Update README.md

dankogai · dankogai · commit 6af8d2bb5203 · 2016-02-11T01:49:05.000+09:00
diff --git a/README.md b/README.md
@@ -9,30 +9,56 @@ Protocol-Oriented Number System in Pure Swift
 
 ````swift
 import PONS                     // Let the fun begin!
+````
+
+BigInt included.  Enjoy unlimited!
 
+````swift
 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 // 1
+````
 
+Rational (number type) is 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 this
+````
+
+Complex numbers.  How can we live without them?
 
+````swift
 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 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!
+
+````swift
+Double.sqrt(-1)             // sadly NaN
+Rational<BigUInt>.sqrt(bq)  // yes, works with Rational, too!
+Complex.sqrt(-1)            // happily i
+Complex.exp(Double.PI.i)    // not exactly -1.0+0.0.i.
+Complex.log(-1)             // Yes, &pi;i
+````
+
 ## USAGE
 
 ### With Playground via Workspace
