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HP Solve: Issue 24 (July 2011)

1. Download the PDF version of newsletter articles Contact the editor From the Editor Learn more about current articles and feedback from the latest Solve newsletter including One Minute Marvels and other community news Learn more gt How Fast is Fast Richard J Nelson Calculator speed is a calculator technical Richard J Nelson This overview of HP s calculator manuals covers the entire history of what HP has done to provide the user with what he or she needs to use an HP calculator Math Series 7 Richard J Nelson What is the difference between average mean median and mode Learn the basics behind these mathematical concepts through data sets and statistics attribute that is often discussed by users This article discusses calculator speed examining how fast is fast and how fast is fast enough A E Update Profile Change Email Support amp Drivers Eo If you received this e mail from an associate and or would like to receive email of this type directly from HP please click here HP respects your privacy If you d like to discontinue receiving these type of e mails from HP please click here For more information regarding HP s privacy policy or to obtain contact information please visit our privacy statement or write to us at Privacy Mailbox 11445 Compaq Center Drive W Houston Texas 77070 ATTN HP Privacy Mailbox Hewlett Packard we
2. 0 246024709841173 Root 0 0706708871132657 N 0302490769565316 Root N The model below shows a linear influence of the values of the roots and the number of duplicated roots on the errors In addition the model has a cross product term that includes both the root values and the number of duplicates HP Solve 24 Page 17 Page 4 of 7 10 1 0 0000001 HP Solve 24 Page 18 Fig 5 A log log plot for the results Page 5 of 7 Series1 H Series t Series3 Series4 Series Series6 Series Series8 Series1 f Series2 amp Series3 Series4 SeriesS Series6 Series Series8 The regression ANOVA table for the above model indicates that it is possible to drop the term for the number of duplicates without significant loss of correlation Doing so yields the following model Number of observations 88 Adjusted R Square 0 96853 F statistic 1339 59 NormEtr 0 984344257243684 0 272775553843399 Root 0 03 14431520006403 Root N Finally I performed a search for the best model that relates the error with the values of the roots and the number of duplicated roots The search employed linearized multiple regression and covered a wide variety of popular transformations Such transformations include functions like the logarithm reciprocal square cube reciprocal square reciprocal cube square root and reciproca
3. About the Author Jake Schwartz has been an HP calculator fan since 1971 after first trying the HP9810A desktop RPN machine at a co op job at RCA in New Jersey He has owned most of the scientific top of the line handhelds since the HP35A in the Bee 1973 joined the PPC Calculator Club in 1977 and contributed to many of _ the clubs since including serving as Peripheral Routines coordinator for the PPC ROM project for the HP41 in 1980 Currently working at Lockheed Martin gt asa software engineer Jake has been presenting at and videotaping the annual U S HP calculator conferences for more than two decades Notes 1 A copy of the HHC2008 conference proceedings which includes Walter s 10 page paper Imagine A Development Since 1988 along with proceedings for 35 conferences between 1979 and 2010 is available as part of the 22 300 page PPC DVD HP calculator historical reference disk For more information check http www pahhc org ppccdrom htm 2 Gene Wright is the current point of contact at present for obtaining an HP serial transfer cable Contact Gene at genewright143 hotmail com 3 Contact Eric Rechlin at http commerce hpcalc org overlay php to order overlays If that link is unavailable check his main commerce page at http commerce hpcalc org 4 The PPC ROM was a custom plug in module containing 122 routines in many disciplines and developed for the HP41 series by members of the PPC club in 1980
4. jis 0 25 es ny i 04 E O 1 0 2 Se 0 0 0 0 0 2 04 06 08 10 12 14 16 18 20 22 3 The mode value is an obvious choice for an odd number of sample data values If the number of data is even it is customary to use certain rules to determine which one to use A data set as a distribution may be bimodal or multimodal See the link above in 2 HP Solve 24 Page 33 Page 4 of 4 Last page of issue 24 From The Editor HP Solve 24 page 34 Article From The Editor Issue 24 Summer is expressing itself 113 degrees worth here in the Sonoran Desert where I write these words In case you haven t noticed HP Solve is quarterly this year Most HP Solve readers are spending their days outdoors but here in the desert being outdoors from June to August is where you do not want to be Triple digit temperatures for 100 plus days in a row during the summer is normal It will start to cool off in September when students go back to school and the HP Hand Held Conference is held See additional comments below Community News HP calculator user activity as reported in issue 23 continues to build This should make HHC 2011 an especially exciting conference with so many new machines 5 to talk about If you have never attended an HHC this year s planned presentations will make it exceptional You will find additional information at hhuc us BTW the cost of attending an HHC 1s very low and you will go home
5. 1 Works with polynomials that have real and complex coefficients and of course a combination of the two 2 Solves for all real and complex roots 3 There is no need to supply guesses for the roots The function PROOT internally determines the initial guesses Article Goals In this article I focus on the following aspects of function PROOT 1 How the function PROOT handles polynomials that have duplicate roots In this article I am using the term duplicate roots to be clear and concise Many articles on the Internet use the term multiple roots which I find a bit ambiguous Typically you must read these articles text to determine if they are referring to several polynomial roots that have the same value or possess unequal values 2 Study the errors in the results of PROOT as how they relate to the values of the duplicated roots and the number of duplicated roots 3 Compare the errors of function PROOT with similar errors in the similar Matlab function roots This article considers univariate polynomials that have a single value for the duplicate roots This is a simple case compared to univariate or mutltivariate polynomials that have several sets of duplicate roots An example of the polynomials I will cover is P x x 1 410 Here is an example of a univariate polynomial with several sets of duplicate roots P x x 1 410 x 1 15 2 x 7 420 Another example of a mutltivariate polynomial with several s
6. 3 020160338 4 241309839 6 408848421 5 521664308 11 16477563 20 0 311436851 0 691337317 0 982268009 1 833327277 2 353802393 3 112862947 6 325574864 9 73553898 18 33327277 23 53802393 31 12862947 25 0 511658272 1 046742843 1 799450896 2 6593 16327 3 319326705 4 833480825 10 46742843 17 996 16639 26 593 16327 33 19556004 48 54449639 30 0 631873293 1 462345524 2 536997271 3 259642713 4 181961208 6 318296467 14 68723352 25 36997271 32 59867889 41 82057503 63 1786003 35 0 796489399 1 975058665 3 0255 19804 4 057980913 5 054055422 8 025091633 19 75058665 30 2545014 40 58167795 50 53939049 80 34521181 40 0 917001403 Error 3 419951916 4 48239371 5 910306454 9 178041139 Error 34 20109414 44 82187293 59 10306454 91 96021967 Figure 4 shows a linear plot for the NormErr results The graph includes a legend Series refers to 5 duplicate roots series 2 refers to 10 duplicate roots and so on The lines are not perfectly linear because of the rounding errors Figure 5 plots the same data using log log scales The series labeling is the same as in Figure 4 Applying simple linear and multiple linearized regressions to the data I found the several empirical models I will share three models that I found most interesting The first model is where N is the number of duplicated roots Number of observations 88 Adjusted R Square 0 96926 F statistic 915 27 NormEtr 0 596421714900844
7. 75C are examples N YR PV PMT FY Anot ED O i 6 Machine repurposing E Eaa es i l The customizing examples given above are features found on older HP machines Has HP exhausted its customizing ideas No the most recent HP customization feature is exhibited in the 2008 HP20b A special calculator connector and HP supplied cable allows the complete calculator to be customized This capability may also be found on the 2010 HP30b Several Rom images have been converted developed that may be loaded into these machines The HP User Community has finally caught up with HP in this regard and the most ambitious Fig 3 The first HP project is the WP 34s This high end scientific calculator is only possible because repurposeable of HPs vision of customization See additional information elsewhere in this issue calculator HP Solve 24 Page 11 Page 3 of 4 7 Expandability High end calculators will often have some form of expandability The best example of this is the HP 41 which is best described as a complete HP calculator system because of its four expansion ports You could customize your HP 41 by simply plugging in ROM and RAM modules You could customize your HP 41 by adding an HP IL module to enable connecting tothe rest of the world You could customize your HP 41 by plugging in a bar code Wit How 3 Caras tack reader printer disc drive cassette drive magnetic card reader or HP Fig 4 Pocket instrument You coul
8. Pi agt O sepleraas ta o A Jn Photos oldcomputermuseum com Educational Aids news Do you understand the basics of computers Do you know Fig 1 Original ad for demonstrator how bits are processed by a computer to perform the De _ a mathematical operations that we use daily with our oy calculators Does your school have a means to demonstrate these concepts in a dramatic interesting and fun way Here is a news item that caught my eye because it would be a neat demonstrator for any school to have Computers were very new in the 60 s and many companies developed machines to demonstrate the underlying digital concepts of computers Fig 1 shows one such machine the DigiComp II and Fig 2 Gaal Cang by Ewl Mad Scent Lab ebones 64 Oversine a raai Of he Digi Core a mechanikai shows a recent version of the same computer I think of it as smz tws amo stonimanrnen msc costg one soe the 8 Ball Computer Watch the video demonstrate the ee eee multiplication problem 3 x 13 39 at the link below Fig 2 Pinball machine like computer No batteries are required just gravity It is a complete automatic binary computer that is big enough for classroom use http laughinesquid com giant digi comp 1i recreates mechanical computer from 1960s Here is the content of this issue 01 Back to School Students are one of the largest group of HP calculator users and HP has great news for st
