labs/lab1-parallel-box-blur-filter/README.md

-# Parallel Box Blur Filter
-
-## Setup
-
-Let's upgrade the IDE support first, close VSCode if it's open and run:
-
-```shell
-code --force --install-extension scalameta.metals
-```
-
-Use the following commands to make a fresh clone of your repository:
-
-```
-git clone -b scalashop git@gitlab.epfl.ch:lamp/student-repositories-s21/cs206-GASPAR.git cs206-scalashop
-```
-
-## Useful links
-
-  * [A guide to the Scala parallel collections](https://docs.scala-lang.org/overviews/parallel-collections/overview.html)
-  * [The API documentation of the Scala parallel collections](https://www.javadoc.io/doc/org.scala-lang.modules/scala-parallel-collections_2.13/latest/scala/collection/index.html)
-  * [The API documentation of the Scala standard library](https://www.scala-lang.org/files/archive/api/2.13.4)
-  * [The API documentation of the Java standard library](https://docs.oracle.com/en/java/javase/15/docs/api/index.html)
-
-**If you have issues with the IDE, try [reimporting the
-build](https://gitlab.epfl.ch/lamp/cs206/-/blob/master/labs/example-lab.md#ide-features-like-type-on-hover-or-go-to-definition-do-not-work),
-if you still have problems, use `compile` in sbt instead.**
-
-## Setup scalashop
-
-In this assignment, we will implement a box blur filter, used in applications
-like Adobe® PhotoShop® to blur images.
-For the purposes of this assignment, a filter is an algorithm that takes an
-input image and transforms it in some way into an output image.
-The box blur filter outputs an image in which every pixel has an average value
-of the surrounding pixels from the original image.
-The box blur filter is an example of an *embarrassingly parallel* problem -- no
-or very little effort is required to separate it into parallel tasks.
-Every pixel of the output image can be computed independently of the other
-pixels, and in parallel.
-
-We will proceed in four steps. First, we will implement the kernel of the box
-blur filter, a method used to compute a single pixel of the output image.
-Then we will implement two versions of the parallel box blur, and measure the
-performance difference.
-Finally, we will try out our parallel box blur implementations on real images,
-using ScalaShop -- the image manipulation tool that would impress even
-the Adobe® folks.
-
-By the time you are finished with this assignment, you will:
-
-- understand how the box blur filter works
-- be able to recognize embarrassingly parallel problems
-- know how to measure the performance of a parallel algorithm
-- see how to agglomerate parallel computations into batches
-- better understand how memory access patterns affect performance of parallel
-  algorithms
-
-
-## Preliminaries
-
-Before we begin, we need to cover some basic data types and helper methods.
-These utilities have already been implemented in the package object (in the file `package.scala`) for this
-exercise.
-First, we will use the `RGBA` type to refer to the value of an image pixel.
-We will limit ourselves to 32-bit pixel depth images, so we define `RGBA` to
-be equal to the 32-bit integer type:
-
-```scala
-type RGBA = Int
-```
-
-Why do we call this type `RGBA`?
-This is because each pixel value is composed from 4 components - red, green,
-blue and alpha, where alpha denotes the amount of transparency in the
-respective pixel.
-These components are referred to as *channels*.
-The value of each channel is at least 0 and at most 255.
-
-We can extract the red, green, blue and alpha channel using the following
-utility methods, which use bit masking and bit shifting:
-
-```scala
-def red(c: RGBA): Int = (0xff000000 & c) >>> 24
-def green(c: RGBA): Int = (0x00ff0000 & c) >>> 16
-def blue(c: RGBA): Int = (0x0000ff00 & c) >>> 8
-def alpha(c: RGBA): Int = (0x000000ff & c) >>> 0
-```
-
-Similarly, given the values of the four channels, we can obtain the pixel value
-like this:
-
-```scala
-def rgba(r: Int, g: Int, b: Int, a: Int): RGBA =
-  (r << 24) | (g << 16) | (b << 8) | (a << 0)
-```
-
-Now that we know how to manipulate individual pixels, we can define our image
-type `Img`:
-
-```scala
-class Img(val width: Int, val height: Int) {
-  private val data = new Array[RGBA](width * height)
-  def apply(x: Int, y: Int): RGBA = data(y * width + x)
-  def update(x: Int, y: Int, c: RGBA): Unit = data(y * width + x) = c
-}
-```
-
-The image is a two-dimensional entity -- to refer to a pixel in an image, we
-need to specify an `x` and `y` component.
