Radio Shack EC-4000 (equiv. of TI-57): Program Library

Radio Shack EC-4000 (equiv. of TI-57):   Program Library

Radio Shack EC-4000/TI-57:  Horner's Method

Let's start with a demonstration of Horner's Method, which allows a quick evaluation of polynomials.   For a quadratic polynomial:

p(x) = a * x^2 + b * x + c = x * (a * x + b) + c

The program demonstrates an example polynomial:

p(x) = 3 * x^2 - 4 * x + 9 = x * (3 * x -  4) + 9

Step:  Key Code [ Key ]

00: 32, 1 [ STO 1 ]

01:  55 [ × ]

02:  03  [ 3 ]

03:  65  [ - ]

04:  04 [ 4 ]

05:  85  [ = ]

06:  55 [ × ]

07:  33, 1 [ RCL 1 ]

08:  75  [ + ]

09:  09  [ 9 ]

10:  85 [ = ]

11:  81  [ R/S ]

12:  71  [ RST ]

Examples:

p(0) = 9

p(5) = 64

p(9) = 216

Horner's Method can apply to higher order polynomials.  

Radio Shack EC-4000/TI-57:  Permutation and Factorial

This is to add two of the common probability functions that are missing with on the calculator.  

nPr = n! / (n - r)!

If n = r, then nPn = n!

Store n in R0 (register 0), r in R1 (register 1), then run the program (RST, R/S).

Other registers used:  R2:  nPr,  R7:  n-r+1 

Note that R7 is also the t-register.  

Step:  Key Code [ Key ]

00:  01  [ 1 ]

01:  32, 2  [ STO 2 ]

02:  33, 0  [ RCL 0 ]

03:  65   [ - ]

04:  33, 1  [ RCL 1 ]

05:  75  [ + ]

06:  01  [ 1 ]

07:  85  [ = ]

08:  32, 7 [ STO 7 ]

09:  86, 5 [ LBL 5 ]

10:  33, 0 [ RCL 0 ]

11:  39, 2  [ Prd 2 ]

12:  01  [ 1 ]

13:  -34, 0 [ INV SUM 0 ]

14:  33, 0 [ RCL 0 ]

15:  76  [ x≥t ]

16:  51, 5 [ GTO 5 ]

17:  33, 2 [ RCL 2 ]

18:  81  [ R/S ]

19:  71  [ RST ]

Examples:

n = 6, r = 6:  6P6 = 6! = 720

n = 5, r = 3:  5P3 = 60

n = 11, r = 6:  11P6 = 332,640

n = 52, r = 5:  52P5 = 3.118752 * 10^8

Radio Shack EC-4000/TI-57:  Snell's Law

There are two subroutines in this program listing.  Subroutines accessed by the [ SBR ] key.  

Snell's Law describes, among other things, the relationship between index of refraction of a medium (n) and refraction angle of the direction of light (Θ) is stated by:

n1 * sin(Θ1) = n2 * sin(Θ2)

Subroutine 1:  Solve for n2.  n2 = (n1 * sin(Θ1)) / sin(Θ2)

Subroutine 2:  Solve for Θ2.  Θ2 = arcsin( n1 * sin(Θ1) / n2 )

The registers used are:  R1 = n1, R2 = n2,  R3 = Θ1, R4 = Θ2

Step:  Key Code [ Key ]

// Solve for n2

00:  86, 1  [ LBL 1 ]

01:  50  [ DEG ]

02:  33, 1 [ RCL 1 ]

03:  55  [ × ]

04:  33, 3  [ RCL 3 ]

05:  28  [ SIN ]

06:  45  [ ÷ ]

07:  33, 4 [ RCL 4 ]

08:  28  [ SIN ]

09:  85  [ = ]

10:  32, 2 [ STO 2 ]

11:  81  [ R/S ]

// Solve for Θ2

12:  86, 2  [ LBL 2 ]

13:  50  [ DEG ]

14:  33, 1 [ RCL 1 ]

15:  55  [ × ]

16:  33, 3 [ RCL 3 ]

17:  28  [ SIN ]

18:  45  [ ÷ ]

19:  33, 2 [ RCL 2 ]

20:  85 [ = ]

21:  -28  [ INV SIN ]

22:  32, 4 [ STO 4 ]

23:  81 [ R/S ]

Examples:

Solve for n2:  n1 = 1.000293 (air), Θ1 = 30°, Θ2 = 19°

1.000293 STO 1

30 STO 3

19 STO 4

GSB 1

Result:  n2:  1.5362267

Solve for Θ2:  n1 = 1.000293 (air), Θ1 = 30°, n2 = 1.333 (water)

1.000293 STO 1

30 STO 3

1.333 STO 2

GSB 2

Result:  Θ2:  22.036902

Radio Shack EC-4000/TI-57:  Pseudorandom Number Generation

This program attempts to generate random numbers using the generator:

x_n+1 = frac(997 * x_n + π)

The random numbers are between 0 and 1.  An initial seed will be required 

The calculator does not have fraction and integer parts, so they have to be simulated:

int(x) ≈ x + 1E10 - 1E10

frac(x) = x - int(x), will require a register 

See steps 10 to 23.  

