Specialize sqrt and cbrt (#6)

* Specialize sqrt and cbrt

* Add tests

* Fix test

Author: jishnub

Project.toml

@@ -1,7 +1,10 @@
 name = "MultiplesOfPi"
 uuid = "b749d01f-fee9-4313-9f11-89ddf7ea9d58"
 authors = ["Jishnu Bhattacharya", "Center for Space Science", "New York University Abu Dhabi"]
-version = "0.5.1"
+version = "0.5.2"
+
+[deps]
+FastRationals = "275e499e-7a09-5551-a1d1-9fe535a2b717"
 
 [compat]
 julia = "1"

README.md

@@ -26,6 +26,12 @@ false
 
 julia> (1//3)Pi + (4//3)Pi == (5//3)Pi
 true
+
+julia> float(sqrt(pi)^2) == float(pi)
+false
+
+julia> float(sqrt(Pi)^2) == float(Pi)
+true
 ```
 
 We may also simplify algebraic expressions involving powers of `Pi` as
@@ -138,6 +144,12 @@ julia> Pi + π
 2Pi
 ```
 
+Note that addition and subtraction are not type-stable at present by design.
+
+# Performance
+
+In general using `Pi` instead of `pi` will be less performant, as `pi` is aggressively promoted to a floating-point value in most calculations. The use of `Pi` is mainly intended for tests where exact fractions of `Pi` are desirable.
+
 # Installation
 
 Install the package using

src/MultiplesOfPi.jl

@@ -1,5 +1,7 @@
 module MultiplesOfPi
 
+using FastRationals: FastRational
+
 export PiExpTimes
 export Pi
 
@@ -246,6 +248,16 @@ Base.:(//)(p::PiExpTimes, ::Irrational{:π}) = PiExpTimes(p.x//1, p.n-1)
 Base.:(//)(y::Real, p::PiExpTimes) = PiExpTimes(y//p.x, -p.n)
 Base.:(//)(::Irrational{:π}, p::PiExpTimes) = PiExpTimes(1//p.x, -p.n+1)
 
+_half(n::Integer) = FastRational(n, 2)
+_half(n::Rational) = n//2
+_half(n) = n/2
+_third(n::Integer) = FastRational(n, 3)
+_third(n::Rational) = n//3
+_third(n) = n/3
+
+Base.sqrt(p::PiExpTimes) = PiExpTimes(sqrt(p.x), _half(p.n))
+Base.cbrt(p::PiExpTimes) = PiExpTimes(cbrt(p.x), _third(p.n))
+
 # Pretty-printing
 
 function Base.show(io::IO, p::PiExpTimes)

test/runtests.jl

@@ -11,7 +11,7 @@ using Test
     @test π == Pi
     @test 2π ≈ 2Pi
 
-    @test float(Pi^0.5) == sqrt(pi)
+    @test float(Pi^0.5) == pi^0.5
 
     @testset "nested" begin
         @test PiExpTimes{PiExpTimes{Int}}(3, 0) == 3
@@ -395,6 +395,20 @@ end
             @test float(@inferred Pi^2.0) === pi^2.0
             @test float(@inferred Pi^-2.0) === pi^-2.0
             @test (@inferred Pi^0.0) == 1.0
+            @test float(@inferred Pi^0.5) == float(@inferred sqrt(Pi))
+            @test BigFloat(@inferred Pi^0.5) == BigFloat(@inferred sqrt(Pi))
+            @test float(@inferred Pi^(1//3)) == float(@inferred cbrt(Pi))
+            @test BigFloat(@inferred Pi^(1//3)) == BigFloat(@inferred cbrt(Pi))
+            for T in [Float64, BigFloat]
+                @test T(sqrt(Pi)^2) == T(Pi)
+                @test T(sqrt(Pi^2)) == T(Pi)
+                @test T(sqrt(Pi^2.0)) == T(Pi)
+                @test T(sqrt(Pi^(2//1))) == T(Pi)
+                @test T(cbrt(Pi)^3) == T(Pi)
+                @test T(cbrt(Pi^3)) == T(Pi)
+                @test T(cbrt(Pi^3.0)) == T(Pi)
+                @test T(cbrt(Pi^(3//1))) == T(Pi)
+            end
         end
 
         @testset "Irrational exponent" begin