9. 2 2 3 4 7 9 7 4 mean gt 9 4 zi lri tetEn Median Middle value separating the greater and 1 2 2 3 4 7 9 3 lesser halves of a data set Mode Most frequent value in a data set 1 2 2 3 4 19 2 Observations and Conclusions The basics of Average Mean Median and Mode have been discussed One of the misunderstandings by many students and technical users is how they relate to each other as the latter three terms are detailed technical terms and average is a casual English term Mean while a technical term implies average in that it is usually understood to be the arithmetic mean which is the same as average Table 2 provides a comparison with examples of each of the terms This topic approaches the very broad topic of statistics which will have to wait for a future article in this series One aspect that is part of a future article is data that occurs multiple times frequency This aspect along with weighted data is the frequency of occurrence of each value and how this is handled by our calculators 1 Mean as used here is the arithmetic mean average vs geometric quadratic or harmonic mean 2 For an excellent distinction of these subtleties see http en wikipedia org wiki Mode_ 2S8statistics 29 Table 2 is taken from that text This text will also provide the mathematical details of the three differences which are illustrated from the following plot from that article mode 1 4 i median mean
10. Solve 24 Page 23 Page 2 of 3 should be fairly straightforward and it would be expected that the PPC ROM code plus the example programs in the PPC ROM manual will begin to take on new relevance thirty years after their original creation Kudos go out to Hewlett Packard for making the 20b 30b hardware open for repurposing and it is hoped that the continued success of the WP 34S project might spur others to attempt to carry this calculating platform even further in the near future Observations and Conclusions Imagine HP considers its graphing machines to be its high end scientific ee calculator entry if you consider there being an entry level model mid range model and high end model Many users however do not need the size or added complexity of a graphing machine and only wished that the scientific product range included one with additional capability Long time HP creative calculator user Walter Bonin gave the product line a lot of thought and with each new model he made his own keyboard arrangement with the functions that he thought should be there Many of his designs may be seen in the HHC 2008 Fig 2 PI of 10 pages of designs conference proceedings His ten full page keyboard layouts build on the HP 42S and HP 15C Walter Bonin Germany teamed up with Paul Dale Australia and Marcus von Cube Germany to implement his concepts into the 20b 30b platform dubbing it the WP 34s The prefix letter choice should be obvious
11. YR Conv k BEG P YR END Depr A Hyp B sin cos Dran E rsp Fairy INPUT ARG Black S l xoy i h STO RCL R f ei h CshFl IRR Bond f RCL PSE 8 _ car view o Rii M He Dota E Ca Wc Wu i i Sums H H d RANY INTG xy tere DEG RAD GRAD TAN Jx iiaa i ATAN J xt IN ex M ENTERT xoy 4 E INPUT Kal ENG ENG UNDO CONST xo NOT cipi Cix Memory EEX B Reset a Fill xa K2 8 t1016 Claf E oi ABS N RIND lt I m CLEAR XEQ 7 8 HMS RAD CHG wie OR MOD 8 e IN M40 ah iaa Maea Pa a HMS DEG l 4 5 6 x MILE F nis T PROB STAT CER STATUS 5 CPyx 2 o REF s SH p TWF x i KM V cm v nPr Vv 1 2 3 egal ECN TESI ECN E I lt gt xox Usv f Yn zW am 3118 eee J SHOW _ PSE Fae fs P R CO ONOFF x RND IP nie Y LBLRIN DSE ISG ae Figure 1 Left to right HP 35s scientific WP 34S scientific repurposed from an HP 20b HP 30b business calculator The 34S utilizes one of Eric Rechlin s professionally made keyboard overlays and individual key covers An Amalgam of Many Predecessors In Walter s manual for the WP 34S it is mentioned that the functionality attempts to encompass the HP 42S scientific functions the fraction mode of the HP 32SH integer and bit manipulation from the HP 16C and probability distributions from the HP 21S In reality this firmware goes much further in several areas such as 1 expanding the complex arithmetic functionality
12. all of your students This would not be absolutely correct however because the average of a group of averages is not the average of all members of each group Let s illustrate this with some real data See Table 1 The grades are given values as 1 A 2 A 3 A 4 B 5 B 6 B 7 C 8 C 9 C 10 D 11 D 12 D and F 13 and is failing There are 15 students in three classes and 17 students in two classes The average grade if the all the grades are averaged 1s 439 79 5 56 B but if the average of the HP Solve 24 Page 31 Page 2 of 4 averages 27 06 5 5 41 is used the grade is B The two may be quite close but that is because the data is closely grouped You may calculate what is called the weighted average of the five classes as follows without having to deal with all 49 values of the data as follows Weighted average of the 5 classes 17 5 23 15 4 27 17 7 88 15 6 27 15 3 87 174 15 4 174 15 15 439 02 79 5 56 Table 1 Student Class Grades Class 1 Class 2 Class 3 Class 4 Class 5 1 8 5 5 9 3 2 5 4 7 5 5 3 3 6 5 9 3 4 8 1 9 3 9 5 10 2 6 7 2 6 4 4 7 5 5 7 3 5 10 2 1 8 4 2 4 9 4 9 2 3 11 6 1 10 6 4 9 6 4 11 3 7 9 6 6 12 7 2 7 8 2 13 4 8 8 2 8 14 2 2 10 8 2 15 7 9 3 9 1 16 4 6 17 9 11 TOT 89 64 134 94 58 AVG 5 23 4 27 7 88 6 27 3 87 Grd B B C B A Average vs Mean Median and Mode Mean In normal life people use the terms average and mean
13. an ideal manual is included with a cost perspective of such a manual using the PPC ROM Manual as an example S07 7 in Fundamentals of Applied Math Series Average Mean Median amp Mode A review of the math related to a general purpose calculator average function that uses a more complex operation data analysis S08 Regular Columns This is a collection of news items and repeating regular columns From the editor This column provides feedback and commentary from the editor One Minute Marvels This OMM provides three routines to provide a rounding function for numbers The method used by our calculators to round numbers is explained and the Astronomers Rule for statistically rounding is provided A reader challenge is to write a program to statistically round S09 How Fast is Fast Calculator speed is a calculator technical attribute that is often discussed by users As you might expect most serious users want more speed This article discusses calculator speed examining how fast is fast and how fast is fast enough A table of typical calculator speeds is provided That is it for this issue I hope you enjoy it If not tell me Also tell me what you liked and what you would like to read about lt a e Richard Email me at hpsolve hp com HP 48 One Minute Marvel No 11 Rounding One Minute Marvels are short efficient unusual and fun HP 48 programs that may be entered into your machine in a m
14. by third parties and he demonstrated firmware support tools for that purpose Soon after a few basic attempts were made to replace the firmware with alternate function sets including one to duplicate the capabilities of the venerable HP45 scientific non programmable calculator from the early 1970s Also at the 2008 conference the commit tee made sure to spotlight a lengthy proceedings paper submitted by Walter Bonin from Germany containing various suggestions for usage of existing HP calculator industrial design to create followon scientific machines boasting powerful capabilities of the great high end non graphing Scientifics of the past such as the HP41 series from 1979 1990 and the HP42S from 1988 1995 With HP s ongoing focus on the financial segment of the market and the HP 35S from 2007 representing merely a contin uation of the scientific mid range as compared to the 41 42 caliber highlighting suggestions for extending this category of machine seemed relevant especially with Hewlett Packard folks in the audience Then in the following year the 20b platform bore additional fruit with the HP 30b advanced business calc with its basic macro programming capability and more complete suite of financial functions And true to form in October at the HHC2009 conference in Fort Collins Colorado attendees were treated to HP presentations detailing the 30b s functional and programming capabilities What was not yet appare
15. interchangeably Statisticians however will consider the mean to be only one form of the average Technical language will usually use the term mean where casual English will use the term average Statistics deals with sets of data and the term average is more of a broad term that describes a data set as a whole whereas mean median and mode are subtle more technical versions of expressing the average of a data set Depending on the distribution of the data mean median and mode may provide a more mathematically accurate description of the average of the data Median This is the central point of the data set In order to determine vs calculate the median of the data set you must first sort the data from low value to high value The sorted values are divided into two equal groups with the value in the middle the value of the mean If the groups are equal the bottom value of the top group is averaged with the top value of the bottom group One difference between the mean and the median is that the mean average or arithmetic mean may be a calculated value whereas the median is usually an actual data value Mode This is the value that occurs most frequently in a data set HP Solve 24 Page 32 Page 3 of 4 The average terms may be briefly summarized in table 2 Table 2 Comparison of Common Averages 2 Examples values 1 2 2 3 4 7 9 Type Description Example Result Arithmetic Sum divided by number of values Se ee van 1
16. its ability to convey an idea without being specific If you listen to advertisements for example and you really hear the words you will be amazed at the ability of the language to convey an image without being exact or precise What does a low price really mean Calculator users are technical people They want to know and express ideas in very specific terms to avoid confusion and misunderstanding The normal way of saying the small nut will not fit on the large screw might be technically expressed as the 6 32 nut will not fit on an 8 32 screw In terms of an advertised price the relative positioning of one product with respect to another is instantly defined if a number is given Numbers are used for precision and included in the use of numbers is what calculator designers call dynamic range the range of numbers that the calculator is able to use The dynamic range for the first scientific calculator the HP 35A in 1972 was described on the first text page 1 of the 36 page operating manual as It will handle numbers as small as 10 and up to 10 If you have ever had to calculate the factorial of a number just for fun you quickly discovered the dynamic range limit of your scientific or graphing calculator The dynamic range of 10 to 10 was considered more than adequate when the HP 35A was introduced The HP 35s extends this dynamic range as described in the User s Guide The smallest numb
