[ruby-core:117409] [Ruby master Feature#20404] `2pi`

["mame (Yusuke Endoh) via ruby-core" <ruby-core@ml.ruby-lang.org>]

Issue #20404 has been updated by mame (Yusuke Endoh).

Status changed from Open to Rejected

April Fools' Day is over. Closing.

This proposal is half joke, half serious. I can think of some reasons why we should introduce `2pi`.

### There are some languages that provide not only `pi` but also commonly used values.

@ko1 and @shyouhei told me that Gauche and C (POSIX) defines the following constants. It seem reasonable to provide frequently used values, even if they can be easily computed from other values.

* Gauche (Scheme): `pi`, `2pi`, `pi/2`, `pi/4`, `pi/180`, `1/pi`, and `180/pi`
* C (POSIX): `pi`, `pi/2`, `pi/4`, `1/pi`, `2/pi`, and `2/sqrt(pi)` (but not `2pi`, why?)

https://practical-scheme.net/gauche/man/gauche-refe/Mathematical-constants.html
https://pubs.opengroup.org/onlinepubs/9699919799/basedefs/math.h.html

### There is no good alternative constant name.

We cannot define `Math::2PI` unfortunately. `Math::PI2` and `Math::PI_2` are in unnatural word order, and also ambiguous as pi^2 or pi/2. `Math::TWO_PI` does not look so good.
I mentioned Tau in the original proposal, and seriously, I don't believe that `Math::Tau` is the way to go at the present. As long as most textbooks use 2pi, programmers will have to replace it with `2pi` in their mind every time they see `Math::Tau`, which is too inconvenient. We should consider this when most textbooks start using Tau. (If I had a time machine, I would try to convince the ancient Greeks to consider the ratio of circumference to radius instead of diameter.)

### `Math::PI` is often the only used one in Math module.

Because Ruby has Complex, it is often not necessary to use `Math.sin` and `cos` directly. When dealing with 2D graphics, we typically use only Complex multiplication and `Math::PI`.

### `Math::PI` leads to a bit cryptic code.

For example, to find the coordinates of the vertices of a hexagon, one would write `Complex.polar(1, 2 * Math::PI / 6 * n)`. However, many people may be bothered by the redundant multiplication and rewrite it as `Complex.polar(1, Math::PI / 3 * n)`. Then the original intent of the hexagon disappears from the code. Since math code tends to be originally cryptic, I think it is better if the intent remains as straightforward as possible. With `2pi`, we could write `Complex.polar(1, 2pi / 6 * n)`.

... Well, but I wonder if a new literal is impossible?

----------------------------------------
Feature #20404: `2pi`
https://bugs.ruby-lang.org/issues/20404#change-107582

* Author: mame (Yusuke Endoh)
* Status: Rejected
----------------------------------------
I propose a new Float literal: `2pi`.

```ruby
p 2pi  #=> 6.283185307179586 == 2 * Math::PI
```

I am not proposing `1pi`, `3pi` or `4pi`. I do only `2pi`. Because in most cases, all you need is `2pi`. Any other multiple of pi is rarely needed.

I've got the statistics. GitHub code search revealed that more than 80% of the occurrences of `n * Math::PI` and `Math::PI * n` had n = 2. [1]

| n |`n * Math::PI`|`Math::PI * n`|sum  | %  |
|--:|-------------:|-------------:|----:|---:|
| 0 |            48|             1|   49|1.4%|
| 1 |            58|             3|   61|1.7%|
| 2 |          2300|           534| 2834|80.4%|
| 3 |           218|            17|  235|6.7%|
| 4 |           200|            23|  223|6.3%|
| 5 |            24|             2|   26|0.7%|
| 6 |            41|             3|   44|1.2%|
| 7 |            14|             0|   14|0.4%|
| 8 |             6|             2|    8|0.2%|
| 9 |             8|             0|    8|0.2%|
|10 |            17|             0|   17|0.5%|
|11 |             2|             0|    2|0.1%|
|12 |             2|             0|    2|0.1%|


Here is the PIe chart

![](https://gist.github.com/assets/21557/1c077af3-f753-4ee1-bc75-5b38a3bd6487)

I know that a new constant name "Tau" is proposed (#4897, #17496). But notice: "2pi" and "Tau" have the same number of characters. Then, it is obvious that familiarity is better. In fact, `2 * Math::PI` is 4 times more than `Math::PI * 2`, indicating that all programmers are copying "2pi" in their textbook.

The idea of 2pi came up regularly in chats among committers. The discussion quickly shifted to its generalization: should we treat `3e` as `3 * Math::E`, or even `42foo` as `42 * foo`? However, I noticed such a generalization is unnecessary because all we need is 2pi. Unneeded generalization is evil.

Here is a patch.

```diff
diff --git a/parse.y b/parse.y
index 55619273b8..93b16a16ac 100644
--- a/parse.y
+++ b/parse.y
@@ -10208,6 +10208,13 @@ parse_numeric(struct parser_params *p, int c)
             return set_number_literal(p, tINTEGER, suffix, 10, 0);
         }
     }
+    else if (c == '2' && peek(p, 'p') && peek_n(p, 'i', 1)) {
+        tokadd(p, c);
+        tokadd(p, nextc(p));
+        tokadd(p, nextc(p));
+        tokfix(p);
+        return set_number_literal(p, tFLOAT, 0, 0, 0);
+    }

     for (;;) {
         switch (c) {
diff --git a/ruby_parser.c b/ruby_parser.c
index 6d85a72c5b..3a6e0b5704 100644
--- a/ruby_parser.c
+++ b/ruby_parser.c
@@ -936,6 +936,9 @@ VALUE
 rb_node_float_literal_val(const NODE *n)
 {
     const rb_node_float_t *node = RNODE_FLOAT(n);
+    if (strcmp(node->val, "2pi") == 0) {
+        return DBL2NUM(2 * M_PI);
+    }
     double d = strtod(node->val, 0);
     if (node->minus) {
         d = -d;

       P I  
Happy a r l fool
```

[1] I used these queries: [`/[^.]\b2 ?\* ?Math::PI/ language:Ruby`](https://github.com/search?type=code&q=%2F%5B%5E.%5D%5Cb2+%3F%5C*+%3FMath%3A%3API%2F+language%3ARuby) and [`/Math::PI *\* *2\b *[^.\/]/ language:Ruby`](https://github.com/search?type=code&q=%2FMath%3A%3API+*%5C*+*2%5Cb+*%5B%5E.%5C%2F%5D%2F+language%3ARuby)




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