# CMath

CMath is a library that provides trigonometric and transcendental functions for complex numbers.

## Usage

To start using this library, simply:

``````require "cmath"
``````

Square root of a negative number is a complex number.

``````CMath.sqrt(-9)  #=> 0+3.0i
``````
Methods
A
C
E
L
S
T
Included Modules
Class Public methods
acos(z)

returns the arc cosine of `z`

Also aliased as: acos!
```# File lib/cmath.rb, line 257
def acos(z)
begin
if z.real? and z >= -1 and z <= 1
acos!(z)
else
(-1.0).i * log(z + 1.0.i * sqrt(1.0 - z * z))
end
rescue NoMethodError
handle_no_method_error
end
end```
acos!(z)
Alias for: acos
acosh(z)

returns the inverse hyperbolic cosine of `z`

Also aliased as: acosh!
```# File lib/cmath.rb, line 314
def acosh(z)
begin
if z.real? and z >= 1
acosh!(z)
else
log(z + sqrt(z * z - 1.0))
end
rescue NoMethodError
handle_no_method_error
end
end```
acosh!(z)
Alias for: acosh
asin(z)

returns the arc sine of `z`

Also aliased as: asin!
```# File lib/cmath.rb, line 243
def asin(z)
begin
if z.real? and z >= -1 and z <= 1
asin!(z)
else
(-1.0).i * log(1.0.i * z + sqrt(1.0 - z * z))
end
rescue NoMethodError
handle_no_method_error
end
end```
asin!(z)
Alias for: asin
asinh(z)

returns the inverse hyperbolic sine of `z`

Also aliased as: asinh!
```# File lib/cmath.rb, line 300
def asinh(z)
begin
if z.real?
asinh!(z)
else
log(z + sqrt(1.0 + z * z))
end
rescue NoMethodError
handle_no_method_error
end
end```
asinh!(z)
Alias for: asinh
atan(z)

returns the arc tangent of `z`

Also aliased as: atan!
```# File lib/cmath.rb, line 271
def atan(z)
begin
if z.real?
atan!(z)
else
1.0.i * log((1.0.i + z) / (1.0.i - z)) / 2.0
end
rescue NoMethodError
handle_no_method_error
end
end```
atan!(z)
Alias for: atan
atan2(y,x)

returns the arc tangent of `y` divided by `x` using the signs of `y` and `x` to determine the quadrant

Also aliased as: atan2!
```# File lib/cmath.rb, line 286
def atan2(y,x)
begin
if y.real? and x.real?
atan2!(y,x)
else
(-1.0).i * log((x + 1.0.i * y) / sqrt(x * x + y * y))
end
rescue NoMethodError
handle_no_method_error
end
end```
atan2!(y,x)
Alias for: atan2
atanh(z)

returns the inverse hyperbolic tangent of `z`

Also aliased as: atanh!
```# File lib/cmath.rb, line 328
def atanh(z)
begin
if z.real? and z >= -1 and z <= 1
atanh!(z)
else
log((1.0 + z) / (1.0 - z)) / 2.0
end
rescue NoMethodError
handle_no_method_error
end
end```
atanh!(z)
Alias for: atanh
cbrt(z)

returns the principal value of the cube root of `z`

Also aliased as: cbrt!
```# File lib/cmath.rb, line 149
def cbrt(z)
z ** (1.0/3)
end```
cbrt!(z)
Alias for: cbrt
cos(z)

returns the cosine of `z`, where `z` is given in radians

Also aliased as: cos!
```# File lib/cmath.rb, line 170
def cos(z)
begin
if z.real?
cos!(z)
else
Complex(cos!(z.real) * cosh!(z.imag),
-sin!(z.real) * sinh!(z.imag))
end
rescue NoMethodError
handle_no_method_error
end
end```
cos!(z)
Alias for: cos
cosh(z)

returns the hyperbolic cosine of `z`, where `z` is given in radians

Also aliased as: cosh!
```# File lib/cmath.rb, line 214
def cosh(z)
begin
if z.real?
cosh!(z)
else
Complex(cosh!(z.real) * cos!(z.imag),
sinh!(z.real) * sin!(z.imag))
end
rescue NoMethodError
handle_no_method_error
end
end```
cosh!(z)
Alias for: cosh
exp(z)

