0).infinite?   #=> 1
```
```VALUE
rb_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
magnitude → float click to toggle source

Returns the absolute value of `float`.

```(-34.56).abs   #=> 34.56
-34.56.abs     #=> 34.56
34.56.abs      #=> 34.56
```

`Float#magnitude` is an alias for `Float#abs`.

```VALUE
rb_float_abs(VALUE flt)
{
double val = fabs(RFLOAT_VALUE(flt));
return DBL2NUM(val);
}```
modulo(other) → float click to toggle source

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

```6543.21.modulo(137)      #=> 104.21000000000004
6543.21.modulo(137.24)   #=> 92.92999999999961
```
```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));
}```
nan? → true or false click to toggle source

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;
}```
negative? → true or false click to toggle source

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;
}```
next_float → float click to toggle source

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:

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

0.01.next_float - 0.01     #=> 1.734723475976807e-18
1.0.next_float - 1.0       #=> 2.220446049250313e-16
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 }
f                           #=> 9.99999999999998       # should be 10.0 in the ideal world.
10-f                        #=> 1.9539925233402755e-14 # the floating point error.
10.0.next_float-10          #=> 1.7763568394002505e-15 # 1 ulp (unit in the last place).
(10-f)/(10.0.next_float-10) #=> 11.0                   # the error is 11 ulp.
(10-f)/(10*Float::EPSILON)  #=> 8.8                    # approximation of the above.
"%a" % 10                   #=> "0x1.4p+3"
"%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, HUGE_VAL);
return DBL2NUM(y);
}```
numerator → integer click to toggle source

Returns the numerator. The result is machine dependent.

```n = 0.3.numerator    #=> 5404319552844595
d = 0.3.denominator  #=> 18014398509481984
n.fdiv(d)            #=> 0.3
```

See also `Float#denominator`.

```static VALUE
float_numerator(VALUE self)
{
double d = RFLOAT_VALUE(self);
VALUE r;
if (isinf(d) || isnan(d))
return self;
r = float_to_r(self);
if (canonicalization && k_integer_p(r)) {
return r;
}
return nurat_numerator(r);
}```
phase → 0 or float click to toggle source

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);
}```
positive? → true or false click to toggle source

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;
}```
prev_float → float click to toggle source

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:

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

0.01 - 0.01.prev_float     #=> 1.734723475976807e-18
1.0 - 1.0.prev_float       #=> 1.1102230246251565e-16
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, -HUGE_VAL);
return DBL2NUM(y);
}```
quo(numeric) → float click to toggle source

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

```static VALUE
flo_quo(VALUE x, VALUE y)
{
return num_funcall1(x, '/', y);
}```
rationalize([eps]) → rational click to toggle source

Returns a simpler approximation of the value (flt-|eps| <= result <= flt+|eps|). If the optional argument `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 also `Float#to_r`.

```static VALUE
float_rationalize(int argc, VALUE *argv, VALUE self)
{
double d = RFLOAT_VALUE(self);

if (d < 0.0)
return rb_rational_uminus(float_rationalize(argc, argv, DBL2NUM(-d)));

if (rb_check_arity(argc, 0, 1)) {
return rb_flt_rationalize_with_prec(self, argv[0]);
}
else {
return rb_flt_rationalize(self);
}
}```
round([ndigits] [, half: mode]) → integer or float click to toggle source

Returns `float` rounded to the nearest value with a precision of `ndigits` decimal digits (default: 0).

When the precision is negative, the returned value is an integer with at least `ndigits.abs` trailing zeros.

Returns a floating point number when `ndigits` is positive, otherwise returns an integer.

```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
```

If the optional `half` keyword argument is given, numbers that are half-way between two possible rounded values will be rounded according to the specified tie-breaking `mode`:

• `:up` or `nil`: round half away from zero (default)

• `:down`: round half toward zero

• `:even`: round half toward the nearest even number

```2.5.round(half: :up)      #=> 3
2.5.round(half: :down)    #=> 2
2.5.round(half: :even)    #=> 2
3.5.round(half: :up)      #=> 4
3.5.round(half: :down)    #=> 3
3.5.round(half: :even)    #=> 4
(-2.5).round(half: :up)   #=> -3
(-2.5).round(half: :down) #=> -2
(-2.5).round(half: :even) #=> -2
```
```static VALUE
flo_round(int argc, VALUE *argv, VALUE num)
{
double number, f, x;
VALUE nd, opt;
int ndigits = 0;
enum ruby_num_rounding_mode mode;

