RealMath

Note: The functions defined here used to use to "*f" versions of the math functions. These turned out to be ISO C functions, and are not available on Mac OSX at the time of writing. Therefore, they were replaced with some C level type cast trickery, which prevent them from being used in a procedure variable, but should work fine otherwise.

Procedure Summary
arccos(REAL): REAL

          Returns the arccosine of x, in the range [0, pi] where -1 <= x <= 1.
arccosh(REAL): REAL

          arccosh(x) is the arc hyperbolic cosine of x.
arcsin(REAL): REAL

          Returns the arcsine of x, in the range [-pi/2, pi/2] where -1 <= x <= 1.
arcsinh(REAL): REAL

          arcsinh(x) is the arc hyperbolic sine of x.
arctan(REAL): REAL

          Returns the arctangent of x, in the range [-pi/2, pi/2] for all x.
arctan2(REAL, REAL): REAL

          arctan2(xn,xd) is the quadrant-correct arc tangent atan(xn/xd).
arctanh(REAL): REAL

          arctanh(x) is the arc hyperbolic tangent of x.
cos(REAL): REAL

          
cosh(REAL): REAL

          cosh(x) is the hyperbolic cosine of x.
exp(REAL): REAL

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

          Returns the natural logarithm of x for x > 0.
power(REAL, REAL): REAL

          Returns the value of the number base raised to the power exponent for base > 0.
round(REAL): LONGINT

          Returns the value of x rounded to the nearest integer.
sin(REAL): REAL

          
sincos(REAL, VAR REAL, VAR REAL)

          More efficient sin/cos implementation if both values are needed.
sinh(REAL): REAL

          sinh(x) is the hyperbolic sine of x.
sqrt(REAL): REAL

          Returns the positive square root of x where x >= 0.
tan(REAL): REAL

          Returns the tangent of x where x cannot be an odd multiple of pi/2.
tanh(REAL): REAL

          tanh(x) is the hyperbolic tangent of x.
Constant Summary
exp1

          
pi

          

Procedure Detail

arccos

PROCEDURE arccos(x: REAL): REAL

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


arccosh

PROCEDURE arccosh(x: REAL): REAL

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


arcsin

PROCEDURE arcsin(x: REAL): REAL

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


arcsinh

PROCEDURE arcsinh(x: REAL): REAL

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


arctan

PROCEDURE arctan(x: REAL): REAL

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


arctan2

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

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: REAL): REAL

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: REAL): REAL

cosh

PROCEDURE cosh(x: REAL): REAL

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


exp

PROCEDURE exp(x: REAL): REAL

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


ln

PROCEDURE ln(x: REAL): REAL

Returns the natural logarithm of x for x > 0.


power

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

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


round

PROCEDURE round(x: REAL): LONGINT

Returns the value of x rounded to the nearest integer.


sin

PROCEDURE sin(x: REAL): REAL

sincos

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

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


sinh

PROCEDURE sinh(x: REAL): REAL

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


sqrt

PROCEDURE sqrt(x: REAL): REAL

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


tan

PROCEDURE tan(x: REAL): REAL

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


tanh

PROCEDURE tanh(x: REAL): REAL

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

Constant Detail

exp1

CONST exp1 

pi

CONST pi