RPN: HP 42S, DM42, Free 42 Tones, Column Vectors, and Songs

RPN: HP 42S, DM42, Free 42 Tones, Column Vectors, and Songs

Making Music of 10 Tones

The HP 42S, and subsequently, the Free42 app, the Plus42 app, and the Swiss Micros DM42, along with the HP 41C and DM41X. Let’s focus on the HP 42S version.

Tone is followed by:

* a single-digit integer (0-9)

* a tone number called indirectly through a stack level (X, Y, Z, T) or a memory register

I asked on the MoHPC (Museum of HP Calculators) forum what scale that the 42S used for the tones. According to Thomas Okken, who programmed the Free42 app, the tones come from the A major scale, with the note A3 called from TONE 1. TONE 0 played the E3 note. Thank you, Thomas!

https://www.hpmuseum.org/forum/thread-23678-post-205315.html#pid205315

The program CTONE plays a collection of tones that is stored in a single-column matrix named MCOL. An example of a collection of tones

[ [ 1 ]

[ 3 ]

[ 5 ]

[ 1 ]

[ 3 ]

[ 5 ]

[ 7 ]

[ 7 ]

[ 7 ]

[ 7 ]

[ 1 ]

[ 3 ]

[ 5 ]

[ 1 ]

[ 3 ]

[ 5 ]

[ 7 ]

[ 8 ]

[ 9 ]

[ 7 ] ]

CTONE: plays tones of the column vector MCOL

00 { 44-Byte Prgm }

01▸LBL "CTONE"

02 INDEX "MCOL"

03 WRAP

04 RCL "MCOL"

05 DIM?

06 X<>Y

07 3

08 10↑X

09 ÷

10 +

11 STO 00

12▸LBL 00

13 RCLEL

14 TONE IND ST X

15 I+

16 ISG 00

17 GTO 00

18 RTN

19 .END.

The following program, CRVCT, creates a matrix with one column named MCOL.

CRVCT: create a vector MCOL

00 { 79-Byte Prgm }

01▸LBL "CRVCT"

02 "SIZE?"

03 PROMPT

04 STO 01

05 1

06 DIM "MCOL"

07 X<>Y

08 3

09 10↑X

10 ÷

11 +

12 STO 00

13 INDEX "MCOL"

14 WRAP

15 ALL

16▸LBL 00

17 "ROW "

18 RCL 00

19 IP

20 ARCL ST X

21 ├"?"

22 PROMPT

23 STOEL

24 ISG 00

25 GTO 01

26 GTO 02

27▸LBL 01

28 I+

29 GTO 00

30▸LBL 02

31 RCL "MCOL"

32 FIX 04

33 RTN

34 .END.

Source

“HP 42S TONE” Museum of HP Calculators. https://www.hpmuseum.org/forum/thread-23678-post-205315.html#pid205315 Retried June 9, 2025.

Have fun,

Eddie

All original content copyright, © 2011-2025. 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.

The author does not use AI engines and never will.

Basic vs. Python: Numeric Guessing Games (Featuring Casio fx-702P and fx-CG100)

Basic vs. Python: Numeric Guessing Games

Calculators Used

Basic: Casio fx-702P

Python: Casio fx-CG100

Task

Generate two simple number guessing games.

Guess the Number

This is the classic guess the number. The game generates a number (positive integer) at random in a given range. The player guess the number and if it doesn’t match the target number, the player is told whether the target number is lower or higher. The objective is to find the target number in the lowest number of turns.

The pricing game, The Clock Game, from the legendary game show The Price Is Right uses the Guess the Number game for two prizes. The Clock Game, the contestant needs to get the three-digit price correct for each prize within a total of 30 seconds, with the host (Drew Carey or the late Bob Barker) informing the contest whether the correct price is higher or lower.

The code is for a game where the target integer is between 10 and 99.

BASIC: Casio fx-702P

10 PRT "GUESS THE NUMBER"

20 T=INT (RAN#*90+10)

30 C=0

40 G=0

100 INP "GUESS (10-99)",G

110 IF G<10 THEN 100

115 IF G>99 THEN 100

120 C=C+1

130 IF G<T;PRT "HIGHER"

140 IF G>T;PRT "LOWER"

150 IF G=T THEN 200

160 GOTO 100

200 PRT "CORRECT! THE # IS ";T

210 PRT "# GUESSES: ";C

PYTHON: Casio fx-CG100

Script: numguess.py

from random import *

print("Guess the number ")

t=int(random()*90+10)

c=0

g=0

# != means not

while t!=g:

  g=int(input("Guess (10-99)? "))

  c+=1

  if g<t:

    print("HIGHER")

  if g>t:

    print("LOWER")

# exact guess leaves the loop

print("CORRECT! The # is "+str(t)+".")

print("# of guesses: "+str(c))

The major difference between the two programs is that the Basic version uses If statements and Goto line statements, while Python code uses a while loop.