-On the other hand, the underlying memory model is one-dimensional -- a single
-offset value specifies the position in the array.
-When we store the image into memory, we need to map between the
-two-dimensional image model and the one-dimensional memory model.
-We will do this by storing consecutive rows of the image one after another, as
-illustrated in the following figure:
-
-![mapping](mapping.png)
-
-Thus, the offset of a pixel at coordinates `x` and `y`, is equal to
-`y * width + x`, where `width` is the number of pixels in a single row.
-Although there are other mappings used in practice, we will restrict to this
-simple mapping throughout the exercise.
-
-To ensure that the value of the `x` and `y` coordinates are confined to the
-dimensions of the image, namely width and height, occasionally we have to call
-the `clamp` method:
-
-```scala
-def clamp(v: Int, min: Int, max: Int): Int
-```
-
-Finally, we will use the `task` construct to start parallel computations.
-Every `task` construct invocation returns an object on which we can call the
-`join` method.
-Calling the `join` method blocks the execution of the program until the parallel
-computation ends.
-Below, we calculate the expression `1 + 1` in parallel to the main program:
-
-```scala
-val computation = task {
-   val result = 1 + 1
-   println("Done!")
-   result
-}
-println("About to wait for some heavy calculation...")
-computation.join()
-```
-
-We now have everything we need to start implementing the parallel box filter.
-
-
-## The Box Blur Filter Kernel
-
-In the first part of the assignment, we will implement the box blur filter
-kernel method.
-A kernel is a method that computes the resulting value of a single pixel.
-The kernel method is typically computationally cheap and is not worth
-parallelizing its implementation.
-However, as we will later see, we can apply the same kernel method to different
-pixels in parallel.
-
-![kernel](kernel.png)
-
-The `boxBlurKernel` method takes the source image `src`, coordinates `x` and `y`
-of the pixel, and the `radius` of the blur.
-It returns the resulting average value of the surrounding pixels.
-We compute the average value by separating the pixel into four channels,
-computing the average of each of the channels,
-and using the four average values to produce the final pixel value.
-In the previous figure, the `radius` parameter is equal to `1` and the average
-is computed from `9` pixels.
-
-You can find its signature in the package object of this assignment:
-
-    def boxBlurKernel(src: Img, x: Int, y: Int, radius: Int): RGBA
-
-Implement the `boxBlurKernel` method.
-Use two nested `while`-loops.
-Make sure that the pixels at the image edges are affected only by the
-pixels inside the image (hint: use the `clamp` method from the package object).
-
-
-## Vertical Stripping Box Blur
-
-We can now implement the parallel box blur filter.
-Note that the `boxBlurKernel` method is relatively inexpensive.
-Executing `boxBlurKernel` might be much faster than starting a parallel
-computation, so having a separate parallel computation for the value of each
-pixel would be far too expensive.
-For this reason, we want to batch together many `boxBlurKernel` calls, and have
-a smaller number of parallel tasks.
-This is sometimes referred to as *agglomeration*, and is present in many
-parallel algorithm implementations.
-
-There are many different ways we can do agglomeration for the parallel box blur.
-One is to divide the image into a fixed number of equally wide vertical strips.
-For each strip, we start a parallel task, and wait for their completion.
-Within each strip, we traverse the pixels going from the top to the bottom of
-the image, as illustrated in the following figure:
-
-![stripping](vertical.png)
-
-We start by implementing the sequential `blur` method in the
-`VerticalBoxBlur.scala` source file, which takes the source image `src`, the
-destination image `dst`, the starting (included) and ending (excluded) `x` coordinates
-(i.e, column indices) of the strip, called `from` and `end`, and the blur `radius`.
-The `blur` method blurs the pixels from the `src` image and writes them to the
-`dst` image:
-
-```scala
-def blur(src: Img, dst: Img, from: Int, end: Int, radius: Int): Unit
-```
-
-The implementation of `blur` should rely on the previously defined `boxBlurKernel`.
-
-Then, implement the `parBlur` method, which divides the image into `numTasks` vertical strips and runs each task in parallel:
-
-```scala
-def parBlur(src: Img, dst: Img, numTasks: Int, radius: Int): Unit
-```
-
-Use Scala ranges to create a list of splitting points
-(hint: use the `by` method on ranges).
