Some RPN Routines: Including Maximum and Minimum of Two Numbers

Some RPN Routines:  Including Maximum and Minimum of Two Numbers

Here are some RPN routines that hopefully you find helpful.   I am assuming that the values are stored in memory registers before calculation and a general four-level stack is used (HP 11C, 12C, 15C, 42S, 32S, 32SII, DM41X, DM32, DM42, DM15, WP34, etc.).  

(a + b + c) × (a + b - c)

Assume that: 

Memory register 1 = a

Memory register 2 = b

Memory register 3 = c

(Your memory registers may have different names or labels)

If recall arithmetic is allowed:

RCL 3

RCL 1

RCL+ 2

+

LST x

RCL- 3

×

(LST x = LAST x)

If recall arithmetic isn't available:

RCL 3

RCL 1

RCL 2

+

+

LST x

RCL 3

-

×

Example:  a= 10, b = 2, c = 7.   Result:  95

 (s + a) × (s + b) × (s + c)

Assume that: 

Memory register 1 = a

Memory register 2 = b

Memory register 3 = c

Memory register 4 = s

(Your memory registers may have different names or labels)

If recall arithmetic is allowed:

RCL 4

ENTER

ENTER

ENTER

RCL+ 1

x<>y

RCL+ 2

×

x<>y

RCL+ 3

×

If recall arithmetic isn't available:

RCL 4

ENTER

ENTER

ENTER

RCL 1

+

x<>y

RCL 2

+

×

x<>y

RCL 3

+

×

Example:  a = 4, b = 8, c = 2, s = 3.   Result:  385

 (s - a) × (s - b) × (s - c)

Assume that: 

Memory register 1 = a

Memory register 2 = b

Memory register 3 = c

Memory register 4 = s

(Your memory registers may have different names or labels)

If recall arithmetic is allowed:

RCL 4

ENTER

ENTER

ENTER

RCL- 1

x<>y

RCL- 2

×

x<>y

RCL- 3

×

If recall arithmetic isn't available:

RCL 4

ENTER

ENTER

ENTER

RCL 1

-

x<>y

RCL 2

-

×

x<>y

RCL 3

-

×

Example:  a = 8, b = 10, c = 3, s = 24.   Result:  4,704

The Maximum and Minimum of the X and Y Stacks

In a program, we can arrange the stack to show the maximum and minimum between two numbers as follows:

Maximum on the X Stack, Minimum on the Y Stack:

...

x≤y   

x<>y

...

If the value of x is less than or equal to y, swap the stack values.  Otherwise, leave the stack as is.

Minimum on the X Stack, Maximum on the X Stack:

HP 12C, HP 11C, HP 10C, and the HP 41C/DM41 family, due to the lack of the  x≥y command:

... 

x≤y

x<>y

x<>y

...

Same routine as the maximum routine, except an extra swap command is placed.

All others:

... 

x≥y

x<>y

...

x≥y is TEST 9 on the HP 15C.  

If the value of x is greater than or equal to y, swap the stack values.  Otherwise, leave the stack as is.

Of course, if your calculator has the maximum (MAX) and minimum (MIN) functions, by all means, use them.  

Eddie

All original content copyright, © 2011-2024.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 

HP 11C: Construction: Calculating the Number of Tiles

HP 11C:  Construction:  Calculating the Number of Tiles

Introduction

The 11C program presented will calculate the number of tiles needed for a rectangular room given:

*  room length and width, in feet
*  tile length and width, in feet
*  grout applied, if any, in inches
*  waste allowance %

For example, for a room of dimensions 12 feet 6 inches by 16 feet 8 inches, enter the room dimensions as 12.5 (12 + 6/12) and 16.66666667 (16 + 8/12), respectively.

