Class: Float

Relationships & Source Files
Super Chains via Extension / Inclusion / Inheritance
Class Chain: self, `::Numeric`
Instance Chain: self, `::Numeric`, `::Comparable`
Inherits:	Numeric `::Object` Numeric Float
Defined in:	numeric.c, complex.c, numeric.rb, rational.c

Overview

A Float object represents a sometimes-inexact real number 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:

You can create a Float object explicitly with:

A floating-point literal.

You can convert certain objects to Floats with:

Method {Kernel.html#method-i-Float }.

What’s Here

First, what’s elsewhere. Class Float:

Inherits from [class Numeric](Numeric.html#class-Numeric-label-What-27s+Here).

Here, class Float provides methods for:

Querying
Comparing
Converting

Querying

#finite?

Returns whether self is finite.
#hash

Returns the integer hash code for self.
#infinite?

Returns whether self is infinite.
#nan?

Returns whether self is a NaN (not-a-number).

Comparing

<

Returns whether self is less than the given value.
<=
Returns whether self is less than
```
or equal to the given value.
```
<=>
Returns a number indicating whether self is less than,
```
equal to, or greater than the given value.
```
== (aliased as #=== and #eql>)

Returns whether self is
```
equal to the given value.
```
>

Returns whether self is greater than the given value.
>=
Returns whether self is greater than
```
or equal to the given value.
```

Converting

#% (aliased as #modulo)

Returns self modulo the given value.
#*

Returns the product of self and the given value.
**

Returns the value of self raised to the power of the given value.
#+

Returns the sum of self and the given value.
#-

Returns the difference of self and the given value.
/

Returns the quotient of self and the given value.
#ceil

Returns the smallest number greater than or equal to self.
#coerce
Returns a 2-element array containing the given value converted to a Float
```
and self
```
#divmod

Returns a 2-element array containing the quotient and remainder results of dividing self by the given value.
#fdiv

Returns the Float result of dividing self by the given value.
#floor

Returns the greatest number smaller than or equal to self.
#next_float

Returns the next-larger representable Float.
#prev_float

Returns the next-smaller representable Float.
#quo

Returns the quotient from dividing self by the given value.
#round

Returns self rounded to the nearest value, to a given precision.
#to_i (aliased as #to_int)

Returns self truncated to an ::Integer.
#to_s (aliased as #inspect)

Returns a string containing the place-value
```
representation of self in the given radix.
```
#truncate

Returns self truncated to a given precision.

Constant Summary

DIG =

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

Usually defaults to 15.

# File 'numeric.c', line 6323
```
INT2FIX(DBL_DIG)
```
EPSILON =

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

Usually defaults to 2.2204460492503131e-16.

# File 'numeric.c', line 6375
```
DBL2NUM(DBL_EPSILON)
```
INFINITY =

An expression representing positive infinity.

# File 'numeric.c', line 6379
```
DBL2NUM(HUGE_VAL)
```
MANT_DIG =

The number of base digits for the double data type.

Usually defaults to 53.

# File 'numeric.c', line 6316
```
INT2FIX(DBL_MANT_DIG)
```
MAX =

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

Usually defaults to 1.7976931348623157e+308.

# File 'numeric.c', line 6368
```
DBL2NUM(DBL_MAX)
```
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.

# File 'numeric.c', line 6351
```
INT2FIX(DBL_MAX_10_EXP)
```
MAX_EXP =

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

Usually defaults to 1024.

# File 'numeric.c', line 6337
```
INT2FIX(DBL_MAX_EXP)
```

MIN =

:MIN. 0.0.next_float returns the smallest positive floating point number including denormalized numbers.

# File 'numeric.c', line 6362

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_10_EXP =

The smallest negative exponent in a double-precision floating point where 10 raised to this power minus 1.

Usually defaults to -307.

# File 'numeric.c', line 6344
```
INT2FIX(DBL_MIN_10_EXP)
```
MIN_EXP =

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

Usually defaults to -1021.

# File 'numeric.c', line 6330
```
INT2FIX(DBL_MIN_EXP)
```
NAN =

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

# File 'numeric.c', line 6383
```
DBL2NUM(nan(""))
```
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.

# File 'numeric.c', line 6310
```
INT2FIX(FLT_RADIX)
```

Instance Attribute Summary

#finite? ⇒ Boolean readonly

Returns true if self is not Infinity, -Infinity, or Nan, false otherwise:
#infinite? ⇒ Boolean readonly

Returns:
#nan? ⇒ Boolean readonly

Returns true if self is a NaN, false otherwise.
#negative? ⇒ Boolean readonly

Returns true if float is less than 0.
#positive? ⇒ Boolean readonly

Returns true if float is greater than 0.
#zero? ⇒ Boolean readonly

Returns true if float is 0.0.

`::Numeric` - Inherited

#finite?	Returns `true` if `num` is a finite number, otherwise returns `false`.
#infinite?	Returns `nil`, -1, or 1 depending on whether the value is finite, `-Infinity`, or `+Infinity`.
#integer?	Returns `true` if `num` is an `::Integer`.
#negative?	Returns `true` if `self` is less than 0, `false` otherwise.
#nonzero?	Returns `self` if `self` is not a zero value, `nil` otherwise; uses method #zero? for the evaluation.
#positive?	Returns `true` if `self` is greater than 0, `false` otherwise.
#real	Returns self.
#real?	Returns `true` if `num` is a real number (i.e.
#zero?	Returns `true` if `zero` has a zero value, `false` otherwise.

