TANH

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Returns the hyperbolic tangent of a number.

Signatures

Returns: Hyperbolic tangent result (between -1 and 1)

TANH(number: T) → DOUBLE

Notes

• Definition: TANH(x) = SINH(x) / COSH(x) = (e^x - e^(-x)) / (e^x + e^(-x))
• Returns values in the range (-1, 1)
• TANH(0) = 0
• Odd function: TANH(-x) = -TANH(x)
• Approaches 1 as x approaches infinity
• Approaches -1 as x approaches negative infinity
• S-shaped (sigmoid) function
• Returns NULL if input is NULL

Examples

SELECT
    f1 := TANH(0e0),  -- Hyperbolic tangent of 0 is 0
    f2 := TANH(1e0),  -- Hyperbolic tangent of 1
    f3 := TANH(-1e0),  -- Odd function: TANH(-1) = -TANH(1)
    f4 := TANH(2e0),  -- Hyperbolic tangent of 2
    f5 := TANH(5e0)  -- Approaches 1 for large positive values
;