Early exit from tanh for values >=20 <=-20 as JS loses precision

[benjoffe]

tanh tends to Infinity very quickly. See the calculations of tanh at the boundary integers of 19 and 20 below. The value is calculated via wolfram alpha then pasted into a JS console to check if JS can represent the value.

tanh(19)
https://www.wolframalpha.com/input/?i=tanh+19
result = 0.99999999999999993721734415903940939665164417761315093858
JS: 0.9999999999999999

tanh(20)
https://www.wolframalpha.com/input/?i=tanh+20
result = 0.999999999999999991503291489416822045438558191190987257130
JS: 1

As can be seen, tanh(20) is equal to 1. Since tanh(Infinity) is also equal to 1 we can treat anything >= 20 as 1.
tanh is an 'odd' function so the same applies to negative values.

Benefits of exiting early:

• speed improvement for a large range of input values
• slightly more accurate for a few values close to 20 (will be 1 instead of 0.999... as was previously being calculated).
• smaller source

Note: there are values between 19 and 20 that also round to 1 but the source should be kept clean at an integer value.

[ljharb]

👏 👏 Well documented, tested, and explained. Thanks!