# LRealMath

Procedure Summary
arccos(LONGREAL): LONGREAL Returns the arccosine of x, in the range [0, pi] where -1 <= x <= 1.
arccosh(LONGREAL): LONGREAL arccosh(x) is the arc hyperbolic cosine of x.
arcsin(LONGREAL): LONGREAL Returns the arcsine of x, in the range [-pi/2, pi/2] where -1 <= x <= 1.
arcsinh(LONGREAL): LONGREAL arcsinh(x) is the arc hyperbolic sine of x.
arctan(LONGREAL): LONGREAL Returns the arctangent of x, in the range [-pi/2, pi/2] for all x.
arctan2(LONGREAL, LONGREAL): LONGREAL arctan2(xn,xd) is the quadrant-correct arc tangent atan(xn/xd).
arctanh(LONGREAL): LONGREAL arctanh(x) is the arc hyperbolic tangent of x.
cos(LONGREAL): LONGREAL
cosh(LONGREAL): LONGREAL cosh(x) is the hyperbolic cosine of x.
exp(LONGREAL): LONGREAL Returns the exponential of x for x < Ln(MAX(REAL).
ln(LONGREAL): LONGREAL Returns the natural logarithm of x for x > 0.
power(LONGREAL, LONGREAL): LONGREAL Returns the value of the number base raised to the power exponent for base > 0.
round(LONGREAL): LONGINT Returns the value of x rounded to the nearest integer.
sin(LONGREAL): LONGREAL
sincos(LONGREAL, VAR LONGREAL, VAR LONGREAL) More efficient sin/cos implementation if both values are needed.
sinh(LONGREAL): LONGREAL sinh(x) is the hyperbolic sine of x.
sqrt(LONGREAL): LONGREAL Returns the positive square root of x where x >= 0.
tan(LONGREAL): LONGREAL Returns the tangent of x where x cannot be an odd multiple of pi/2.
tanh(LONGREAL): LONGREAL tanh(x) is the hyperbolic tangent of x.

Constant Summary
exp1
pi

Procedure Detail

### arccos

    PROCEDURE arccos(x: LONGREAL): LONGREAL

> Returns the arccosine of x, in the range [0, pi] where -1 <= x <= 1.

### arccosh

    PROCEDURE arccosh(x: LONGREAL): LONGREAL

> arccosh(x) is the arc hyperbolic cosine of x. All arguments greater than or equal to 1 are legal.

### arcsin

    PROCEDURE arcsin(x: LONGREAL): LONGREAL

> Returns the arcsine of x, in the range [-pi/2, pi/2] where -1 <= x <= 1.

### arcsinh

    PROCEDURE arcsinh(x: LONGREAL): LONGREAL

> arcsinh(x) is the arc hyperbolic sine of x. All arguments are legal.

### arctan

    PROCEDURE arctan(x: LONGREAL): LONGREAL

> Returns the arctangent of x, in the range [-pi/2, pi/2] for all x.

### arctan2

    PROCEDURE arctan2(xn: LONGREAL;
                      xd: LONGREAL): LONGREAL

> arctan2(xn,xd) is the quadrant-correct arc tangent atan(xn/xd). If the denominator xd is zero, then the numerator xn must not be zero. All arguments are legal except xn = xd = 0.

### arctanh

    PROCEDURE arctanh(x: LONGREAL): LONGREAL

> arctanh(x) is the arc hyperbolic tangent of x. |x| < 1 - sqrt(em), where em is machine epsilon. Note that |x| must not be so close to 1 that the result is less accurate than half precision.

### cos

    PROCEDURE cos(x: LONGREAL): LONGREAL

### cosh

    PROCEDURE cosh(x: LONGREAL): LONGREAL

> cosh(x) is the hyperbolic cosine of x. The argument x must not be so large that exp(|x|) overflows.

### exp

    PROCEDURE exp(x: LONGREAL): LONGREAL

> Returns the exponential of x for x < Ln(MAX(REAL).

### ln

    PROCEDURE ln(x: LONGREAL): LONGREAL

> Returns the natural logarithm of x for x > 0.

### power

    PROCEDURE power(base: LONGREAL;
                    exponent: LONGREAL): LONGREAL

> Returns the value of the number base raised to the power exponent for base > 0.

### round

    PROCEDURE round(x: LONGREAL): LONGINT

> Returns the value of x rounded to the nearest integer.

### sin

    PROCEDURE sin(x: LONGREAL): LONGREAL

### sincos

    PROCEDURE sincos(x: LONGREAL;
                     VAR sin: LONGREAL;
                     VAR cos: LONGREAL)

> More efficient sin/cos implementation if both values are needed.

### sinh

    PROCEDURE sinh(x: LONGREAL): LONGREAL

> sinh(x) is the hyperbolic sine of x. The argument x must not be so large that exp(|x|) overflows.

### sqrt

    PROCEDURE sqrt(x: LONGREAL): LONGREAL

> Returns the positive square root of x where x >= 0.

### tan

    PROCEDURE tan(x: LONGREAL): LONGREAL

> Returns the tangent of x where x cannot be an odd multiple of pi/2.

### tanh

    PROCEDURE tanh(x: LONGREAL): LONGREAL

> tanh(x) is the hyperbolic tangent of x. All arguments are legal.

Constant Detail

### exp1

    CONST exp1

### pi

    CONST pi