Instance Method Summary

#%(other) ⇒ Float (also: #modulo)

Returns self modulo other as a float.
#*(other) ⇒ Numeric

Returns a new Float which is the product of self and other:
#**(other) ⇒ Numeric

Raises self to the power of other:
#+(other) ⇒ Numeric

Returns a new Float which is the sum of self and other:
#-(other) ⇒ Numeric

Returns a new Float which is the difference of self and other:
#- ⇒ Float

Returns float, negated.
#/(other) ⇒ Numeric

Returns a new Float which is the result of dividing self by other:
#<(other) ⇒ Boolean

Returns true if self is numerically less than other:
#<=(other) ⇒ Boolean

Returns true if self is numerically less than or equal to other:
#<=>(other) ⇒ 1, ...

Returns a value that depends on the numeric relation between self and other:
#==
#===
#>(other) ⇒ Boolean

Returns true if self is numerically greater than other:
#>=(other) ⇒ Boolean

Returns true if self is numerically greater than or equal to other:
#abs ⇒ Float

Returns the absolute value of float.
#angle ⇒ 0, Float

Alias for #arg.
#arg ⇒ 0, Float (also: #angle, #phase)

Returns 0 if the value is positive, pi otherwise.
#ceil(ndigits = 0) ⇒ Float, Integer

Returns the smallest number greater than or equal to self with a precision of ndigits decimal digits.
#coerce(other) ⇒ Array

Returns a 2-element array containing other converted to a Float and self:
#denominator ⇒ Integer

Returns the denominator (always positive).
#divmod(other) ⇒ Array

Returns a 2-element array [q, r], where.
#eql? ⇒ Boolean
#fdiv(other) ⇒ Numeric

Alias for #quo.
#floor(ndigits = 0) ⇒ Float, Integer

Returns the largest number less than or equal to self with a precision of ndigits decimal digits.
#hash ⇒ Integer

Returns the integer hash value for self.
#inspect ⇒ String

Alias for #to_s.
#magnitude
#modulo(other) ⇒ Float

Alias for #%.
#next_float ⇒ Float

Returns the next-larger representable Float.
#numerator ⇒ Integer

Returns the numerator.
#phase ⇒ 0, Float

Alias for #arg.
#prev_float ⇒ Float

Returns the next-smaller representable Float.
#quo(other) ⇒ Numeric (also: #fdiv)

Returns the quotient from dividing self by other:
#rationalize([eps]) ⇒ Rational

Returns a simpler approximation of the value (flt-|eps| <= result <= flt+|eps|).
#round(ndigits = 0, half: :up]) ⇒ Integer, Float

Returns self rounded to the nearest value with a precision of ndigits decimal digits.
#to_f ⇒ self

Since float is already a Float, returns self.
#to_i ⇒ Integer (also: #to_int)

Returns self truncated to an ::Integer.
#to_int ⇒ Integer

Alias for #to_i.
#to_r ⇒ Rational

Returns the value as a rational.
#to_s ⇒ String (also: #inspect)

Returns a string containing a representation of self; depending of the value of self, the string representation may contain:
#truncate(ndigits = 0) ⇒ Float, Integer

Returns self truncated (toward zero) to a precision of ndigits decimal digits.

`::Numeric` - Inherited

#%	Returns `self` modulo `other` as a real number.
#+@	Returns `self`.
#-@	Unary Minus—Returns the receiver, negated.
#<=>	Returns zero if `self` is the same as `other`, `nil` otherwise.
#abs	Returns the absolute value of `self`.
#abs2	Returns square of self.
#angle	Alias for Numeric#arg.
#arg	Returns 0 if the value is positive, pi otherwise.
#ceil	Returns the smallest number that is greater than or equal to `self` with a precision of `digits` decimal digits.
#clone	Returns `self`.
#coerce	Returns a 2-element array containing two numeric elements, formed from the two operands `self` and `other`, of a common compatible type.
#conj	Returns self.
#conjugate	Alias for Numeric#conj.
#denominator	Returns the denominator (always positive).
#div	Returns the quotient `self/other` as an integer (via #floor), using method `/` in the derived class of `self`.
#divmod	Returns a 2-element array `[q, r]`, where.
#dup	Returns `self`.
#eql?	Returns `true` if `self` and `other` are the same type and have equal values.
#fdiv	Returns the quotient `self/other` as a float, using method `/` in the derived class of `self`.
#floor	Returns the largest number that is less than or equal to `self` with a precision of `digits` decimal digits.
#i	Returns `Complex(0, self)`:
#imag	Returns zero.
#imaginary	Alias for Numeric#imag.
#magnitude	Alias for Numeric#abs.
#modulo	Alias for Numeric#%.
#numerator	Returns the numerator.
#phase	Alias for Numeric#arg.
#polar	Returns an array; [num.abs, num.arg].
#quo	Returns the most exact division (rational for integers, float for floats).
#rect	Returns an array; [num, 0].
#rectangular	Alias for Numeric#rect.
#remainder	Returns the remainder after dividing `self` by `other`.
#round	Returns `self` rounded to the nearest value with a precision of `digits` decimal digits.
#step	Generates a sequence of numbers; with a block given, traverses the sequence.
#to_c	Returns the value as a complex.
#to_int	Returns `self` as an integer; converts using method #to_i in the derived class.
#truncate	Returns `self` truncated (toward zero) to a precision of `digits` decimal digits.
#singleton_method_added	Trap attempts to add methods to `::Numeric` objects.

