Returns a new Complex object formed from the arguments, each of which must be an instance of Numeric, or an instance of one of its subclasses: Complex, Float, Integer, Rational; see Rectangular Coordinates:
Complex.rect(3) # => (3+0i) Complex.rect(3, Math::PI) # => (3+3.141592653589793i) Complex.rect(-3, -Math::PI) # => (-3-3.141592653589793i)
Complex.rectangular is an alias for Complex.rect.
Returns the imaginary value for self:
Complex(7).imaginary #=> 0 Complex(9, -4).imaginary #=> -4
If self was created with polar coordinates, the returned value is computed, and may be inexact:
Complex.polar(1, Math::PI/4).imag # => 0.7071067811865476 # Square root of 2.
Returns the argument (angle) for self in radians; see polar coordinates:
Complex.polar(3, Math::PI/2).arg # => 1.57079632679489660
If self was created with rectangular coordinates, the returned value is computed, and may be inexact:
Complex.polar(1, 1.0/3).arg # => 0.33333333333333326
Returns the array [self.real, self.imag]:
Complex.rect(1, 2).rect # => [1, 2]
If self was created with polar coordinates, the returned value is computed, and may be inexact:
Complex.polar(1.0, 1.0).rect # => [0.5403023058681398, 0.8414709848078965]
Complex#rectangular is an alias for Complex#rect.
Returns the denominator of self, which is the least common multiple of self.real.denominator and self.imag.denominator:
Complex.rect(Rational(1, 2), Rational(2, 3)).denominator # => 6
Note that n.denominator of a non-rational numeric is 1.
Related: Complex#numerator.
Returns a string representation of self:
Complex(2).inspect # => "(2+0i)" Complex('-8/6').inspect # => "((-4/3)+0i)" Complex('1/2i').inspect # => "(0+(1/2)*i)" Complex(0, Float::INFINITY).inspect # => "(0+Infinity*i)" Complex(Float::NAN, Float::NAN).inspect # => "(NaN+NaN*i)"
Returns true if both self.real.finite? and self.imag.finite? are true, false otherwise:
Complex(1, 1).finite? # => true Complex(Float::INFINITY, 0).finite? # => false
Related: Numeric#finite?, Float#finite?.
Returns zero if self is positive, Math::PI otherwise.
Returns array [self, 0].
Returns the remainder after dividing self by other.
Of the Core and Standard Library classes, only Float and Rational use this implementation.
Examples:
11.0.remainder(4) # => 3.0 11.0.remainder(-4) # => 3.0 -11.0.remainder(4) # => -3.0 -11.0.remainder(-4) # => -3.0 12.0.remainder(4) # => 0.0 12.0.remainder(-4) # => 0.0 -12.0.remainder(4) # => -0.0 -12.0.remainder(-4) # => -0.0 13.0.remainder(4.0) # => 1.0 13.0.remainder(Rational(4, 1)) # => 1.0 Rational(13, 1).remainder(4) # => (1/1) Rational(13, 1).remainder(-4) # => (1/1) Rational(-13, 1).remainder(4) # => (-1/1) Rational(-13, 1).remainder(-4) # => (-1/1)
Returns self truncated (toward zero) to a precision of digits decimal digits.
Numeric implements this by converting self to a Float and invoking Float#truncate.
Generates a sequence of numbers; with a block given, traverses the sequence.
Of the Core and Standard Library classes,
Integer, Float, and Rational use this implementation.
A quick example:
squares = []
1.step(by: 2, to: 10) {|i| squares.push(i*i) }
squares # => [1, 9, 25, 49, 81]
The generated sequence:
- Begins with +self+.
- Continues at intervals of +by+ (which may not be zero).
- Ends with the last number that is within or equal to +to+;
that is, less than or equal to +to+ if +by+ is positive,
greater than or equal to +to+ if +by+ is negative.
If +to+ is +nil+, the sequence is of infinite length.
If a block is given, calls the block with each number in the sequence;
returns +self+. If no block is given, returns an Enumerator::ArithmeticSequence.
