Speed Test - Casio Calculators

Hi everyone! Today I am blogging from home.

Last time I posted a speed test for various Texas Instruments, which you can go to by clicking on this link.

For each calculator, I timed how long does the calculator take until it "counts down" from 2013 to 0. I ran the program on each calculator twice.

The Program TEST2013

TEST2013:
2013 → A
Lbl 1
A - 1 → A
A > 0 ⇒ Goto 1 : 1

The program returns 1 when completed.

For the Casio ClassPad 330, I had to modify the program a bit, as the ⇒ symbol means "store" (instead of "jump") for the ClassPad.

TEST2013 for ClassPad 330:
2013 ⇒ a
Lbl one
a
a - 1 ⇒ a
If a > 0
Then
Goto one
IfEnd

Results

I will start from the oldest made model. Thanks to rskey.org and Wikipedia for the dates.

fx-7000GA (1990): 31.11 sec, 30.89 sec
(The fx-7000GA is as close to the original 7000G as I will probably get).

fx-6300G (1991): 38.91 sec, 38.90 sec

CFX-9850G (1997): 28.58 sec, 28.00 sec

fx-9750G Plus (2002): 28.50 sec, 28.44 sec

fx-3650P (2002) Solar Powered: 3 min 6 sec, 3 min 6.31 sec

ClassPad 330, Operating System 3.04.4000 (2007): 35.89 sec, 36.01 sec

Prizm (fx-CG 10) (2010), Operating System 1.04.3200 : 9.53 sec, 9.44 sec
(I am very happy with this!)

Note that the fx-3650P is a solar powered-calcualtor. I had no idea that this model was released in 2002. I had to get it from eBay, as it is not sold in stores in the United States.

I did not test any of the modern fx-9860g family (GII, Slim, etc...), but I guess that these calculators are fast of the Prizm. From these results, it is apparent that Casio knows how to maximize their processor speed.

Next time I will review the calculator app MyScript. Until next time,

Eddie



This blog is property of Edward Shore. 2013

Casio Programming Part II

This blog entry is an extension of the list of programs made with the Casio fx-6300G and the fx-7000GA. Most of the program steps can be transferred verbatim to today's Casio graphing calculators.

Note:
Pol( and Rec( on the fx-6300G and fx-7000GA returns results in variables I and J. I gets r and x, respectively while J gets y and θ, respectively.

The fx-9xxx series (at least the fx-9860 series) returns the conversions from Pol( and Rec( as lists. Adjust accordingly.

However this list of programs will bring more of the complex features offered by today's higher-end calculators.

Here are the links to my two previous posts:

Casio and the Programming Language

Program Library Part 1


Comments:

The batteries run out on the fx-7000GA fast, or maybe not. It seems to work well after hours of rest.

The programs listed (except for the Quadratic Formula program) on this blog requires a second program, which I designated Program 0. I use program 0 to store my function.

Calculus

Numeric Derivative Approximation

The difference quotient method is used with Δ = 10^-5. Accuracy may vary. Machine accuracy not guaranteed.

Program 0: Enter as a function of X. (example: "2 sin x")

D is the derivative.

Main Program:
"X0"?→Z:
Z + 10^x -5→X: Prog 0: Ans→A:
Z - 10^x -5 → X: Prog 0: Ans→B:
(A - B) ÷ (2 10^x -5) → D

51 steps

Sum of a Function

Σ f(x) from a to b

S is the sum

Program 0: Function of X

Main Program:
"A"?→A:"B"?→B:
A→X: 0→S: Lbl 1:
Prog 0:Ans + S → S:
X + 1 →X:X ≤ B ⇒ Goto 1: S

48 steps

Simpson's Rule - Numeric Integration

I modified the program in the Casio fx-6300G handbook, to try to make it shorter.

N must be even. I is the integral.

Program 0: Function of X

Main Program:
"A"?→ A: "B"?→ B:
"N"?→ N: A→ X: Prog 0: Ans → I:
(B - A) ÷ N → D: N- 2 → O:
Lbl 2:
X + D → X: Prog 0: I + 4 Ans → I:
X + D → X: Prog 0: I + 2 Ans → I:
O - 1 → O: O ≠ 0 ⇒ Goto 2 :
B → X : Prog 0 : (I - Ans) D ÷ 3 → I

113 steps

Graphing: Parametric Equations

Program 0: X(T) to be stored in X, Y(T) to be stored in Y
(Example: 2T sin T→ X: 3T cos T→ Y)

Note: You will have set up the Range in advance which takes intuition, knowledge, and maybe luck to get a "perfect" graph. Once the Range is set up, as I understand it, the graph screen clears.