-Then use collection combinators on the list of splitting points to create a list
-of start and end tuples, one for each strip
-(hint: use the `zip` and `tail` methods).
-Finally, use the `task` construct to start a parallel task for each strip,
-and then call `join` on each task to wait for its completion.
-
-### Benchmarking VerticalBoxBlur
-
-Before running the benchmarking program, go to the top of `VerticalBoxBlur.scala`
-and replace the line:
-```scala
-    Key.verbose -> true
-```
-by:
-```scala
-    Key.verbose -> false
-```
-
-
-Now you can run the `VerticalBoxBlur` program with the following sbt command:
-
-```
-> runMain scalashop.VerticalBoxBlurRunner
-```
-
-Change the number of tasks and the radius parameter.
-How does the performance change?
-
-
-## Horizontal Stripping Box Blur
-
-In this part of the exercise we will pick an alternative agglomeration for the
-box blur algorithm.
-Instead of dividing the image into vertical strips, we will divide it into
-horizontal strips in a similar way:
-
-![stripping](horizontal.png)
-
-We implement the two methods, `blur` and `parBlur` in a similar way as before:
-
-```scala
-def blur(src: Img, dst: Img, from: Int, end: Int, radius: Int): Unit
-def parBlur(src: Img, dst: Img, numTasks: Int, radius: Int): Unit
-```
-
-Note that the arguments `from` (included) and `end` (excluded) this time denote the values of the
-`y` coordinate (i.e, row indices), and that we traverse the pixels left-to-right within each strip.
-
-### Benchmarking HorizontalBoxBlur
-
-Before running the benchmarking program, go to the top of `HorizontalBoxBlur.scala`
-and replace the line:
-```scala
-    Key.verbose -> true
-```
-by:
-```scala
-    Key.verbose -> false
-```
-
-
-Now you can now run the `HorizontalBoxBlur` program from sbt with:
-
-```
-> runMain scalashop.HorizontalBoxBlurRunner
-```
-
-If you implemented the two blur versions correctly, you should observe that the
-horizontal stripping is slightly faster.
-This is because the pixel traversal order visits the pixels which are closer
-together in memory (remember the mapping between the pixel coordinates and the
-memory addresses). As a result, each core can reuse some of the pixels that it
-fetched from the memory during the previous invocation of `boxBlurKernel`.
-The processor cores spend less time fetching pixels from memory and lower the
-pressure on the memory bus.
-
-
-## ScalaShop
-
-Now we have everything we need to start ScalaShop, from sbt run:
-
-```
-> runMain scalashop.ScalaShop
-```
-
-Change the blur implementation, parallelism level and blur radius, and study the
-effect your changes have on performance.
-
- * Which of the two blur implementations is faster?
- * For which values of the `radius` parameter is the difference most significant?
-   * Why?
- * What if we split the image into rectangles? Will this be faster?
-
-*"Adobe" and "Photoshop" are either registered trademarks or trademarks of Adobe
-Systems Incorporated in the United States and/or other countries.*

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labs/lab2-reductions-and-prefix-sums/README.md

-# Reductions and Prefix Sums
-
-Use the following commands to make a fresh clone of your repository:
-
-```
-git clone -b reductions git@gitlab.epfl.ch:lamp/student-repositories-s21/cs206-GASPAR.git cs206-reductions
-```
-
-## Useful links
-
-  * [A guide to the Scala parallel collections](https://docs.scala-lang.org/overviews/parallel-collections/overview.html)
-  * [The API documentation of the Scala parallel collections](https://www.javadoc.io/doc/org.scala-lang.modules/scala-parallel-collections_2.13/latest/scala/collection/index.html)
-  * [The API documentation of the Scala standard library](https://www.scala-lang.org/files/archive/api/2.13.4)
-  * [The API documentation of the Java standard library](https://docs.oracle.com/en/java/javase/15/docs/api/index.html)
-
-**If you have issues with the IDE, try [reimporting the
-build](https://gitlab.epfl.ch/lamp/cs206/-/blob/master/labs/example-lab.md#ide-features-like-type-on-hover-or-go-to-definition-do-not-work),
-if you still have problems, use `compile` in sbt instead.**
-
-## Introduction
-
-In this assignment, you will implement several variants of reduction and prefix
-sum algorithms. Each of the three parts of the assignment will exercise a
-different aspect of parallel programming:
-
-- choosing the right parallelization threshold
-- identifying the correct reduction operator
-- identifying the correct prefix sum operator
-
-We will use the `parallel` construct, defined in the file `package.scala`, as in the lecture to start parallel
-computations. Every `parallel` construct invocation takes two tasks as input and
-outputs the corresponding results as a tuple of two elements. You are not allowed
-to use the `task` construct in this assignment.
