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Additional mathematical functions

Less common mathematical functions defined in REF NUMBERS include:

phase(NUM)
    Returns the complex phase angle of NUM as a floating-point
    quantity.

cis(REALANGLE)
    Returns the float-complex number cos(REALANGLE) +: sin(REALANGLE)

arctan2(REAL_X, REAL_Y) -> REALANGLE
    Computes the arctangent of REAL_Y / REAL_X, but using the signs of
    the two numbers to derive quadrant information.


sinh(ANGLE)
cosh(ANGLE)
tanh(ANGLE)
    These procedures compute the hyperbolic sine, hyperbolic cosine and
    hyperbolic tangent of ANGLE. The result is a floating-point, or a
    float-complex if ANGLE is complex.

arcsinh(NUM)
arccosh(NUM)
arctanh(NUM)
    These procedures compute the hyperbolic arcsine, hyperbolic
    arccosine and hyperbolic arctangent of NUM. For NUM complex, the
    result is a float-complex. For NUM real, the result will be a real
    float, except in the following cases:

        arccosh:    NUM < 1
        arctanh:    abs(NUM) > 1

    For -arctanh-, it is an error if NUM = 1 or -1.


linearfit(LIST) -> (M,C)
    The library LIB LINEARFIT makes available the procedure linearfit,
    which takes a list of pairs of numbers representing co-ordinates of
    points, works out the best straight line through the points, and
    returns its slope M, and its Y-intercept C.

        linearfit([% conspair(0,0), conspair(1.01, 0.98),
            conspair(1.85, 2.005), conspair(3.0, 3.0) %]) =>
        ** 1.015095 0.009136

    For vertical or nearly vertical lines it will produce an error.


Aaron Sloman
Fri Jan 2 03:17:44 GMT 1998