So, we have already set up coding with AROAPL. And, we learned various unique features of AROAPL.
In this chapter, let’s code and learn about practical numerical calculations in scalar operations.
Scalar means, single value. So, there is also multiple values, called “array”, or more strictly, “tensor” in AROAPL. For more details, we shall discuss in next chapter.
In scalar operations, all things you need to learn are able to been explained in only this page.

It may be a bit late to mention this, but AROAPL … or rather, languages in the APL familiars are characterized by the use of far more symbols (glyphs) than typical languages, and if you’re a beginner, you’re probably already bewildered by the sheer chaos of it all.

Also, while most languages typically cover conditional branching and iterative processing in this chapter, but in case of AROAPL, those topics will be covered much later.
Honestly, you may skip and learn them previously at chapter 5 and chapter 8, if you want to learn about the abstract of controlling at first. However, in any case, you’ll eventually hit a wall unless you understand the contents from this chapter through chapter 4, so come back here later.

So, let’s start.

2.1. Boolean Operations

2.1.1. AND Operation

⎕ ← ⊥∧⊥;
⎕ ← ⊥∧⊤; 
⎕ ← ⊤∧⊥; 
⎕ ← ⊤∧⊤;

⊥
⊥
⊥
⊤

2.1.2. OR Operation

⎕ ← ⊥∨⊥;
⎕ ← ⊥∨⊤;
⎕ ← ⊤∨⊥;
⎕ ← ⊤∨⊤;

⊥
⊤
⊤
⊤

2.1.3. NOT Operation

⎕ ← ⊤ = ¬⊥;
⎕ ← ⊤ = ¬⊤;

⊤
⊥

2.1.4. Questions: XOR/XNOR

1. How to express XOR/XNOR operation with using AND/OR/NOT operation?
2. How to express XOR/XNOR operation without using AND/OR/NOT operation?

2.2. Numeric Operations

2.2.1. Negate Value

-2;
-¯2.8;

¯2
2.8

2.2.2. Direction

×5.3;
×0;
ׯ10;

1
0
¯1

2.2.3. Reciprocal

Only integers are allowed as the arguument.

÷4;
÷¯6;

0.25
¯0.16666666666

2.2.4. Magnitude

%1;
%1.72;
%¯1;
%¯1.72;

1
1.72
1
1.72

2.2.5. Rounding

Only real numbers are allowed as the arguument.

in case of positive number:

⌈3.45;
⌊3.45;

4
3

in case of negative number:

⌈¯3.45;
⌊¯3.45;

3
4

2.2.6. Conjugate

Only complex numbers are allowed as the arguument.

+3.J4.;
+8.J¯4;
+¯5.J¯7.;

3.J¯4.
8.J4;
¯5.J7.;

2.3. Numeric Calculations

2.3.1. Basic Dyadic Calculations

You can calculate if the pair is the same type of integer, real number, or complex number.

in case of integer:

⎕ ← 5 + 2;
⎕ ← 5 - 2;
⎕ ← 5 × 2;
⎕ ← 5 ÷ 2;
⎕ ← 5 % 2;

7
3
10
2
1

in case of real number:

⎕ ← 5.5 + 2.7;
⎕ ← 5.5 - 2.7;
⎕ ← 5.5 × 2.7;
⎕ ← 5. ÷ 2.;
⎕ ← 5.5 ÷ 2.7;
⎕ ← 5.5 % 2.7;

8.2
2.8
14.85
2.5
2.03703703704
0.1

in case of complex number:

⎕ ← 5.5 + 2.7;
⎕ ← 5.5 - 2.7;
⎕ ← 5.5 × 2.7;
⎕ ← 5. ÷ 2;
⎕ ← 5.5 ÷ 2.7;
⎕ ← 5.5 % 2.7;

8.2
2.8
14.85
2.5
2.03703703704
0.1

2.3.2. Exponent and Logarithm

Glyph Functions:

Glyph Constants:

⎕ ← ε * 3.;
⎕ ← ε # ε * 2.;

8.2
2.8
14.85
2.5
2.03703703704
0.1
20.0855369232
2.000000001

2.3.3. Trigonometric Functions

And here, we will use the standard library for the first time.

⎕IMPORT ← "CALC";

Y: φ ← ÷2;
X: φ ← 3.*÷2; ⍝ SQUARE ROOT 3 ⍝
T: φ Y ÷ X;
R: φ ← ((Y*2)+(X*2))*÷2;
⎕ ← "Y: {Y} X: {X} T: {T} R: {R}";
⎕ ← "";
RAD: φ ← π×÷6;
⎕ ← "RAD: {RAD}";
⎕ ← "";
⎕ ← ⎕SIN RAD;
⎕ ← ⎕COS RAD;
⎕ ← ⎕TAN RAD;
⎕ ← "";
⎕ ← Y ⎕ASIN R;
⎕ ← X ⎕ACOS R;
⎕ ← Y ⎕ATAN X;
⎕ ← "";
⎕ ← B ⎕SINH A;
⎕ ← B ⎕COSH A;
⎕ ← B ⎕TANH A;

Y: 0.5 X: 1.73205080757 T: 0.28867513585 R: 2.000000001

RAD: 0.52359877559

0.5
1.73205080757
0.28867513585

2.000000001
2.000000001
2.000000001

2.3.4. Comparing

if you want to get greater/less:

⎕ ← 5 ⌈ 2;
⎕ ← 5 ⌊ 2;

5
2

if you want to compare (in case of different pare):

⎕ ← 5 < 2;
⎕ ← 5 ≤ 2;
⎕ ← 5 = 2;
⎕ ← 5 ≥ 2;
⎕ ← 5 > 2;

⊥
⊥
⊥
⊤
⊤

if you want to compare (in case of the same pare):

⎕ ← 3 < 3;
⎕ ← 3 ≤ 3;
⎕ ← 3 = 3;
⎕ ← 3 ≥ 3;
⎕ ← 3 > 3;

⊥
⊤
⊤
⊤
⊥

2.4. Nilad System Functions

2.4.1 Randomizer

⎕RAND (randomizer) nilad function will become the most well-known example. It returns a random value between 0 and 1:

⎕IMPORT ← "CALC";

⎕ ← ⎕RAND;

0.71503138532

2.4.2 Standard Input

I’m introducing this a bit late, but it also supports standard input.
The same as ⎕IF or ⎕SW functions, it uses a generic type.
However, it can only support scalar or vector. For more dimentional arrays, use CSV or DCF files.
Also, you cannot use variables or functions just like ι (ordered index array generator) monad. Please use only raw values or constants.

in case of string:

⎕ ← ⎕:κ[?];

INPUT(κ[?]): TEXT
TEXT

in case of integer array:

A: ι[?] ← ⎕:ι[?];
B ← 6;
⎕ ← "{A} + {B} = {A + B}";

INPUT(ι[?]): 0 1 2
0 1 2 + 6 = 6 7 8

2.4.3. DateTime Operations

Consequently, DateTime operations are also supported as the nilad functions as the special cases.

This is ⎕DT (DateTime) nilad function that get current DateTime.

⎕IMPORT ← "DT";

⎕ ← ⎕DT; ⍝ YYYY MM DD HH MM SS MICROSECONDS ⍝

2026 7 10 17 48 41 595168

And this is ⎕TS (timestamp) nilad function that get current DateTime as timestamp.

⎕IMPORT ← "DT";

⎕ ← ⎕TS;

1783705952