<b>Keyword Arguments</b>
With keyword arguments +by+ and +to+,
their values (or defaults) determine the step and limit:
# Both keywords given.
squares = []
4.step(by: 2, to: 10) {|i| squares.push(i*i) } # => 4
squares # => [16, 36, 64, 100]
cubes = []
3.step(by: -1.5, to: -3) {|i| cubes.push(i*i*i) } # => 3
cubes # => [27.0, 3.375, 0.0, -3.375, -27.0]
squares = []
1.2.step(by: 0.2, to: 2.0) {|f| squares.push(f*f) }
squares # => [1.44, 1.9599999999999997, 2.5600000000000005, 3.24, 4.0]
squares = []
Rational(6/5).step(by: 0.2, to: 2.0) {|r| squares.push(r*r) }
squares # => [1.0, 1.44, 1.9599999999999997, 2.5600000000000005, 3.24, 4.0]
# Only keyword to given.
squares = []
4.step(to: 10) {|i| squares.push(i*i) } # => 4
squares # => [16, 25, 36, 49, 64, 81, 100]
# Only by given.
# Only keyword by given
squares = []
4.step(by:2) {|i| squares.push(i*i); break if i > 10 }
squares # => [16, 36, 64, 100, 144]
# No block given.
e = 3.step(by: -1.5, to: -3) # => (3.step(by: -1.5, to: -3))
e.class # => Enumerator::ArithmeticSequence
<b>Positional Arguments</b>
With optional positional arguments +to+ and +by+,
their values (or defaults) determine the step and limit:
squares = []
4.step(10, 2) {|i| squares.push(i*i) } # => 4
squares # => [16, 36, 64, 100]
squares = []
4.step(10) {|i| squares.push(i*i) }
squares # => [16, 25, 36, 49, 64, 81, 100]
squares = []
4.step {|i| squares.push(i*i); break if i > 10 } # => nil
squares # => [16, 25, 36, 49, 64, 81, 100, 121]
Implementation Notes
If all the arguments are integers, the loop operates using an integer counter. If any of the arguments are floating point numbers, all are converted to floats, and the loop is executed <i>floor(n + n*Float::EPSILON) + 1</i> times, where <i>n = (limit - self)/step</i>.
Returns true if self is a finite number, false otherwise.
Returns zero.
Returns the denominator (always positive).
Returns 0 if self is positive, Math::PI otherwise.
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 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 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 the denominator (always positive). The result is machine dependent.
See also Float#numerator.
Returns a copy of the storage hash for the fiber. The method can only be called on the Fiber.current.
Sets the storage hash for the fiber. This feature is experimental and may change in the future. The method can only be called on the Fiber.current.
You should be careful about using this method as you may inadvertently clear important fiber-storage state. You should mostly prefer to assign specific keys in the storage using Fiber::[]=.
You can also use Fiber.new(storage: nil) to create a fiber with an empty storage.
Example:
while request = request_queue.pop # Reset the per-request state: Fiber.current.storage = nil handle_request(request) end
Returns the current execution stack of the fiber. start, count and end allow to select only parts of the backtrace.
def level3 Fiber.yield end def level2 level3 end def level1 level2 end f = Fiber.new { level1 } # It is empty before the fiber started f.backtrace #=> [] f.resume f.backtrace #=> ["test.rb:2:in `yield'", "test.rb:2:in `level3'", "test.rb:6:in `level2'", "test.rb:10:in `level1'", "test.rb:13:in `block in <main>'"] p f.backtrace(1) # start from the item 1 #=> ["test.rb:2:in `level3'", "test.rb:6:in `level2'", "test.rb:10:in `level1'", "test.rb:13:in `block in <main>'"] p f.backtrace(2, 2) # start from item 2, take 2 #=> ["test.rb:6:in `level2'", "test.rb:10:in `level1'"] p f.backtrace(1..3) # take items from 1 to 3 #=> ["test.rb:2:in `level3'", "test.rb:6:in `level2'", "test.rb:10:in `level1'"] f.resume # It is nil after the fiber is finished f.backtrace #=> nil