Due to the internal 10 digits and the simulations, expect possible roundoff errors as random numbers are continuously generated.  

Step:  Key Code [ Key ]

00:  55 [ × ]

01:  09  [ 9 ]

02:  09  [ 9 ]

03:  07 [ 7 ]

04:  75  [ + ]

05:  30  [ π ]

06:  85  [ = ]

07:  32, 6 [ STO 6 ]

08:  75  [ + ]

09:  01  [ 1 ]

10:  42  [ EE ]

11:  01  [ 1 ] 

12:  00 [ 0 ]

13:  65  [ - ]

14:  01  [ 1 ]

15:  42  [ EE ]

16:  01  [ 1 ] 

17:  00 [ 0 ]

18:  85 [ = ]

19:  -42  [  INV EE ]

20:  -34,6  [ INV SUM 6 ]

21:  33, 6 [ RCL 6 ]

22:  81  [ R/S ]

23:  71  [ RST ]

Example:

Seed:  0.98

Generation:

0.2015927

0.1294647

0.2178986

0.3864470

0.4292517

Until next time,

Eddie 

All original content copyright, © 2011-2023.  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. 

Tandy PC-4: What Can You Do With 1,568 Bytes in Basic?

Tandy PC-4: What Can You Do With 1,568 Bytes in Basic?

On December 1, 2019, reviewed the Tandy Pocket Computer PC-4.  (link here:  http://edspi31415.blogspot.com/2019/12/retro-review-tandy-pc-4-pocket-computer.html ).  The PC-4 comes with 544 bytes, but with an OR-1 RAM card, the memory goes up to 1,568 bytes. 

How much can I fit in 1,568 bytes?  Here's an attempt. 

P0:  Factorial

10 PRINT "N!"
20 INPUT "N",N
25 F=0
30 FOR I=1 TO N
40 F= LOG(I)+F
50 NEXT I
60 E= INT(F)
70 R=10↑( FRAC(F))
80 PRINT N;"! ="
90 PRINT R;"*10↑";E

P1:  Quadratic Equation

100 PRINT "AX↑2+BX+C=0"
105 INPUT "A",A
110 INPUT "B",B
115 INPUT "C",C
120 D=B↑2-4*A*C
125 S=-B/(2*A)
130 T=SQR( ABS(D))/(2*A)
135 IF D<0 300="" font="" then="">
200 R=S-T
205 T=S+T
210 S=R
215 PRINT "X1 =";S
220 PRINT "X2 =";T
225 GOTO 400
300 PRINT "REAL: ";S
305 PRINT "IMAG: ";T
400 PRINT "AGAIN?"
405 INPUT "0 FOR NO ",R
410 IF R≠0 THEN 105
415 END

P2:  Horizontal Curve

10 MODE 4     (Degrees Mode)
15 INPUT "TAN. LNGTH",T    (tangent length)
20 INPUT "ANGLE",D
25 R=T/ TAN(D/2)
30 L=R*D*π/180
35 C=2*R* SIN(D/2)
40 PRINT "R =";R     (radius)
45 PRINT "L=";L     (arc length)
50 PRINT "C =";C    (chord length)
55 END

P3:  Amortizing a Monthly Loan (Annual Principal and Interest)

50 SET F2  (Fix 2)
100 INPUT "LOAN",L
105 INPUT "RATE",I
110 I=I/1200
115 INPUT "YEARS",T
120 N=12*T
125 U=(1-(1+I)↑(-N))/I
130 P= RND(L/U,-2)   (note the -2 in the round command)
135 PRINT "PMT: $";P
140 B=L
200 FOR Y=1 TO T
201 S=0
202 C=0
205 FOR K=1 TO 12
210 E= RND(B*I,-2)
215 S=S+E
220 A=P-E
225 C=C+A
230 B=B-A
235 NEXT K
240 PRINT "YEAR: ";Y
245 PRINT "INT= $";S
250 PRINT "PRN= $";C
255 PRINT "BAL= $";B
260 NEXT Y
270 PRINT "LAST= ";P+B   (last payment)
275 SET N   (floating decimal)
280 END

