tanh()

Returns the hyperbolic tangent of a double value.

Syntax

Numeric tanh()

Usage

The hyperbolic tangent of x is defined to be (ex - e-x)/(ex + e-x), in other words, sinh(x)/cosh(x).

Note: The absolute value of the exact tanh is always less than 1.

Special cases:

  • If the value is NaN, then the result is NaN.
  • If the value is zero, then the result is a zero with the same sign as the value.
  • If the value is positive infinity, then the result is +1.0.
  • If the value is negative infinity, then the result is -1.0.

The computed result must be within 2.5 ulps of the exact result. The result of tanh for any finite input must have an absolute value less than or equal to 1. Note that once the exact result of tanh is within 1/2 of an ulp of the limit value of ±1, correctly signed ±1.0 should be returned.