`::Comparable` - Included

#<	Compares two objects based on the receiver’s #<=> method, returning true if it returns a value less than 0.
#<=	Compares two objects based on the receiver’s #<=> method, returning true if it returns a value less than or equal to 0.
#==	Compares two objects based on the receiver’s #<=> method, returning true if it returns 0.
#>	Compares two objects based on the receiver’s #<=> method, returning true if it returns a value greater than 0.
#>=	Compares two objects based on the receiver’s #<=> method, returning true if it returns a value greater than or equal to 0.
#between?	Returns `false` if obj #<=> min is less than zero or if obj #<=> max is greater than zero, `true` otherwise.
#clamp	In `(min, max)` form, returns min if obj #<=> min is less than zero, max if obj #<=> max is greater than zero, and obj otherwise.

Instance Attribute Details

#finite? ⇒ `Boolean` (readonly)

Returns true if self is not Infinity, -Infinity, or Nan, false otherwise:

f = 2.0      # => 2.0
f.finite?    # => true
f = 1.0/0.0  # => Infinity
f.finite?    # => false
f = -1.0/0.0 # => -Infinity
f.finite?    # => false
f = 0.0/0.0  # => NaN
f.finite?    # => false

[ GitHub ]

# File 'numeric.c', line 2022


VALUE
rb_flo_is_finite_p(VALUE num)
{
    double value = RFLOAT_VALUE(num);

    return RBOOL(isfinite(value));
}

#infinite? ⇒ `Boolean` (readonly)

Returns:

1, if self is Infinity.
-1 if self is -Infinity.
nil, otherwise.

Examples:

f = 1.0/0.0  # => Infinity
f.infinite?  # => 1
f = -1.0/0.0 # => -Infinity
f.infinite?  # => -1
f = 1.0      # => 1.0
f.infinite?  # => nil
f = 0.0/0.0  # => NaN
f.infinite?  # => nil

[ GitHub ]

# File 'numeric.c', line 1992


VALUE
rb_flo_is_infinite_p(VALUE num)
{
    double value = RFLOAT_VALUE(num);

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

    return Qnil;
}

#nan? ⇒ `Boolean` (readonly)

Returns true if self is a NaN, false otherwise.

f = -1.0     #=> -1.0
f.nan?       #=> false
f = 0.0/0.0  #=> NaN
f.nan?       #=> true

[ GitHub ]

# File 'numeric.c', line 1961


static VALUE
flo_is_nan_p(VALUE num)
{
    double value = RFLOAT_VALUE(num);

    return RBOOL(isnan(value));
}

#negative? ⇒ `Boolean` (readonly)

Returns true if float is less than 0.

[ GitHub ]

# File 'numeric.rb', line 327


def negative?
  Primitive.attr! 'inline'
  Primitive.cexpr! 'RBOOL(RFLOAT_VALUE(self) < 0.0)'
end

#positive? ⇒ `Boolean` (readonly)

Returns true if float is greater than 0.

[ GitHub ]

# File 'numeric.rb', line 316


def positive?
  Primitive.attr! 'inline'
  Primitive.cexpr! 'RBOOL(RFLOAT_VALUE(self) > 0.0)'
end

#zero? ⇒ `Boolean` (readonly)

Returns true if float is 0.0.

[ GitHub ]

# File 'numeric.rb', line 305


def zero?
  Primitive.attr! 'inline'
  Primitive.cexpr! 'RBOOL(FLOAT_ZERO_P(self))'
end

Instance Method Details

#%(other) ⇒ `Float` Also known as: #modulo

Returns self modulo other as a float.

For float f and real number r, these expressions are equivalent:

f % r
f-r*(f/r).floor
f.divmod(r)[1]

See Numeric#divmod.

Examples:

10.0 % 2              # => 0.0
10.0 % 3              # => 1.0
10.0 % 4              # => 2.0

10.0 % -2             # => 0.0
10.0 % -3             # => -2.0
10.0 % -4             # => -2.0

10.0 % 4.0            # => 2.0
10.0 % Rational(4, 1) # => 2.0

#modulo is an alias for %.

[ GitHub ]

# File 'numeric.c', line 1416


static VALUE
flo_mod(VALUE x, VALUE y)
{
    double fy;

    if (FIXNUM_P(y)) {
	fy = (double)FIX2LONG(y);
    }
    else if (RB_BIGNUM_TYPE_P(y)) {
	fy = rb_big2dbl(y);
    }
    else if (RB_FLOAT_TYPE_P(y)) {
	fy = RFLOAT_VALUE(y);
    }
    else {
	return rb_num_coerce_bin(x, y, '%');
    }
    return DBL2NUM(ruby_float_mod(RFLOAT_VALUE(x), fy));
}

#*(other) ⇒ Numeric

Returns a new Float which is the product of self and other:

f = 3.14
f * 2              # => 6.28
f * 2.0            # => 6.28
f * Rational(1, 2) # => 1.57
f * Complex(2, 0)  # => (6.28+0.0i)

[ GitHub ]