17. marvels attracts an incredible amount of research resources and leading edge technological advancements excel if they are used in a smart phone Antenna battery display key radio semiconductor and sensor technology advances as used in smart cell phones could eventually impact calculators because high volume manufacturing lowers cost Color displays for example are common in cell phones When a color display costs the same as a monochromic display the possibility of a color displays being used in a calculator increases Touch screens when low enough in cost will eventually be used in calculators As I mention in the Customization article The basic idea is that a calculator has a key per function 1 e a calculator has to have as efficient a user interface as possible Efficiency is vital for a calculator One technology to watch is haptic touch displays and this topic was discussed by Jake Schwartz in issue 19 This technology allows you to feel what you touch so that a flat screen may also become an effective keyboard One of the more sensitive issues with HP calculator users is the feel of the keyboard Does this technology offer a solution for calculators A recent article Haptics Adds New Dimensions to Touchscreens in BusinessWeek provided an update and based on the list of very large companies investigating the technology the promise looks interesting http www businessweek com magazine content 11_26 b4234043549730 htm
18. of the 42S or 15C as well as offering an optional 8 level RPN stack mode 2 enhancing the integer capabilities of the 16C by providing conversions to and math in any integer base between 2 and 16 being not restricted solely to binary octal decimal and hexadecimal 3 offering over 50 constants plus 80 unit conversions and 4 expanding programming features in many areas Also it should be stressed that due to the high speed CPU in the 20b 30b programs run on the order of 50 to 100 times as fast as the HP 42S and even moreso compared to the 35S With its 111 storage registers 100 flags and 506 program steps in its basic memory as well as 3 additional 506 step program banks available for storage in flash memory this powerhouse of capability is something no serious calculator user of science and or math should overlook It has recently been announced that Marcus will be attending and speaking at the HHC2011 calculator conference this September in San Diego California to present his insider s perspective on the project and we very much look forward to meeting and hearing him Activities have begun with respect to creating user programs to augment the built in 34S capabilities especially in the matrix manipulation area The natural starting point for these has been to adapt and update the M1 through M5 matrix routines from the PPC ROM for the HP41 series Since the programming languages are very similar this adaptation HP
19. to include lots of examples for any publication is simply beyond the resources that are available The PPC ROM Manual was able to provide the much needed examples because of the donated 100 man years 876 528 man hours which the User Community put into the project Can you imagine HP or any calculator manufacturer spending these kinds of resources on any similar project At a value of 20 hr for the time that would be 17 5 million dollars or 35 000 dollars per document page to produce the content Even the world s largest technology company does not have that level or resources for a calculator product I mention these things because of the chatter often seen on the various HP web sites that users complain about HP s manuals I am sensitive to these complaints because I have been writing HP s manuals for over 30 years I have probably met with in person face to face the majority of the manual writers at HP for most of their machines Back in the days when HP had all of their operations engineering marketing and manufacturing in one location in Corvallis I would visit the factory for three days meeting with many different teams dedicated to calculators I especially remember one meeting with the documentation group at a mutual HP Solve 24 Page 26 Page 1 of 3 request because of some of the things I had written that mentioned that they thought that their manuals were some of the best in the industry Aft
20. 6 174838817 12 42682286 18 93328928 24 85364572 29 93058001 59 861 16002 35 0 766216523 1 465711962 2 22172822 2 997573651 3 748654527 7 564532863 15 12906573 22 55593546 30 25813145 37 49176674 73 79690739 40 0 901217991 1 775271906 2 633223623 3 550543811 4 440941079 8 881882158 17 76376432 26 86599005 35 34012844 43 07384657 86 07878242 Comparing the data in tables 1 and 2 you can see that the errors increase with the values of the roots and the number of their duplicates You can also notice that the errors in PROOT for 5 10 and 15 duplicates are less than that of Matlab s roots function For 20 duplicates the errors for both functions PROOT and roots are close to each other In the case of 25 30 35 and 40 duplicates the errors of PROOT exceed those of Matlab s function roots the difference is not overwhelming So you can say that function PROOT stacks up well against a powerful tool like Matlab s roots function I was also able to obtain similar models for the errors with Matlab s roots function The first two models match the ones for the PROOT function Here is the first model HP Solve 24 Page 19 Page 6 of 7 Number of observations 88 Adjusted R Square 0 99577 F statistic 6827 06 NormEtr 0 1354891060389 0 182209523189305 Root 0 008075 18594388061 N 0 0260245276550454 Root N The second model is Number of observations 88 Adjusted R Square 0 99580 F
21. 81 Copies of the complete 500 page user manual including scannable program barcode and the 32 page pocket guide appear in the PPC DVD reference disk mentioned earlier HP Solve 24 Page 24 Page 3 of 3 HP s Calculator Manuals HP Solve 24 page 25 Article HP s Calculator Manuals Richard J Nelson Note Most of the opinions expressed here are my own and they reflect my obsessive belief that examples and a high index rating are vital to every technical manual Experience has shown that providing them however is very very difficult Introduction Legacy users of HP s Calculators usually remember the manuals that came with their machines in a positive way Popular opinion seems to suggest that newer manuals are not as good as the older manuals and certainly every manual user old or new seems to complain that there are never enough examples Most commonly the manual that describes the machine and how to use it is called the owner s manual This is a generic term for a manual that comes with your car refrigerator or calculator The owner s manual is assumed to contain the important information related to the product and how to use it HP didn t start out calling their calculator manuals Owner s Manuals and they don t call them by that name today The HP 35A 1972 came with an HP 35 operating manual 36 pp The lower case is HP s choice The HP 65A 1974 came with an HP 65 Owner s Hand
22. HP Solve Calculating solutions powered by HP Hot Deals Back To School Summer Savings 10 off Calculators at the HP Home amp Home Office Store and more Your articles ie fh An ip eda Customization Richard J Nelson One of HP s greatest contributions to calculators is the feature of customization Read through a list of features found on HP calculators past and present HP Mobile Calculating Lab Kits Learn how the HP Mobile Calculating Lab MCL helps educators teach math and science in a dynamic way Be is L1 1 N Ase TEET Using PROOT with Duplicate Roots Namir Shammas In this article Namir focuses on how the function PROOT handles polynomials that have duplicate roots in addition to studying and comparing errors within the function PROOT y Repurposing the HP 20b 30b Calculator Platform Jake Schwartz As mentioned in the Customization article repurposing is a form of customizing your calculator Jake provides an updated overview of an interesting user community repurposing project HP s Calculator Manuals Fundamentals of Applied Issue 24 July 2011 Welcome to the twenty forth edition of the HP Solve newsletter Learn calculation concepts get advice to help you succeed in the office or the classroom and be the first to find out about new HP calculating solutions and special offers
23. HP Solve 24 Page 9 Page 1 of 4 1 Programming This feature was first seen on the HP 65A calculator in 1974 Running a program allows the user to perform hundreds and even thousands of keystroke pressings by running a single program The user customizes the program to perform the computation task exactly as he or she needs The requirement for having a calculator programmable has always been a debatable issue for just about every level of machine Will the user make the effort to write a program Research shows that the number of users who program is very small less than 1 of the total machines sold are user programmed Adding programming to a model requires more ROM memory more RAM memory a programming language of sorts and documentation The issue of what the user Fig 1 The HP 65 expects is also a factor Most users are familiar with electronically transferring had customization information to their machines They expect to be able to down load the more features intricate programs into their machines without thinking or effort This adds some form of input output to the calculator which further increases the programmable calculator cost I argue that even the low end scientific calculator should have some very simple keystroke remembering basic programming capability for quick simple keystroke repeatable calculations 2 Dedicated program Keys Being programmable does not completely meet the requirement of being truly
24. bject in the variable PC This program takes the value of the duplicate root and the number of duplicates from levels 2 and 1 respectively The program performs the following tasks HP Solve 24 Page 16 Page 3 of 7 1 Creates the array of roots Duplicates the array of roots in the stack Invokes the PCOEF function to create the array of polynomial coefficients Calls the function PROOT to calculate the roots of the polynomial Subtracts the array of calculated roots from the array of supplied roots Se se Calculates the norm of the array of root differences or errors in the calculated roots if you prefer by using the ABS function 7 Divides the norm by the square root of the number of duplicated roots The result 1s a measure for the square root of the mean squared errors I will call this result NormErr Table 1 shows the results the square root of the mean squared errors in a two dimensional table of duplicate root values and number of duplicate roots Table 1 The resulting square roots of the mean squared errors NormErr Number of Duplicate Roots 7 57356E 07 1 11504E 06 2 0398 1E 06 3 09378E 06 4 01014E 06 6 03879E 06 1 10905E 05 2 52447E 05 3 02134E 05 3 36434E 05 7 57356E 05 10 0 023712099 0 019690194 0 009003057 0 015701459 0 118694337 0 2368645 13 0 204998177 0 641002908 0 149300066 1 187462764 2 371209903 15 0 111591213 0 313862912 0 357305746 0 640147421 0 714660864 1 761367587
