Class

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:

You can convert certain objects to Floats with:

What's Here

First, what's elsewhere. Class Float:

Here, class Float provides methods for:

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.


Constants


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

Usually defaults to 15.

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

Usually defaults to 2.2204460492503131e-16.

An expression representing positive infinity.

The number of base digits for the double data type.

Usually defaults to 53.

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

Usually defaults to 1.7976931348623157e+308.

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

Usually defaults to 308.

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

Usually defaults to 1024.

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.

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

Usually defaults to -307.

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

Usually defaults to -1021.

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.

Instance Methods


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

Float#modulo is an alias for Float#%.

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)

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)

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)

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)

Returns float, negated.

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)

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.

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.

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.

Returns true if other has the same value as self, false otherwise:

2.0 == 2              # => true
2.0 == 2.0            # => true
2.0 == Rational(2, 1) # => true
2.0 == Complex(2, 0)  # => true

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

Related: Float#eql? (requires other to be a Float).

An alias for ==

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.

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.

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.

Returns 0 if the value is positive, pi otherwise.

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: Float#floor.

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.

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

See also Float#numerator.

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]

Returns true if other is a Float with the same value as self, false otherwise:

2.0.eql?(2.0)            # => true
2.0.eql?(1.0)            # => false
2.0.eql?(1)              # => false
2.0.eql?(Rational(2, 1)) # => false
2.0.eql?(Complex(2, 0))  # => false

Float::NAN.eql?(Float::NAN) returns an implementation-dependent value.

Related: Float#== (performs type conversions).

An alias for quo

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

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: Float#ceil.

Returns the integer hash value for self.

See also Object#hash.

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
An alias for to_s
No documentation available
An alias for %

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

Returns true if float is less than 0.

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 0x1.47ae147ae147bp-7 0.01
 1 0x1.47ae147ae147cp-7 0.010000000000000002
 2 0x1.47ae147ae147dp-7 0.010000000000000004
 3 0x1.47ae147ae147ep-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: Float#prev_float

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.

Returns true if float is greater than 0.

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 0x1.47ae147ae147bp-7 0.01
1 0x1.47ae147ae147ap-7 0.009999999999999998
2 0x1.47ae147ae1479p-7 0.009999999999999997
3 0x1.47ae147ae1478p-7 0.009999999999999995

Related: Float#next_float.

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)

Float#fdiv is an alias for Float#quo.

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.

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: Float#truncate.

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.

Since float is already a Float, returns self.

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 (!)

Float#to_int is an alias for Float#to_i.

An alias for to_i

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.

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”

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: Float#round.

Returns true if float is 0.0.