Find the Coin

This is a guessing game where the player is tasked to find a coin in a 10 by 10 grid. The rows and columns are labeled 0 through 9.

BASIC: Casio fx-702P

10 PRT "FIND THE COIN ($)"

30 A=INT (RAN#*10)

40 B=INT (RAN#*10)

50 C=0

60 PRT "GRID 0-9,0-9"

70 INP "X (0-9)",X

80 INP "Y (0-9)",Y

90 R=ABS (A-X)

100 S=ABS (Y-B)

105 C=C+1

110 IF R=S THEN 200

120 PRT S;" ROW";R;" COL"

150 GOTO 70

200 PRT "YOU FOUND IT!"

210 PRT "SCORE= ";C

PYTHON: Casio fx-CG100

Script: findcoin.py

# find the coin, 10 x 10 grid

from random import *

print("FIND THE COIN")

# random integer from 0 to 9

a=randint(0,9)

b=randint(0,9)

c=0

print("GRID 0-9,0-9")

# set up 

r=-1

s=-2

while r!=s:

  x=int(input("X 0-9: "))

  y=int(input("Y 0-9: "))

  r=abs(a-x)

  s=abs(b-y)

  c+=1

  if r==s:

    break

  print(str(s)+" rows "+str(r)+" col")

print("You found it!")

print("SCORE= ",str(c))

Note: Both numguess.py and findcoin.py use the random module, hence it can be adopted on every calculator with a random module. The HP Prime’s random module is urandom.

Have fun, and modify as you like,

Eddie

 All original content copyright, © 2011-2025. 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.

The author does not use AI engines and never will.

fx-991 CW: Gamma Function

fx-991 CW: Gamma Function

All screenshots were made with Casio’s classpad.net website.

No Gamma Function? No Problem!

The gamma function is used a lot in advanced mathematics. The gamma functions with a lot of definition functions, but the most common one is for values t>0 (in particular Re(t)>0):

Γ(t) = ∫( x^(t-1) × e^(-x) dx, 0, ∞)

This integral is an improper integral and unless we have a calculator that handles infinite limit, we need to use the following:

Γ(t) =

lim ∫( x^(t-1) × e^(-x) dx, 0, w)

w → ∞

Calculators with the integral function can use the above for estimating the gamma function.

Use Basic Properties for Shortcuts

If t is a positive integer, we can use the factorial function:

Γ(t) = (t – 1)!

Example: Γ(16) = (16 – 1)! = 15! ≈ 1.31 × 10^12

If t is in the form n/2 where n is odd (i.e. 1/2 = 0.5, 3/2 = 1.5, 5/2 = 2.5, 7/2 = 3.5, etc.). we can use the product..

Γ(n / 2) = (n – 2) / 2 × (n – 4) / 2 × (n – 6) / 2 × … × 1 / 2 × √π

Example: Γ(3.5) = Γ(7 / 2) = 5 / 2 × 3 / 2 × 1 / 2 × √π = 15 / 8 × √π ≈ 3.32335097

The following pictures demonstrate the use of the above equivalency along with integral estimate:

I hope you find this helpful,

Eddie

 All original content copyright, © 2011-2025. 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.

The author does not use AI engines and never will.

Numworks Python: Days Between Days Without Converting to Julian Dates

Numworks Python: Days Between Days Without Converting to Julian Dates

Introduction

The script daysbtwn.py find the number days between two days given the month and year. The program is designed to find the dates, not including the last date (to match most financial calculators and spreadsheets), within one calendar year. The program will ask if February 29 is included.