A = Tmin
B = Tmax
N = number of points

Main Program:
"A"?→A: "B"?→ B:
"N"→ N: (B - A) ÷ N → H: Cls : A - H → T:
Lbl 1: T + H →T:Prog 0: Plot X,Y : T ≠ B ⇒ Goto 1

61 steps


Graphing: Polar Equations

Program 0: R(T) with T being θ
(Example: .5T)

Note: You will have set up the Range in advance which takes intuition, knowledge, and maybe luck to get a "perfect" graph. Once the Range is set up, the graph screen clears.

A = Tmin
B = Tmax
N = number of points

I had better luck with this program on the fx-6300G than on the fx-7000GA.

Main Program:
"A"?→A: "B"?→ B:
"N"→ N: (B - A) ÷ N → H: Cls : A - H → T:
Lbl 1: T + H →T:Prog 0: Rec(Ans,T: Plot I,J : T ≠ B ⇒ Goto 1

67 steps

Note: these are dot plots and are not traceable. I tried using SD2 mode (Scatterplot Mode) but was not able to use comparison commands. Also Line is not the command that it is today.

And now to a favorite program...

Quadratic Formula

AX^2 + BX + C = 0

D = B^2 - 4AC

If D <0, then the roots are complex, X is the real part, Y is the imaginary part, X ± Yi
If D >0, then the roots are X and Y, both real

Program displays D, X, and Y

Preload A, B, and C before running!

B^2 - 4AC → D ◢
D < 0 ⇒ Goto 1:
(-B + √ D) ÷ (2A) → X:
(-B - √ D) ÷ (2A) → Y: Goto 2:
Lbl 1: -B ÷ (2A) → X : √ Abs D ÷ (2A) → Y :
Lbl 2 : X ◢ Y

79 steps

I leave you with some graphs.

Until next time, Eddie


This blog is property of Edward Shore. © 2012

Casio Program Library Part 1

Here is a list of programs I did over the course of the last few days (since 6/14/2012). These programs were done using the Casio fx-6300G and fx-7000GA calculators. These programs can be ported to almost any Casio calculator that has programming.

Note: for the fx-3650P, there are no strings, graphics, and variables are limited to A, B, C, D, X, Y, and M.

If you need summary of the programming commands, check out this page.

Programs are listed in blue, Courier font. Enjoy! Eddie

Binomial Distribution

B
Σ N nCr K × P^K × (1-P)^(N-K) = M
K=A

A = lower limit
B = upper limit
P = probability of success (0 ≤ P ≤ 1)
M = total probability

For a single point, enter A and B as the same value

**You can shave off steps by pre-storing all the variables before execution and leaving out some the beginning prompt commands. I do that in some of these programs.

"A"?→A:"B"?→B:"N"?→N:"P"?→P:
0→M:Lbl 1:
M+(N!×P^A×(1-P)^(N-A))÷(A!(N-A)!)→M:
A+1→A:A>B⇒Goto 2:Goto 1:
Lbl 2:M
91 steps

Roots of a Complex Number

Uses the polar form of the complex number x+yi to find the n roots of it.

Note: fx-6300G and fx-7000G Rectangular and Polar Conversions

Pol(x,y) stores r in I and θ in J.
Rec(r,θ) store x in I and y in J.

For the fx-9000s series (i.e. fx-9860), lists are returned. Adjust accordingly.

(x+yi)^1/n = r^1/n cos((θ + 2k π)/n) + i r^1/n sin((θ + 2k)/n)

"X"?→X:"Y"?→Y:"N"?→N:
0→K:Rad:
Pol(X,Y:Lbl 1:"RE"◢
N x√ I × cos((J+2K π ) ÷ N ◢
"IM" ◢ N x√ I sin((J+2K π ) ÷ N ◢
1 + K → K ◢ K < N ⇒ Goto 1
89 steps

Horizontal Curves

Given the radius (R) and angle in Radians ( θ ):

L = R θ
C = 2 R sin(θ/2)

where L=length of arc and C=chord length

Let T be θ.

