Plus42: The FOR Function

Plus42:  The FOR Function

About the Plus42 App

Author:  Thomas Okken

App: 

Android:  $9.99

iOS:  $9.99

PC/MacOS/Linux:  Free

Donations Accepted

Link:  https://thomasokken.com/plus42/

Please give Okken some love!   Free42 and Plus42 are both awesome apps and emulators, both emulate the HP 42S engine.  The Plus42 adds the solver of the HP 17B/19B/27S and unit conversions of the HP 48/49/50 family.   The Plus42 can also graph functions.   You can find a lot more information on the link above!

(Disclaimer:  I am not being paid.)

I am now including apps like the Plus42 in my rotation for blogs, please be on the look out for those.  

Today's blog entry will cover one of the additional solver functions for the Plus42:  FOR.

Plus42 FOR Syntax

FOR(INIT:COND:NEXT:EXPR)

INIT:  Initial commands

COND:  condition

If the condition is true:  execute EXPR (there can be more than one EXPR statements), then NEXT

If the condition is false:  the loop ends

NEXT:  next command,  this is where the counter variable is incremented or decremented

EXPR:  the main loop

Examples 

Example 1:  Add from 1 to 4.

HP 39G/Prime Code:

A:=0;

FOR K FROM 1 TO 4 DO  (STEP 1)

A:=A+K;

END;

Plus42 Equation Code:

S=FOR((L(A:0)+L(I:1))×0:G(I)≤4:L(I:G(I)+1):L(A:G(A)+G(I)))

Variables:

S = sum_final answer

A = sum

I = counter variable

Result:  S = 10

S=:   set the result to the variable S, S = A

INIT:  (L(A:0)+L(I:1))×0;  set A = 0 and I = 1

COND:  G(I)≤4;  test if I≤4; if true continue, if false exit the loop

NEXT:  L(I:G(I)+1); this happens at the end of the loop, this is like the general STEP incr/decr command

EXPR: L(A:G(A)+G(I))

The use of the Get function allows the variable to used automatically and not be displayed in the CALC menu.  

Something that threw me off is that the order of NEXT and EXPR, which the EXPR (which I think there could be more than one EXPR statements), I am used to NEXT either at the end of the FOR loop or implied (end of indentation in Python, for example).

Example 2:  Product

Calculate Π(n/4, n=1 to m) = 1/4 * 2/4 * 3/4 * ... * m/4

Plus42 Equation Code:

P=FOR((L(A:1)+L(N:1)+M)×0:G(N)≤IP(M):L(N:G(N)+1):L(A:G(A)×(G(N)÷4)))

Variables:

P = product_final answer

N = counter

M = higher limit

P=:   set the result to the variable P, P = A

INIT:  (L(A:1)+L(N:1)+M)×0; set A = 1, N = 1, ask for M

COND: G(N)≤IP(M); if N ≤ IP(M); if true continue, if false exit the loop

NEXT:  L(N:G(N)+1)

EXPR: L(A:G(A)×(G(N)÷4))

Results:

3 → M; P → 0.0938

6 → M; P → 0.1758

12 → M; P → 28.5507

Example 3:  Recursive

Given an initial condition u_0, calculate the recursion:

u_n = 2 * u_n-1 - 3

for n terms.

Plus42 Equation Code:

S=FOR((U+N+L(I:1))×0:G(I)≤N:L(I:G(I)+1):L(U:2×G(U)-3))

Variables:

S = final answer

U = recursive variable

N = number of terms

S=:  final answer

INIT:  (U+N+L(I:1))×0

COND: G(I)≤N

NEXT:  L(I:G(I)+1)

EXPR:  L(U:2×G(U)-3)

Results, enter U, N first before calculating for S:

2 → U, 3 → N; S → -5

5 → U, 2 → N; S → 11

Enjoy and hope this helps,

Eddie 

All original content copyright, © 2011-2022.  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. 

Numworks Python Scripts: Basic Graphics

Numworks Python Scripts:  Basic Graphics

Script:  atari.py

Draws the basic-eight color palette of the classic 1977 Atari 2600.

Atari Palette Python Script

from math import *
from kandinsky import *
# 2020-05-28 atari 2600 colors
# kandinsky module

fill_rect(0,0,320,240,color(245,245,245))

fill_rect(15,15,55,55,color(0,0,0))
fill_rect(85,15,55,55,color(255,0,0))
fill_rect(155,15,55,55,color(255,255,0))
fill_rect(15,85,55,55,color(255,0,255))
fill_rect(155,85,55,55,color(0,255,0))
fill_rect(15,155,55,55,color(0,255,255))
fill_rect(85,155,55,55,color(0,0,255))
fill_rect(155,155,55,55,color(255,255,255))

draw_string("8",107,107)


Script:  firstdigit.py

The tenths digit from n random numbers is extracted and a bar chart is generated based on the results.  I recommend a sample size of at least 20.

A Sample of 100 data points

from math import *
from random import *
from matplotlib.pyplot import *

# set up lists
x=[0,1,2,3,4,5,6,7,8,9]
y=[0,0,0,0,0,0,0,0,0,0]

# user iput
print("EWS 2020-05-29")
print("Bar Chart: First Digit")
print("Recommended at least 20")
n=int(input("n? "))

# generate list
for i in range(n):
  s=int(random()*10)
  y[s]=y[s]+1

# bar plot
h=int(n/2)
d=-int(h/4)
axis([-0.5,9.5,d,h])
bar(x,y)

# turn axis off
axis("off")

# labels at the bottom
# results at top
m=max(y)
for i in range(10):
  text(i-0.25,d+1,str(i))
  text(i-0.25,m+2,str(y[i]))
  
show()

Script:  colorfulrings.py

The script cycles through a set of nine colors, four times.   The Kandinsky module is used to generate the flowery circles as well as cycle through the colors.  This module works with integer pixels.

Color rings script in progress

from math import *
from kandinsky import *
from time import *

# color lists
r=[255,255,255,0,0,0,51,128,255]
g=[0,102,255,128,255,0,102,128,255]
b=[0,0,0,0,0,255,255,128,255]

# angles
a=list(range(128))
for i in range(128):
  a[i]=i/128*2*pi

# draw circles
for k in range(36):
  n=int(fmod(k,9))
  for j in range(50):
    for i in range(128):
      x=int(160+(20+j)*cos(a[i]))
      y=int(120+(20+j)*sin(a[i]))
      set_pixel(x,y,color(r[n],g[n],b[n]))
  sleep(0.1)

Script:  modulusplot.py

Generate a pixel plot of the equation (x^n + y^n) mod m

Input Screen  (n = 3.9, m = 15.6)

Modulus Plot result, n = 3.9, m = 15.6

from math import *
from kandinsky import *
print("EWS 2020-05-28")
print("x**n + y**n mod m")
n=float(input("power? "))
m=float(input("modulus? "))

for x in range(320):
  for y in range(240):
    t=fmod(pow(x,n)+pow(y,n),m)  
    c=floor(t/m*255)
    set_pixel(x+1,y+1,color(c,c,c))


Eddie

BLOG UPDATE:
The HP Prime:  Conversion to Binary and IEEE-754 Binary blog entry that was posted on June 27, 2020 may contain errors.  In this case, I have taken that entry back to draft status and my intention is to repost the entry as soon as I can.  Apologies for any inconvenience. 

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.