-
-## Parallel Counting Change
-
-If you took the course Functional Programming in Scala, you surely recall the
-assignment in which you had to count the number of ways in which you can make
-the change for a given amount of money.
-The text of that assignment was as follows:
-
-> Write a recursive function that counts how many different ways you can
-> make change for an amount, given a list of coin denominations. For
-> example, there are 3 ways to give change for 4 if you have coins with
-> denomination 1 and 2: 1+1+1+1, 1+1+2, 2+2.
-
-In this assignment, you will repeat the same task, but this time, your
-implementation will be parallel.
-Start with the sequential version of this problem once more -- the `countChange`
-function takes the amount of money and the list of different coin denominations.
-It returns the total number of different ways you can give change:
-
-```scala
-def countChange(money: Int, coins: List[Int]): Int
-```
-
-Note that the solution to this problem is recursive.
-In every recursive call, we either decide to continue subtracting the next coin
-in the `coins` list from the `money` amount, or we decide to drop the coin from the list of coins.
-For example, if we have 4 CHF, and coin denominations of 1 and 2, the call
-graph, in which every node depicts one invocation of the `countChange` method,
-is as follows:
-
-                                     4,[1, 2]
-                       3,[1, 2]          +            4,[2]
-               2,[1, 2]    +     3,[2]          2,[2]   +   4,[]
-          1,[1, 2] + 2,[2]   1,[2] + 3,[]    0,[2] + 2,[]    0
-    0,[1, 2] + 1,[2]   1       0      0       1       0
-        1        0
-
-We can take advantage of this recursive structure by evaluating different
-subtrees in parallel.
-This is the next part of the assignment -- implement the method `parCountChange`
-that counts the amount of change in parallel:
-
-```scala
-def parCountChange(money: Int, coins: List[Int], threshold: Threshold): Int
-```
-
-As we learned in the lectures, the `parCountChange` should not spawn parallel
-computations after reaching the leaf in the call graph -- the synchronization
-costs of doing this are way too high.
-Instead, we need to *agglomerate* parts of the computation.
-We do this by calling the sequential `countChange` method when we decide that
-the amount of work is lower than a certain value, called the *threshold*.
-To separate the concern of deciding on the threshold value from the
-implementation of our parallel algorithm, we implement the threshold
-functionality in a separate function, described by the `Threshold` type alias:
-
-```scala
-type Threshold = (Int, List[Int]) => Boolean
-```
-
-When a `threshold` function returns `true` for a given amount of money and the
-given list of coins, the sequential `countChange` implementation must be called.
-
-Implement `parCountChange`!
-
-Now that we have the `parCountChange` method, we ask ourselves what is the right
-implementation of the `threshold` function?
-Recall the examples from the lectures, such as summing the array values and
-computing the norm, where this was easy -- we exactly knew the amount of work
-required to traverse a subrange of the array, so `threshold` could return `true`
-when the length of the subrange was smaller than a certain value.
-
-Sadly, the total amount of work for a given `parCountChange` invocation is hard
-to evaluate from the remaining amount of money and a list of coins.
-In fact, the amount of work directly corresponds to the count that
-`parCountChange` returns, which is the value that we are trying to compute.
-Counting change is a canonical example of a task-parallel problem in which the
-partitioning the workload across processors is *solution-driven* -- to know how
-to optimally partition the work, we would first need to solve the problem
-itself.
-
-For this reason, many parallel algorithms in practice rely on heuristics to
-assess the amount of work in a subtask.
-We will implement several such heuristics in this exercise, and assess the
-effect on performance.