Instructions:

Outside of User Mode:
Enter room length [ENTER] room width [ f ] [ A ]
Enter tile length [ENTER] tile width [ f ] [ B ]
Enter grout width [ f ] [ C ]
Enter waste allowance [ f ] [ D ]
Calculate the number of tiles, [ f ] [ E ]

In User Mode:
Enter room length [ENTER] room width [ √ ] (A)
Enter tile length [ENTER] tile width [ e^x ] (B)
Enter grout width [ 10^x ] (C)
Enter waste allowance [ y^x ] (D)
Calculate the number of tiles, [ 1/x ] (E)

Variables:
R1 = tile length (ft)
R2 = tile width (ft)
R3 = grout (in)
R4 = room length (ft)
R5 = room width (ft)
R6 = waste %

Number of tiles =

ceiling( (room length * room width) / ((tile length + grout) * (tile width + grout)) * (1 + waste%)

ceiling:  next highest integer

HP 11C Program: Number of Tiles

Step:  Key Code:  Key

001:  42,21,11:  LBL A
002:  44,5:  STO 5
003:  34:   X<>Y
004:  44, 4:  STO 4
005:  43, 32:  RTN

006:  42, 21, 12:  LBL B
007:  44, 1:  STO 1
008:  34:  X<>Y
009:  44, 2:  STO 2
010:  43, 32:  RTN

011:  42, 21, 13:  LBL C
012:  1:  1
013:  2:  2
014:  10:  ÷
015:  44, 3:  STO 3
016:  43, 32:  RTN

017:  42, 21, 14:  LBL D
018:  44, 6:  STO 6
019:  43, 32:  RTN

020:  42, 21, 15:  LBL E
021:  45, 5:  RCL 5
022:  45, 4:  RCL 4
023:  20:  *
024:  45, 1:  RCL 1
025:  45, 3:  RCL 3
026:  40:  +
027:  45, 2:  RCL 2
028:  45, 3:  RCL 3
029:  40:  +
030:  20:  *
031:  10:  ÷
032:  45, 6:  RCL 6
033:  43, 14:  %
034:  40:  +
035:  36:  ENTER
036:  42, 44:  X=0
037:  43, 40:  FRAC
038:  22, 0:  GTO 0
039:  33:  R↓
040: 1:  1
041: 40: +
042: 22,1:  GTO 1 
043: 42,21,0:  LBL 0
044: 33: R↓
045: 42,21,1:  LBL 1
046: 43, 44: INT
047: 43, 32: RTN

Example

Room Dimensions:  14 feet by 13.5 feet
Tile Dimensions:  1 foot by 1 foot
Grout: 1/8 inch (0.125 inch)
Waste Percentage:  5

Result:  Number of Tiles:  195

Eddie

All original content copyright, © 2011-2020.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

HP 12C and HP 11C: Loan Amount Using the Annual Loan Constant

HP 12C and HP 11C:  Loan Amount Using the Annual Loan Constant

Introduction

The program calculates the theoretical loan amount using the following factors:

*  NOI:  Net Operating Income. The estimated net operating income the property is expected to earn annually.  An average is usually used.

*  DCR:  Debt Coverage Ratio.  The ratio of net operating income to annual debt service, describing a company's ability to pay its debts.  Generally, the larger the DCR, the better.  We really don't want DCR to be below 1.

*  Number of payments per year, number of years, and annual interest rate of the potential loan. 

The ALC, or the annual loan constant is calculated by:

*  Either divided the annual debt service by the loan amount (when the amount is known), or

*  Determining the periodic payment to amortize a $100 loan given number of payments and interest rate.

Set up:
Number of payments -> N
Interest Rate -> I%YR  (or periodic interest rate -> i)
-100 -> PV
0 -> FV
Solve for PMT

The ALC is expressed as a percentage. 

