Protocol-Oriented Number System in Pure Swift
import PONS // Let the fun begin!Big integer included. Enjoy unlimited!
let bn = BigInt(1)<<64 + 1 // 18446744073709551617
bn.asUInt64 // nil; bn > UIntMax.max
(bn - 2).asUInt64 // 18446744073709551615 == UIntMax.max
bn + bn // 36893488147419103234
bn - bn // 0
bn * bn // 340282366920938463500268095579187314689
bn / bn // 1Rational number also included.
let bq = BigInt(1).over(bn) // (1/18446744073709551617)
bq + bq // (2/18446744073709551617)
bq - bq // (0/1)
bq * bq // (1/340282366920938463500268095579187314689)
bq / bq // (1/1)
bq.denominator == bn // true, of course!
bq.reciprocal.numerator == bn // so is thisComplex numbers. How can we live without them?
let bz = bq + bq.i // ((1/18446744073709551617)+(1/18446744073709551617).i)
bz + bz // ((2/18446744073709551617)+(2/18446744073709551617).i)
bz - bz // ((0/1)+(0/1).i)
bz * bz // ((0/1)+(2/340282366920938463500268095579187314689).i)
bz / bz // ((1/1)+(0/1).i)Elementary functions (as in <math.h>) are supported as static functions,
By default it just converts to Double, let Darwin (or Glibc on Linux) do the work,
and convertsit back by default.
TODO: rewrite elementary functions generically!
Double.sqrt(-1) // sadly NaN
Rational<BigUInt>.sqrt(bq) // (1/4294967296) == yes, works with Rational, too!
Complex.sqrt(-1) // happily `0.0+1.0.i`
Complex.exp(Double.PI.i) // not exactly -1.0+0.0.i.
Complex.log(-1) // Yes, πiBuild the framework before having fun.
To do so, all you need is choose Framework-OSX from the scheme and build it. With framework done, get back to the OSX playground and enjoy.
- Just copy pons/*.swift to your project
- Or build framework and copy it to your project
Simply make repl in the top directory.
make SWIFTPATH=${YOUR_SWIFT_PATH} repl # ${YOUR_SWIFT_PATH}=~/swift/usr/bin in my case
Swift 2.1 or better. Linux supported.
With Swift 2.2 you get some deprecation warnings like:
pons/pocomplex.swift:13:5: warning: use of 'typealias' to declare associated types is deprecated; use 'associatedtype' instead
typealias RealType:POSignedNumber
^~~~~~~~~
```
Just ignore them for the time being. They are needed in 2.1.