## Feature #10255

open### Math.log: check domain of base argument

**Description**

I suppose Math.log with base 0 or 1 is undefinable or has no meaning, so I think it should be raise `Math::DomainError`

It is helpful to prevent unnecessary concern or misunderstand.

Yes I know there are many controversial issue about that, specially treating Math.log(0.0, 0.0), Math.log(1.0, 0.0) and Math.log(1.0, 1.0).

Even if there are some reason it had better return value,

I suppose `Math.log(2.0,1.0)`

should not be `Infinity`

and `Math.log(1.0, 0.0)`

should not be `-0.0`

.

In terms of `raises Math::DomainError instead of returning NaN if the base is less than 0`

at the (https://bugs.ruby-lang.org/issues/9797)

, this PATCH make sense.

But please feel free to point out my unsatisfactory points. (Actually this is first time to write c-lang thoroughly)

Thank you. gogo.

Before

```
# For all 0 <= n < 1
Math.log(n, 1.0)
=> -Infinity
Math.log(1.0, 1.0)
=> NaN
# For all n > 1
Math.log(n, 1.0)
=> Infinity
Math.log(0.0,0.0)
=> NaN
# For all 0 < n < 1
Math.log(n, 0.0)
=> 0.0
# For all n >= 1
Math.log(n, 0.0)
=> - 0.0
```

After

```
# For all n >= 0. Actually for all n <- R (a real number) because of checking domain of first argument
Math.log(n, 1.0)
Math::DomainError: Numerical argument is out of domain - “log”
Math.log(n, 0.0)
Math::DomainError: Numerical argument is out of domain - “log”
```

**Files**

#### Updated by gogotanaka (Kazuki Tanaka) about 8 years ago

I'd forgotten to update RDoc. So I add new patch for updating RDoc.

gogo.

#### Updated by gogotanaka (Kazuki Tanaka) about 8 years ago

After I thought twice about that,

I came to the conclusion that `1.0`

should be considered as `1 + ε (infinitesimal)`

In terms of ↓

```
1/0.0
=> Infinity
```

so below behave does make sense.↓

```
# For all 0 <= n < 1
Math.log(n, 1.0)
=> -Infinity
# For all n > 1
Math.log(n, 1.0)
=> Infinity
```

But when a base is exact `1`

, it doesn't make sense still.↓

```
# For all 0 <= n < 1
Math.log(n, 1)
=> -Infinity
# For all n > 1
Math.log(n, 1)
=> Infinity
```

We can say some for `0.0`

or exact `0`

So I wanna make changes in patchs, if anybody have free time, please remove these patchs.

thank you. gogo.

#### Updated by gogotanaka (Kazuki Tanaka) about 8 years ago

Associated revision 10474

#### Updated by gogotanaka (Kazuki Tanaka) about 8 years ago

Associated revision 10487

#### Updated by gogotanaka (Kazuki Tanaka) about 8 years ago

Hi there. I'm just gonna add a explain.

```
Math.log(1,-1)
#=> NaN
Math.log(0.0,-1)
#=> -Infinity
Math.log(0,-1)
#=> -Infinity
Math.log(-0.0,-1)
#=> -Infinity
Math.log(-1,-1)
#=> Math::DomainError: Numerical argument is out of domain - "log"
```

All these examples should raise Math::DomainError. right?

I wish this issue would be solved by 12/25(JST).

Anyway I can't wait for 2.2.0, thank you for your jobs always :)

P.S. I've just make sure `Math::log`

with a negative base is fixed at #9797, thank you so much!!!

I'm really appreciate it! but, this issue about `Math.log with base 0 or 1`

still remain.

#### Updated by gogotanaka (Kazuki Tanaka) almost 8 years ago

Related to https://bugs.ruby-lang.org/issues/10785