P4:  Linear Regression, Y=A+BX with correlation, R

100 VAC    (clear variables A-Z)
200 N=N+1   (N: counter)
205 PRINT "POINT ";N
210 PRINT "X",X
215 PRINT "Y",Y
220 C=C+X:F=F+X↑2
230 D=D+Y:G=G+Y↑2
240 E=E+X*Y
245 INPUT "DONE? NO=0 ",Z
250 IF Z=0 THEN 200
300 H = SQR((F-C↑2/N)/N)
305 I= SQR((G-D↑2/N)/N)
310 B=((N*E-C*D)/(N*F-C↑2))
315 A=(D-B*C)/N:R=B*H/I
325 PRINT "SLP=";B
330 PRINT "ITC=";A
335 PRINT "CORR=";R
340 END

P5:  Snell's Law

10 MODE 4      (degrees mode)
15 INPUT "N1",M    (index of refraction - 1st medium)
20 INPUT "INCIDENCE",T   (angle of incidence)
25 INPUT "N2",N     (index of refraction - 2nd medium)
30 H = ASN(M/N* SIN(T))
35 R= SIN(T-H)↑2/ SIN(T+H)↑2
40 R=1/2*R*100
50 PRINT "REFRACTION=";H;"°"
55 PRINT "REFLECT=";R;"%"
60 END

°  (degree character):  EXT mode, SHIFT C
% (percent character):  EXT mode, SHIFT Q

P6:  Rectangular/Polar Conversions

100 MODE 4
105 INPUT "1.P>R 2.R>P",C
110 IF C=1 THEN 200
115 IF C=2 THEN 300
120 GOTO 105
200 INPUT "RADIUS",R
205 INPUT "ANGLE,"T
210 X=R* COS(T)
215 Y=R* SIN(T)
220 PRINT "X=";X
225 PRINT "Y=";Y
230 GOTO 900
300 INPUT "X",X
305 INPUT "Y",Y
310 R= SQR(X↑2+Y↑2)
315 IF X>0 THEN 500
320 IF X<0 600="" font="" then="">
325 IF X=0 THEN 700
500 IF Y≥0 THEN T= ATN(Y/X)
505 IF Y<0 t="ATN(Y/X)+360</font" then="">
510 GOTO 800
600 IF Y≥0 THEN T= ATN(Y/ ABS(X))+180
605 IF Y<0 t="ATN(Y/X)+180</font" then="">
610 GOTO 800
700 IF Y>0 THEN T=90
705 IF Y=0 THEN T=0
710 IF Y<0 t="270</font" then="">
715 GOTO 800
800 PRINT "RADIUS=";R
805 PRINT "ANGLE=";T
900 PRINT "AGAIN (NO=0)",C
905 IF C≠0 THEN 105
910 END

P7:  Area and Circumference on a Circle

10 INPUT "R",R
25 PRINT "C=";2*π*R
35 PRINT "A=";π*R↑2

Remaining:  8 bytes

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 Prime: Law of Refraction

HP Prime: Law of Refraction 

Introduction

The program DRAWREFRACT, visually demonstrates the Law of Refraction, or Snell's Law:

n1 sin θi = n2 sin θt

The program asks for n1, θi, and n2; and calculates θt.  The program draws the incident ray (in red) and the refracted ray (in blue).  The calculator is set to Degrees mode and the Function app. 

Note: you can find the angle character ∡, by pressing [SHIFT] [ × ]. 

HP Prime: Law of Refraction: DRAWREFRACT

Program:
EXPORT DRAWREFRACT(n1,θ1,n2)
BEGIN
// EWS 2018-08-20
// drawing Descates law
HAngle:=1; // Degrees
LOCAL θ2,x1,y1,x2,y2;
LOCAL str1,str2;
// window setup
STARTAPP("Function");
STARTVIEW(11,0);  // Decimal zoom
// calculation
θ2:=ASIN(n1*SIN(θ1)/n2);
x1:=RE(16∡(θ1+90));
y1:=IM(16∡(θ1+90));
x2:=RE(16∡(270+θ2));
y2:=IM(16∡(270+θ2));
// plot
RECT();
// draw axis
LINE(0,−16,0,16,0);
LINE(16,0,−16,0,0);
// draw analysis
LINE(0,0,x1,y1,#FF0000h);
LINE(0,0,x2,y2,#0000FFh);
str1:="n = "+STRING(n1)+
", θi = "+STRING(θ1);
str2:="-> n = "+STRING(n2)+
", θt = "+STRING(θ2);
TEXTOUT(str1,−15,−5,4,#FF0000h);
TEXTOUT(str2,−15,−8,4,#0000FFh);
WAIT(0);
// display home
STARTVIEW(−1);
END;

Example

n1 = 1.001
θ = 34.5°
n2= 1.205

DRAWREFRACT(1.001, 34.5, 1.205)

Result:
θt = 28.0678429359°

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.