# File 'numeric.c', line 1233


VALUE
rb_float_mul(VALUE x, VALUE y)
{
    if (FIXNUM_P(y)) {
	return DBL2NUM(RFLOAT_VALUE(x) * (double)FIX2LONG(y));
    }
    else if (RB_BIGNUM_TYPE_P(y)) {
	return DBL2NUM(RFLOAT_VALUE(x) * rb_big2dbl(y));
    }
    else if (RB_FLOAT_TYPE_P(y)) {
	return DBL2NUM(RFLOAT_VALUE(x) * RFLOAT_VALUE(y));
    }
    else {
	return rb_num_coerce_bin(x, y, '*');
    }
}

#**(other) ⇒ Numeric

Raises self to the power of other:

f = 3.14
f ** 2              # => 9.8596
f ** -2             # => 0.1014239928597509
f ** 2.1            # => 11.054834900588839
f ** Rational(2, 1) # => 9.8596
f ** Complex(2, 0)  # => (9.8596+0i)

[ GitHub ]

# File 'numeric.c', line 1510


VALUE
rb_float_pow(VALUE x, VALUE y)
{
    double dx, dy;
    if (y == INT2FIX(2)) {
	dx = RFLOAT_VALUE(x);
        return DBL2NUM(dx * dx);
    }
    else if (FIXNUM_P(y)) {
	dx = RFLOAT_VALUE(x);
	dy = (double)FIX2LONG(y);
    }
    else if (RB_BIGNUM_TYPE_P(y)) {
	dx = RFLOAT_VALUE(x);
	dy = rb_big2dbl(y);
    }
    else if (RB_FLOAT_TYPE_P(y)) {
	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));
}

#+(other) ⇒ Numeric

Returns a new Float which is the sum of self and other:

f = 3.14
f + 1                 # => 4.140000000000001
f + 1.0               # => 4.140000000000001
f + Rational(1, 1)    # => 4.140000000000001
f + Complex(1, 0)     # => (4.140000000000001+0i)

[ GitHub ]

# File 'numeric.c', line 1172


VALUE
rb_float_plus(VALUE x, VALUE y)
{
    if (FIXNUM_P(y)) {
	return DBL2NUM(RFLOAT_VALUE(x) + (double)FIX2LONG(y));
    }
    else if (RB_BIGNUM_TYPE_P(y)) {
	return DBL2NUM(RFLOAT_VALUE(x) + rb_big2dbl(y));
    }
    else if (RB_FLOAT_TYPE_P(y)) {
	return DBL2NUM(RFLOAT_VALUE(x) + RFLOAT_VALUE(y));
    }
    else {
	return rb_num_coerce_bin(x, y, '+');
    }
}

#-(other) ⇒ Numeric

Returns a new Float which is the difference of self and other:

f = 3.14
f - 1                 # => 2.14
f - 1.0               # => 2.14
f - Rational(1, 1)    # => 2.14
f - Complex(1, 0)     # => (2.14+0i)

[ GitHub ]

# File 'numeric.c', line 1203


VALUE
rb_float_minus(VALUE x, VALUE y)
{
    if (FIXNUM_P(y)) {
	return DBL2NUM(RFLOAT_VALUE(x) - (double)FIX2LONG(y));
    }
    else if (RB_BIGNUM_TYPE_P(y)) {
	return DBL2NUM(RFLOAT_VALUE(x) - rb_big2dbl(y));
    }
    else if (RB_FLOAT_TYPE_P(y)) {
	return DBL2NUM(RFLOAT_VALUE(x) - RFLOAT_VALUE(y));
    }
    else {
	return rb_num_coerce_bin(x, y, '-');
    }
}

#- ⇒ `Float`

Returns float, negated.

[ GitHub ]

# File 'numeric.rb', line 294


def -@
  Primitive.attr! 'inline'
  Primitive.cexpr! 'rb_float_uminus(self)'
end

#/(other) ⇒ Numeric

Returns a new Float which is the result of dividing self by other:

f = 3.14
f / 2              # => 1.57
f / 2.0            # => 1.57
f / Rational(2, 1) # => 1.57
f / Complex(2, 0)  # => (1.57+0.0i)

[ GitHub ]

# File 'numeric.c', line 1288


VALUE
rb_float_div(VALUE x, VALUE y)
{
    double num = RFLOAT_VALUE(x);
    double den;
    double ret;

    if (FIXNUM_P(y)) {
        den = FIX2LONG(y);
    }
    else if (RB_BIGNUM_TYPE_P(y)) {
        den = rb_big2dbl(y);
    }
    else if (RB_FLOAT_TYPE_P(y)) {
        den = RFLOAT_VALUE(y);
    }
    else {
	return rb_num_coerce_bin(x, y, '/');
    }

    ret = double_div_double(num, den);
    return DBL2NUM(ret);
}

#<(other) ⇒ `Boolean`

Returns true if self is numerically less than other:

2.0 < 3              # => true
2.0 < 3.0            # => true
2.0 < Rational(3, 1) # => true
2.0 < 2.0            # => false

Float::NAN < Float::NAN returns an implementation-dependent value.

