About the speed of animated models in MS Excel part #2

Transcription

1 About the speed of animated models in MS Excel part #2 by George Lungu - This is the second part of a presentation concerning the calculation speed in Excel workbooks. - The first half contained a speed test run on both, a reduced size window and a full screen window for the following series of formula sizes:,,,,,, and million formulas. Medium worksheets Small worksheets 5 Large worksheets Excel Computation Speed 4 3 Hardware: Gateway SX284-2 Monitor resolution: 28 x 24 Mega Operation/second Million Formulas = rand( ) Number of kilo-formulas in the worksheet < - All the series of tests were run on both 23 and 27 versions of Excel, the results are presented in the chart to the left. - As seen in the chart, it looks like for relatively small worksheets (with less than ten thousand single formula calculations) Excel 23 is 5- times faster that Excel 27 when the window is kept very small (2-3 inches). - The speed in 23 for small worksheets drops significantly when the window is increased at full screen size. - Even within the 27 version the speed can be increased dramatically (2-3 times) just by decreasing the window size during the calculation for small to medium size worksheets (below million formulas). - It must be noted the formulas were all =rand() and there was no charting within these worksheets.

2 Benchmarking Excel calculation speed for complex formulas: - Up to this point we filled ranges of various sizes with the same formula ( =rand() ) and measured the calculation speed. - Let s now keep the array of formulas at the unique size of one million (2 columns x 5 rows) and do a series of average speed measurements while progressively increasing the complexity of the formulas in each cell. - It would be a good idea to use a product of the same function ( rand() ) and just use a product of them with an increasing number of factors (from to ). - What we expect to see is a calculation time which is proportional to the total number of rand() functions contained in the worksheet (our assumption will prove to be right). - We upgraded the speed_test_() macro so it can be started and stopped from the same button. We called this new macro speed_test_2(). - We will also upgrade the macros which fill the worksheet with the formulas. For this we first copied the two previous worksheets and used a rename scheme as seen below. Dim N As Boolean Dim p As Double Dim Measurement_Start As Double Sub speed_test_2() N = Not N p = Measurement_Start = Timer() Do Until N = False Or (Timer() - Measurement_Start) > 5 [B4] = p / (Timer - Measurement_Start +.) DoEvents p = p + Loop < 2

3 The formula generator macros: - These macros are used one by one to alter the formulas in an array of 2 x 5 cells so that they are a product of rand() functions with different number of factors, starting with one factors and ending with ten factors. Cell formula: rand() * rand() *.. * rand() - We run one macro at a time and after each macro we run the speed test on sheet Test2 and when the speed test is over we write the iteration frequency results in a table in worksheet Test2_results - We then repeat the same process for the rest of the macros one by one. - The charted result of this procedure is shown in the next page. n =, 2, 3,, Sub generate_array_m_rands() [A:GR5].Formula = "=rand()*rand()*rand()*rand()*rand()*rand()*rand()*rand()*rand()*rand()" Sub generate_array_m_9rands() [A:GR5].Formula = "=rand()*rand()*rand()*rand()*rand()*rand()*rand()*rand()*rand()" Sub generate_array_m_8rands() [A:GR5].Formula = "=rand()*rand()*rand()*rand()*rand()*rand()*rand()*rand()" Sub generate_array_m_7rands() [A:GR5].Formula = "=rand()*rand()*rand()*rand()*rand()*rand()*rand()" Sub generate_array_m_6rands() [A:GR5].Formula = "=rand()*rand()*rand()*rand()*rand()*rand()" Sub generate_array_m_5rands() [A:GR5].Formula = "=rand()*rand()*rand()*rand()*rand()" Sub generate_array_m_4rands() [A:GR5].Formula = "=rand()*rand()*rand()*rand()" Sub generate_array_m_3rands() [A:GR5].Formula = "=rand()*rand()*rand()" Sub generate_array_m_2rands() [A:GR5].Formula = "=rand()*rand()" Sub generate_array_m_rand() [A:GR5].Formula = "=rand()" < 3

4 Average Loop Iteration Period [sec.] (average worksheet calculation time) Charted results: - Below is the average worksheet calculation time in seconds charted against the formula complexity (n). As expected the calculation (update) time is proportional to the formula complexity (or in other words to the total number of rand() functions used in the worksheet). - There are also some products to evaluate within these functions but it seems from the chart below (and the one next page) that this multiplication is not taking significant resources..9.8 The worksheet calculation time seems to scale proportionally to formula complexity The number cells containing formulas is constant = Million The size of the window is reduced (about 4"x4").7.6 Hardware: Gateway SX284- Monitor resolution: 28 x 24 Excel Excel Number of "rand()" functions in the product in each cell Cell formula: "=rand()*rand()*..*rand()" < 4

5 Single Formula Calculation Time [ns] Charted results (continuation): - Below is the average calculation time per function used (in nanoseconds). If we use let s say a product of rand() functions in million cells we have a total of millions functions. If we divide the worksheet calculation time with the total number of functions we get a point on the chart below. As expected this is a fairly constant number and of course dependent on the Excel version and the machine used. 4 The calculation time per function seems to stay relatively constant 2 The number cells with formulas in the worksheet is constant = Million The size of the window is reduced (about 4"x4") Hardware: Gateway SX284-8 Monitor resolution: 28 x 24 Excel 23 6 Excel Number of "rand()" functions in the product in each cell Cell formula: "=rand()*rand()*..*rand()" < 5

6 Single Formula Calculation Time [ns] Lets benchmark a few mathematical functions against each other - A new speed benchmarking worksheet (Test_3) was run for eight different functions (using eight different macros to fill the worksheet with one million formulas). - The results are shown below: 2 8 Calculation time for various built-in mathematical functions sqrt() exp() sin() tan() abs() trunc() rand() < The end 6