PCalc 42 User Functions ( iOS )

PCalc 42 User Functions ( iOS )

Programs for the iOS App PCalc 42 from Previous Posts (during May 2014):

http://edspi31415.blogspot.com/2014/05/pcalc-programming-introduction.html

Mohr’s Circle:  http://edspi31415.blogspot.com/2014/05/pcalc-and-hp-50g-mohr-circle.html

Period of Orbit Around the Sun:  http://edspi31415.blogspot.com/2014/05/pcalc-and-hp-50g-period-of-orbit-around.html

Horizontal Pipe Discharge:  http://edspi31415.blogspot.com/2014/05/pcalc-and-hp-50g-horizontal-pipe.html

Newton’s law of Gravity Solver:  http://edspi31415.blogspot.com/2014/05/pcalc-and-hp-50g-newton-law-of-gravity.html

Distance of a Star by Parallax:  http://edspi31415.blogspot.com/2014/05/pcalc-and-hp50g-distance-of-star-by.html

Escape Velocity:  http://edspi31415.blogspot.com/2014/05/pcalc-and-hp-50g-escape-velocity.html

Time to revisit this app:

PCalc42 Decimal to Degrees-Minutes-Seconds (d.mmssss form): 

D > DMS

Switch to Decimal

Set R0 to X

Truncate X

Set R1 to R0

Subtract X from R1

Multiply R1 by 60

Set R2 to R1

Subtract X from R1

Multiply R1 by 60

Set R2 to R1

Truncate R1

Multiply R1 by 0.01

Add R1 to X

Set R3 to R2

Truncate R3

Subtract R3 from R2

Multiply R2 by 0.006

Add R2 to X

Example:   1.85 in DMS form is 1.51 (1° 51’)

PCalc42 Degrees-Minutes-Seconds (d.mmssss form) to Decimal

DMS > D

Switch to Decimal

Set R0 to X

Truncate X

Set R1 to R0

Subtract X from R1

Multiply R1 by 100

Set R2 to R1

Truncate R1

Subtract R1 from R2

Divide R2 by 60

Multiply R2 by 100

Add R1 to R2

Divide R2 by 60

Add R2 to X

Example:  1.3052 (1° 30’ 52”) in decimal form is 1.514444444

PCalc42 Snell’s Law of Refraction

Input: Y: n1, X: n,  n1 ≤ n2

Switch to Degrees

Invert X

Multiply Y by X

Inverse Sine X

Example:  n1 = 1.33, n2 = 1.50.   Output:  62.4573248455

PCalc42 Doppler Effect (RPN)  (SI Units)

Input:  Z:  emitted frequency (Hz), Y:  receiver velocity (m/s), X: source velocity (m/s)

Output:  observed frequency (Hz) on stack X

Negate X

Add Y to X

RPN Swap

RPN Roll Down

Divide X by 299752458

Add 1 to X

Multiply Y by X

RPN Roll Down

Example: 

Z:  Emitted Frequency:  525 Hz

Y:  Receiver Velocity:  214,000,000 ft/s

X:  Source Velocity:  208,000,000 ft/s

Output:  Observed Frequency:  535.5086711249 Hz

PCalc42 Sums (RPN) Σ m, Σ m^2, Σ m^3

The sum of Σ m^X from m = 1 to m = Y, where X is the power, Y is the power (up to 3).  If Y > 3, an error condition occurs. 

Formulas:

Σ m = (X^2 + X) / 2

Σ m^2 = (2*X^3 + 3*X^2 + X) / 6

Σ m^3 = (X * (X+1))^2 / 4

Set R0 to Y

Truncate X

Skip 3 if X = 1

Skip 7 if X = 2

Skip 16 if X = 3

Error

RPN Roll Down

X To Power of 2

Add R0 to X

Divide X by 2

Stop

RPN Roll Down

X To Power of 3

Multiply X by 2

Set R1 to R0

R1 To Power of 2

Multiply R1 by 3

Add R1 to X

Add R0 to X

Divide X by 6

Stop

RPN Roll Down

Add 1 to X

Multiply X by R0

X To Power of 2

Divide X by 4

Example:

Y = 6, X = 1:  Sum is 21

Y = 6, X = 2:  Sum is 91

Y = 6, X = 3:  Sum is 441

PCalc42 Present Value Factor of a Single Sum

PV:  (1 + Y/100)^-X

Y:  interest rate

X:  periods

Negate X

Divide Y by 100

Add 1 to Y

Y To Power of X

RPN Roll Down

Example:  Y = 7 (7%), X =  5 (n = 5)

Output:  0.7129861795

Happy New Year’s Everyone! See you in 2017!    

Eddie

This blog is property of Edward Shore, 2016.