The theoretical loan amount is calculated by:

Loan = NOI / (DCR * ALC%)

HP 12C Program: Loan Amount Using the Annual Loan Constant

Instructions:
Store the following:
NOI in R1
DCR in R2
Number of payments per year in R3
Number of periods in [ n ]
Periodic Interest rate in [ i ]

Program:
Step;  Key;  Code
01;  1;  1
02;  0;  0
03;  0;  0
04;  CHS;  16
05;  PV;  13
06;  0;  0
07;  FV;  15
08;  PMT;  14
09;  RCL 3;  45, 3
10;  *;  20
11;  RCL 2; 45, 2
12;  x<>y;  34
13;  %;  25
14;  RCL 1; 45, 1
15;  x<>y;  34
16;  ÷;  10
17;  GTO 00;  43, 33, 00

(* HP 12C Platinum, step 17:  GTO  000; 43, 33, 000)

HP 11C Program:    Loan Amount Using the Annual Loan Constant

Instructions:
Store the following:
NOI in R1
DCR in R2
Number of payments per year in R3
Number of periods in R4
Periodic Interest rate in R5

Program:
Step; Key; Code
001;  LBL A; 42, 21, 11
002;  1;  1
003;  ENTER; 36
004;  ENTER; 36
005;  RCL 5;  45, 5
006; %;  43, 14
007;  +;  40
008;  RCL 4;  45, 4
009;  CHS;  16
010;  y^x; 14
011;  *;  30
012;  1;  1
013;  RCL 5; 45, 5
014;  %;  43, 14
015;  x<>y;  34
016;  R↓;  33
017;  ÷;  10
018;  1;  1
019;  0;  0
020;  0;  0
021;  x<>y; 34
022;  ÷;  10
023;  RCL 3; 45, 3
024;  *;  20
025;  RCL 2; 45, 2
026;  x<>y; 34
027;  %;  43, 14
028;  RCL 1; 45, 1
029;  x<>y;  34
030;  ÷; 10
031;  RTN; 43, 32

Examples

Example 1: 

NOI:  $58,000.00
DCR:  1.25
P/Y:  12
Number of Years: 30
Annual Interest Rate:  5%

Loan Amount:  $720,288.92

Example 2:

NOI:  $40,000.00
DCR:  1.35
P/Y:  12
Number of Years: 20
Annual Interest Rate:  6.8%

Loan Amount: $323,464.95

Source: 

Goldman, Mark H. and Stephen D. Messner "HP 12C Real Estate Applications Handbook"  Hewlett Packard Rev. B. March 1984

Eddie

All original content copyright, © 2011-2019.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

HP 11C (and Emulators): Sun's Approximate Declination, Altitude, and Azimuth

HP 11C (and Emulators):  Sun's Approximate Declination, Altitude, and Azimuth

Introduction

The following program calculates three positions for our Sun in our Solar System:

1.  Declination of the Sun (δ = 0° at the Equinoxes)
2.  Altitude of the Sun (height of the sun)
3.  Azimuth of the Sun (degree from latitude ground-wise north)
 
Formulas Used:

Inputs:
D = days after the vernal equinox (usually March 20 or March 21)
L = latitude given in D.MMSS format (avoid ±90°)
T = time before solar noon (12 PM).  Example: 9 AM, T= 3.  3 PM, T = -3.

Declination:
δ = 23.45 * sin(D * 0.9856)

Altitude:
H = asin(cos L * cos D * cos(15 * T)) + sin L * sin D)

Azimuth:
A = acos((sin H * sin L - sin D) / (cos L * cos H))

Before running the program, store D in R1, L in R2, and T in R3.

HP 11C Program: Sun Declination, Altitude, Azimuth

001 42, 21, 13 LBL C
002 43, 7 DEG
003 45, 1 RCL 1
004 48 .
005 9 9
006 8 8
007 5 5
008 6 6
009 20 ×
010 23 SIN
011 2 2
012 3 3
013 48 .
014 4 4
015 5 5
016 20 ×
017 44, 4 STO 4
018 31 R/S
019 24 COS
020 45, 2 RCL 2
021 43, 2 →H
022 24 COS
023 20 ×
024 45, 3 RCL 3
025 1 1
026 5 5
027 20 ×
028 24 COS
029 20 ×
030 45, 2 RCL 2
031 43, 2 →H
032 23 SIN
033 45, 4 RCL 4
034 23 SIN
035 20 ×
036 40 +
037 43, 23 ASIN
038 44, 5 STO 5
039 31 R/S
040 23 SIN
041 45, 2 RCL 2
042 43, 2 →H
043 23 SIN
044 20 ×
045 45, 4 RCL 4
046 23 SIN
047 30 -
048 45, 2 RCL 2
049 43, 2 →H
050 24 COS
051 45, 5 RCL 5
052 24 COS
053 20 ×
054 10 ÷
055 43, 24 ACOS
056 44, 6 STO 6
057 43,32 RTN