if (rb_scan_args(argc, argv, "01:", &nd, &opt)) {
ndigits = NUM2INT(nd);
}
mode = rb_num_get_rounding_option(opt);
number = RFLOAT_VALUE(num);
if (number == 0.0) {
return ndigits > 0 ? DBL2NUM(number) : INT2FIX(0);
}
if (ndigits < 0) {
return rb_int_round(flo_to_i(num), ndigits, mode);
}
if (ndigits == 0) {
x = ROUND_CALL(mode, round, (number, 1.0));
return dbl2ival(x);
}
if (isfinite(number)) {
int binexp;
frexp(number, &binexp);
if (float_round_overflow(ndigits, binexp)) return num;
if (float_round_underflow(ndigits, binexp)) return DBL2NUM(0);
f = pow(10, ndigits);
x = ROUND_CALL(mode, round, (number, f));
return DBL2NUM(x / f);
}
return num;
}```
to_d → bigdecimal click to toggle source
to_d(precision) → bigdecimal

Returns the value of `float` as a `BigDecimal`. The `precision` parameter is used to determine the number of significant digits for the result (the default is `Float::DIG`).

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

0.5.to_d         # => 0.5e0
1.234.to_d(2)    # => 0.12e1
```

See also `BigDecimal::new`.

```# File ext/bigdecimal/lib/bigdecimal/util.rb, line 47
def to_d(precision=Float::DIG)
BigDecimal(self, precision)
end```
to_f → self click to toggle source

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

```static VALUE
flo_to_f(VALUE num)
{
return num;
}```
to_i → integer click to toggle source
to_int → integer

Returns the `float` truncated to an `Integer`.

```1.2.to_i      #=> 1
(-1.2).to_i   #=> -1
```

Note that the limited precision of floating point arithmetic might lead to surprising results:

```(0.3 / 0.1).to_i  #=> 2 (!)
```

`to_int` is an alias for `to_i`.

```static VALUE
flo_to_i(VALUE num)
{
double f = RFLOAT_VALUE(num);

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

return dbl2ival(f);
}```
to_int → integer click to toggle source

Returns the `float` truncated to an `Integer`.

```1.2.to_i      #=> 1
(-1.2).to_i   #=> -1
```

Note that the limited precision of floating point arithmetic might lead to surprising results:

```(0.3 / 0.1).to_i  #=> 2 (!)
```

`to_int` is an alias for `to_i`.

```static VALUE
flo_to_i(VALUE num)
{
double f = RFLOAT_VALUE(num);

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

return dbl2ival(f);
}```
to_r → rational click to toggle source

Returns the value as a rational.

```2.0.to_r    #=> (2/1)
2.5.to_r    #=> (5/2)
-0.75.to_r  #=> (-3/4)
0.0.to_r    #=> (0/1)
0.3.to_r    #=> (5404319552844595/18014398509481984)
```

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.

```0.3.to_r   == 3/10r  #=> false
"0.3".to_r == 3/10r  #=> true
```

See also `Float#rationalize`.

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

float_decode_internal(self, &f, &n);
{
long ln = FIX2LONG(n);

if (ln == 0)
return rb_rational_new1(f);
if (ln > 0)
return rb_rational_new1(rb_int_lshift(f, n));
ln = -ln;
return rb_rational_new2(f, rb_int_lshift(ONE, INT2FIX(ln)));
}
#else
if (RB_TYPE_P(f, T_RATIONAL))
return f;
return rb_rational_new1(f);
#endif
}```
to_s → string click to toggle source

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`.

```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)) {
static const char minf[] = "-Infinity";
const int pos = (value > 0); /* skip "-" */
return rb_usascii_str_new(minf+pos, strlen(minf)-pos);
}
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;
}```
Also aliased as: inspect
truncate([ndigits]) → integer or float click to toggle source

Returns `float` truncated (toward zero) to a precision of `ndigits` decimal digits (default: 0).

When the precision is negative, the returned value is an integer with at least `ndigits.abs` trailing zeros.

Returns a floating point number when `ndigits` is positive, otherwise returns an integer.

```2.8.truncate           #=> 2
(-2.8).truncate        #=> -2
1.234567.truncate(2)   #=> 1.23
34567.89.truncate(-2)  #=> 34500
```

Note that the limited precision of floating point arithmetic might lead to surprising results:

```(0.3 / 0.1).truncate  #=> 2 (!)
```
```static VALUE
flo_truncate(int argc, VALUE *argv, VALUE num)
{
if (signbit(RFLOAT_VALUE(num)))
return flo_ceil(argc, argv, num);
else
return flo_floor(argc, argv, num);
}```
zero? → true or false click to toggle source

Returns `true` if `float` is 0.0.

```static VALUE
flo_zero_p(VALUE num)
{
return flo_iszero(num) ? Qtrue : Qfalse;
}```