Math::E raised to the `z` power

``````exp(Complex(0,0))      #=> 1.0+0.0i
exp(Complex(0,PI))     #=> -1.0+1.2246467991473532e-16i
exp(Complex(0,PI/2.0)) #=> 6.123233995736766e-17+1.0i
``````
Also aliased as: exp!
```# File lib/cmath.rb, line 52
def exp(z)
begin
if z.real?
exp!(z)
else
ere = exp!(z.real)
Complex(ere * cos!(z.imag),
ere * sin!(z.imag))
end
rescue NoMethodError
handle_no_method_error
end
end```
exp!(z)
Alias for: exp
log(*args)

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

``````log(Complex(0,0)) #=> -Infinity+0.0i
``````
Also aliased as: log!
```# File lib/cmath.rb, line 71
def log(*args)
begin
z, b = args
unless b.nil? || b.kind_of?(Numeric)
raise TypeError,  "Numeric Number required"
end
if z.real? and z >= 0 and (b.nil? or b >= 0)
log!(*args)
else
a = Complex(log!(z.abs), z.arg)
if b
a /= log(b)
end
a
end
rescue NoMethodError
handle_no_method_error
end
end```
log!(*args)
Alias for: log
log10(z)

returns the base 10 logarithm of `z`

Also aliased as: log10!
```# File lib/cmath.rb, line 107
def log10(z)
begin
if z.real? and z >= 0
log10!(z)
else
log(z) / log!(10)
end
rescue NoMethodError
handle_no_method_error
end
end```
log10!(z)
Alias for: log10
log2(z)

returns the base 2 logarithm of `z`

Also aliased as: log2!
```# File lib/cmath.rb, line 93
def log2(z)
begin
if z.real? and z >= 0
log2!(z)
else
log(z) / log!(2)
end
rescue NoMethodError
handle_no_method_error
end
end```
log2!(z)
Alias for: log2
sin(z)

returns the sine of `z`, where `z` is given in radians

Also aliased as: sin!
```# File lib/cmath.rb, line 155
def sin(z)
begin
if z.real?
sin!(z)
else
Complex(sin!(z.real) * cosh!(z.imag),
cos!(z.real) * sinh!(z.imag))
end
rescue NoMethodError
handle_no_method_error
end
end```
sin!(z)
Alias for: sin
sinh(z)

returns the hyperbolic sine of `z`, where `z` is given in radians

Also aliased as: sinh!
```# File lib/cmath.rb, line 199
def sinh(z)
begin
if z.real?
sinh!(z)
else
Complex(sinh!(z.real) * cos!(z.imag),
cosh!(z.real) * sin!(z.imag))
end
rescue NoMethodError
handle_no_method_error
end
end```
sinh!(z)
Alias for: sinh
sqrt(z)

Returns the non-negative square root of Complex.

``````sqrt(-1)            #=> 0+1.0i
sqrt(Complex(-1,0)) #=> 0.0+1.0i
sqrt(Complex(0,8))  #=> 2.0+2.0i
``````
Also aliased as: sqrt!
```# File lib/cmath.rb, line 124
def sqrt(z)
begin
if z.real?
if z < 0
Complex(0, sqrt!(-z))
else
sqrt!(z)
end
else
if z.imag < 0 ||
(z.imag == 0 && z.imag.to_s[0] == '-')
sqrt(z.conjugate).conjugate
else
r = z.abs
x = z.real
Complex(sqrt!((r + x) / 2.0), sqrt!((r - x) / 2.0))
end
end
rescue NoMethodError
handle_no_method_error
end
end```
sqrt!(z)
Alias for: sqrt
tan(z)

returns the tangent of `z`, where `z` is given in radians

Also aliased as: tan!
```# File lib/cmath.rb, line 185
def tan(z)
begin
if z.real?
tan!(z)
else
sin(z) / cos(z)
end
rescue NoMethodError
handle_no_method_error
end
end```
tan!(z)
Alias for: tan
tanh(z)

returns the hyperbolic tangent of `z`, where `z` is given in radians

Also aliased as: tanh!
```# File lib/cmath.rb, line 229
def tanh(z)
begin
if z.real?
tanh!(z)
else
sinh(z) / cosh(z)
end
rescue NoMethodError
handle_no_method_error
end
end```
tanh!(z)
Alias for: tanh