Numworks Python Code: daysbtwn.py

from math import *

# days between dates within a year

# no conversion to julian approach

# store basic calendar

# 0th is 0 to match the months

cal=[0,31,28,31,30,31,30,31,31,30,31,30,31,31,28,31,30,31,30,31,31,30,31,30,31]

# ask for dates

m1=int(input("Month 1? "))

d1=int(input("Day 1? "))

m2=int(input("Month 2? "))

d2=int(input("Day 2? "))

# leap year question

l=0

l=int(input("Include Feb. 29?\nYES=1, NO=0: "))

# sum

if m1==m2:

  s=d2-d1

  if s<=0:

    s+=365+l  

else:

  if m2<m1:

    m2+=12

  s=cal[m1]-d1

  s+=sum(cal[m1+1:m2])

  s+=d2+l

print("DAYS = ",s)

The code has the math module, which can be used with any calculator with Python or the computer version.

Examples

March 14 – March 13 (of next year)

Month 1? 3, Day 1? 14

Month 2? 3, Day 2? 13

Include Feb. 29? 0

Number of Days: 364

March 14 – March 14 (of next year)

Month 1? 3, Day 1? 14

Month 2? 3, Day 2? 14

Include Feb. 29? 0

Number of Days: 365

March 14 – March 15 (of the same year)

Month 1? 3, Day 1? 14

Month 2? 3, Day 2? 15

Include Feb. 29? 0

Number of Days: 1

January 1 – December 31 (of the same year – leap year)

Month 1? 1, Day 1? 1

Month 2? 12, Day 2? 31

Include Feb. 29? 1

Number of Days: 365

In the U.S., wishing you a safe, sane, and Happy Thanksgiving.

Eddie

All original content copyright, © 2011-2025. 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.

Basic (TI-81) vs. Python (TI-84 Plus CE Python): First and Second Derivative and Integral by Simpson’s Rule

Basic vs. Python: First and Second Derivative and Integral by Simpson’s Rule

Calculators Used

Basic: TI-81

Python: TI-84 Plus CE Python

Task

Estimate the numerical first derivative by the Nearby Secant Line Method:

f'(x) = lim (f(x + h) - f(x - h)) / (2 * h) as h → 0

Estimate the numerical second derivative by:

f''(x) = lim (f(x + h) - 2 * f(x) + f(x - h)) / h^2 as h → 0

Estimate the definite integral by Simpson’s rule:

∫( Y1 dx, x = a to x = b) ≈

(b - a)/(3 * n) + (f(a) + 4 * f1 + 2 * f2 + 4 * f3 + 2 * f4 + ... + 2 * f_n-2 + 4 * f_n-1 + f(b))

n must be an even integer.

fi = f(a + i * (b – a) / n)

BASIC: TI-81

First let’s look at the TI-Basic version with the classic TI-81:

First Order Derivative  (Nearby Secant Line Method)

f'(x) ≈ (f(x + h) - f(x - h)) / (2 * h)

DER1  (61 bytes)

Function

Rad

Disp "D/DX Y1"

1E-4 -> H

Disp "X?"

Input A

A+H -> X

Y1 -> D

A-H -> X

(D-Y1)/(2H)->D

Disp D

Second Order Derivative

f''(x) ≈ (f(x + h) - 2 * f(x) + f(x - h)) / h^2

DER2  (75 bytes)

Function

Rad

Disp "D²/DX² Y1"

1E-4 -> H

Disp "X?"

Input A

A+H -> X

Y1 -> D

A -> X

D-2*Y1 -> D

A-H -> X

(D+Y1)/(H^2) -> D

Disp D

INTGY1  (134 bytes)

Function 

Rad

Disp "SIMPSONS RULE"

Disp "A,B,N?"

Input A

Input B

Input N

A -> X

Y1 -> S

B -> X

S+Y1 -> S

1 -> I

Lbl 1

A+I*(B-A)/N -> X

S+2*Y1 -> S

If Fpart (I/2)≠0

S+2*Y1 -> S

IS>(I,N-1)

Goto 1

S*(B-A)/(3*N) -> S

Disp S

Examples

f(x) = 3*x^3 + 4*x – 1

Y1 = 3 * X³ + 4 * X – 1

f’(2.4): DER1 returns: 55.84

f’’(2.4): DER2 returns: 43.2

∫( 3 * X³ + 4 * X – 1 dX, 0.5, 1.5):

INTGY1 returns with N = 40 returns 6.75

Notes for BASIC

Before running the programs, store the function to the variable Y1. Calling Y1 evaluates the function of the value stored in variable X. Evaluate Y1 at X: [2nd], (Y-VARS), 1

The TI-81 MUST be in Function mode to evaluate Y1, unless an error occurs. The programs set the angle mode to Radians. The value of h is set to a "default" value of 10^-4. We want h to be small, but not too small. A value of h too small can run the risk of floating point errors.