25. book 107 pp The HP 67A 1976 came with an HP 67 Owner s Handbook and Programming Guide 353 pp The HP 41C 41CV came with an Operating manual A Guide for the Experienced User 71 pp The HP48G Series machines 1993 came with a User s Guide 592pp All of these manuals were printed most spiral bound and heavy User s Guide makes sense because it is simple short and descriptive After 16 years of calculator manuals the eleven Pioneer Series of machines 1988 1991 came with an Owner s Manual larger size 250 pp More recent machines now come with a User s Guide or Quick Start Guide The name has changed from manual to handbook to guide Another often remembered feature of HP s manuals is the use of humor when illustrating examples that include people Especially memorable are the unusual names for people used in the example One reason that users tend to remember these things is that they desperately need examples in manuals The PPC ROM Manual demonstrated this need by providing extensive examples for every one of the 153 routines described in the 500 page 8 1 2 x 11 US letter size 2 1 2 pound 1 1 Kilo tome Why is this completely obvious aspect of the user s need not emphasized by HP when it produces its manuals After 35 years of writing about this issue especially after producing the PPC ROM Manual I believe that I know the answer The resources required
26. bsite Sign up for Driver and Support Alerts Back To School Summer Savings HP Solve 24 page 3 Article This school year HP is offering something for everybody The best line up of scientific graphing and financial calculators for every level of education Elementary School Business School EasyCalc 10bI1 smartCalc 300 30b Middle School Engineering amp Science 10s 35S 39gs 50g smartCalc 300 Approved for most college entrance exams High School Approved for the CFP Certification Exam 10s 39gs 40gs smartCalc 300 Find these HOT Summer Savings at your favorite office supply store E tail site or 10 off at the HP Home and Home Office Store Supplies are limited SO Act Fast These HOT Deals Won t Last www shopping hp com Promo code BTS2011 Offer Ends 9 30 2011 How does the calculator you are now using stack up To find out use it to calculate the number of cubic inches in a Cosmic Cube a million light years on each edge You should be able to easily get the answer to at least three digits of precision For the 12 digit answer see below ANSWER Cosmic cube volume Coupon is valid through 9 20 11 Valid for HP Direct hpdirect com internet and call center purchases only Coupon valid while supplies last Any unused portion will be forfeited Each coupon code is limited to one usage per customer one coupon code per checkout Offer void where prohibited taxed or restricted by law Non
27. ct mathematics to the students everyday experiences through mathematical modeling The HP MCL kit is unlike any other lab kit as it allows students to stream data continuously instead of logging data at certain time intervals The benefit is that there is very little students have to set up They just start monitoring the experimental setup When they see something of interest they can stop and zoom in on the data they want and make conjectures or start analyzing the data The following experiment illustrates the benefits of data streaming An accelerometer is connected to the HP MCL and the StreamSmart He neraee wince nei application is launched An accelerometer is strapped to a ruler with a rubber band One end of the ruler is clamped to a table top and the other end is flexed and released to set the ruler in motion This is done x 761 4 0 1325 nest ra EMPRTISTART several times over a 5 second period The result is shown in Figure 1 Figure 1 where 2 or 3 of the events can be seen as small peaks HP Solve 24 Page 6 Page 1 of 2 Zooming in horizontally in time and vertically on one of the peaks reveals the detail shown in Figure 2 What looked like just a bump or two is actually a clearly defined set of dampened oscillations The simple ruler can behave in a way that is both complex and beautiful Using the StreamSmart Application the student can trace to each peak and add the point to a data set manually Figure 3 sho
28. customizable as defined above The HP 65A also added dedicated program keys to start a program previously keyed into memory Press one of five top row keys and you run five of your programs 3 Off line storage The HP 65A had a built in card reader to load and store programs see Fig 1 The stick of gum sized magnetic cards were used to store share and sell buy programs You could fill program memory with large programs that could completely customize your machine and make it into a dedicated surveyors medical engineering or financial calculator 4 Key assignments The HP 41 is the prime example of a machine with a full set of customization features and it had everything Programming allows the features to be customized but it was the User Mode key that converted the meaning of every key to be customized so the user could run any operation function or program by pressing a single key A running program could also redefine the complete keyboard so customization was also dynamic The 41 also had a feature not seen on other calculators Since any key could have any function assigned to it the user may not know what to expect If however you held down the key the assigned or internal native function would be displayed If you continued to hold down the key the display would switch to NULL and you could release it and no action was performed The HP 41C manual concludes with You have just completed the HP 41C Owners Handbook and Pr
29. d also plug in a host of third party accessories as well customization example Observations and Conclusions The vital character of a calculator is defined in terms of the current market environment and the power of a convenient and simple user interface of a single key press 1s emphasized with customization HP excels when it comes to providing customization features in its calculators The best example of the full gamut of customizing features 1s represented by the legacy HP 41C CV CX series of calculators The seven customizing features of programming dedicated program keys off line program and data storage key assignments overlays repurposing and expandability are discussed Reference links are included to further explore the subject 1 Examples are HHC Conferences user Group meetings CES Show meetings and HP facility visits 2 Camera manufacturers provide a cable to connect to the camera to the USB port of a computer to down load photos High end graphing calculators connect to computers to upload and download programs and even operating system upgrades 3 The next calculator the 1976 HP 67A also had a built in card reader The most popularly programmed calculator ever was the 1979 HP 41C CV CX There were several off line I O storage options available for the HP 41 including an HP IL interface a card reader and a barcode wand 4 See HP Solve issue 16 for an article The HP 41 system 30 Years Old that explains the re
30. e 12 and the book was previewed in issue 19 page 23 The extensive photography provided in this book may also be sampled with illustrations of installing the 41CL board at http www hpmuseum ore ce1 sys ceiwrap hpmuseum archvO20 ce1 read 186300 1 86300 Yet another very exciting project uses one of HP s business calculators to create a new calculator dubbed the WP 34s In this case the very recent HP 30b s feature of being repurposed is used to create a new high end scientific calculator Jake Schwartz delves into some of the features of this community project created by an HP user in Germany This project will be discussed in detail and machines can be repur posed at HHC 2011 The WP 34s is a true RPN machine not an RPL based RPN machine The PPC ROM manual based on the HP 41 is an excellent resource for programs Matrix operations are an example of functions not included in the WP 34s but the PPC ROM routines provides a rich resource for easily adding them Third party news A new business book dealing with the HPIOBII is now in type setting Written by John Webber it is titled Get Rich Slow In addition to being an author John is a lecturer and his books and other activities may be found at www webbertext com You may email John at jwebber olympuspub com HP Solve 24 Page 35 Page 1 of 4 Technology News One of the most technologically complex consumer electronics devices is the smart phone The sales volume of these handheld
31. e project is often behind schedule and not going back to add to the index entries is easily justified HP Solve 24 Page 28 Page 3 of 3 Fundamentals of Applied Math Series 7 HP Solve 24 page 29 Article 7 in Fundamentals of Applied Math Series Average Mean Median amp Mode Richard J Nelson Introduction What is the difference Everyone remembers from school what an average is The average cost for a student s five text books is calculated by adding the five prices e g 83 52 72 44 amp 70 321 and dividing the sum by the total number of items being averaged 321 5 64 20 What does the average text book cost asks the parent thinking of budget planning For the example above it is 64 20 but is this the Fig 1 HP35s X key same for all students Is this the same for the average student Sometimes we hear about a news report that mentions a median value when the expected term is the average value A similar situation may also apply to the mean or mode How are these different Like many mathematical concepts there are sometimes different levels to a meaning You may think of this situation as the normal meaning and the purist s meaning If you can t depend on mathematics as being exact what is Human nature even influences mathematics Data Sets and Statistics Previous calculator functions reviewed in this series were simple unary functions e g given x calcula
