Added the SimpsonEvenFast method.

Author: dextorious

.travis.yml

@@ -3,9 +3,9 @@ language: julia
 os:
   - linux
   - osx
+  - windows
 julia:
   - release
-  - nightly
 notifications:
   email: false
 # uncomment the following lines to override the default test script

README.md

@@ -31,5 +31,6 @@ The currently available methods are:
 - TrapezoidalFast
 - TrapezoidalEvenFast
 - SimpsonEven
+- SimpsonEvenFast
 
-All methods containing "Even" in the name assume evenly spaced data. All methods containing "Fast" omit basic correctness checks and focus on performance. The fast methods will crash horribly if you supply invalid data.
+All methods containing "Even" in the name assume evenly spaced data. All methods containing "Fast" omit basic correctness checks and focus on performance. Consequently, the fast methods will segfault or produce incorrect results if you supply incorrect data (vectors of different lengths, etc.).

appveyor.yml

@@ -2,8 +2,6 @@ environment:
   matrix:
   - JULIAVERSION: "julialang/bin/winnt/x86/0.5/julia-0.5-latest-win32.exe"
   - JULIAVERSION: "julialang/bin/winnt/x64/0.5/julia-0.5-latest-win64.exe"
-  - JULIAVERSION: "julianightlies/bin/winnt/x86/julia-latest-win32.exe"
-  - JULIAVERSION: "julianightlies/bin/winnt/x64/julia-latest-win64.exe"
 
 branches:
   only:

src/NumericalIntegration.jl

@@ -6,6 +6,7 @@ immutable TrapezoidalEven     <: IntegrationMethod end
 immutable TrapezoidalFast     <: IntegrationMethod end
 immutable TrapezoidalEvenFast <: IntegrationMethod end
 immutable SimpsonEven         <: IntegrationMethod end # https://en.wikipedia.org/wiki/Simpson%27s_rule#Alternative_extended_Simpson.27s_rule
+immutable SimpsonEvenFast     <: IntegrationMethod end
 
 integrate{T<:AbstractFloat}(x::Vector{T}, y::Vector{T}, method::IntegrationMethod=Trapezoidal()) = integrate(x, y, method)
 
@@ -42,16 +43,25 @@ end
 
 function integrate{T<:AbstractFloat}(x::Vector{T}, y::Vector{T}, ::SimpsonEven)
     @assert length(x) == length(y) "x and y vectors must be of the same length!"
-    retval = 17*y[1] + 59*y[2] + 43*y[3] + 49*y[4] + 49*y[end-3] + 43*y[end-2] + 59*y[end-1] + 17*y[end]
-    retval /= 48
+    retval = (17*y[1] + 59*y[2] + 43*y[3] + 49*y[4] + 49*y[end-3] + 43*y[end-2] + 59*y[end-1] + 17*y[end]) / 48
     for i in 5 : length(y) - 1
         retval += y[i]
     end
     return (x[end] - x[1]) / (length(y) - 1) * retval
 end
 
+function integrate{T<:AbstractFloat}(x::Vector{T}, y::Vector{T}, ::SimpsonEvenFast)
+    @inbounds retval = 17*y[1] + 59*y[2] + 43*y[3] + 49*y[4]
+    @inbounds retval += 49*y[end-3] + 43*y[end-2] + 59*y[end-1] + 17*y[end]
+    retval /= 48
+    @fastmath @inbounds for i in 5 : length(y)-1
+        retval += y[i]
+    end
+    @inbounds return (x[end] - x[1]) / (length(y) - 1) * retval
+end
+
 export integrate
 export Trapezoidal, TrapezoidalEven, TrapezoidalFast, TrapezoidalEvenFast
-export SimpsonEven
+export SimpsonEven, SimpsonEvenFast
 
 end

test/runtests.jl

@@ -1,7 +1,7 @@
 using NumericalIntegration
 using Base.Test
 
-methods = [Trapezoidal(), TrapezoidalEven(), TrapezoidalFast(), TrapezoidalEvenFast(), SimpsonEven()]
+methods = [Trapezoidal(), TrapezoidalEven(), TrapezoidalFast(), TrapezoidalEvenFast(), SimpsonEven(), SimpsonEvenFast()]
 x = collect(-π : π/1000 : π)
 y = sin(x)
 for method in methods