In the integral program:

* I/2 - Ipart (I/2) is Fpart(I/2), but the long way. Python does not have a built-in fractional part function.

* IS>(I,N-1) translates to:

I=I+1

If I>N-1

Goto 1

IS> is the increment (by 1) and skip, a command in TI-Calculator Basic.

In general BASIC languages, evaluation Y1 may take a different approach, depending on the calculator, pocket computer, or computer:

General Basic:

### ...

### X = g(A)

### GOSUB ***

### ...

*** Y = <evaluate f(X)>

*** RETURN

Another approach on a calculator: Use another program

Prog <main>

...

g(A) -> X

Prog "FX" (see below, answer is stored in Y)

...

Prog "FX" (or any name of your choosing)

<evaulate f(X)> -> Y

<end program, an implied Return is executed here>

PYTHON: TI-84 Plus CE Python Edition

The code presented here uses the math module and built-in functions, and should work with any calculator with Python.

DERINTG.py

from math import *

# derivatives and integrals

# 2025-06-01

print("MATH MODULE IS IMPORTED")

# first derivative function

def der1(fx,x,h=1E-3):

  # fx is a string

  # h is optional (def 1E-3)

  # set up lambda

  f=eval("lambda x:"+fx)

  d=(f(x+h)-f(x-h))/(2*h)

  return d

# second derivative function

def der2(fx,x,h=1E-3):

  # fx is a string

  # h is optional (def 1E-3)

  # set up lambda

  f=eval("lambda x:"+fx)

  d=(f(x+h)-2*f(x)+f(x-h))/(h**2)

  return d

# integrals by simpsons rule

def intg(fx,a,b,n=64):

  # fx is a string

  # n is even, optional (def 64)

  # set up lambda

  f=eval("lambda x:"+fx)

  s=f(a)+f(b)

  for i in range(1,n):

    w=f(a+i*(b-a)/n)

    s+=(2*w) if (i/2-int(i/2)==0) else (4*w)

  s*=(b-a)/(3*n)

  return s

I decided to make a script of three functions.

Python uses binary arithmetic, so be prepared to possibly see answers such as 2.999999999999 and 5.00000000000001. The code leaves the answer in floating point form. Feel free to use the round function and/or format specifiers as you see fit.

f(x) = 3*x^3 + 4*x – 1

In Python:

f(x) = 3*x**3+4*x-1

Examples

Store the string to s:

s=”3*x**3+4*x-1”

der1(s,2.4) returns 55.84000299999303

der2(s,2.4) returns 43.19999999324864

intg(s,0.5,1.5) returns 6.75

I hope you find this useful. Enjoy,

Eddie

All original content copyright, © 2011-2025. 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.

RPN: Certain Integrals to Positive Infinity

RPN: Certain Integrals to Positive Infinity

Introduction

Today’s RPN session deals with improper integrals where the upper limit is positive infinity (∞).

∫( f(x) dx, a, ∞) → lim ∫( f(x) dx, a, t) as t → ∞

Some properties that will be use:

lim 1/t^n as t → ∞ approaches 0

lim e^(-t) as t → ∞ approaches 0

lim p(t) ÷ q(t) as t → ∞ approaches 0 where p(t) and q(t) are polynomials and

degree p(t) < degree q(t)

lim p(t) ÷ q(t) as t → ∞ approaches p_n ÷ q_n where p(t) and q(t) are polynomials and

degree p(t) = degree q(t). p_n and q_n are the leading coefficients of p(t) and q(t), respectively.

All integrals presented will have closed formulas because they have very friendly anti-derivatives.