32. easons with a third characteristic that it is a calculator 1 Itis convenient easy to use Convenience means that it is consistent and always ready to solve your problem s It instantly turns on and its battery life is very long so it usually works when you pick it up 2 Itis low cost The three devices listed above usually start in price above the high end calculator models 3 The last requirement is in its name calculator Have you noticed that most computer the three devices listed above are actually computers calculator emulations are those of well known calculator models Basically a calculator is optimized with a completely different design vision than that which is used for a computer handheld or otherwise The basic idea is that a calculator has a key per function i e a calculator has to have as efficient a user interface as possible What is more efficient Customization defined HP was the first calculator manufacturer to add customization features to its machines and to this day HP has created more methods and has put more types of customization features into its machines than any other manufacturer Basically a customization feature is one that helps make a calculator what is has to be convenient and low cost Let me repeat the last sentence of the paragraph above What is more efficient than pressing a single key Let s go through the list of customizing features found on HP calculators past and present
33. ed This is in sharp contrast to accumulated sums based statistics which essentially destroys each data point when it is entered Each method has its advantages and disadvantages The accumulated sums method is simpler faster and easier to use The data list method is busier requires more thought allows data entry verifying and is more suitable for multiple uses such as calculating the median and mode of large sets of data The HP 35s key we need to calculate the average is shown in fig 1 but this key is used for only half of the problem Fig 2 shows another key located just to the left that is needed to enter the data Assuming that the statistics registers are clear you key the first data point and press the key The data is processed and the display will show 1 to indicate that the first data point or x y pair is input Continue keying in the values and the key pressings will count your data points When you are finished you will then press the left shifted gold X key to calculate the Fig 2 HP35s X key average See you User s Guide for the details of clearing and calculating all of the statistics values d A m p pi hi 7y Suppose you are a teacher and the principal asks you for the average grade for all of your five classes Without thinking you may think that since you have the average grade for each class that you could just add these five averages and divide the total by five to a get the average grade for
34. er all they had won awards for their manuals Of course I was coming from a perspective of what is desired from the user s perspective and these experiences drove the decision to include extensive examples and a formal format of section headings extensive index etc in the PPC ROM Manual The Ideal Manual Manuals for computer related products have always and will always fall short from the user s perspective simply because of resources complexity cost and time The needs of the user don t change it is the manufacturer s continuous attempts to competitively meet those needs that changes If resources were unlimited is a prerequisite that every complainer should use when writing about manuals From the user s perspective I personally would like to see a manual approach similar to the following 1 A photograph of the keyboard with each and every key identified with a description of what the notations and symbols mean This should be a straight on photo not one at an unreadable angle 2 A key response description of what happens when any key is pressed Presenting this matrix of key responses will require that the user understand that keys change in their meanings depending on the mode or environment at the moment the key 1s pressed 3 A reference organization that recognizes that the manual is used at least five times more frequently for reference than it is used for explanation initial reading 4 Each page is numb
35. er available on the calculator is 9 99999999999 x 10 while the largest number is 9 99999999999 x 10 One of the lesser advertised aspects of HP s calculators are that all functions work over the full dynamic range Many competing machines have restrictions in their manuals that provide limits for various operations and functions so that even though the calculator may work with a specified dynamic range the algorithms they use are not robust enough to always work and be accurate correct AS aT i gs 4 Ly Po r a i j n esws Stee mSS i Sees s oaea tld Speed numbers Calculator speed was a major specification for the HP 35A and the early 4 literature even listed the numbers Addition subtraction multiplication and division were 60 to 100 milliseconds The slowest functions were Trigonometric functions at 500 milliseconds Half a second is considered a noticeable amount of time for the user to wait ite tii PIJI TTT IHH He Bae TETE PPH 4 tetepa yi P The newer models are programmable and how fast the calculator runs becomes increasingly important as elaborate programs perform very ee ee ee ey ee complex operations and analysis Fig 1 Calculator speed has been of concern since the very The question is How fast is fast beginning HP Solve 24 Page 40 Page l of 3 The popular press has reported in the past that Bill Hewlett the internal champion of HP Calculat
36. eral places 4 15 4 16 5 See the HP Museum site for the data as of February 2007 http www hpmuseum org cgi sys cgiwrap hpmuseum articles cgi read 700 HP Solve 24 Page 42 Page 3 of 3
37. ered sequentially Bill Wickes addressed the page numbering issue of section numbering vs sequential page numbering in his famous trilogy of HP48 books by using both 5 Many Examples practical real world timely and meaningful 3 6 Consistent Writing Style Manuals should be written following a published style that dictates what must be covered in an owner s manual handbook or guide 7 A two tier index While examples are omitted because of necessity the sparse indexes in most calculator manuals are a classic example of inconsistency Using modern computer software it is an easy task to produce an index with a minimum index rating of 3 or higher Index rating number of index entries divided by the number of text pages Certainly every technical document that is to be used as a reference has at least three words terms or important ideas per page Simply write down these index items with the page number as the proofing is being done Word and most other document software have an index capability 8 Format Most of HP s recent User s Guides follow a standard format Section one is usually Getting Started and the last part is Appendixes and References If the manual is printed it has a soft cover using a perfect bound style of binding HP calculator teams have reinvented themselves during the 39 years of calculators How should the manual issue be viewed using today s highly competitive ma
38. ets of duplicate roots appears next P x y Z x 2 412 y 1 14 4 z 7 422 The last two examples refer to polynomials whose root error analysis is very complicated Why Bother with Duplicate Roots If you apply math in practical calculations you may ask why you should bother with worrying about duplicate roots since they may rarely occur in your field To be honest I have not found a practical case that yields polynomials with duplicate roots at least with 5 or more duplicates I have stumbled on the topic of duplicate polynomial roots while researching general solutions for polynomial roots The cases of polynomials with duplicate roots that I have encountered on the Internet are purely mathematical in HP Solve 24 Page 14 Page 1 of 7 nature It may be one of these cases where we have the knowledge and the algorithms in case a real world application requires a solution Demonstrating PROOT Errors Duplicate polynomial roots are surprisingly difficult to solve for causing many popular algorithms to stumble or even fail To give you a quick idea about errors in calculating duplicate roots enter the following program object in the stack lt lt gt XN lt lt 1 N START X NXT N gt ARRY DUP PCOEFF PROOT ARR Y gt DROP gt gt gt gt Store the above program object in the variable TDR short for Test Duplicate Roots or you can use any other name you prefer To use the TDR program enter the value for the root t
39. even last roots out of ten roots It s easy to notice the deterioration of the results as the real component values fall above and below 1 In addition the results include imaginary parts that are not so small as in the simple test you did earlier If you clear the first seven stack levels you get the output shown in Figure 3 RAD ave HEn R a THOME re Eis Je 4 1111111111 J 1 He H HH zi 1 He H HH l 1 BHs H HE OTOR FAD cazr l Fig 3 The first three roots Levels 1 to 3 show the first three roots which are exact You can conclude that the algorithm used by PROOT may experience deterioration of results due to deflation of the targeted polynomial Analyzing PROOT Errors How are the errors in calculating the duplicate roots affected by their values and their count I will attempt to answer this question in this section First I will define a domain of values for the duplicate roots and the number of duplicates I studied the roots of 1 2 3 4 5 10 20 30 40 50 and 100 As far as the number of duplicates I considered the values in the range of 5 to 40 in increments of 5 As the number of duplicates exceeds 40 the PROOT function experiences runtime errors I used the following program object to calculate a single value that summarizes the errors in the obtained roots lt lt gt XN lt lt 1 N START X NXT N gt ARRY DUP PCOEFF PROOT ABS N SQRT gt gt Store the above program o
40. ges should be sequentially numbered on all documents over four pages in length The writers were surprised that I should mention this until I showed them a 72 page example that had obviously slipped through the cracks Perhaps I am overly sensitive to page numbering because I so often reference page numbers in review articles 3 When I asked if an HP Style Manual existed most of the people in the room were hesitant to talk about it They implied that they had one but when I asked if I could get a copy I received a blank look Privately a writer later explained that each writer used his or her own references and that they did not have an official HP Style Manual This older HP confident writer explained that there was an official HP Style manual but it hadn t been updated in many years at that time and the younger writers didn t know about it That was over twenty years ago Today technology and language change so fast that corporate style manuals are seldom used 4 In the spirit of the famous numerical calculation philosophy of Prof William Kahn there are avoidable errors and unavoidable errors Perhaps the lack of examples could be justified to be in the latter category but having a poor index is most certainly in the former category An index value of three or higher is most desirable and it greatly extends the usefulness of the User s Guide One reason that many manuals have a sparse index is that the Index is often done last th