"R"?→R: "T"?→T:
Rad: "L" ◢ RT ◢
"C" ◢ 2R sin(T ÷ 2

34 steps

Lens Equation: Image Length and Magnitude

O^-1 +I^-1 = F^-1
M = F (F-O)^-1

Where
O = object length
F = focal length
I = image length
M = magnification

Notes:

Focal Length
F<0 for concave lens and convex mirrors (diverging light)
F>0 for convex lens and concave mirrors (converging light)

Magnification
M>0 image is upright
M<0 image is upside down
0<|M|<1 image is shrunk
|M|>1 image is enlarged

"O"?→O: "F"?→F:
"I" ◢ (F^-1 - O^-1)^-1 ◢
"M" ◢ F(F-O)^-1

38 bytes

Ellipse

With semi-axis of lengths X and Y:

Area = π X Y

Perimeter ≈ 2 π √ ((X^2 + Y^2) / 2)
(best when X and Y are close, this came from the Fundamentals of Engineering Handbook)

"X"→ X: "Y"→ Y:
"P" ◢ 2 π √ (.5 (X^2+Y^2→ P ◢
"A" ◢ π XY → A

42 steps

2 by 2 Matrices: Determinant, Inverse, Solution

[[A B][C D]] [[X][Y]] = [[E][F]]

det = AD-CB = Z

inverse = [[D/Z -B/Z][-C/Z A/Z]] = [[G H][I J]]

solution = M^-1 b = [[G H][I J]] [[E][F]] = [[X][Y]]

If Z = 0, the matrix is singular and only the determinant is displayed.

Store A, B, C, D, E, and F before running the program


"DET" ◢
AD-BC→Z ◢ Z = 0 : Goto 1 : "INV" ◢
D ÷ Z → G ◢ -B ÷ Z → H ◢ -C ÷ Z → I ◢
A ÷ Z → J ◢ "X,Y" ◢ GE + HF → X ◢
IE + JF → Y

74 steps

Picking Random Numbers - Repeats are Allowed

N random numbers from A to B, with repeats allowed

"A"?-> A: "B"? → B:
"N"?→ N: Lbl 1: Int((B-A+1)Ran#) ◢ Dsz N : Goto 1

40 steps

There will be a Part 2 - which I will aim to post during the next week. Until then,

Eddie

This blog is property of Edward Shore. © 2012

Casio fx-7000GA and the Programming Language

Greetings all!

I finally got my hands on it! The Casio fx-7000GA calculator. OK, it is not the original fx-7000G that launched the world of graphing calculators, but it is the second edition of it. The 7000G was originally launched in 1985. After some research, i found that the fx-7000GA was first launched in 1990. The fx-7000G series continued with the fx-7000GB (1992) and the fx-7200g (1986). This series is like the Texas Instruments TI-83/84+ family (1996-present), except that the latter family eventually added flash ROM and textbook math input on its later models.

Why?

I spent a week playing with the Casio fx-3650P, a solar programming Calcualtor that is sold today (had to buy one off of eBay). And being a collector, the fx-7000G is on my wish list.


An excellent page on programming calculators: http://www.rskey.org/CMS/

The fx-7000GA arrived at my house on 6/14/2012. I was bummed at first because the calculator acted weird. Thankfully, three fresh CR2032 batteries later, the calculator is back in working order. However I read that the batteries get used quickly. Bummer.

I am amazed on how light the fx-7000GA is. I was expecting a heavy machine, being one of the first graphing calculators to ever be mass produced. However the calculator is thin, which hopefully you can see in a picture comparing the fx-7000GA and the TI-84+ below.

Features of the FX-7000GA

Graph Types: Function, Scatterplot, Histogram
Memories: 26, but can be expanded to 78
Program Steps: 422, 10 program slots
Linear Regression
Base Operations: Decimal, hexadecimal, octal, binary


The fx-7000G's smaller cousin, the fx-6300G, which I got several years back in Hollywood, CA (new of the box!), has only 400 program steps but adds the XNOR function. The fx-6300G has a lot of clones.

Programming Language

The programming language is a simple, tokenized one. Tokenized means that symbols and characters are used instead of words to symbolize commands. This minimizes the memory used in programs. This type of programming language is prevalent in today's graphing calculators from Casio. It also requires us bloggers to purchase and use Unicode apps to get these symbols.

The commands featured are:

: This colon separates commands.

? Input Command. The calculator prompts for a value.

"prompt message"? Input Command with a prompt message.

◢ Output Command. The calculator stops and shows output. Continue the program by pressing EXE. On the fx-3650P and fx-6300G, when ◢ is encounter during program execution, the calculator stops and a Disp indicator is present.

Goto n The Goto command, n is any number 0-9.

Lbl n The Label command, n is any number 0-9.

⇒ The Jump command. This is the basic If-Then-Else structure. On the fx-7000G and fx-6300G, the command is entered by pressing SHIFT, 7.

Syntax:

test statement ⇒ do if test is true : skip to here if test is false

Isz and Dsz Increase and decrease a memory, by 1, respectively. This is akin to the For-Next loops.

Syntax:

Isz var : do if var ≠ 0 : skip to here if var=0

Syntax is the same for Dsz.

My next blog entry will have some of the programs I entered over the last few days since I got the fx-7000GA. Until then, Cheers! Eddie


This blog is property of Edward Shore. © 2012