[ GitHub ]

# File 'numeric.c', line 1838


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

    a = RFLOAT_VALUE(x);
    if (RB_INTEGER_TYPE_P(y)) {
        VALUE rel = rb_integer_float_cmp(y, x);
        if (FIXNUM_P(rel))
            return RBOOL(-FIX2LONG(rel) < 0);
        return Qfalse;
    }
    else if (RB_FLOAT_TYPE_P(y)) {
	b = RFLOAT_VALUE(y);
#if MSC_VERSION_BEFORE(1300)
	if (isnan(b)) return Qfalse;
#endif
    }
    else {
	return rb_num_coerce_relop(x, y, '<');
    }
#if MSC_VERSION_BEFORE(1300)
    if (isnan(a)) return Qfalse;
#endif
    return RBOOL(a < b);
}

#<=(other) ⇒ `Boolean`

Returns true if self is numerically less than or equal to other:

2.0 <= 3              # => true
2.0 <= 3.0            # => true
2.0 <= Rational(3, 1) # => true
2.0 <= 2.0            # => true
2.0 <= 1.0            # => false

Float::NAN <= Float::NAN returns an implementation-dependent value.

[ GitHub ]

# File 'numeric.c', line 1881


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

    a = RFLOAT_VALUE(x);
    if (RB_INTEGER_TYPE_P(y)) {
        VALUE rel = rb_integer_float_cmp(y, x);
        if (FIXNUM_P(rel))
            return RBOOL(-FIX2LONG(rel) <= 0);
        return Qfalse;
    }
    else if (RB_FLOAT_TYPE_P(y)) {
	b = RFLOAT_VALUE(y);
#if MSC_VERSION_BEFORE(1300)
	if (isnan(b)) return Qfalse;
#endif
    }
    else {
	return rb_num_coerce_relop(x, y, idLE);
    }
#if MSC_VERSION_BEFORE(1300)
    if (isnan(a)) return Qfalse;
#endif
    return RBOOL(a <= b);
}

#<=>(other) ⇒ `1`, ...

Returns a value that depends on the numeric relation between self and other:

-1, if self is less than other.
0, if self is equal to other.
1, if self is greater than other.
nil, if the two values are incommensurate.

Examples:

2.0 <=> 2              # => 0
  2.0 <=> 2.0            # => 0
  2.0 <=> Rational(2, 1) # => 0
  2.0 <=> Complex(2, 0)  # => 0
  2.0 <=> 1.9            # => 1
  2.0 <=> 2.1            # => -1
  2.0 <=> 'foo'          # => nil

This is the basis for the tests in the ::Comparable module.

Float::NAN <=> Float::NAN returns an implementation-dependent value.

[ GitHub ]

# File 'numeric.c', line 1700


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

    a = RFLOAT_VALUE(x);
    if (isnan(a)) return Qnil;
    if (RB_INTEGER_TYPE_P(y)) {
        VALUE rel = rb_integer_float_cmp(y, x);
        if (FIXNUM_P(rel))
            return LONG2FIX(-FIX2LONG(rel));
        return rel;
    }
    else if (RB_FLOAT_TYPE_P(y)) {
	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);
}

#==

[ GitHub ]

#===

[ GitHub ]

#>(other) ⇒ `Boolean`

Returns true if self is numerically greater than other:

2.0 > 1              # => true
2.0 > 1.0            # => true
2.0 > Rational(1, 2) # => true
2.0 > 2.0            # => false

Float::NAN > Float::NAN returns an implementation-dependent value.

[ GitHub ]

# File 'numeric.c', line 1753


VALUE
rb_float_gt(VALUE x, VALUE y)
{
    double a, b;

    a = RFLOAT_VALUE(x);
    if (RB_INTEGER_TYPE_P(y)) {
        VALUE rel = rb_integer_float_cmp(y, x);
        if (FIXNUM_P(rel))
            return RBOOL(-FIX2LONG(rel) > 0);
        return Qfalse;
    }
    else if (RB_FLOAT_TYPE_P(y)) {
	b = RFLOAT_VALUE(y);
#if MSC_VERSION_BEFORE(1300)
	if (isnan(b)) return Qfalse;
#endif
    }
    else {
	return rb_num_coerce_relop(x, y, '>');
    }
#if MSC_VERSION_BEFORE(1300)
    if (isnan(a)) return Qfalse;
#endif
    return RBOOL(a > b);
}

#>=(other) ⇒ `Boolean`

Returns true if self is numerically greater than or equal to other:

2.0 >= 1              # => true
2.0 >= 1.0            # => true
2.0 >= Rational(1, 2) # => true
2.0 >= 2.0            # => true
2.0 >= 2.1            # => false

Float::NAN >= Float::NAN returns an implementation-dependent value.

[ GitHub ]

# File 'numeric.c', line 1796


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

    a = RFLOAT_VALUE(x);
    if (RB_TYPE_P(y, T_FIXNUM) || RB_BIGNUM_TYPE_P(y)) {
        VALUE rel = rb_integer_float_cmp(y, x);
        if (FIXNUM_P(rel))
            return RBOOL(-FIX2LONG(rel) >= 0);
        return Qfalse;
    }
    else if (RB_FLOAT_TYPE_P(y)) {
	b = RFLOAT_VALUE(y);
#if MSC_VERSION_BEFORE(1300)
	if (isnan(b)) return Qfalse;
#endif
    }
    else {
	return rb_num_coerce_relop(x, y, idGE);
    }
#if MSC_VERSION_BEFORE(1300)
    if (isnan(a)) return Qfalse;
#endif
    return RBOOL(a >= b);
}

#abs ⇒ `Float` #magnitude ⇒ `Float`

Returns the absolute value of float.