41. inute or less These programs were developed on the HP 48 but they will usually run on HP Solve 24 Page 37 Page 3 of 4 the HP 49 and HP 50 as well Note that the byte count is for the program only Rounding is an important numerical practice and is used for just about every numerical problem you solve HP s calculators provide display settings that will automatically round the answer to the display setting without changing the number itself Here are three rounding programs by Joseph K Horn that provide additional rounding scenarios A second input is required in addition to the number being rounded These special cases allow the rounding to be up or down as desired The number being rounded is obj2 and the basis for the rounding is obj1 1 Round obj2 up to a multiple of objl UP lt lt SWAP OVER CEIL gt gt Examples 153 25 UP 175 167 25 UP 175 2 Round obj2 down to a multiple of objl DOWN lt lt OVER SWAP MOD gt gt Examples 153 25 DOWN gt 150 167 25 DOWN gt 150 3 Round obj2 to the closest multiple of obj1 NEAR lt lt SWAP OVER 0 RND gt gt Examples 153 25 NEAR gt 150 167 25 NEAR gt 175 Rounding is an interesting statistical issue and the use of calculators with their industry standard rounding practices have clouded the issue of rounding Suppose you need to calculate a financial value and the result is put int
42. l square root The best model that I obtained is Number of observations 88 F statistic 4229 83 Adjusted R Square 0 98982 In NormErr 0 112444241487657 1 0193 1043509749 In Root 357 981953542852 N 2 Figure 5 agrees with the above model as it shows logarithmic lines that are somewhat straight Comparing PROOT with the Matlab roots Function How do the results of PROOT stack up against other polynomial solving tools Iran a similar analysis on Matlab s roots function and obtained the data in Table 2 Table 2 The resulting square roots of the mean squared errors NormErr for Matlab s roots function 0 00110017 0 002200341 0 003448921 0 004400682 0 0059033 1 0 01180662 0 02361324 0 030521903 0 047226479 0 0604 143 0 1208286 Number 10 0 046654747 0 088936771 0 14421786 0 175477828 0 261612309 0 523224619 1 047740343 1 247066378 2 095480686 2 253174036 4 506348071 Of 15 0 190355923 0 382060543 0 543322189 0 764121085 0 7753 1048 1 550620961 3 101241921 5 337837594 6 202483842 8 700136175 17 40027235 Duplicate 20 0 315265272 0 652304998 0 997975469 1 274225415 1 590484639 3 180969278 6 361938555 9 428758046 12 72387711 16 37453381 32 74906762 Roots 25 0 460383822 0 955636607 1 461086619 1 868542293 2 272848794 4 974854445 8 925339062 14 14962977 18 18279036 23 88436412 48 02155301 30 0 620049177 1 235873769 1 870331984 2 400188501 3 087419409
43. n devised and the participation from users who frequented the HP Museum Forum increased steadily Soon after the first version actually made it to the 20b 30b hardware and with HP making serial interface PC firmware transfer cables available by request the number of beta testers using real calculators began to take off Copies of the 34S firmware along with a complete user manual are available for free download at http sourceforge net projects wp34s files One final piece of the puzzle was related to the fact that the entire calculator keyboard was redefined A method was therefore needed to re label all the keys as well as the land around them to mark the shifted functions Based on life size keyboard images posted by Walter on the HP Museum people began fashioning their own rudimentary keyboard overlays as well as stick on key covers Users posted images of their efforts and virtually all these attempts remained crude until Eric Rechlin purchased a cutting HP Solve 24 Page 22 Page 1 of 3 machine and began to offer vinyl preprinted adhesive backed overlays and peel off adhesive key covers An image of the HP 20b transformed into the 34S is shown in the center with its peers in Figure 1 below HP 35s hn ny Scientific Calculator ae tial RPN SCIENTIFIC C Z ai iy ix J ie i j id 1 RTN x2y FLAGS Tx s XEQ MODE A A Bj BB Ors Bae 68 aa Bo TT x0 t DISPLAY i o CONST AU Fix sci ENG CONV WODE xP
44. ne of HP s fastest calculators available and the reader could argue that it is fast enough Because it is programmable however it cannot ever be fast enough 1 The HP 35A was called a pocket calculator A shirt pocket was implied and it was intended to replace a slide rule the only other computational device that average person could hope town and use on a personal basis The operating manual all lower case letters were used by HP was also a shirt pocket size of 3 11 16 wide 6 high and very thin I checked the shirt I was wearing while writing this and it fits 2 Calculating the factorial of a number is a problem function that challenges the calculator for accuracy dynamic range and speed The factorial of a number n is the product of each integer from n to 1 e g 9 9x SxX7xX6xXx5x4x3x2x 1 362 880 A single digit input produces a six digit answer 3 One HP internal publication describing the HP 35A pocket calculator news n notes article used the example of calculating the number of cubic inches of a Cosmic Cube a million light years on an edge to illustrate that the dynamic range of 10 to 10 covered all practical calculations Today the calculator is used as much for analysis as for problem solving and an even wider dynamic range is desirable 4 There appears to be an error in the HP25s User s guide in that the negative number is missing a sign for the smallest number exponent in sev
45. ngle data set is usually represented as X HP Solve 24 Page 30 Page 1 of 4 We could just key in the values and add as we go This would be the approach used for most simple calculators and the approach you would use for a calculator you are not familiar with In general terms more advanced scientific and graphing calculators provide a means of inputting the data set storing the complete set and then calculating a wide range of functions on the data The category of functions of which the average is only one is statistical functions The HP35s uses what may be called accumulated sums based statistics A more advanced machine such as the HP50g will use list based statistics Usually more advanced calculators have more memory and they will handle larger sets of data In the early days of calculators memory was much more expensive than it presently is and the data was stored as sums There are usually Six statistics registers for two data sets designated as x and y see Fig 1 and each time you keyed a data point the data went into the six dedicated statistics registers These are 1 number of data points or ordered pairs 2 sum of x 3 sum of y 4 sum of x squared 5 sum of y squared and 6 sum of the product of x amp y More advanced calculators will store the data points into a list which is only limited by the total memory of the machine The user then performs the desired operations and the individual data is always preserv
46. nt however was that Walter had teamed up with fellow HP enthusiast Paul Dale from Australia to embark on a very sophisticated repurposing project for the 20b 30b hardware whose goal was to provide just the type of high end scientific machine he had proposed the year before As 2010 rolled around Walter and Paul were using the HP Museum Forum at http www hpmuseum org curated by Dave Hicks and independent of HP to announce their fledgling project now known as WP 34S show early keyboard layouts and to solicit input from the community for suggesting improvements By the summer the design was taking solid shape and attention was beginning to build There was an emulator which would run under the Linux operating system but nothing yet for Windows nor had they achieved a way to transfer their code to real hardware for testing As the season flew by and interest in this important project seemed to be waning it was thought that making the HHC2010 conference attendees aware of it might reinvig orate the community As a result I presented a synopsis of the capabilities included an abridged copy of Walter s detailed manual in the conference proceedings and made a plea to the group to anyone with the appropriate expertise to offer assistance in order to give the project the push needed to succeed In early 2011 Marcus von Cube also in Germany jumped in with some crucial assistance and by March a Windows version of the WP 34S emulator had bee
47. o a document The dollars and cents value will need to be rounded to the nearest cent The rounded number needs to be to two decimal places e g 245 735952341 becomes 245 74 Rounding is a simple concept Round the desired digit to the value that is closest to the longer value being rounded If the digits after the rounded place are 4 they are dropped and if the digits are 6 9 the rounded place is increased by 1 The issue is the middle digit of 5 following the rounded place digit The vast majority of calculators in the world use the rule of adding 1 if the digits are 5 9 From a statistics perspective this means that statistically many rounded numbers are too high I learned what is called the Astronomers Rule of rounding You only round up one digit if the following digit is 5 if it will make the rounded number even In the cents rounding case 245 735 1s rounded to 245 74 as given above but if the number was 245 765 it would be rounded to 245 76 not adding 1 because 6 is already even and the following digits are dropped Statistically the rounded numbers are balanced in the special 5 case Reader challenge How would you write a rounding program to implement the statistically more accurate Astronomers Rule of rounding HP Solve 24 Page 38 Page 4 of 4 How Fast is Fast HP Solve 24 page 39 Article How Fast is Fast Richard J Nelson Introduction One of the more powerful aspects of English is
48. o duplicate and the number of duplicates in the stack Then run the TDR program This program performs the following tasks 1 Builds an array of duplicate roots 2 Creates a copy of the array 3 Calculates the corresponding polynomial coefficients 4 Solves for the polynomial roots 3 Converts the array of roots into single stack values This step allows you to examine the calculated roots without using a matrix editor Let s use the program object TDR in a simple case Enter 1 and then 5 in the stack to build the array 1 1 1 1 1 Next run the TDR program Figure 1 shows the output generated using Fix 2 display mode RAD ave HES R fn THOME i z 4 2 1 OTOR PAb casti Fig 1 Solving for a polynomial with duplicate roots The stack level 6 shows a copy of the array of roots that the program built The stack levels 1 to 5 show the roots obtained by PROOT The values in levels 3 to 5 are exact albeit in complex form values By contast the values in levels 1 and 2 show minor deteriorations in the form of small imaginary parts of the complex numbers Now clear the entire stack and rerun program TDR This time enter 1 and 10 in the stack to build an array of ten duplicate roots Run program TDR to obtain the output in Figure 2 HP Solve 24 Page 15 Page 2 of 7 RAD ave HES R fn THOME ce z E 2 i or ran caso T Fig 2 The last seven roots Levels 1 to 7 in Figure 2 show the s
