Reference · Math

math.tanh

math.tanh(num) -> float

What it does

The hyperbolic tangent of a number, as a float, as Python's math.tanh: sinh(x) / cosh(x). The answer is always between -1 and 1, and it takes any number without overflowing. Its inverse is math.atanh.

Examples

print(math.tanh(0), math.tanh(1), math.tanh(-1))print(math.tanh(0.5), math.atanh(math.tanh(0.5)))

0.0 0.7615941559557649 -0.76159415595576490.46211715726000974 0.5

Edge cases

• Past about 19 the answer is exactly 1.0 (and -1.0 below -19); a huge input is not an error.
• inf gives 1.0, -inf gives -1.0, NaN gives NaN.
• The function is odd: math.tanh(-x) is -math.tanh(x).

print(math.tanh(20), math.tanh(-20), math.tanh(1e300))print(math.tanh(math.inf), math.tanh(-math.inf), math.tanh(math.nan))print(math.tanh(-2) == -math.tanh(2))

1.0 -1.0 1.01.0 -1.0 NaNtrue

Errors

There is no domain or range error. A value that is not a number is a runtime error, not an error value: it stops the request; a decimal is converted first with float.

print(math.tanh(dec("1")))

line 1: `math.tanh` expects a number as argument 1, got dec (this works on floats: convert a dec with float(x))

Chaining

A squashing function: any number ends up in -1..1.

print(3 | math.tanh)print([-100, -1, 0, 1, 100] | map(math.tanh))

0.9950547536867305[-1.0, -0.7615941559557649, 0.0, 0.7615941559557649, 1.0]

See also

math.sinh, math.cosh, math.atanh, math.tan

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