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

#magnitude is an alias for abs.

[ GitHub ]

# File 'numeric.rb', line 278


def abs
  Primitive.attr! 'inline'
  Primitive.cexpr! 'rb_float_abs(self)'
end

#arg ⇒ `0`, `Float` #angle ⇒ `0`, `Float` #phase ⇒ `0`, `Float`

Alias for #arg.

#arg ⇒ `0`, `Float` #angle ⇒ `0`, `Float` #phase ⇒ `0`, `Float`
Also known as: #angle, #phase

Returns 0 if the value is positive, pi otherwise.

[ GitHub ]

# File 'complex.c', line 2253


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 = 0) ⇒ `Float`, Integer

Returns the smallest number greater than or equal to self with a precision of ndigits decimal digits.

When ndigits is positive, returns a float with ndigits digits after the decimal point (as available):

f = 12345.6789
f.ceil(1) # => 12345.7
f.ceil(3) # => 12345.679
f = -12345.6789
f.ceil(1) # => -12345.6
f.ceil(3) # => -12345.678

When ndigits is non-positive, returns an integer with at least ndigits.abs trailing zeros:

f = 12345.6789
f.ceil(0)  # => 12346
f.ceil(-3) # => 13000
f = -12345.6789
f.ceil(0)  # => -12345
f.ceil(-3) # => -12000

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

(2.1 / 0.7).ceil  #=> 4 (!)

Related: #floor.

[ GitHub ]

# File 'numeric.c', line 2247


static VALUE
flo_ceil(int argc, VALUE *argv, VALUE num)
{
    int ndigits = flo_ndigits(argc, argv);
    return rb_float_ceil(num, ndigits);
}

#coerce(other) ⇒ Array

Returns a 2-element array containing other converted to a Float and self:

f = 3.14                 # => 3.14
f.coerce(2)              # => [2.0, 3.14]
f.coerce(2.0)            # => [2.0, 3.14]
f.coerce(Rational(1, 2)) # => [0.5, 3.14]
f.coerce(Complex(1, 0))  # => [1.0, 3.14]

Raises an exception if a type conversion fails.

[ GitHub ]

# File 'numeric.c', line 1146


static VALUE
flo_coerce(VALUE x, VALUE y)
{
    return rb_assoc_new(rb_Float(y), x);
}

#denominator ⇒ Integer

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

#divmod(other) ⇒ Array

Returns a 2-element array [q, r], where

q = (self/other).floor      # Quotient
r = self % other            # Remainder

Examples:

11.0.divmod(4)              # => [2, 3.0]
11.0.divmod(-4)             # => [-3, -1.0]
-11.0.divmod(4)             # => [-3, 1.0]
-11.0.divmod(-4)            # => [2, -3.0]

12.0.divmod(4)              # => [3, 0.0]
12.0.divmod(-4)             # => [-3, 0.0]
-12.0.divmod(4)             # => [-3, -0.0]
-12.0.divmod(-4)            # => [3, -0.0]

13.0.divmod(4.0)            # => [3, 1.0]
13.0.divmod(Rational(4, 1)) # => [3, 1.0]

[ GitHub ]

# File 'numeric.c', line 1471


static VALUE
flo_divmod(VALUE x, VALUE y)
{
    double fy, div, mod;
    volatile VALUE a, b;

    if (FIXNUM_P(y)) {
	fy = (double)FIX2LONG(y);
    }
    else if (RB_BIGNUM_TYPE_P(y)) {
	fy = rb_big2dbl(y);
    }
    else if (RB_FLOAT_TYPE_P(y)) {
	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? ⇒ `Boolean`

[ GitHub ]

#quo(other) ⇒ Numeric #fdiv(other) ⇒ Numeric

Alias for #quo.

#floor(ndigits = 0) ⇒ `Float`, Integer

Returns the largest number less than or equal to self with a precision of ndigits decimal digits.

When ndigits is positive, returns a float with ndigits digits after the decimal point (as available):

f = 12345.6789
f.floor(1) # => 12345.6
f.floor(3) # => 12345.678
f = -12345.6789
f.floor(1) # => -12345.7
f.floor(3) # => -12345.679

When ndigits is non-positive, returns an integer with at least ndigits.abs trailing zeros:

f = 12345.6789
f.floor(0)  # => 12345
f.floor(-3) # => 12000
f = -12345.6789
f.floor(0)  # => -12346
f.floor(-3) # => -13000

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

(0.3 / 0.1).floor  #=> 2 (!)

Related: #ceil.

[ GitHub ]

# File 'numeric.c', line 2204


static VALUE
flo_floor(int argc, VALUE *argv, VALUE num)
{
    int ndigits = flo_ndigits(argc, argv);
    return rb_float_floor(num, ndigits);
}

#hash ⇒ Integer

Returns the integer hash value for self.

#to_s ⇒ String #inspect ⇒ String

Alias for #to_s.

#magnitude

[ GitHub ]

# File 'numeric.rb', line 283


def magnitude
  Primitive.attr! 'inline'
  Primitive.cexpr! 'rb_float_abs(self)'
end

#%(other) ⇒ `Float` #modulo(other) ⇒ `Float`

Alias for #%.

#next_float ⇒ `Float`

Returns the next-larger representable Float.