49. ogramming Guide You have certainly noticed that programming the HP 41C is simple and even fun HP Solve 24 Page 10 Page 2 of 4 Yet the capability of the system 1s astounding Your programming expertise will increase as you continue to use your HP 41C And you will find it an easy matter to completely customize your HP 41C The 41C has 130 functions The HP 48 49 50 series of machines has 2 000 functions The key assignment ability for these machines extends to six planes of key assignments with the most powerful calculator key assignment capability ever 5 Overlay capability Obviously anyone may cut a piece of paper with holes for the keys and place an overlay on any calculator to re label the keys Overlays may be made of paper plastic or electrostatic cling material The HP 41 included the use of full keyboard overlays in the case design so that the overlays could be easily managed as part of the system See HP Solve issue 1 6 Fig 2 is reproduced from that article Overlay D was called the rubber duck because it completely covered the keyboard to protect it from splashing water CLE BST T SHIFT RCL SST ASN CATALOG ASPLIT REG CLEAR Fig 2 Typical keyboard overlays provided by HP for HP 41 PACs A amp B and general use C amp D HP provided overlays with their HP 41software sold as plug in modules A few other machines also included a hardware overlay capability the HP 71B and HP
50. ors insisted that all operations or functions should take less than one second to provide an answer The HP 35A cut that specification in half The solver in HP s financial calculators uses an iterative method that may take a noticeable much longer amount of time to arrive at an answer The question is How fast is fast How fast is fast enough From a practical point of view perhaps the question should really be How fast is fast enough The business calculator user might realize that it would take him or her half an hour to solve the IRR problem by hand and that five seconds is fast enough If you simply can t solve the problem any other way five seconds is certainly fast enough Calculator enthusiasts are similar to race car enthusiasts and the technical challenge of going ever faster is what makes the competition interesting This also applies to all things electronic in which the smaller the circuits are the faster they respond A faster response means that more is done in less time and as the old adage says time is money The obsession for speed hasn t changed in the 39 years that personal handheld calculators have been in use Many calculators are programmable an essential feature for serious and very convenient problem solving and using a common program to measure speed allows the technical user to compare machines The HP 30b calculator is one of HP s most recent technological advancements There are three aspects
51. our desires with HP and being prepared to reach ever deeper into your wallet for printed good quality manuals handbooks or guides Most calculator owners use their manual mostly in a reference mode How does HP s more recent manuals stack up A quick look at the HP35s manual index shows 1152 page references for the 338 indexed pages for an Index rating of 3 4 This is great Paper is heavy and manuals take valuable packaging space so the trend of putting the manual on a CD and making it available for free down load is really a win win solution Electronic searching is facilitated production time is saved cost is reduced and if you really need a bound paper version you can do it yourself See one method of low cost binding at http www pahhc org 2004 HHC2004 Low_Cost_Book Binding R4 dist pdf Notes 1 Technology changes the way we use information Manuals are provided on CD s Examples as mentioned here are usually associated with a manual printed downloaded or provided by HP on a CD What is an example It is a step by step procedure process or algorithm that shows you how to solve a problem or use a process Today HP is using video technology in the form of Training Guides for their machines The Training Guides may be found on their web site and they are being produced by experienced users of their machines 2 One of the comments I had written over 20 years ago regarding HP documentation was the fact that at least the pa
52. quirements for HP 41 overlay use must allow at least 3 reversible overlays on the machine with 12 examples photos A pdf file of the article is at http h71028 www7 hp com enterprise downloads The 20HP 41 20System 20V3 pdf 5 Three Slots at the bottom of the keyboard provided space for the tabs at the bottom of the overlau to be inserted A sliding lever tab at the top of the keyboard held the overlay in place at the top This design allowed the overlay to be easily replaced as needed the thickness of the slots allowed three reversible overlays to be stacked on the machine at one time One overlay has the standard notations printed on it so that the machine looked normal You then have five additional overlays that you could easily swap around as needed 6 Details of this capability with extensive photos may be found at htip nhuc us 2008Anterfacing 20t0 20the 20H P20b 20V3 pdf HP Solve 24 Page 12 Page 4 of 4 Using PROOT with Duplicate Roots HP Solve 24 page 13 Article Using PROOT with Duplicate Roots Namir Shammas Introduction The PROOT function in the HP 50G returns the real and complex roots for polynomials with real and complex coefficients This function appeared in the HP 48G GX G graphing models HP has implemented a nice algorithm based on the Laguerre method to handle a wide variety of polynomial coefficients As mentioned in an earlier article the PROOT function has the following features
53. rket place Many of you reading this have watched HP up close and personal during their active participation at HHC s since 2002 when Fred Valdez broke the mold for HP User Community relationships Attendees of HHC 2007 witnessed the manual changes that are taking place A new calculator GM Wing first met at HHC demonstrated that HP has changed in ways that brings a smile to the face of the legacy user Product indicators of this very positive change are the HP50g and the HP35s Regarding the latter the very nice HP 35s manual is available to be down loaded at HP Solve 24 Page 27 Page 2 of 3 http h10010 www1 hp com wwpc pscmisc vac us product_pdfs user_guide pdf Printed manuals is still an HP challenge and there have been several solutions proposed to solve this problem Still having a manual in a useful downloadable form as illustrated at the link above is most helpful If you must have a printed copy you may print it yourself or have it done at a copy store and bind it using the method described in my HHC 2004 paper Personal Low Cost Binding system It is clear that manuals will become ever smaller and be more of a Quick Start Guide The primary User s guide is available on a CD DVD and or downloaded from HP s web site Observations and Conclusions Manuals will always be a topic of discussion by users young and old newbie and experienced What is most important however is to understand the issues involved sharing y
54. sonal Calculator Has Key to Solve Any Equation f X 0 Hewlett Packard Journal December 1979 About the Author Eip as L Namir Shammas is a native of Baghdad Iraq He resides in Richmond Virginia USA Namir graduated with a degree in Chemical Engineering He received a master degree in Chemical engineering from the University of Michigan Ann Arbor He worked for a few years in the field of water treatment before focusing for 17 years on writing programming books and articles Later he worked in corporate technical documentation He is a big fan of HP calculators and collects many vintage models His hobbies also include traveling music movies especially French movies chemistry cosmology Jungian psychology mythology statistics and math As a former PPC and CHHU member Namir enjoys attending the HHC conferences Email me at nshammas aol com HP Solve 24 Page 20 Page 7 of 7 Repurposing the HP 20b 30b Calculator Plattorm HP Solve 24 page 21 Article Repurposing the HP 20b 30b Calculator Platform Jake Schwartz Introduction In June of 2008 Hewlett Packard released the new HP 20b business financial calculator which repre sented the initial iteration of a new calculator hardware platform At the HHC2008 calculator conference in Corvallis Oregon in September of that year HP s Cyrille de Brebisson gave a 20b presentation where he explained that the hardware had been designed for repurposing
55. statistic 10313 99 NormEtr 0 0462025776984127 0 18530488 1350049 Root 0 0261620991288563 Root N The third model 1s Number of observations 88 Adjusted R Square 0 99953 F Statistic 92299 51 In NormErr 0 783443710801719 0 99705546254637 In Root 37 86063845 16461 N The above model is somewhat similar to the third model for the PROOT errors The term for the duplicate count is the reciprocal of the count instead of the reciprocal squared Conclusion The results indicate that the results of function PROOT deteriorate as the number of duplicates and the values of the duplicate roots increases It is worth pointing out that the deterioration is relatively small for duplicate roots up to 20 To better handle duplicate roots one must use specialized algorithms The question is how much effort do we need to employ to hunt for duplicate roots when such roots don t occur very frequently in real world problems Of course when they do they can be a headache References 1 Wikipedia The Laguerre s Method March 2010 2 W M Press et al Numerical Recipes The Art of Scientific Computing third edition 2007 Cambridge University Press 3 A Ralston and P Rabinowitz A First Course in Numerical Analysis second edition 1978 Dover Publications 4 Hewlett Packard Company HP 50 49 48elII graphing calculator advanced user s reference manual Edition 2 July 2009 5 W Kahan Per
