Class: Float

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

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 self is less than 0, false otherwise.

Returns true if self is greater than 0, false otherwise.

Returns true if self is 0.0, false otherwise.

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 self, 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 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 self:

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

Alias for #arg.

Returns 0 if self is positive, Math::PI otherwise.

:markup: markdown

Returns a numeric that is a “ceiling” value for self, as specified by the given ndigits, which must be an [integer-convertible object](implicit_conversion.rdoc@Integer-Convertible+Objects).

When ndigits is positive, returns a Float with ndigits decimal digits after the decimal point (as available, but no fewer than 1):

“‘ f = 12345.6789 f.ceil(1) # => 12345.7 f.ceil(3) # => 12345.679 f.ceil(30) # => 12345.6789 f = -12345.6789 f.ceil(1) # => -12345.6 f.ceil(3) # => -12345.678 f.ceil(30) # => -12345.6789 f = 0.0 f.ceil(1) # => 0.0 f.ceil(100) # => 0.0 “`

When ndigits is non-positive, returns an Integer based on a computed granularity:

• The granularity is 10 ** ndigits.abs.

• The returned value is the largest multiple of the granularity that is less than or equal to self.

Examples with positive self:

| ndigits | Granularity | 12345.6789.ceil(ndigits) | |——–:|————:|————————-:| | 0 | 1 | 12346 | | -1 | 10 | 12350 | | -2 | 100 | 12400 | | -3 | 1000 | 13000 | | -4 | 10000 | 20000 | | -5 | 100000 | 100000 |

Examples with negative self:

| ndigits | Granularity | -12345.6789.ceil(ndigits) | |——–:|————:|————————–:| | 0 | 1 | -12345 | | -1 | 10 | -12340 | | -2 | 100 | -12300 | | -3 | 1000 | -12000 | | -4 | 10000 | -10000 | | -5 | 100000 | 0 |

When self is zero and ndigits is non-positive, returns Integer zero:

“‘ 0.0.ceil(0) # => 0 0.0.ceil(-1) # => 0 0.0.ceil(-2) # => 0 “`

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

“‘ (2.1 / 0.7).ceil #=> 4 # Not 3 (because 2.1 / 0.7 # => 3.0000000000000004, not 3.0) “`

Related: #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 #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]

Alias for #quo.

:markup: markdown

Returns a float or integer that is a “floor” value for self, as specified by ndigits, which must be an [integer-convertible object](implicit_conversion.rdoc@Integer-Convertible+Objects).

When self is zero, returns a zero value: a float if ndigits is positive, an integer otherwise:

“‘ f = 0.0 # => 0.0 f.floor(20) # => 0.0 f.floor(0) # => 0 f.floor(-20) # => 0 “`

When self is non-zero and 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.floor(30) # => 12345.6789 f = -12345.6789 f.floor(1) # => -12345.7 f.floor(3) # => -12345.679 f.floor(30) # => -12345.6789 “`

When self is non-zero and ndigits is non-positive, returns an integer value based on a computed granularity:

• The granularity is 10 ** ndigits.abs.

• The returned value is the largest multiple of the granularity that is less than or equal to self.

Examples with positive self:

| ndigits | Granularity | 12345.6789.floor(ndigits) | |——–:|————:|————————–:| | 0 | 1 | 12345 | | -1 | 10 | 12340 | | -2 | 100 | 12300 | | -3 | 1000 | 12000 | | -4 | 10000 | 10000 | | -5 | 100000 | 0 |

Examples with negative self:

| ndigits | Granularity | -12345.6789.floor(ndigits) | |——–:|————:|—————————:| | 0 | 1 | -12346 | | -1 | 10 | -12350 | | -2 | 100 | -12400 | | -3 | 1000 | -13000 | | -4 | 10000 | -20000 | | -5 | 100000 | -100000 | | -6 | 1000000 | -1000000 |

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

“‘ (0.3 / 0.1).floor # => 2 # Not 3, (because (0.3 / 0.1) # => 2.9999999999999996, not 3.0) “`

Related: #ceil.

Returns the integer hash value for self.

See also Object#hash.

Alias for #to_s.

Alias for #abs.

Alias for #%.

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

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 #denominator.

Alias for #arg.

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.

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)

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 #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: #truncate.

Returns self (which is already a Float).

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 (!)

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 #rationalize.

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

• A fixed-point number.

  3.14.to_s         # => "3.14"

• A number in “scientific notation” (containing an exponent).

  (10.1**50).to_s   # => "1.644631821843879e+50"

• ‘Infinity’.

  (10.1**500).to_s  # => "Infinity"

• ‘-Infinity’.

  (-10.1**500).to_s # => "-Infinity"

• ‘NaN’ (indicating not-a-number).

  (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: #round.