Example 1:
Stored Data: 
R0 = 184 (approximately September 21),
R1 = -14° 50' 12" (entered as -14.5012)
R2 = 0 (noon)

Output:
δ ≈ 13.1576°
H ≈ 62.0058°
A = 180.0000°

Example 2:
Stored Data: 
R0 = 68 
R1 = 46°
R2 = 4 (8 AM)

Output:
δ ≈ 21.5892°
H ≈ 35.9899°
A ≈ 84.4083°

Sources:

Hewlett Packard.  "Sun Altitude, Azimuth, Solar Pond Absorption", HP 67/97 Energy Conservation December 1978.
Shore, Edward.  "HP 35S: Sun Altitude, Azimuth, Solar Pond Absorption"  Eddie's Math and Calculator Blog:  http://edspi31415.blogspot.com/2013/06/hp-35s-sun-altitude-azimuth-solar-pond.html  June 7, 2013

Eddie

All original content copyright, © 2011-2018.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.  Please contact the author if you have questions.

HP 11C (and Emulators): The Four Means

HP 11C (and Emulators):  The Four Means

Introduction

The following program uses the statistical registers to calculate four types of mean:

Arithmetic Mean:  μ = Σx / n

Harmonic Mean:  HM = n / Σ(1/x)

Geometric Mean:  GM = (Πx) ^ (1/n)

Root Mean Square:  RMS = √(Σx^2 / n)


The HP 11C uses the following registers in statistical analysis.  Be sure to clear registers by pressing [ f ] [ x<>y ] (CLEAR REG) before beginning.  Also, after clearing the registers, store 1 in register 7 (R7).  

R0 = n
R1 = Σx
R2 = Σx^2
R3 = Σy
R4 = Σy^2
R5 = Σxy

LBL A:  Enter data
LBL B:  Analysis: μ [R/S], HM [R/S], GM [R/S], RMS

HP 11C Program: The Four Means

Don't forget to store 1 in R7 prior to running the program. 

001 42, 21, 11 LBL A
002 49 Σ+
003 43, 36 LAST x
004 44, 20, 7 STO× 7
005 15 1/x
006 44, 40, 6 STO+ 6
007 43, 32 RTN

008 42, 21, 12 LBL B
009 43, 0         x-bar 
010 32 R/S
011 45, 6         RCL 6
012 15 1/x
013 45, 0 RCL 0
014 20 *
015 31 R/S
016 45, 7         RCL 7
017 45, 0         RCL 0
018 15 1/x
019 14 y^x
020 31 R/S
021 45, 2         RCL 2
022 45, 0         RCL 0
023 10 ÷
024 11 √
025 43, 32 RTN

Example:
Sample set:  4.25, 4.08, 5.63, 6.13, 4.48, 7.02 ( 6 data points )

Keystrokes:

4.25 [ f ] [ √ ] (A)
4.08 [ f ] [ √ ] (A)
5.63 [ f ] [ √ ] (A)
6.13 [ f ] [ √ ] (A)
4.48 [ f ] [ √ ] (A)
7.02 [ f ] [ √ ] (A)

[ f ] [e^x] (B)   5.2650 (arithmetic mean, μ)
[R/S] 5.0556 (harmonic mean, HM)
[R/S] 5.1575 (geometric mean, GM)
[R/S] 5.3748 (root mean square, RMS)


Eddie
All original content copyright, © 2011-2018.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.  Please contact the author if you have questions.

HP 11C (and Emulator Apps): Thin Lens Analysis

HP 11C (and Emulator Apps):  Thin Lens Analysis

Given the distance from the object to the lens (U) and the focal distance (F), the program calculates object from the image from the lens (V) and magnification (M) of the image by the following equations:

V = 1 / (1/F - 1/U)
M = -V / U

HP 11C Program: Thin Lens Analysis

Note:  The keystrokes are also applicable for any HP 11C emulator apps. 

