Numbers and constants

Swix defines several convince constants including π (or pi), φ (or phi), e, inf, as well as the smallest possible difference between a float or double, FLOAT_EPSILON and DOUBLE_EPSILON

It should be noted that this library defaults to the type double. While it does use the most memory, it’s the most precise. If the compiler ever complains about conversion or can’t find a function, try calling it with a double value.

I’ve extended the native types to include a dot syntax. That is, Int(3).double will return 3.0. These are included for Int, Double, CInt, and Float. For integrating with C, use Int(3).cint. For integrating with vDSP, use Int(1).stride or Int(N).length to get a vDSP_Stride or vDSP_Length respectively.

The library includes both ScalarArithmetic and swift-complex. This means that numbers have handy conversions and we can access complex numbers through 1.0+1.0.i respectively.

Docs

numbers_swix.DOUBLE_EPSILON = 'smaller'

The smallest possible difference between two doubles. See machine epsilon for more detail.

numbers_swix.FLOAT_EPSILON = 'small'

The smallest possible difference between two floats. See machine epsilon for more detail.

numbers_swix.PYTHON_PATH = '~/anaconda/bin/ipython'

Where is Python found? Used for imshow and savefig (testing on MacOSX only!). Assumes pylab is installed.

numbers_swix.S2_PREFIX = '\\(NSHomeDirectory())/Developer/swix/swix/swix/swix/'

The path that should point to the swix directory. The file imshow.py, numbers.swix would be found by appending to this path.

numbers_swix.S2_TOLEANCE = 1e-09

The determines how close two numbers have to be equal.

numbers_swix.binom(n, k)

Calculate the binomial coeffecint or n choose k.

Parameters:

• n (Double) – n as in on the wiki page.
• k (Double) – k as in on the wiki page.

Return type:

The Binomial coeff

numbers_swix.close(x, y)

See if two numbers are approximately equal.

Parameters:

• x – Double. An input value.
• y – Double. Another value.

Return type:

Bool. True only if the two values are close numerically.

Specifically, true only if \(|x-y|<\textrm{tol}\).

>>> assert(close(0, 1e-10) == true)

numbers_swix.convience_elements()

The built in numeric classes have convience elements.

• {Float|Double|Int|CInt}.int. Returns the integer value
• {Float|Double|Int|CInt}.float. The floating point value
• {Float|Double|Int|CInt}.double. The double value.
• String.floatValue, String.doubleValue. Converts the string to a numeric value by interpetting a NSString.
• String.nsstring. For interfacing with C.

Additionally,

• Int has an element cint, length, stride. Length and stride of for interacting with vDSP.
• Double has element cdouble,
• Float has element cfloat.

>>> assert(3.14.int == 3)
>>> assert("3.14".floatValue == 3.14)
>>> assert(vDSP_Stride(1) == 1.stride)
>>> assert(vDSP_Length(N) == N.length)

numbers_swix.deg2rad(x)

Convert from degrees to radians.

Parameters:x (Double) – Angle in degrees. Return type:Double. Angle in radians.

numbers_swix.e = 2.718281828459045

Euler’s number

numbers_swix.euler = 0.5772156649015329

Euler’s constant

numbers_swix.factorial(n)

Computes \(n \cdot (n-1) \ldots 2 \cdot 1 = n!\)

Parameters:n (Int) – The number to compute the factorial of. Return type:The factorial of n.

numbers_swix.inf = inf

Infinity.

numbers_swix.isNumber(x)

See if the input object is a number.

Parameters:x – AnyObject. Return type:Bool. True only if x is a number (a float, double, cint, int). Returns false for vector and matrix.

numbers_swix.operator_slash(lhs, rhs)

Operator / converts integer divison to double division.

Parameters:

• lhs – Int.
• rhs – Int.

Return type:

Double = lhs / rhs

numbers_swix.phi = 1.618033988749895

The golden ratio Also callable with φ

numbers_swix.pi = 3.141592653589793

The classic circle constant, pi and \(\pi\).

numbers_swix.rad2deg(x)

Convert from radians to degrees.

Parameters:x (Double) – Angle in radians. Return type:Double. Angle in degrees.

numbers_swix.tau = 6.283185307179586

The much more intuitive circle constant, tau and \(\tau\).