These examples show the internally stored values (64-bit hexadecimal) for each Float f and for the corresponding f.next_float:

f = 0.0      # 0x0000000000000000
f.next_float # 0x0000000000000001

f = 0.01     # 0x3f847ae147ae147b
f.next_float # 0x3f847ae147ae147c

In the remaining examples here, the output is shown in the usual way (result #to_s):

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

f = 0.01
(0..3).each_with_index {|i| printf "%2d %-20a %s\n", i, f, f.to_s; f = f.next_float }

Output:

 0 0x1ae147ae147bp-7 0.01
 1 0x1ae147ae147cp-7 0.010000000000000002
 2 0x1ae147ae147dp-7 0.010000000000000004
 3 0x1ae147ae147ep-7 0.010000000000000005

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.

Related: #prev_float

[ GitHub ]

# File 'numeric.c', line 2083


static VALUE
flo_next_float(VALUE vx)
{
    return flo_nextafter(vx, HUGE_VAL);
}

#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

#arg ⇒ `0`, `Float` #angle ⇒ `0`, `Float` #phase ⇒ `0`, `Float`

Alias for #arg.

#prev_float ⇒ `Float`

Returns the next-smaller representable Float.

These examples show the internally stored values (64-bit hexadecimal) for each Float f and for the corresponding f.pev_float:

f = 5e-324   # 0x0000000000000001
f.prev_float # 0x0000000000000000

f = 0.01     # 0x3f847ae147ae147b
f.prev_float # 0x3f847ae147ae147a

In the remaining examples here, the output is shown in the usual way (result #to_s):

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

f = 0.01
(0..3).each_with_index {|i| printf "%2d %-20a %s\n", i, f, f.to_s; f = f.prev_float }

Output:

0 0x1ae147ae147bp-7 0.01
1 0x1ae147ae147ap-7 0.009999999999999998
2 0x1ae147ae1479p-7 0.009999999999999997
3 0x1ae147ae1478p-7 0.009999999999999995

Related: #next_float.

[ GitHub ]

# File 'numeric.c', line 2124


static VALUE
flo_prev_float(VALUE vx)
{
    return flo_nextafter(vx, -HUGE_VAL);
}

#quo(other) ⇒ Numeric Also known as: #fdiv

Returns the quotient from dividing self by other:

f = 3.14
f.quo(2)              # => 1.57
f.quo(-2)             # => -1.57
f.quo(Rational(2, 1)) # => 1.57
f.quo(Complex(2, 0))  # => (1.57+0.0i)

#fdiv is an alias for quo.

[ GitHub ]

# File 'numeric.c', line 1328


static VALUE
flo_quo(VALUE x, VALUE y)
{
    return num_funcall1(x, '/', y);
}

#rationalize([eps]) ⇒ Rational

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)

#round(ndigits = 0, half: :up]) ⇒ Integer, `Float`

Returns self rounded to the nearest value with a precision of ndigits decimal digits.

When ndigits is non-negative, returns a float with ndigits after the decimal point (as available):

f = 12345.6789
f.round(1) # => 12345.7
f.round(3) # => 12345.679
f = -12345.6789
f.round(1) # => -12345.7
f.round(3) # => -12345.679

When ndigits is negative, returns an integer with at least ndigits.abs trailing zeros:

f = 12345.6789
f.round(0)  # => 12346
f.round(-3) # => 12000
f = -12345.6789
f.round(0)  # => -12346
f.round(-3) # => -12000

If keyword argument half is given, and self is equidistant from the two candidate values, the rounding is according to the given half value:

:up or nil: round away from zero:

2.5.round(half: :up)      # => 3
3.5.round(half: :up)      # => 4
(-2.5).round(half: :up)   # => -3

:down: round toward zero:

2.5.round(half: :down)    # => 2
3.5.round(half: :down)    # => 3
(-2.5).round(half: :down) # => -2

:even: round toward the candidate whose last nonzero digit is even:

2.5.round(half: :even)    # => 2
3.5.round(half: :even)    # => 4
(-2.5).round(half: :even) # => -2

Raises and exception if the value for half is invalid.

Related: #truncate.

[ GitHub ]

# File 'numeric.c', line 2506


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);
        if (ndigits > 14) {
            /* In this case, pow(10, ndigits) may not be accurate. */
            return rb_flo_round_by_rational(argc, argv, num);
        }
	f = pow(10, ndigits);
	x = ROUND_CALL(mode, round, (number, f));
	return DBL2NUM(x / f);
    }
    return num;
}

#to_f ⇒ `self`

Since float is already a Float, returns self.

[ GitHub ]

# File 'numeric.rb', line 261


def to_f
  return self
end

#to_i ⇒ Integer Also known as: #to_int

Returns self truncated to an ::Integer.

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

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

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

#to_int is an alias for to_i.

[ GitHub ]

# File 'numeric.c', line 2599


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_i ⇒ Integer #to_int ⇒ Integer

Alias for #to_i.

#to_r ⇒ Rational

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

#to_s ⇒ String Also known as: #inspect

Returns a string containing a representation of self; depending of the value of self, the string representation may contain:

A fixed-point number.
A number in “scientific notation” (containing an exponent).
‘Infinity’.
‘-Infinity’.
‘NaN’ (indicating not-a-number).