001 42, 21, 13 LBL C
002 15 1/x
003 34 x<>y
004 15 1/x
005 43, 36 LAST x
006 33 R↓
007 30 -
008 15 1/x
009 31 R/s
010 36 ENTER
011 16 CHS
012 43, 33 R↑
013 10 ÷
014 43, 32 RTN

To run:  enter U (object distance) then F (focal distance).  Then run label C ([ f ] [10^x] (C)).  The first result is V (image distance).  Press [R/S] to get M (magnification).

Example 1:
Input:  U = 0.24 ft, F = 0.16 ft
Output:  V = 0.4800 ft (R/S) M = -2.0000

Example 2:
Input: U = 1.5 ft, F = 0.8 ft
Output: V ≈ 1.7143 ft, M ≈ -1.1429

Eddie

All original content copyright, © 2011-2018.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.  Please contact the author if you have questions.

Retro Review: Hewlett Packard HP 11C

Retro Review:  Hewlett Packard HP 11C

HP 11C 

This is one calculator I sought after for a long time.  Thanks to Mark Hardman for donating the door prize at HHC 2018. 

General Information

Company:  Hewlett Packard
Type:  RPN Programmable
Display:  10 digits with 2 digit exponents
Power:  3 LR44 or A76 batteries
Memory:  up to 21 storage registers, up to 203 programming lines
Years:  1981-1989
Original Cost: $80
Documentation:  Manual

The HP 11C is an RPN programmable scientific calculator from Hewlett Packard. The calculator has four stacks (X, Y, T, Z) to use for calculations.  The 11C is part of the landscape series that Hewlett Packard produced in the 1980s, including the long-standing and still current selling HP 12C, the HP 15C, which got a short reprise in 2011-2012, and the beloved HP 16C.  The HP 11C does not have as many functions as the HP 15C, and we'll get to the comparisons later. 

Programming and Memory

The HP 11C has memory that shared between registers and program lines.   The HP 11C has 63 permanent lines of memory and one permanent register, R_I.  Note that R_I is also used as an indirect register.  The rest of the memory is a combination of up to a maximum of 20 registers or 140 additional program lines.  Each numerical register costs 7 lines of program lines.  Conversion from numerical register to program lines are automatic as program space increased in size.

The HP 11C allows for labels A, B, C, D, and E with numeric labels 0-9.  Program execution from labels A-E can be run directly from the keyboard. 
There are eight comparisons tests:  x ≤ y, x < 0, x > y, x > 0, x ≠ y, x ≠ 0, x = y, and x = 0.  If the comparison test is true, then the next step is executed.  Otherwise, the next step is skipped.

DSE (decrease, skip if equal) and ISG (increase, skip if greater) are present, uses the current value in R_I.  DSE and ISG are used for FOR loops, the format of R_I is nnnn.xxxyy, n is the current value, x is the final value, and y is the increment/decrements. 
There are two flag variables for the HP 11C: 0 and 1.  The three commands with flags are SF (set flag), CF (clear flag), and F? (is flag set?). There is no indicator when flags are set.

The Back of the HP 11C 

The back of the HP 11C contains important information:  four conversion formulas, two variable functions, statistics registers, ISG/DSE diagrams, and the meaning of seven error codes (0-6). 

Statistics

The HP 11C has linear regression (y = a*x + b).  The L.R. displays the intercept (b) in the X stack and slope (a) in the Y stack. 

Stat registers used:  R0 = n, R1 = ⅀x, R2 = ⅀x^2, R3 = ⅀y, R4 = ⅀y^2,  R5 = ⅀xy.   You will need at least 6 memory registers.

The Keyboard

The keyboard of the HP 11C matches the legendary reputation of Hewlett Packard calculators  have for keyboards. 

Final Verdict

Yes, I recommend the HP 11C for the collection.  If you want to find an HP 11C for sale, you are going to have shop for the best price because they are popular, like the HP 15C. 

