Module: Math
Relationships & Source Files | |
Namespace Children | |
Exceptions:
| |
Defined in: | math.c |
Overview
The Math module contains module functions for basic trigonometric and transcendental functions. See class ::Float for a list of constants that define Ruby's floating point accuracy.
Domains and codomains are given only for real (not complex) numbers.
Constant Summary
-
E =
Definition of the mathematical constant
E
(e) as a ::Float number.DBL2NUM(M_E)
-
PI =
Definition of the mathematical constant
PI
as a ::Float number.DBL2NUM(M_PI)
Class Method Summary
-
.acos(x) ⇒ Float
mod_func
Computes the arc cosine of
x
. -
.acosh(x) ⇒ Float
mod_func
Computes the inverse hyperbolic cosine of
x
. -
.asin(x) ⇒ Float
mod_func
Computes the arc sine of
x
. -
.asinh(x) ⇒ Float
mod_func
Computes the inverse hyperbolic sine of
x
. -
.atan(x) ⇒ Float
mod_func
Computes the arc tangent of
x
. -
.atan2(y, x) ⇒ Float
mod_func
Computes the arc tangent given
y
andx
. -
.atanh(x) ⇒ Float
mod_func
Computes the inverse hyperbolic tangent of
x
. -
.cbrt(x) ⇒ Float
mod_func
Returns the cube root of
x
. -
.cos(x) ⇒ Float
mod_func
Computes the cosine of
x
(expressed in radians). -
.cosh(x) ⇒ Float
mod_func
Computes the hyperbolic cosine of
x
(expressed in radians). -
.erf(x) ⇒ Float
mod_func
Calculates the error function of
x
. -
.erfc(x) ⇒ Float
mod_func
Calculates the complementary error function of x.
-
.exp(x) ⇒ Float
mod_func
Returns e**x.
- .frexp(x) ⇒ Array, exponent mod_func
-
.gamma(x) ⇒ Float
mod_func
Calculates the gamma function of x.
-
.hypot(x, y) ⇒ Float
mod_func
Returns sqrt(x**2 + y**2), the hypotenuse of a right-angled triangle with sides
x
andy
. -
.ldexp(fraction, exponent) ⇒ Float
mod_func
Returns the value of
fraction
*(2**exponent
). -
.lgamma(x) ⇒ Array, 1
mod_func
Calculates the logarithmic gamma of
x
and the sign of gamma ofx
. -
.log(x) ⇒ Float
mod_func
Returns the logarithm of
x
. -
.log10(x) ⇒ Float
mod_func
Returns the base 10 logarithm of
x
. -
.log2(x) ⇒ Float
mod_func
Returns the base 2 logarithm of
x
. -
.sin(x) ⇒ Float
mod_func
Computes the sine of
x
(expressed in radians). -
.sinh(x) ⇒ Float
mod_func
Computes the hyperbolic sine of
x
(expressed in radians). -
.sqrt(x) ⇒ Float
mod_func
Returns the non-negative square root of
x
. -
.tan(x) ⇒ Float
mod_func
Computes the tangent of
x
(expressed in radians). -
.tanh(x) ⇒ Float
mod_func
Computes the hyperbolic tangent of
x
(expressed in radians).
Class Method Details
.acos(x) ⇒ Float (mod_func)
Computes the arc cosine of x
. Returns 0..PI.
Domain: [-1, 1]
Codomain: [0, PI]
Math.acos(0) == Math::PI/2 #=> true
.acosh(x) ⇒ Float (mod_func)
Computes the inverse hyperbolic cosine of x
.
Domain: [1, INFINITY)
Codomain: [0, INFINITY)
Math.acosh(1) #=> 0.0
.asin(x) ⇒ Float (mod_func)
Computes the arc sine of x
. Returns -PI/2..PI/2.
Domain: [-1, -1]
Codomain: [-PI/2, PI/2]
Math.asin(1) == Math::PI/2 #=> true
.asinh(x) ⇒ Float (mod_func)
Computes the inverse hyperbolic sine of x
.
Domain: (-INFINITY, INFINITY)
Codomain: (-INFINITY, INFINITY)
Math.asinh(1) #=> 0.881373587019543
.atan(x) ⇒ Float (mod_func)
Computes the arc tangent of x
. Returns -PI/2..PI/2.
Domain: (-INFINITY, INFINITY)
Codomain: (-PI/2, PI/2)
Math.atan(0) #=> 0.0
.atan2(y, x) ⇒ Float (mod_func)
Computes the arc tangent given y
and x
. Returns a ::Float in the range -PI..PI. Return value is a angle in radians between the positive x-axis of cartesian plane and the point given by the coordinates (x
, y
) on it.
