The Transcendental library implements some common mathematical functions and constants, such as sine and cosine. All functions in the Transcendental library signal errors when given invalid arguments, and Dylan floating point precision contagion rules are obeyed. Precise contagion rules are given for each function below.

*Note*: The Transcendental library is not available on all platforms. At present, it will work only under HP/UX and Microsoft Windows.

The following names are exported from the Transcendental module of the Transcendental library:

**$single-pi** [Constant]

- The value of pi as a

**$double-p**i [Constant]

- The value of pi as a

**sin** (*x* :: <real>) => (*y* :: <float>) [Function]
**cos** (*x* :: <real>) => (*y* :: <float>) [Function]
**tan** (*x* :: <real>) => (*y* :: <float>) [Function]

- Returns the sine, cosine, or tangent of

- The floating point precision of the result is given by the precision of

**asin** (*y* :: <real>) => (*x* :: <float>), -1 <= *y* <= +1 [Function]
**acos** (*y* :: <real>) => (*x* :: <float>), -1 <= *y* <= +1 [Function]

- Returns the arc sine or arc cosine of

- The floating point precision of the result is given by the precision of

**atan** (*y* :: <real>) => (*x* :: <float>) [Function]

- Returns the arc tangent of

- The floating point precision of the result is given by the precision of

**atan2** (*y* :: <real>, *x* :: <real>) => (*z* :: <float>) [Function]

- Returns the arc tangent of

- The floating point precision of the result is given by the precision of

**sinh** (*x* :: <real>) => (*y* :: <float>) [Function]
**cosh** (*x* :: <real>) => (*y* :: <float>) [Function]
**tanh** (*x* :: <real>) => (*y* :: <float>) [Function]

- Returns the hyperbolic sine, hyperbolic cosine, or hyperbolic tangent of

- The floating point precision of the result is given by the precision of

**$single-e** [Constant]

- The value of

**$double-e** [Constant]

- The value of

**log** (*x* :: <real>, #key base) => (*y* :: <float>), *x* > 0, base > 1 [Function]

- Returns the natural logarithm of

- The floating point precision of the result is given by the precision of

**exp** (*x* :: <real>) => (*y* :: <float>) [Function]

- Returns

- The floating point precision of the result is given by the precision of

**\^** (*b* :: <real>, *x* :: <real>) => (*y* :: <float>) [G.F. method]

- Returns

- The floating point precision of the result is given by the precision of

**\^** (*b* :: <integer>, *x* :: <integer>) => (*y* :: <integer>) [G.F. method]

- Returns an integer result giving

**sqrt** (*x* :: <real>) => (*y* :: <float>), *x* >= 0 [Function]

- Returns the square root of

- The floating point precision of the result is given by the precision of

**isqrt** (*x* :: <integer>) => (*y* :: <integer>), *x* >= 0 [Function]

- Returns the integer square root of

- If

We intend to someday implement the following functions, but haven’t done so yet:

**asinh** (*y* :: <real>) => (*x* :: <float>) [Function]
**acosh** (*y* :: <real>) => (*x* :: <float>) [Function]
**atanh** (*y* :: <real>) => (*x* :: <float>) [Function]

- Returns the hyperbolic arc sine, hyperbolic arc cosine, or hyperbolic arc tangent of

- The floating point precision of the result is given by the precision of

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