And Now for the Comparison

HP 11C (top), HP 15C Limited Edition (bottom, sorry for the light blocking out the text)

The HP 11C does not have as many functions of the HP 15C.  First, the memory space is not as great (203 for the 11C, 448 for the 15C).  Also the HP 15C has integration, a solver, matrix, and complex numbers.  The tests for the 11C are right on the keyboard (the shifted functions of the arithmetic functions), while the 15C has the majority of tests through the TEST n command.

Eddie

All original content copyright, © 2011-2018.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.  Please contact the author if you have questions.

HP 15C: Pricing Calculations (Gamo)

HP 15C:  Pricing Calculations (Gamo)

Introduction

The following program is a solver for cost, price, markup, and margin – developed by Gamo, which was emailed to me. The program (shown for the HP 15C).  Program listed here with permission and much thanks and gratitude to Gamo. 

HP 11C and HP 15C Program:  Pricing Calculations

Note:  Key codes are for the HP 15C. 

Step	Key Code	Key	Comment
001	42, 21, 11	LBL A	Start Cost Routine
002	44, 1	STO 1
003	0	0
004	43, 30, 6	TEST 6, x≠y
005	43, 32	RTN
006	45, 2	RCL 2
007	1	1
008	45, 3	RCL 3
009	43, 14	%
010	40	+
011	10	÷
012	43, 32	RTN
013	42, 21, 12	LBL B	Start Price Routine
014	44, 2	STO 2
015	0	0
016	43, 30, 6	TEST 6 , x≠y
017	43, 32	RTN
018	45, 1	RCL 1
019	45, 3	RCL 3
020	43, 14	%
021	40	+
022	43, 32	RTN
023	42, 21, 13	LBL C	Enter Markup Routine
024	44, 3	STO 3
025	0	0
026	43, 30, 6	TEST 6, x≠ y
027	43, 32	RTN
028	45, 1	RCL 1
029	45, 2	RCL 2
030	43, 15	Δ%
031	43, 32	RTN
032	42, 21, 14	LBL D	Margin to Markup routine
033	44, 4	STO 4
034	0	0
035	43, 30, 6	TEST 6, x≠y
036	43, 32	RTN
037	45, 3	RCL 3
038	15	1/x
039	26	EEX
040	16	CHS
041	2	2
042	40	+
043	15	1/x
044	43, 32	RTN
045	42, 21, 15	LBL E	Markup to Margin routine
046	44, 3	STO 3
047	0	0
048	43, 30, 6	TEST 6, x≠y
049	43, 32	RTN
050	45, 4	RCL 4
051	15	1/x
052	26	EEX
053	16	CHS
054	2	2
055	30	-
056	15	1/x
057	43, 32	RTN

Registers: 

R1 = Cost

R2 = Price

R3 = Markup

R4 = Margin

Instructions:

The program primary runs on the cost-price-markup calculation, which belongs to labels A, B, and C, respectively.

Conversions between margin and markup are used between labels D and E.  Gamo recommends that you set the calculator in FIX 2 mode and press [ f ] (USER) prior to running this program.

This program is set up to be a solver similar to the HP 12C and Hewlett Packard other financial calculators. 

Examples

It is assumed that FIX 2 is set and USER mode is turned on.

Example 1: (from Gamo)

Cost = 66.46

Price = 105.00

Keystrokes:

66.46 [ A ]

105.00 [ B ]

[ C ], Markup =  57.99

[ C ] [ D ], Margin = 36.70

Example 2: 

Cost = 2500.00

Margin = 10.00

2500 [ A ]

10 [ D ]

[ E ] [ C ] [ B ],  Price = 2777.78

Example 3:

Price = 48.75

Markup = 10.00

48.75 [ B ]

10.00 [ C ]

[ A ], Cost = 44.32

Example 4:  Margin/Markup Calculation

Markup = 54.00

54.00 [ E ]

[ D ],  Margin = 35.06

Eddie

 All original content copyright, © 2011-2018.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.  Please contact the author if you have questions.