Domain: (-INFINITY, INFINITY)
Codomain: [-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
Math.atan2(INFINITY, INFINITY) #=> 0.7853981633974483
Math.atan2(INFINITY, -INFINITY) #=> 2.356194490192345
Math.atan2(-INFINITY, INFINITY) #=> -0.7853981633974483
Math.atan2(-INFINITY, -INFINITY) #=> -2.356194490192345
.atanh(x) ⇒ Float (mod_func)
Computes the inverse hyperbolic tangent of x
.
Domain: (-1, 1)
Codomain: (-INFINITY, INFINITY)
Math.atanh(1) #=> Infinity
.cbrt(x) ⇒ Float (mod_func)
Returns the cube root of x
.
Domain: (-INFINITY, INFINITY)
Codomain: (-INFINITY, INFINITY)
-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]
.cos(x) ⇒ Float (mod_func)
.cosh(x) ⇒ Float (mod_func)
Computes the hyperbolic cosine of x
(expressed in radians).
Domain: (-INFINITY, INFINITY)
Codomain: [1, INFINITY)
Math.cosh(0) #=> 1.0
.erf(x) ⇒ Float (mod_func)
Calculates the error function of x
.
Domain: (-INFINITY, INFINITY)
Codomain: (-1, 1)
Math.erf(0) #=> 0.0
.erfc(x) ⇒ Float (mod_func)
Calculates the complementary error function of x.
Domain: (-INFINITY, INFINITY)
Codomain: (0, 2)
Math.erfc(0) #=> 1.0
.exp(x) ⇒ Float (mod_func)
Returns e**x.
Domain: (-INFINITY, INFINITY)
Codomain: (0, INFINITY)
Math.exp(0) #=> 1.0
Math.exp(1) #=> 2.718281828459045
Math.exp(1.5) #=> 4.4816890703380645
.frexp(x) ⇒ Array, exponent
(mod_func)
.gamma(x) ⇒ Float (mod_func)
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]
.hypot(x, y) ⇒ Float (mod_func)
Returns sqrt(x**2 + y**2), the hypotenuse of a right-angled triangle with sides x
and y
.
Math.hypot(3, 4) #=> 5.0
.ldexp(fraction, exponent) ⇒ Float (mod_func)
Returns the value of fraction
*(2**exponent
).
fraction, exponent = Math.frexp(1234)
Math.ldexp(fraction, exponent) #=> 1234.0
.lgamma(x) ⇒ Array, 1
(mod_func)
Returns the logarithm of x
. If additional second argument is given, it will be the base of logarithm. Otherwise it is e
(for the natural logarithm).
Domain: (0, INFINITY)
Codomain: (-INFINITY, INFINITY)
Math.log(0) #=> -Infinity
Math.log(1) #=> 0.0
Math.log(Math::E) #=> 1.0
Math.log(Math::E**3) #=> 3.0
Math.log(12, 3) #=> 2.2618595071429146
.log10(x) ⇒ Float (mod_func)
Returns the base 10 logarithm of x
.
Domain: (0, INFINITY)
Codomain: (-INFINITY, INFINITY)
Math.log10(1) #=> 0.0
Math.log10(10) #=> 1.0
Math.log10(10**100) #=> 100.0
.log2(x) ⇒ Float (mod_func)
Returns the base 2 logarithm of x
.
Domain: (0, INFINITY)
Codomain: (-INFINITY, INFINITY)
Math.log2(1) #=> 0.0
Math.log2(2) #=> 1.0
Math.log2(32768) #=> 15.0
Math.log2(65536) #=> 16.0
.sin(x) ⇒ Float (mod_func)
.sinh(x) ⇒ Float (mod_func)
Computes the hyperbolic sine of x
(expressed in radians).
Domain: (-INFINITY, INFINITY)
Codomain: (-INFINITY, INFINITY)
Math.sinh(0) #=> 0.0
.sqrt(x) ⇒ Float (mod_func)
Returns the non-negative square root of x
.
Domain: [0, INFINITY)
Codomain:[0, INFINITY)
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]
.tan(x) ⇒ Float (mod_func)
Computes the tangent of x
(expressed in radians).
Domain: (-INFINITY, INFINITY)
Codomain: (-INFINITY, INFINITY)
Math.tan(0) #=> 0.0
.tanh(x) ⇒ Float (mod_func)
Computes the hyperbolic tangent of x
(expressed in radians).
Domain: (-INFINITY, INFINITY)
Codomain: (-1, 1)
Math.tanh(0) #=> 0.0