Module: Math

Computes the inverse hyperbolic cosine of x.

Computes the arc sine of x. Returns -PI/2 .. PI/2.

Computes the inverse hyperbolic sine of x.

Computes the arc tangent of x. Returns -PI/2 .. PI/2.

Computes the arc tangent given y and x. Returns -PI..PI.

Math.atan2(-0.0, -1.0) #=> -3.141592653589793
Math.atan2(-1.0, -1.0) #=> -2.356194490192345
Math.atan2(-1.0, 0.0)  #=> -1.5707963267948966
Math.atan2(-1.0, 1.0)  #=> -0.7853981633974483
Math.atan2(-0.0, 1.0)  #=> -0.0
Math.atan2(0.0, 1.0)   #=> 0.0
Math.atan2(1.0, 1.0)   #=> 0.7853981633974483
Math.atan2(1.0, 0.0)   #=> 1.5707963267948966
Math.atan2(1.0, -1.0)  #=> 2.356194490192345
Math.atan2(0.0, -1.0)  #=> 3.141592653589793

Computes the inverse hyperbolic tangent of x.

Returns the cube root of numeric.

-9.upto(9) {|x|
  p [x, Math.cbrt(x), Math.cbrt(x)**3]
}
#=>
[-9, -2.0800838230519, -9.0]
[-8, -2.0, -8.0]
[-7, -1.91293118277239, -7.0]
[-6, -1.81712059283214, -6.0]
[-5, -1.7099759466767, -5.0]
[-4, -1.5874010519682, -4.0]
[-3, -1.44224957030741, -3.0]
[-2, -1.25992104989487, -2.0]
[-1, -1.0, -1.0]
[0, 0.0, 0.0]
[1, 1.0, 1.0]
[2, 1.25992104989487, 2.0]
[3, 1.44224957030741, 3.0]
[4, 1.5874010519682, 4.0]
[5, 1.7099759466767, 5.0]
[6, 1.81712059283214, 6.0]
[7, 1.91293118277239, 7.0]
[8, 2.0, 8.0]
[9, 2.0800838230519, 9.0]

Computes the cosine of x (expressed in radians). Returns -1..1.

Computes the hyperbolic cosine of x (expressed in radians).

Calculates the error function of x.

Calculates the complementary error function of x.

Returns e**x.

Math.exp(0)       #=> 1.0
Math.exp(1)       #=> 2.718281828459045
Math.exp(1.5)     #=> 4.4816890703380645

Returns a two-element array containing the normalized fraction (a Float) and exponent (a Fixnum) of numeric.

fraction, exponent = Math.frexp(1234)   #=> [0.6025390625, 11]
fraction * 2**exponent                  #=> 1234.0

Calculates the gamma function of x.

Note that gamma(n) is same as fact(n-1) for integer n > 0.
However gamma(n) returns float and can be an approximation.

 def fact(n) (1..n).inject(1) {|r,i| r*i } end
 1.upto(26) {|i| p [i, Math.gamma(i), fact(i-1)] }
 #=> [1, 1.0, 1]
 #   [2, 1.0, 1]
 #   [3, 2.0, 2]
 #   [4, 6.0, 6]
 #   [5, 24.0, 24]
 #   [6, 120.0, 120]
 #   [7, 720.0, 720]
 #   [8, 5040.0, 5040]
 #   [9, 40320.0, 40320]
 #   [10, 362880.0, 362880]
 #   [11, 3628800.0, 3628800]
 #   [12, 39916800.0, 39916800]
 #   [13, 479001600.0, 479001600]
 #   [14, 6227020800.0, 6227020800]
 #   [15, 87178291200.0, 87178291200]
 #   [16, 1307674368000.0, 1307674368000]
 #   [17, 20922789888000.0, 20922789888000]
 #   [18, 355687428096000.0, 355687428096000]
 #   [19, 6.402373705728e+15, 6402373705728000]
 #   [20, 1.21645100408832e+17, 121645100408832000]
 #   [21, 2.43290200817664e+18, 2432902008176640000]
 #   [22, 5.109094217170944e+19, 51090942171709440000]
 #   [23, 1.1240007277776077e+21, 1124000727777607680000]
 #   [24, 2.5852016738885062e+22, 25852016738884976640000]
 #   [25, 6.204484017332391e+23, 620448401733239439360000]
 #   [26, 1.5511210043330954e+25, 15511210043330985984000000]

Returns sqrt(x**2 + y**2), the hypotenuse of a right-angled triangle with sides x and y.

Math.hypot(3, 4)   #=> 5.0

Returns the value of flt*(2**int).

fraction, exponent = Math.frexp(1234)
Math.ldexp(fraction, exponent)   #=> 1234.0

Calculates the logarithmic gamma of x and

the sign of gamma of x.

Math.lgamma(x) is same as
 [Math.log(Math.gamma(x).abs), Math.gamma(x) < 0 ? -1 : 1]
but avoid overflow by Math.gamma(x) for large x.

Returns the natural logarithm of numeric. If additional second argument is given, it will be the base of logarithm.

Math.log(1)          #=> 0.0
Math.log(Math::E)    #=> 1.0
Math.log(Math::E**3) #=> 3.0
Math.log(12,3)       #=> 2.2618595071429146

Returns the base 10 logarithm of numeric.

Math.log10(1)       #=> 0.0
Math.log10(10)      #=> 1.0
Math.log10(10**100) #=> 100.0

Returns the base 2 logarithm of numeric.

Math.log2(1)      #=> 0.0
Math.log2(2)      #=> 1.0
Math.log2(32768)  #=> 15.0
Math.log2(65536)  #=> 16.0

Computes the sine of x (expressed in radians). Returns -1..1.

Computes the hyperbolic sine of x (expressed in radians).

Returns the non-negative square root of numeric.

0.upto(10) {|x|
  p [x, Math.sqrt(x), Math.sqrt(x)**2]
}
#=>
[0, 0.0, 0.0]
[1, 1.0, 1.0]
[2, 1.4142135623731, 2.0]
[3, 1.73205080756888, 3.0]
[4, 2.0, 4.0]
[5, 2.23606797749979, 5.0]
[6, 2.44948974278318, 6.0]
[7, 2.64575131106459, 7.0]
[8, 2.82842712474619, 8.0]
[9, 3.0, 9.0]
[10, 3.16227766016838, 10.0]

Returns the tangent of x (expressed in radians).

Computes the hyperbolic tangent of x (expressed in radians).