sin  

Elementary math library function.
 
::§Float → §Float  
Dynamic references:  none 
Sine of argument in radians. 
cos  

Elementary math library function.
 
::§Float → §Float  
Dynamic references:  none 
Cosine of argument in radians. 
tan  

Elementary math library function.
 
::§Float → §Float  
Dynamic references:  none 
Tangent of argument in radians. 
cot  

Elementary math library function.
 
::§Float → §Float  
Dynamic references:  none 
Coangent of argument in radians. 
arcsin  

Elementary math library function.
 
::§Float → §Float  
Dynamic references:  none 
Inverse of sine, with result in radians. 
arccos  

Elementary math library function.
 
::§Float → §Float  
Dynamic references:  none 
Inverse of cosine, with result in radians. 
arctan  

Elementary math library function.
 
::§Float → §Float  
Dynamic references:  none 
Inverse of tangent, with result in radians. 
floor  

Elementary math library function.
 
::§Float → §Integer  
Dynamic references:  none 
Rounding towards negative infinity, giving the largest integer which is not greater than the argument.

ceil  

Elementary math library function.
 
::§Float → §Integer  
Dynamic references:  none 
Rounding towards positive infinity, giving the smallest integer which is not less than the argument.

round  

Elementary math library function.
 
::§Float → §Integer  
Dynamic references:  none 
Rounding to nearest integer, with halfway cases rounded away from zero.

Remainder functions  

The three remainder functions, illustrated for both §Integer and §Float cases, and for both positive (left column) and negative (right column) divisors. Lines show the §Float case, with unattained limit values indicated with empty circles. Spots show the §Integer case. It is seen that the §Float case coincides with the §Integer case at integer points.
The illustration is included just for fun — when determining which remainder function to use, it is strongly recommended to do that based on the mathematical characterizations rather than this illustration.
 
Source: show/hide — visit 
modulo  

dividend::§Integer divisor::§Integer → §Integer  
Dynamic references:  none 
Remainder consistent with Euclidean division, always being nonnegative. That is, let z denote the result of [modulo x y], where x is the divident and y is the divisor. Then z is the unique number that satisfies both 0 ≤ z < y and n y + z = x for some integer n.
Equivalently, z can be compuated as x  [abs y] * [floor (1.0 * x) / [abs y]]..
 
dividend::§Float divisor::§Float → §Float  
Dynamic references:  none 
Generalization of the §Integer case to real values.  
dividend::§Length divisor::§Length → §Length  
Dynamic references:  none 
Analogous to the §Float case. 
mod  

dividend::§Integer divisor::§Integer → §Integer  
Dynamic references:  none 
Remainder induced by floored division. That is, let z denote the result of [mod x y], where x is the divident and y is the divisor. Then z solves the equation n y + z = x, where the integer n is the fraction x / y rounded towards negative infinity.
Since n y ≤ x if y > 0 and vice versa, the definition implies that z will have the same sign as y and magnitude less than that of y.
 
dividend::§Float divisor::§Float → §Float  
Dynamic references:  none 
Generalization of the §Integer case to real values.  
dividend::§Length divisor::§Length → §Length  
Dynamic references:  none 
Analogous to the §Float case. 
rem  

dividend::§Integer divisor::§Integer → §Integer  
Dynamic references:  none 
Remainder induced by division rounded towards zero. That is, let z denote the result of [rem x y], where x is the divident and y is the divisor. Then z solves the equation n y + z = x, where the integer n is the fraction x / y rounded towards zero.
Since the magnitude of n y will be no greater than that of x, the definition implies that z will have the same sign as x, and the magnitude of z will be less than that of y.
 
dividend::§Float divisor::§Float → §Float  
Dynamic references:  none 
Generalization of the §Integer case to real values.  
dividend::§Length divisor::§Length → §Length  
Dynamic references:  none 
Analogous to the §Float case. 
sqrt  

Elementary math library function.
 
::§Float → §Float  
Dynamic references:  none 
Square root of nonnegative number.

abs  

This is the function invoked by the syntax abscall. The binding is useful when the function needs to be passed around as a value, or if one does not like the special syntax.
 
::§Float → §Float  
Dynamic references:  none 
Absolute value.  
::§Integer → §Integer  
Dynamic references:  none 
Absolute value.  
::§Length → §Length  
Dynamic references:  none 
Unsigned length.  
::§FloatPair → §Float  
Dynamic references:  none 
Euclidean norm.  
::§Coords → §Length  
Dynamic references:  none 
Euclidean norm.  
::§FloatTriple → §Float  
Dynamic references:  none 
Euclidean norm.  
::§Coords3D → §Length  
Dynamic references:  none 
Euclidean norm.  
::§Path → §Length  
Dynamic references:  none 
Length of path.  
::§Path3D → §Length  
Dynamic references:  none 
Length of path.  
::§Dash → §Length  
Dynamic references:  none 
Length of dash pattern. 