-First, implement the `moneyThreshold` method, which creates a threshold function
-that returns `true` when the amount of money is less than or equal to `2 / 3` of
-the starting amount:
-
-```scala
-def moneyThreshold(startingMoney: Int): Threshold
-```
-
-Remember that `a / b` will return the integer division of `a` and `b` when both
-operands are `Int`s. To avoid this problem, be sure to always do the multiplication of
-`startingMoney` by `2` before doing the division by `3`.
-
-Now run the `ParallelCountChange` application in sbt and observe the speedup:
-
-```
-> runMain reductions.ParallelCountChangeRunner
-```
-
-The previous heuristic did not take into account how many coins were left on the
-coins list, so try two other heuristics.
-Implement the method `totalCoinsThreshold`, which returns a threshold function
-that returns `true` when the number of coins is less than or equal to the `2 / 3` of the
-initial number of coins:
-
-```scala
-def totalCoinsThreshold(totalCoins: Int): Threshold
-```
-
-Again, be careful about the order of operations.
-
-Then, implement the method `combinedThreshold`, which returns a threshold
-function that returns `true` when the amount of money multiplied with the number
-of remaining coins is less than or equal to the starting money multiplied with
-the initial number of coins divided by `2`:
-
-```scala
-def combinedThreshold(startingMoney: Int, allCoins: List[Int]): Threshold
-```
-
-Which of the three threshold heuristics gives the best speedup?
-Can you think of a heuristic that improves performance even more?
-
-
-## Parallel Parentheses Balancing
-
-In this part of the assignment, we recall the Parenthesis Balancing assignment
-that might be familiar to you from the Functional Programming in Scala course.
-Here, the task is to, given an array of characters, decide if the parentheses in
-the array are balanced.
-
-Let us recall a few examples of strings in which parentheses are correctly
-balanced:
-
-```
-(if (zero? x) max (/ 1 x))
-I told him (that it's not (yet) done). (But he wasn't listening)
-```
-
-Similarly, the parentheses in the following strings are not balanced:
-
-```
-(o_()
-:-)
-())(
-```
-
-Implement a sequential function `balance`, which returns `true` iff the
-parentheses in the array are balanced:
-
-```scala
-def balance(chars: Array[Char]): Boolean
-```
-
-Next, you will implement a parallel version of this method.
-By now, you're already an expert at implementing the structure of a reduction
-algorithm, so you should have no problem there.
-The tricky part in parallel parentheses balancing is choosing the reduction
-operator -- you probably implemented `balance` by keeping an integer
-accumulator, incrementing it for left parentheses and decrementing it for the
-right ones, taking care that this accumulator does not drop below zero.
-Parallel parentheses balancing will require a bit more ingenuity on your part,
-so we will give you a hint -- you will need two integer values for the
-accumulator.
-
-Implement the `parBalance` method, which checks if the parentheses in the input
-array are balanced using two helper methods `reduce` and `traverse`.
-These methods implement the parallel reduction and the sequential traversal
-part, respectively:
-
-```scala
-def parBalance(chars: Array[Char], threshold: Int): Boolean = {
-  def traverse(idx: Int, until: Int, _???_: Int, _???_: Int): ???
-
-  def reduce(from: Int, until: Int): ??? = ???
-
-  reduce(0, chars.length) == ???
-}
-```
-
-In this case, we again use the fixed threshold parameter, as we did in the
-lectures. Sections with size smaller or equal to the threshold should be processed sequentially.
-For maximum performance, use a `while` loop in the `traverse` method, or make
-`traverse` tail-recursive -- do not use a `Range`.
-
-Now, run the `ParallelParenthesesBalancing` application from sbt:
-
-```
-> runMain reductions.ParallelParenthesesBalancingRunner
-```
-
-How large was your speedup?
-
-If you are looking for additional challenges, prove that your reduction operator
-is associative!
-
-
-## Line of Sight
-
-In the last part of the exercise, you will be implementing an entirely new
-parallel algorithm -- you will apply the prefix sum algorithm to computing the
-line-of-sight in two-dimensional terrain.
-
-Imagine that you are standing at the zero of a coordinate system.
-The curve to your right describes the terrain that you are facing.
-This is shown in the following figure:
-
-![terrain](terrain.png)
-
-The task of the line-of-sight algorithm is to compute the visibility of each
-point of the terrain, as shown in the following figure, where the visible area
-is above of the full line, and the obscured terrain is shown with a dotted
-line.