56. sys com HP Solve 24 Page 7 Page 2 of 2 Customization HP Solve 24 page 8 Article Customization Richard Y Melsou Introduction I have attended many meetings with HP managers and one of the most common topics of conversation may be summarized by the question How may HP distinguish its products from others in the market place In other words what makes HP calculators special and unique Obviously these managers from the GM on down were asking a classical marketing question My marketing background is much less than my engineering background so I resonate best with the technical features and benefits of HP s machines One vital distinguishing feature at least to me is described in the title of this article Customization Before we explore what this means let s agree or at least read what I think are the two most important requirements for a calculator We have all seen many handheld boxes with a display microprocessor and an input device usually a keyboard PDA s notebook computers and cell phones are examples especially the latter in the smart phone category Each of you has at least one of these devices and an integrated calculator is usually one of its features What makes an HP handheld calculator important enough to also buy and use To me the reason a handheld scientific business or graphing calculator is essential and sustains a billion dollar a year business is due to two basic r
57. te LN x given n calculate the cube root of n etc When multiple data called sets are involved the calculated answer provides perspective and is a form of analysis of the data The calculations are more involved and in many cases they are quite complex with the calculated values providing a comparative measure or a Statistic of the data set The average value of a data set provides a means of using the set without knowing each value in the set Let s imagine the problem of clearing out the rocks in a length of a stream flowing through your property If you know how many rocks there are and the average weight for a rock you could calculate the size of the truck you need to rent Let s say that the average rock weighs 35 pounds and there are 73 rocks total The previous owner was going to do the job and he gave you the numbers The total weight 35 x 73 1s 2 555 pounds You might possibly be able to lift and load a 35 pound rock but the analysis average and total is such that you may actually have a bunch of small rocks with a few rocks that weigh hundreds of pounds In fact no rock may weigh 35 pounds and you really don t have enough information to get the job done In the real world a personal visual inspection of the stream would tell you that you may need more than just a truck How may we calculate the average of a data set on our calculator The HP35s is our typical calculator we are using for this series The average of a si
58. that make it especially stand out 1 it is fast 2 it is customizable and 3 it is repurposeable All of these advancements are discussed in this issue The first of these outstanding technological accomplishments are being discussed here by trying to answer How fast is fast If you are technologically interested you will want to know two things How fast is the HP 30b and how does it stack up with other machines The HP User Community has addressed this issue by publishing benchmark speed Fig 2 HP 30b numbers for a full gamut of machines Table 1 provides a few of those HP calculator comparisons When attempting to answer How fast is fast it is very important to compare machines under similar conditions Many machines will run in several modes using various languages The two most common are user code and assembly code Assembly code programs will almost always run faster than user code programs All machines in the HP Museum data base are solving the same problem called the N Queens problem Not all machines are able to run programs in a similar manner and the details including program listings are provided as well If you study the values in Table 1 you will notice that the 30b is 360 times faster than the 12C As a point of interest the 30b repurposing capability will most likely produce a version or program that puts it near the bottom of the table And as Internet rumor has it we haven t seen
59. the last of the 15C either HP Solve 24 Page 41 Page 2 of 3 Table 1 Typical HP Calculator Speed Comparisons Model Conditions Speed Time in decreasing order Ratio HP 15C User code 1 19 10 4 750 sec REF HP 12C User Code 55 52 3 352 sec 1 42x HP 41C User Code 17 35 1 055 sec 4 5x HP 35s User Code 2 49 169 sec 28 1x HP 50g User RPL 1 07 67 sec 70 9x HP 30b User Code 9 31 sec 510x HP 41CX Assembly 11 sec 431x HP 50g Assembly Arm 9 75 MHz 0 000404 sec 404 us 11 757 426x HP 50g Assembly Fast mode 2 7x 0 000150 sec 150 us 31 666 667x Observations and Conclusions The word fast doesn t convey very much technical information To say a 75 001 MHz clock is fast when the nearest competitor is 75 000 MHz is accurate but not very informative This is especially true when you consider that engineers consider a significant change as twice as much Calculator users are technical people who need numeric values in order to reach conclusions The first scientific calculator provided an answer in 500 ms or less and this was considered fast enough Today s machines are orders of magnitude faster and the user cannot detect the difference between 50 ms and 5 ms in terms of the answer calculation time Programmable calculators however need to be much faster because complex programs demand it Data analysis involving large data sets are common problems being worked on by today s programmable calculators The HP 30b is o
60. transferable Not valid retroactively on previously purchased items Not valid for any resale activity as defined by HP Direct Coupons may not be used to purchase gift cards May not be permitted with certain bundle offers Products and support acquired by Customer under these Terms are solely for Customer s personal use and not for immediate resale or sub licensing Not valid on purchases from HP download store hp digitalriver com Offer not combinable with Instant Rebates For complete coupon conditions see Coupon Information in the Customer Service section at www hpdirect com HP Solve 24 Page 4 Page of 1 HP Mobile Calculating Lab Kits HP Solve 24 page 5 Article HP Mobile Calculating Lab A Dynamic way to Teach Math and Science As technology advances the ability to challenge today s tech savvy students in the fields of math and science has become increasingly difficult Educators have the need for a more challenging curriculum that offers students real life hands on experiments to keep them fully engaged HP provides Educators the solution with the HP Mobile Calculating Lab MCL The HP MCL consists of the HP 39gs graphing calculator the HP StreamSmart 410 data streamer and a set of Fourier sensors For science teachers the HP MCL gives students direct experiences with the laws of nature For math teachers these same laws of nature can be explored to develop the concepts of variable and function and to conne
61. udents a special sale S02 MCL kits School learning is more than ever hands on with integrated measurement data recording and analysis using HP calculators HP s DataStream compatibility is now further improved HP Solve 24 Page 36 Page 2 of 4 S03 Customization One of HP s greatest contributions to calculators is the feature of customization as exemplified by the HP 41 series of machines This vital feature is an HP calculator first You may also read about other HP calculator firsts at http h20331 www2 hp com Hpsub cache 392617 0 0 225 121 html S04 PROOT with Duplicate Roots by Namir Shammas who is a familiar author to HP Solve readers He has written articles for HP Solve and given papers at HHCs on Solvers The solver first appeared as a feature on any calculator with the 1973 introduction of HP 80 Namir examines the HP 50g command PROOT S05 Repurposing the HP 20b 30b Calculator Platform by Jake Schwartz As mentioned in the Customization article repurposing is a form of customizing your calculator Jake provides an updated overview of this interesting user community repurposing project S06 HPs Manuals Every user has an opinion on what a calculator manual should look like how it should be organized and what its content should be This overview of HPs manual covers the entire history of what HP has done to provide the user with what he or she needs to use an HP calculator A list of the features of
62. with more than you came with in all aspects HP has always inspired its users to build on its leadership machines with new applications ideas and even new hardware The most unbelievable inspiration is one user redesigning the HP nut microprocessor Monte Darymple not only cloned the nut microprocessor used for the famous HP 41 series calculators but he actually had it made He then redesigned the HP 41 CPU circuit board and built a replacement board that has been shipped to 21 early adopters This unique group of HP calculator users have been testing the resulting machine called the HP 41CL This board swap brings the 1979 HP calculator up to a typical 2011 calculator capability in terms of speed ROM and RAM capacity Not only is the HP 41CL 50 times faster but it is a system compatible with more I O options more accessories and more software than any other calculator on the planet past or present When you install the 41CL circuit board you also install more than 100 of the best software ROM modules programmed for the HP 41 system At a bargain basement price of 25 each many of them sell for two or three times this price on eBay that is 2 500 worth of software at your command with a 235 upgrade Follow Monte and this exciting project at http systemyde com hp41 Another topic being presented at HHC 2011 is anew HP calculator restoration book by Geoff Quickfall HP Solve readers will remember that Geoff was interviewed in HP Solve issu
63. ws the final data set graphically Students can see that the oscillations are fairly regular that is the peaks are evenly spaced even though the amplitude decreases over time Connecting phenomena of growth and decay to exponential models is natural here Figure 4 shows an exponential fit for the data set In this experiment there was very little for students to set up simply the ruler and accelerometer The HP MCL automatically identified the sensor selected a graphing window for the data stream and began streaming the data The students saw something interesting to examine interesting to them and zoomed in to find the data they wanted from the data stream They went on to analyze create a Han eis LH e J Chi wccal Kier S 4 4 202 nese PHA AL a F Figure 2 Figure 3 SOOM iTRACE GOTO FIT IEFH HEHU Figure 4 model make predications etc Using the HP MCL was fast easy and best of all brought exploration to the forefront of classroom activities The HP Mobile Calculating Lab is a comprehensive STEM solution that is available in 2 kits The Starter Kit has just the sensors you need to get started in either math or science The Advanced Kit has a more extensive collection of sensors which lets you complete all the experiments in the enclosed HP MCL Experiment Guide To access more information about the HP MCL Kit and Fourier Systems sensors visit www hp com go MCL and www fourier

HP Solve: Issue 24 (July 2011)

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