3.14.to_s # => “3.14” (10.1**50).to_s # => “1.644631821843879e+50” (10.1**500).to_s # => “Infinity” (-10.1**500).to_s # => “-Infinity” (0.0/0.0).to_s # => “NaN”

[ GitHub ]

# File 'numeric.c', line 1055


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 {
        goto exp;
    }
    return s;

  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;
}

#truncate(ndigits = 0) ⇒ `Float`, Integer

Returns self truncated (toward zero) to a precision of ndigits decimal digits.

When ndigits is positive, returns a float with ndigits digits after the decimal point (as available):

f = 12345.6789
f.truncate(1) # => 12345.6
f.truncate(3) # => 12345.678
f = -12345.6789
f.truncate(1) # => -12345.6
f.truncate(3) # => -12345.678

When ndigits is negative, returns an integer with at least ndigits.abs trailing zeros:

f = 12345.6789
f.truncate(0)  # => 12345
f.truncate(-3) # => 12000
f = -12345.6789
f.truncate(0)  # => -12345
f.truncate(-3) # => -12000

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

(0.3 / 0.1).truncate  #=> 2 (!)

Related: #round.

[ GitHub ]

# File 'numeric.c', line 2645


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);
}

Class: Float

Overview

What’s Here

Querying

Comparing

Converting

Constant Summary

Instance Attribute Summary

::Numeric - Inherited

Instance Method Summary

::Numeric - Inherited

::Comparable - Included

Instance Attribute Details

#finite? ⇒ Boolean (readonly)

#infinite? ⇒ Boolean (readonly)

#nan? ⇒ Boolean (readonly)

#negative? ⇒ Boolean (readonly)

#positive? ⇒ Boolean (readonly)

#zero? ⇒ Boolean (readonly)

Instance Method Details

#%(other) ⇒ Float Also known as: #modulo

#*(other) ⇒ Numeric

#**(other) ⇒ Numeric

#+(other) ⇒ Numeric

#-(other) ⇒ Numeric

#- ⇒ Float

#/(other) ⇒ Numeric

#<(other) ⇒ Boolean

#<=(other) ⇒ Boolean

#<=>(other) ⇒ 1, ...

#==

#===

#>(other) ⇒ Boolean

#>=(other) ⇒ Boolean

#abs ⇒ Float #magnitude ⇒ Float

#arg ⇒ 0, Float #angle ⇒ 0, Float #phase ⇒ 0, Float

#arg ⇒ 0, Float #angle ⇒ 0, Float #phase ⇒ 0, Float Also known as: #angle, #phase

#ceil(ndigits = 0) ⇒ Float, Integer

#coerce(other) ⇒ Array

#denominator ⇒ Integer

#divmod(other) ⇒ Array

#eql? ⇒ Boolean

#quo(other) ⇒ Numeric #fdiv(other) ⇒ Numeric

#floor(ndigits = 0) ⇒ Float, Integer

#hash ⇒ Integer

#to_s ⇒ String #inspect ⇒ String

#magnitude

#%(other) ⇒ Float #modulo(other) ⇒ Float

#next_float ⇒ Float

#numerator ⇒ Integer

#arg ⇒ 0, Float #angle ⇒ 0, Float #phase ⇒ 0, Float

#prev_float ⇒ Float

#quo(other) ⇒ Numeric Also known as: #fdiv

#rationalize([eps]) ⇒ Rational

#round(ndigits = 0, half: :up]) ⇒ Integer, Float

#to_f ⇒ self

#to_i ⇒ Integer Also known as: #to_int

#to_i ⇒ Integer #to_int ⇒ Integer

#to_r ⇒ Rational

#to_s ⇒ String Also known as: #inspect

#truncate(ndigits = 0) ⇒ Float, Integer

`::Numeric` - Inherited

`::Numeric` - Inherited

`::Comparable` - Included

#finite? ⇒ `Boolean` (readonly)

#infinite? ⇒ `Boolean` (readonly)

#nan? ⇒ `Boolean` (readonly)

#negative? ⇒ `Boolean` (readonly)

#positive? ⇒ `Boolean` (readonly)

#zero? ⇒ `Boolean` (readonly)

#%(other) ⇒ `Float` Also known as: #modulo

#- ⇒ `Float`

#<(other) ⇒ `Boolean`

#<=(other) ⇒ `Boolean`

#<=>(other) ⇒ `1`, ...

#>(other) ⇒ `Boolean`

#>=(other) ⇒ `Boolean`

#abs ⇒ `Float` #magnitude ⇒ `Float`

#arg ⇒ `0`, `Float` #angle ⇒ `0`, `Float` #phase ⇒ `0`, `Float`

#arg ⇒ `0`, `Float` #angle ⇒ `0`, `Float` #phase ⇒ `0`, `Float`
Also known as: #angle, #phase

#ceil(ndigits = 0) ⇒ `Float`, Integer

#eql? ⇒ `Boolean`

#floor(ndigits = 0) ⇒ `Float`, Integer

#%(other) ⇒ `Float` #modulo(other) ⇒ `Float`

#next_float ⇒ `Float`

#arg ⇒ `0`, `Float` #angle ⇒ `0`, `Float` #phase ⇒ `0`, `Float`

#prev_float ⇒ `Float`

#round(ndigits = 0, half: :up]) ⇒ Integer, `Float`

#to_f ⇒ `self`

#truncate(ndigits = 0) ⇒ `Float`, Integer