-
-![visibility](visibility.png)
-
-What is the necessary and sufficient condition for a point on the terrain to be
-visibile from the zero of the coordinate system, where you are standing?
-Imagine that the terrain heights are represented with an array of numbers.
-We can compute (the tangent of) the viewing angle of each point on the terrain by dividing the
-height of the terrain `xs(i)` with the distance from the viewing point `i`,
-as shown in the following figure:
-
-![angle](angle.png)
-
-It turns out that if the viewing angle of some point B is **lower** than the
-viewing angle of an earlier point A, then the point B is not visible, as shown
-in the following figure:
-
-![angle](angle2.png)
-
-This simple realization allows us to easily compute the line-of-sight on the
-terrain -- if you were a sequential programmer, you would traverse the array of
-height values from the beginning to the end, and write the maximum angle seen so
-far into the output array.
-
-Implement the sequential `lineOfSight` method, which, for each height entry in
-the `input` array (except for input(0) which is the location of the observer and
-is always zero), writes the maximum angle until that point into the `output`
-array (output(0) should be 0):
-
-```scala
-def lineOfSight(input: Array[Float], output: Array[Float]): Unit
-```
-
-We keep things simple -- instead of outputting an array of booleans denoting the
-visibilities, we only output the angles.
-
-Note that what we call an angle in this assignment is actually the tangent
-of the angle. Indeed, `xs(i)` is the opposing side of the angle and `i` the adjacent side.
-The ratio `xs(i) / i` that you compute is in fact the tangent of the angle!
-Since the tangent of an angle is strictly increasing between
-0° and 90°, it is a perfectly good replacement for the actual angle in our use case.
-Keep this in mind and make sure that you do not apply any trigonometic functions on the tangent!
-
-When we see a sequential algorithm that produces a sequence of values by
-traversing the input from left to right, this is an indication that the
-algorithm might have a parallel prefix sum variant.
-So let's try to implement one!
-
-Recall what you learned in the lectures -- the first phase of the parallel
-prefix sum algorithm is the *upsweep* phase.
-Here, the algorithm constructs the reduction tree by traversing parts of the
-input array in parallel.
-Implement the method `upsweepSequential`, which returns the maximum angle in a
-given part of the array, and the method `upsweep`, which returns the reduction
-tree over parts of the input array. If the length of the given part of the input
-array is less than or equal to `threshold`, then `upsweep` calls `upsweepSequential`.
-Note that the part of the input array that needs to traversed is represented
-using indices 'from' (inclusive) and 'until' (or 'end') (exclusive).
-
-```scala
-def upsweepSequential(input: Array[Float], from: Int, until: Int): Float
-```
-
-```scala
-def upsweep(input: Array[Float], from: Int, end: Int, threshold: Int): Tree
-```
-
-The `Tree` data type is either a `Leaf` or an inner `Node`, and it contains the
-maximum angle in the corresponding part of the array.
-Note that when the number of elements in a part of the input array,
-which is `(end - from)`, is smaller or equal to the threshold, the sequential `upsweepSequential`
-has to be invoked, and you should return a `Leaf`.
-Otherwise, you should process the part of the input array in parallel, and return
-a `Node`. Make sure that the work is evenly distributed between the parallel computations.
-
-The second phase is called *downsweep* -- here, the algorithm uses the tree to
-push the maximum angle in the corresponding *prefix* of the array to the leaves
-of the tree, and outputs the values.
-Implement the methods `downsweep` which processes parts of the tree in parallel,
-and the method `downsweepSequential`, which traverses the parts of the array
-corresponding to leaves of the tree and writes the final angles into the
-`output` array:
-
-```scala
-def downsweep(input: Array[Float], output: Array[Float],
-  startingAngle: Float, tree: Tree): Unit
-
-def downsweepSequential(input: Array[Float], output: Array[Float],
-  startingAngle: Float, from: Int, until: Int): Unit
-```
-
-Finally, implement `parLineOfSight` using the `upsweep` and `downsweep` methods:
-
-```scala
-def parLineOfSight(input: Array[Float], output: Array[Float],
-  threshold: Int): Unit
-```
-
-Now, run the `LineOfSight` application in sbt and observe the relative speedups:
-
-```
-> runMain reductions.LineOfSightRunner
-```
-
-How large is the speedup compared to the number of cores in your processor?
-Can you explain your results?

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