∫( 1 ÷ (x^n) dx, a, ∞)

∫( 1 ÷ (x^n) dx, a, ∞) = 1 ÷ ((n - 1) * a^(n - 1))

(Abbreviated) Derivation:

∫( 1 ÷ (x^n) dx, a, ∞)

= lim (1 ÷ x^(n - 1) * -1 ÷ (n – 1) as x → ∞) - (1 ÷ a^(n – 1) * -1 ÷ (n – 1))

= ( 0 * -1 ÷ (n – 1) ) + 1 ÷ ((n – 1) * a^(n – 1))

= 1 ÷ ((n – 1) * a^(n – 1))

∫( 1 ÷ (x^n) dx, a, ∞) = 1 ÷ ((n - 1) * a^(n - 1))

HP 15C Code:

[42, 21, 11]: LBL A

[         1]: 1

[        30]: -

[    43, 36]: LSTx

[        20]: ×

[        15]: 1/x

[    43, 32]: RTN

Stack:

Y: a

X: n

Examples:

a = 2.75, n = 2: 4/11 ≈ 0.36364

a = 4.9, n = 3: ≈ 0.02082

∫( 1 ÷ ((x - r)*(x - s)) dx, a, ∞)

∫( 1 ÷ ((x - r)*(x - s)) dx, a, ∞)

= 1 ÷ (r - s) * ln( abs((a - s) ÷ (a – r)) )

For best results, a > max(s, r)

(Abbreviated) Derivation:

∫( 1 ÷ ((x - r)*(x - s)) dx, a, ∞)

Simply by partial fractions:

1 ÷ ((x - r)*(x – s)) = 1 ÷ ((r – s) * (x – r)) – 1 ÷ ((r – s) * (x – s))

Anti-derivative:

∫( 1 ÷ ((x - r)*(x - s)) dx)

= 1 ÷ (r – s) * ( ln(abs(x – r)) – ln(abs(x – s)) )

= 1 ÷ (r – s) * ln ( abs((x – r) ÷ (x – s)) )

Limit as x → ∞:

1 ÷ (r – s) * ln ( abs((x – r) ÷ (x – s)) )

= 1 ÷ (r – s) * ln ( abs((1 – r ÷ x) ÷ (1 – s ÷ x)) )

= 1 ÷ (r – s) * ln ( abs(1) )

= 1 ÷ (r – s) * ln(1)

= 0

When x = a

1 ÷ (r – s) * ln ( abs((a – r) ÷ (a – s)) )

= 1 ÷ (r – s) * ln ( abs(1 ÷ [(a – r) * (a -s)]) )

= 1 ÷ (r – s) * ln ( 1 ÷ [abs((a – s) ÷ (a – r))] )

= -1 ÷ (r – s) * ln ( abs((a – s) ÷ (a – r)) )

Then:

∫( 1 ÷ ((x - r)*(x - s)) dx, a, ∞) = 0 - (-1 ÷ (r – s) * ln ( abs((a – s) ÷ (a – r)) ))

= 1 ÷ (r - s) * ln ( abs((a - s) ÷ (a – r)) )

Code:

[42, 21, 12]: LBL B

[    44,  1]: STO 1

[        33]: R↓

[    44,  2]: STO 2

[        33]: R↓

[    44,  3]: STO 3

[45, 30,  1]: RCL- 1

[    45,  3]: RCL 3

[45, 30,  2]: RCL- 2

[        10]: ÷

[    43, 16]: ABS

[    43, 12]: LN

[    45,  2]: RCL 2

[45, 30,  1]: RCL- 1

[        15]: 1/x

[        20]: ×

[    43, 32]: RTN

Stack:

Z: a

Y: r

X: s

Examples:

a = 7.25, b = -3, s = 6: (ln 41 - ln 5) ÷ 9 ≈ 0.23379

a = 11, b = 4, s = 9: (ln 7 - ln 2) ÷ 5 ≈ 0.25055

∫( 1 ÷ e^x dx, a, ∞)

∫( 1 ÷ e^x dx, a, ∞) = 1 ÷ e^a

Code:

[42, 21, 13]: LBL C

[        12]: e^x

[        15]: 1/x

[    43, 32]: RTN

Stack:

X: a

Examples:

a = 4: e^(-4) ≈ 0.01832

a = 6: e^(-6) ≈ 0.00248

∫( x ÷ e^x dx, a, ∞)

∫( x ÷ e^x dx, a, ∞) = (a + 1) ÷ e^a

Code:

[42, 21, 14]: LBL D

[        12]: e^x

[    43, 36]: LSTx

[         1]: 1

[        40]: +

[        34]: x<>y

[        10]: ÷

[    43, 32]: RTN

Stack:

X: a

Examples:

a = 4: 5 ÷ e^(-4) ≈ 0.09158

a = 6: 7 ÷ e^(-6) ≈ 0.01735

Eddie

All original content copyright, © 2011-2025. 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.

The author does not use AI engines and never will.