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Is there a name for the range of numbers $[-1,1]$, or the name by which a non-zero number is brought to be in this range$^1$?

I am aware that a Unit Interval is the name for the range $[0, 1]$, and the page does make mention of $[-1, 1]$ but offers no specific name for the range.

$^1$If there is a number -123.456 and I want to represent it in the range $[-1, 1]$ I would expect the resultant number to be -0.123456, but I am not certain of the name of the function that has just been performed.

The closest term I can think of is norm (or normalize to use the verb form) in the sense of a normalized vector such that $x = (3,4)$ and $\hat x = (0.6, 0.8)$

But how would one look to apply such terms outside of vectors and what would the correct terms be?

JLN
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    I'm thinking "unit ball" but that's the best I have... – Sean Roberson May 23 '22 at 14:39
  • "$[-1,1]$" is already pretty clear and concise. – Karl May 23 '22 at 14:40
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    The "normalization" operation you described seems unnatural because it depends on the base-10 representation of numbers, and it's not injective or continuous. What are you using that function for? – Karl May 23 '22 at 14:43
  • @Karl this is something that has just been bugging me for quite a few years. It's a problem I've run into in a couple different forms while programming, and I've found it very irksome to not have a proper name to describe what I am doing. The "normalizing" of a vector has stuck in my head as a kind of analogues process to what I hope to achieve. – JLN May 23 '22 at 14:54
  • In programming terms, it sounds like you're discarding the exponent of a floating point number and keeping only the significand. I imagine in many situations an order-preserving function like tanh might be more useful. – Karl May 23 '22 at 15:03
  • Keeping only the significand would be the goal in this context. The following would be the function in python 
    def to_be_named(value):
    return 0 if value == 0 else value / pow(10, ceil(log10(fabs(value))))```
In the link there is mention of Scmid's "true normalized form" which is akin to what I'm searching for, but for the range [-1, 1] instead of (0.1, 1) since I want to keep the sign of the number.

Hadn't known about tanh before, so certainly useful to learn that bit!
    – JLN May 23 '22 at 15:25

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